In the present study we tested the effects of different transcranial direct current stimulation (tDCS) protocols in the formation of visuo-spatial contextual learning (VSCL). The study comprised three experiments designed to evaluate tDCS-induced changes in VSCL measures collected during the execution of a visual search task widely used to examine statistical learning in the visuo-spatial domain. In Experiment 1, we probed for the effects of left-posterior parietal cortex (PPC) anodal-tDCS (AtDCS) at different timings (i.e. offline and online) and intensities (i.e. 3 mA and 1.5 mA). The protocol producing the more robust effect in Experiment 1 was used in Experiment 2 over the right-PPC, while in Experiment 3, cathodal-tDCS (CtDCS) was applied over the left-PPC only at a high intensity (i.e. 3 mA) but varying timing of application (offline and online). Results revealed that high intensity offline AtDCS reduced VSCL regardless of the stimulation side (Experiment 1 and 2), while no significant behavioral changes were produced by both online AtDCS protocols (Experiment 1) and offline/online CtDCS (Experiment 3). The reduced VSCL could result from homeostatic regulatory mechanisms hindering normal task-related neuroplastic phenomena. It consists in the application of weak direct electrical currents  for a few minutes  via a pair of electrodes positioned on the scalp. The electrical field generated by the current is capable to modulate membrane permeability and post-synaptic neuronal activity in both excitatory and inhibitory fashion. Because of single neuron registrations, we know that anodal-tDCS (AtDCS) induces an increase (depolarization) and cathodal-tDCS (CtDCS) causes a decrease (hyperpolarization) in permeability of the of neuronal membrane potential of stimulated neurons6. In the long run , the two processes are thought to promote neuroplasticity through the induction of long-term potentiation (LTP) and long-term depression (LTD) -like effects9.Transcranial electrical stimulation (tES) is a non-invasive brain stimulation technique extensively used in cognitive neuroscience to produce transient modifications of brain activity. Among the various existing tES protocols, transcranial direct current stimulation (tDCS) is doubtless the most known and a wealth of works have demonstrated its capability to modulate neural responses and to shape behaviour3. It is plausible that, at least part, of the reported non-linear effects could arise from a limited comprehension of the interactions occurring between tDCS-induced modifications and the state of the system or its governing mechanisms12. Accordingly, it has been demonstrated that the effects of tDCS can be greatly influenced by the ongoing brain activity given that the level of engagement during the execution of an experimental task can even reverse the expected effects of the stimulation16. In addition, we also know that the brain is anything but a passive system and is endowed with adaptive mechanisms enabling it to dynamically react to external inputs or changes in the environmental demands. Homeostatic regulatory mechanisms are an evidence of this. They consist in the ability of the brain to dynamically stabilize its own activity around a physiologically reasonable range in order to prevent itself from hyper-/hypo-excitability17. In this view, when within the same cortical area/network a prolonged tES-induced brain activity (increase/decrease) is associated with a task-induced (increase) brain activity , we could expect the two processes to dynamically interact. Previous works confirmed this idea and provided wide behavioural and neurophysiological support for the presence of homeostatic regulatory principles in the human brain. Reported evidence mainly pertain the effects produced by tDCS applied over the primary motor cortex in close temporal sequence with a task involving motor learning20. For example, Kuo and colleagues demonstrated that prior application of AtDCS (1 mA) reduced implicit motor learning in a serial reaction time task but left performance unchanged in a simple reaction time task18. Amadi and colleagues reported that AtDCS (1 mA) applied before a motor task decreased learning rates and increased GABAA activity as revealed by short interval intracortical inhibition protocol19. Stagg and colleagues found that AtDCS (1 mA) applied during a motor learning task enhanced the learning process while the same stimulation protocol applied before the task, reduced learning20. Similarly, Bortoletto and colleagues observed that AtDCS (1.5 mA) facilitated motor learning but only when applied in association with a slow motor practice, not producing learning on its own. With the same protocol, learning was inhibited when AtDCS was applied in association with a fast motor practice that usually generate learning on its own by increasing cortical excitability14. Interestingly, even reversing the order of tES application and motor practice produced results consistent with mechanisms of homeostatic regulation as revealed by Cantanero and colleagues who reported an occluded motor learning when AtDCS (1 mA) was applied after a sequential visual isometric pinch task21. What is less documented is whether similar regulatory mechanisms are retrievable also outside the motor cortex and/or primary sensory areas. Further, it is not clear whether the abovementioned interactions between tES- and task-related brain activity occur also when the learning paradigm involves a more distributed network of cortical activity. For instance, during visuo-spatial statistical learning where a complex interplay between primary and higher order areas is necessary for the learning to occur24. Finally, the effects produced by stimulation intensities exceeding the standard 1–2 mA has been rarely tested in the literature casting out the possibility to fully understand whether increased/decreased learning could be obtained with increased stimulation intensities.At the behavioural level, using the stimulation-dependent model, it is generally expected that AtDCS applied during the execution of a task leads to enhanced behavioural performances on the task while the opposite is expected for CtDCS. These assumptions are primarily related to the abovementioned effects of tDCS on membrane permeability. Nevertheless, this model directly and simplistically associates the effects at the neuronal level to the effects at the behavioural level. Moreover, this description clearly represents an approximation mainly assuming the brain as a passive system. The coarseness of this picture has been confirmed by several studies revealing the non-linearity of tDCS-induced effects, an evidence suggesting that much remains to be understood about tDCS-brain interactions25. Based on previously described works on the motor domain, we expected AtDCS applied before the task (offline) to significantly interfere with VSCL on a stimulation intensity gradient providing evidence of homeostatic regulatory principles in the PPC. Furthermore, we expected AtDCS applied during the task (online) to potentially facilitate learning, based on intensity and individual ability to perform the task. Experiment 2 was post-hoc designed to control whether results obtained from Experiment 1 could be explained in the framework of a balance between left and right PPC activity. For this reason, the stimulation protocol that produced the more robust effect was used with a reversed electrodes montage . Finally, in Experiment 3, offline and online 3 mA CtDCS protocols  were used to test the conceivable effects of neuronal excitability reduction on task performance. In this case, we expected offline CtDCS to produce facilitatory effects on VSCL, while online CtDCS to significantly interfere with VSCL.In the present study, we developed three separate experiments in order to test the effects produced by different tDCS protocols  on visuo-spatial contextual learning (VSCL). In Experiment 1, left-posterior parietal cortex (PPC) AtDCS  applied at different timings (offline/online) and intensities (3 mA and 1.5 mA) was associated with the execution of a VSCL task widely used in previous studies examining statistical learning in the visuo-spatial domainhttps://osf.io/rwx29.The present study was preregistered prior to data collection at the Centre for Open Science through the Open Science Framework and is visible at the present address: confirmatory analyses) from those not reported , an indication adhering to the following code has been added alongside each result both in the Manuscript and in the Supplementary Information. (CF) = Confirmatory Analyses; (EX) = Exploratory Analyses.The original preregistered project comprised additional data and statistical analysis that are not included in the main body of the manuscript. These elements are however retrievable in the Supplementary Information (Appendix A–C). Moreover, both Experiment 2 and Experiment 3 were not included in the preregistration since they have been post-hoc designed to explore additional aspects related to results obtained in Experiment 1. To ease the identification of those analyses originally reported in the preregistration form  all naïve to the purpose of the study, right handed (as assessed by the Edinburgh Handedness Inventory27) and with normal or corrected to normal visual acuity. Participants were pseudo-randomly assigned to one of the different electrical stimulation protocols chosen for the present study . This resulted in the selection of 14 participants  per stimulation group.One hundred and fourteen healthy participants were screened for the presence of any contraindications to the use of tESBefore taking part to the experiment, all participants were informed about the procedures of the study and provided written informed consent in accordance with the Declaration of Helsinki. The study was approved by the University of Trento Human Research Ethics Committee and was carried out in accordance with approved guidelines.25. The task was to search for a rotated “T” (90° clockwise or 90° counterclockwise) target stimulus amongst eleven heterogeneously rotated “L” distractors and to report target stimulus orientation by pressing “-“ (counterclockwise) or “z” (clockwise) keys on the keyboard.The visual task used in the present experiment was an adapted version of the spatial contextual cueing paradigm elaborated by Chun and JiangEach trial started with a fixation cross at the center of the screen (jittered time between 500 and 800 ms) followed by the presentation of the search array. Participants had to report the orientation of the target stimulus within 1500 ms. Each response was followed by an auditory feedback (200 ms) that varied based on response provided . The search array disappeared whenever participants provided a response and was followed by a blank black screen (variable duration) which ensured a constant trial duration regardless of individual RTs. If no response was provided within 1500 ms, a new trial began  plus 3 training blocks (~4 minutes) performed before the experiment which served to get participants familiarized with the task.Participants seated in a dimly lit and sound attenuated room with their head placed on a chinrest at 57 cm from a LED monitor .new arrays and 12 old arrays per block). In new arrays, the position, the colour and the rotation of the items were pseudo-randomly assigned. Target stimulus could appear at the centre of one of twelve predetermined grids, could have a random rotation (90° clockwise or counterclockwise) and a random color . Each distractor could appear in one of the remaining grids (jittered position within grid’s possible coordinates), could have a random rotation  and a pseudo-random colour. In old arrays, the position, the colour and the orientation of items were a priori defined within a set of twelve predetermined arrangements that were repeated across blocks. Only rotation of the target stimulus (90° clockwise or 90° counterclockwise) was randomly varied. In both new and old trials, an equal number of red, blue, green and yellow items was presented for each search array and an equal number of targets was presented for each colour at the end of each block. Furthermore, in order to control for any effect of proximity to the fixation cross, the eccentricities of target locations were balanced across new and old arrays.In search displays, stimuli could appear within an invisible array of 8 × 6 grids , were heterogeneously colored  and were presented amongst a black background. Search arrays could be either “new” or “old”  in order to blind participants to the stimulation manipulation. Half of the participants included in the sham tDCS protocol received a current ramping to 3 mA while the other half received a current ramping to 1.5 mA.Electrical stimulation (3 or 1.5 mA) was delivered by a battery-driven DC stimulator  via two rubber electrodes inserted in saline-soaked sponges. The target electrode size was 5 × 5 cm while the return electrode size was 6 × 7 cm. To reduce skin impedance, electro-conductive gel  was applied under the sponges and impedance levels were kept below ~5 kΩ. Electrodes were kept in place with the use of elastic bands, which ensured a homogeneous pressure on the electrode surface and minimized the probability of drops in current density2 and 0.06 mA/cm2 for the 3 mA and 1.5 mA protocols respectively.In Experiment 1, five different stimulation protocols were administered , while one stimulation protocol was included in Experiment 2 (P4 as in the 10/20 EEG system - 3 mA offline AtDCS) and two in Experiment 3 . Current densities were 0.12 mA/cmIn the offline protocols, real stimulation was applied before the execution of the task while participants listened to an audiobook, whereas in the online protocols real stimulation was applied during the execution of the task. Furthermore, in order to blind participants with respect to the timing of the real stimulation , a sham stimulation was also administered before or after the real stimulation  and the second referring to the online stimulation .At the end of all experiments, participants completed a questionnaire about the sensations experienced during the tES in which they were asked to give a score from 0 (none) to 4 (strong) to rate their perception of tES-induced Irritation, Pain, Burning, Heat, Itch, Iron Taste and Fatiguenew trials minus RTs on old trials) were used as the main outcome measure. Only hit trials and trials with VSCL scores within 3sd from the individual mean were considered in the analysis. For each experiment, data were analysed using a mixed design analysis of covariance (ANCOVA) which compared the effects of different stimulation protocols on VSCL scores after controlling for general task performance . The rationale of using ANCOVA arose from the significant correlation found between VSCL scores and mean accuracy scores on new trials which suggested a possible influence of general task performance on the main outcome measure (see Multivariate Outliers’ Detection section below). In Experiment 2 and Experiment 3, results obtained from the real stimulation protocols were compared with those obtained from the Sham protocol from Experiment 1. Further analyses comprised mixed design analyses of variance (ANOVA) of the RTs and the accuracy scores on new trials which were performed for control purposes. Fisher’s Least Significant Difference (LSD) method was used to test the limited number of contrasts of interest . For all the other comparisons, Bonferroni correction was applied. Data from the sensations induced by tDCS were analysed using appropriate non-parametric statistics. A p-value <0.05 was considered significant for all statistical analyses.VSCL scores  A correlation analysis revealed a significant correlation between general task performance  and VSCL scores (r(111) = 0.271, p = 0.004) suggesting that the main outcome measure  could be influenced by participants’ individual ability to perform visual search.34. Specifically, participants who had values of Cook’s distance greater than 1 were excluded. This resulted in the exclusion of one participant initially assigned to the P3 - 3 mA offline AtDCS stimulation group.For this reason, a multivariate outliers’ detection procedure combining individual general task performance (independent variable) and VSCL scores (dependent variable) was used to exclude those participants who had performance greatly departing from the average distribution of the group(CF) A 5 × 13 mixed design ANCOVA with the between factor Stimulation , the within factor Blocks (13 levels) and General Task Performance  as covariate factor, was performed to evaluate the influence of different AtDCS protocols on VSCL. Mean hit trials for each stimulation group were: 0.84 (P3 - 3 mA offline AtDCS), 0.85 (P3 - 3 mA online AtDCS), 0.81 (P3 - 1.5 mA offline AtDCS), 0.83 (P3 - 1.5 mA online AtDCS) and 0.85 (Sham). The analysis revealed a significant main effect of Stimulation  = 2.542; p = 0.048; ƞp2 = 0.14; observed power = 0.69). Compared to the Sham group, a significant reduction of VSCL scores for the P3 – 3 mA offline AtDCS group  and a trend in the direction of a significant reduction for the P3 – 1.5 mA offline AtDCS group  was revealed by the post-hoc analysis  = 9.073; p = 0.004; ƞp2 = 0.13; observed power = 0.84) suggesting, once again, an important influence of general task performance on VSCL scores. No other main effect or interactions were significant to the statistical analysis .is Figs.  and 4A. (EX)In order to control whether differences in VSCL scores could be attributable to between groups differences in general task performance, two 5 × 13 mixed ANOVAs with the between factor Stimulation (5 levels) and the within factor Blocks (13 levels) were performed on accuracy scores and RTs to new trials. Both analyses revealed a main effect of Blocks  = 4.050; p < 0.001; ƞp2 = 0.06; observed power = 0.99; RTs: F = 4.22; p < 0.001; ƞp2 = 0.06; observed power = 0.99) explained by enhanced accuracy scores and a significant reduction of RTs as the task progresses. No main effect of Stimulation  = 0.576; p = 0.681; ƞp2 = 0.03; RTs: F = 0.70; p = 0.595; ƞp2 = 0.04) and Blocks*Stimulation interaction  = 0.965; p = 0.542; ƞp2 = 0.06; RTs: F = 1.13; p = 0.257; ƞp2 = 0.06) was revealed by the analysis suggesting that general task performances were correctly equated between groups .(EX)Given the strong dependency of tDCS effects on the neural activity level induced by the task16, an exploratory additional analysis was conducted after dividing participants into “low performers” and “high performers” based on group accuracy scores’ median values on new trials  = 2.854; p = 0.031; ƞp2 = 0.16; observed power = 0.74) that was explained by a reduction of VSCL scores in the two offline AtDCS groups with respect to the Sham group . As expected, a main effect of Performance was evident  = 7.413; p = 0.008; ƞp2 = 0.11; observed power = 0.76) suggesting that low and high performers significantly differed with respect to VSCL scores regardless of Stimulation. More interestingly, a significant Stimulation*Performance interaction was found  = 3.102; p = 0.022; ƞp2 = 0.17; observed power = 0.78). Post-hoc analysis revealed that the P3 – 3 mA offline AtDCS group’s reduction in VSCL scores with respect to the Sham group was significant only for low performers  though this result could be due to a reduced statistical power consequent to the halving of the sample as low performers broadly revealed a greater interference with respect to high performers A 2 × 13 mixed design ANCOVA with the between factor Stimulation (2 levels: P4 - 3 mA offline AtDCS and Sham), the within factor Blocks (13 levels) and General Task Performance as covariate factor, was performed to evaluate the contribution of right-PPC in the reduction of VSCL scores reported in Experiment 1. The analysis compared data obtained from a stimulation protocol in which the target electrode was placed over P4 with data obtained during Sham stimulation administered in Experiment 1. Mean hit trials were: 0.81 (P4 - 3 mA offline AtDCS) and 0.81 (Sham). Results revealed a main effect of Stimulation  = 5.604; p = 0.026; ƞp2 = 0.18; observed power = 0.62). A significant reduction in VSCL scores was evident on P4 - 3 mA offline stimulation protocol  with respect to the Sham protocol  = 1.907; p = 0.179; ƞp2 = 0.07) and no other main effects or interactions were significant to the statistical analysis .(EX) Also in this case, two 2 × 13 mixed ANOVAs were performed on accuracy scores and RTs to new trials with the between factor Stimulation (3 levels) and the within factor Blocks (13 levels) to control whether differences in VSCL scores could be attributable to between groups differences in general task performance. Both analyses revealed a main effect of Blocks  = 2.371; p = 0.006; ƞp2 = 0.08; observed power = 0.96; RTs: F = 1.963; p = 0.027; ƞp2 = 0.07; observed power = 0.91) explained by a general increase in accuracy and reduced RTs as the task progressed. Both the main effect of Stimulation  = 0.087; p = 0.771; ƞp2 = 0.003; RTs: F = 0.429; p = 0.518; ƞp2 = 0.01) and the Stimulation*Block interaction  = 0.770; p = 0.681; ƞp2 = 0.03; RTs: F = 0.816; p = 0.633; ƞp2 = 0.03) were not significant, revealing that the two stimulation groups were correctly equated with respect to general task performance .(EX)Again, for explorative purposes, an additional analysis was conducted after dividing participants into “low performers” and “high performers” based on group accuracy scores’ median values on new trials  = 6.437; p = 0.018; ƞp2 = 0.21; observed power = 0.68) that was explained by a significant reduction of VSCL scores on P4 - 3 mA offline stimulation protocol (p = 0.018) with respect to the Sham protocol. As expected, a main effect of Performance was evident  = 4.818; p = 0.038; ƞp2 = 0.17; observed power = 0.58). However, the interaction Stimulation*Performance was not significant  = 0.008; p = 0.928; ƞp2 = 0.0003) suggesting that stimulation affected VSCL on both low and high performers  A 3 × 13 mixed design ANCOVA with the between factor Stimulation , the within factor Blocks (13 levels) and General Task Performance  as covariate factor was performed to evaluate the effect of offline and online CtDCS on VSCL scores. Again, data from the Sham protocol were taken from Experiment 1. Mean hit trials were: 0.83 (P3 – 3 mA offline CtDCS), 0.81 (P3 – 3 mA online CtDCS) and 0.85 (Sham). The analysis revealed no significant main effects  or interactions  suggesting that the three stimulation protocols had similar effects on VSCL  Two 3 × 13 ANOVAs on accuracy scores and RTs on new trials were performed to ensure comparable performances between groups on the task. A main effect of Blocks was evident both for accuracy scores and RTs  = 2.024; p = 0.021; ƞp2 = 0.05; observed power = 0.92; RTs: F = 1.98; p = 0.024; ƞp2 = 0.05; observed power = 0.92) explained by increased accuracy and decreased RTs as the task progressed. Neither the main effect of Stimulation  = 0.743; p = 0.482; ƞp2 = 0.04; RTs: F = 1.17; p = 0.321; ƞp2 = 0.06), nor the Stimulation*Blocks interaction  = 0.606; p = 0.930; ƞp2 = 0.03; RTs: F = 1.10; p = 0.339; ƞp2 = 0.05) were significant to the statistical analysis, confirming that the three stimulation groups were correctly equated with respect to general task performance .(EX) Wilcoxon Signed-Ranks Test was used to first evaluate whether sensations induced by online and offline Sham stimulations were statistically comparable29. Results revealed no statistical differences between online Sham ranks and offline Sham ranks for all the examined sensations . Data from the offline and online questionnaires were then collapsed into a single Sham condition. For the other stimulation protocols, only sensations referring to the real (offline or online) stimulation were examined.(CF) The Kruskal-Wallis test was used to compare the different stimulations for each sensation. The analysis revealed no significant difference between the stimulation protocols for any of the examined sensation  suggesting that sensations experienced by different stimulation groups were comparable  though we cannot exclude replication also with lower intensities. Regarding tolerability aspects, we found that even higher stimulation intensities (3 mA) were well tolerated by participants who reported sensations similar to those induced by lower intensities (1.5 mA) and that were also mostly indistinguishable from those evoked by the control Sham protocol. From the numerical point of view, the augmentation from 1.5 to 3 mA led to an increase of the means of the aggregate sensations from 0.58 to 0.62 (P3 - and P4 – 3 mA offline AtDCS conditions collapsed) for the offline AtDCS conditions (0.71 for the CtDCS) and from 0.53 to 0.73 for the online AtDCS conditions (0.39 for the CtDCS). The aggregate sensations from the Sham condition was 0.57. Even when considering the most reported sensations . The reason we decided to use such intensities is twofold. On the one hand, we aimed at testing the possibility to induce more robust behavioural outcomes as a consequence of stronger electric fields targeting the brainIn general, only few subjects reported scores equal or higher than 3 . Participants who reported scores equal or higher than 3 for Burning were 2 out of 27 in the 3 mA offline AtDCS (P3 - and P4 – 3 mA offline AtDCS conditions collapsed), 2 out of 14 in the 3 mA online AtDCS and 0 for all the other stimulation protocols. Similarly, participants reporting scores equal or higher than 3 for Itch were 2 out of 27 in the 3 mA offline AtDCS (P3 - and P4 – 3 mA offline AtDCS conditions collapsed), 5 out of 14 in the 3 mA online AtDCS, 1 out of 14 in the 3 mA offline CtDCS, 1 out of 14 for the 3 mA online CtDCS, 0 out of 14 in the 1.5 mA offline AtDCS and 1 out of 14 in the 1.5 mA online AtDCS. Crucially, no participant reported relevant cutaneous or other adverse effect.39.In the present study, we used a series of tDCS protocols to test the effects of various parameters of application in shaping VSCL. We provided evidence of relevant tDCS-brain interactions in both left and right PPC possibly related to homeostatic regulatory mechanisms similar to those originally observed in the motor cortexnew trials were considered40. Furthermore, it is unlikely that this result could be attributed to differences in the sensations induced by the stimulation protocols as the analysis of the sensations questionnaires revealed statistically comparable results between all the stimulation protocols administered. Finally, this result unlikely arose from a reduced activation of the right PPC consequent to a tDCS-induced alteration of the interhemispheric rivalry between left and right PPC41. Given the prominent role of the right-PPC in visuo-spatial processing43, an alternative interpretation could consider a tDCS-induced hyperactivation of the left PPC and a consequent hypoactivation of the right PPC producing the VSCL reduction here reported. However, if it was the case, we would expect that applying the same stimulation protocol over the right-PPC would lead to an increase of VSCL. We tested this hypothesis in Experiment 2, where the stimulation protocol that produced the more robust interference in Experiment 1  was used with a reversed electrodes montage  and results revealed overlapping effects with those obtained after left PPC intervention, suggesting an equal contribution of left and right PPC in VSCL.In Experiment 1, we showed that AtDCS applied on left-PPC before the execution of the task strongly reduced VSCL with respect to the control Sham protocol. This was evident both for the 3 mA and for the 1.5 mA AtDCS, though a more robust reduction was produced by the 3 mA protocol. This result was not due to the influence of tDCS on general task performance or response speed, as no differences between stimulation protocols were made evident when the sole performances on θm), that is the level of post-synaptic activity above or below which LTP or LTD are respectively induced44. In this view, the prolonged excitatory input produced by AtDCS could have led to an increase in the modification threshold producing a consequent decrease in the probability of subsequent excitatory events  to induce LTP.We concluded that PPC offline AtDCS selectively influenced the ability of participants to store new visuo-spatial contextual information. A plausible explanation is that the interaction of two excitability-increasing events  hindered the normal task-related neuroplastic phenomena. As conceptualized by an influential model of synaptic plasticity elaborated by Bienenstock, Cooper and Munro model (BCM model), the stabilization of neuronal activity from an excessive increase or decrease in neuronal firing rate would be ensured by the dynamic adaptation of the modification threshold , one might wonder why no homeostatic mechanisms had been observed in this case. One possibility is that AtDCS produced an increase of the modification threshold only when VSCL had already occurred and thus did not influence its occurrence. Indeed, homeostatic mechanisms are not instantaneous and are known to develop after few or tens of minutes of prolonged plasticity-inducing protocols45. Furthermore, the length of breaks intervening between the two events  could have played a relevant role. In this regard, Fricke and colleagues reported that homeostatic plasticity in the motor cortex occurred only when 3 or 10 minutes breaks intervened between the two activity enhancing protocols, while no homeostatic mechanisms were observed for both longer and shorter breaks46. In the offline conditions, the time lapse between AtDCS and VSCL ideally matched with those reported by Fricke and colleagues whereas the same does not hold true for the online conditions. Another interesting point to be examined concerns the lack of a behavioural facilitation expected to occur in the online AtDCS conditions20. One possibility is that some sort of ceiling/floor effect intervened in our case, as VSCL in the control Sham protocol was overall high  and possibly no intervention could have been able to further enhance it. At the same time, we cannot a priori assume a sharp direct relationship between online PPC AtDCS application and VSCL increase given that a distributed network of cortical activity is involved in this type of learning.Contrary, when AtDCS was applied during the execution of the task no significant changes in VSCL were produced as compared to the Sham group. This result is in line with a recent study reporting no behavioural changes induced by AtDCS applied during the execution of the same task47. Some studies reported that old trials presentation was associated with a reduced activation of these areas likely reflecting a more fluid processing of the stored visual scenes47. Conversely, other studies showed an enhanced activation interpreted as a memory-mediated attentional capture of repeated spatial contexts33. It is possible that both mechanisms are at play. In this regard, Manginelli and colleagues showed that different temporo-parietal areas were associated with opposite activations during old trials presentation33. However, regardless of the exact neural mechanisms at play, it seems clear that distinct neuronal activity levels in response to new and old trials are an important correlate of VSCL. Given the direct relationship found between the ability to perform the task  and VSCL scores, we could predict high performers to show a greater difference in the neural activation produced by new and old trial with respect to low performers. If it was the case, the different pattern of results obtained by low and high performers reported in Experiment 1 could be explained in the light of two possible interpretations. The first interpretation would consider the raising up of the modification threshold as the main mechanism at play. In this view, those subjects showing higher differences in neural activation produced by new and old trials presentation  would still be able to exceed modification threshold and achieve VSCL. This would not happen for low performers whose VSCL would be mostly cancelled after the raising up of the modification threshold  the difference between new and old trials-induced activation in low performers. The same mechanism could have only marginally affected high performers for whom the difference between new and old trials-induced activation would have been mostly preserved (Fig. At the neural level, the spatial contextual cueing paradigm has been associated with a pattern of multifaceted cortical responses including primary visual areas, parietal and frontal cortices as well as various medial temporal lobe structuresold Fig. . The secved Fig. . HoweverDespite this interpretation, it remains to be clarified why in Experiment 2 the difference between low and high performers was not confirmed and only a main effect of Stimulation was evidenced by the statistical analysis. It is possible that this was due to differences in how participants were assigned to low and high performers groups as the median accuracy values of general task performance were slightly different between the two stimulation groups (P3 - 3 mA AtDCS: 83.3%; P4 - 3 mA AtDCS: 76.9%; Table 12. It could be argued that higher or lower CtDCS stimulation intensities are potentially necessary to reverse the behavioural effect produced by AtDCS. What is maybe more surprising is the null effect of the online CtDCS. We expected this protocol to produce a significant reduction of VSCL like the one observed after offline AtDCS. Nevertheless, the lack of a symmetrical relationship between the effects produced by AtDCS and CtDCS have been reported in various studies. For example, in a meta-analytical review Jacobson and collaborators2 reported that the relationship anodal-excitatory and cathodal-inhibitory have been mainly shown within motor and sensory domains. Conversely, when higher cognitive functions are involved, findings are much more controversial and a lack of significant behavioural modifications after CtDCS are frequently evidenced. Though it is still debated what is the reason for this asymmetry within higher cognitive domains, various explanations have been proposed. These mainly pertain the recruitment of larger cortical networks, mechanisms of contralateral compensation and the initial activation state of the brain2. In his view, the not-significant change produced by CtDCS intervention in our study could be attributed to one of the abovementioned mechanisms. Furthermore, given that online effects of tDCS are thought to primarily affect resting membrane potential while offline effects to be dependent on synaptic plasticity1, we can hypothesize that plasticity-mediated interference has a much stronger impact on behaviours with respect to changes in resting state potentials.Experiment 3 was designed to take a further step in the direction of disclosing homeostatic principles in the PPC. We probed for facilitatory behavioural effects after offline and online application of 3 mA CtDCS to the left PPC. Results revealed that CtDCS produced no significant changes in VSCL with respect to the control Sham protocol neither when applied before nor when applied during task execution. Though to some extent inconsistent with the BCM model, the lack of a significant effect of the offline CtDCS protocol on VSCL could be explained in several ways. On the one hand, we could again hypothesize that a ceiling/floor effect intervened or that CtDCS induced small changes that were not retrievable at the behavioural level. On the other hand, a sharp inverse relationship between AtDCS and CtDCS-induced behavioural changes cannot be a priori assumed given the non-linearity effects of tDCSIn summary, the present study revealed that the exposure to a prolonged excitability increasing stimulation of the PPC reduces VSCL when applied before task execution but left VSCL unaffected when applied during task execution. We consider the present results relevant in the context of a deeper understanding of the effects produced by tDCS in brain regions outside the motor cortex together with the potential interactions of these effects with other plasticity inducing events.Supplementary information


The plasmon resonance can cover a broad spectral range from the terahertz (40 μm) to the telecom (1.55 μm) region, which is further tunable by changing thickness and dielectric environments. The plasmon dispersion flattens at large wave vectors, resulted from the universal screening effect of interband transitions. More interestingly, anomalous temperature dependence of plasmon resonances associated with CDW excitations is observed. In the CDW phase, the plasmon peak close to the CDW excitation frequency becomes wider and asymmetric, mimicking two coupled oscillators. Our study not only reveals the universal role of the intrinsic screening on 2D plasmons, but also opens an avenue for tunable plasmons in 2D correlated materials.Plasmons in two-dimensional (2D) materials beyond graphene have recently gained much attention. However, the experimental investigation is limited due to the lack of suitable materials. Here, we experimentally demonstrate localized plasmons in a correlated 2D charge-density-wave (CDW) material: 2H-TaSe Here, arrays of 2H-TaSe2 nanoribbons are shown to exhibit a broadband plasmonic response that can be tuned from THz to telecom range. These localized plasmons can also couple to charge density wave excitations, offering insights on the physics of plasmonic excitations in 2D correlated materials. In the long wavelength limit, the plasmon frequency of 2D free electron gas is proportional to 12, with q as the wave vector. Such dispersion may give us an illusion that the plasmon frequency can go as high as one wishes. However, recent theoretical studies suggest that the plasmon dispersion in real 2D materials flattens universally due to the intrinsic dielectric screening from interband transitions15, which is inevitable for almost every crystal. The flattened dispersion renders slow plasmon group velocity and facilitates plasmon localization15. Though with importance, the experimental verification of such flattened dispersion remains elusive up to date.With strong tunability and extraordinary light field confinement, plasmons in 2D materials show great promise in reconfigurable photonics2 belongs to a transition metal dichalcogenide (TMDC), which attracts much attention due to the appearance of CDW orders16. It exhibits a normal-incommensurate charge-density-wave (CDW) phase transition at about TC1 = 122 K, followed by an incommensurate–commensurate CDW phase transition at TC2 = 90 K17. Previously, the bulk plasmon of metallic TMDCs was studied by electron energy-loss spectroscopy (EELS) and the anomalous negative plasmon dispersion was observed19. The interactions between CDW and plasmons were proposed as the physics origin of the negative dispersion21. In contrast, some later theoretical calculations and doping experiments revealed that the narrow d bands near the Fermi level may account for the negative dispersion24. All these studies based on EELS are for bulk plasmons, while the coupling between 2D plasmons and CDW excitations in TaSe2 thin films is still unclear.2H-TaSe2 van der Waals (vdW) thin films. We patterned the vdW thin films of 2H-TaSe2 into ribbon arrays and measured the plasmon resonances by Fourier-transform infrared spectroscopy (FTIR). The plasmonic excitations correspond to the collective oscillations of carriers with the moving direction perpendicular to the ribbon1, analogous to localized plasmons in traditional metallic nanostructures. Of course, propagating surface plasmons can be expected to show up in TaSe2 thin films through momentum compensation techniques, such as an atomic force microscopy (AFM) tip in near field imaging experiments3. We find that the resonance frequency of the plasmon in TaSe2 thin films covers a broad spectra range and extends to the telecom region, which is unattainable for graphene plasmons6. In addition, TaSe2 plasmons sensitively depend on the layer thickness and dielectric environments. Particularly, we reveal that the plasmon dispersion becomes flat at large wave vectors due to the screening of interband transitions, fully consistent with theoretical predictions15. More interestingly, we find that the CDW phase has profound influence on the plasmon resonance. In our study, we observe the coupling effects between TaSe2 plasmons and CDW excitations, which causes non-monotonic change of the peak height and linewidth when the temperature decreases. For comparison, thin films of 2H-NbSe2 were fabricated into ribbon arrays as well. On the contrary to TaSe2, the plasmon peak of NbSe2 continually becomes sharper with decreasing temperature.Here, we report the experimental studies of localized 2D plasmons in 2H-TaSe2 exhibits hexagonal structures as illustrated in Fig. 2 were mechanically exfoliated from bulk crystals onto diamond substrates, as displayed in Fig. 2 film, we fabricated more than 10 plasmonic arrays with various ribbon widths. The extinction spectra, which are directly determined by the optical conductivity, were measured by FTIR as illustrated in Fig. −1), as shown in Fig. d = 40 nm, ribbon width W = 500 nm), whereas plasmon resonances are observed with perpendicular polarization. The optical conductivity of plasmons is fitted by a Lorentz oscillator model  regions as well, with the resonance light wavelength readily beyond 40 μm  and comparable to that of ultrathin gold films (1.8 × 1016 cm−2 for d = 3 nm25).Figure 12ε0 is the vacuum permittivity, εe is the relative dielectric constant of the surrounding environment, ns is the sheet carrier density, and m is the effective mass of carriers. The wave vector q is W6. As shown in Fig. 7 m−1. As suggested by Jornada et al.15, the deviation from the ideal 2D plasmon dispersion is originated from the screening effect of interband transitions, and the flattening of plasmon dispersion at large q appears to be universal for 2D metals. For metallic TMDCs, there are multiple interband transitions between bands near the Fermi level, namely, the occupied (unoccupied) bands just below (above) the Femi level, whose onset energy is around 1–2 eV according to optical measurements28 and first-principles calculations23. The plasmon dispersion can be modified by introducing screening effects of interband transitions into the effective dielectric constant εe15, which becomes q-dependent in Keldysh model29. In the long-wavelength limit, the effective dielectric constant is approximately expressed as εs is the dielectric constant of the substrate, ρ0 is the screening length of the 2D film. For thin films with finite thickness d, the screening length is ε is the intrinsic dielectric constant due to interband transitions29. By incorporating the q-dependent dielectric constant εe(q) into Eq.  Å and the intrinsic dielectric constant ε is about 3.5 ± 1.3 for 2H-TaSe2 with thickness of 40 nm. The plasmon dispersion can also be simulated by the loss function1115, which holds promise for highly sensitive detection of local and non-local electronic structures.The plasmon dispersion as well as the saturation behavior at large wave vectors are well fitted by Eq. , as dispis 710 ± 60 Å and −1 at 1.6 × 106 m−1 and increases to 3200 cm−1 at 5.2 × 107 m−1. Due to the retardation effect31, the plasmon peak width at small wave vectors is less than its Drude scattering rate. At relatively large wave vectors, where the retardation effect is already negligible, the plasmon width gradually increases with the wave vector increases. We attribute such peak width enhancement to the more pronounced edge scattering of carriers6 and the inevitable nanofabrication imperfections and inhomogeneities.As shown in Fig. 2 plasmons is also strongly influenced by the interband screening. For the relatively wide ribbons, the spectral weight of the first-order plasmon is less than that of the second-order plasmon  and Si substrates , in addition to diamond substrates (εs = 5.7). Low dielectric constant substrates facilitate the observation of higher energy plasmon in experiments. The plasmon frequency of the sample on BaF2 substrates is about twice as high as that on Si, as illustrated in Fig. ρ0 for the film with thickness of 40 nm is (700 ± 280) Å and thus the intrinsic dielectric constant ε is 3.5 ± 1.4, which agrees with the value fitted from the plasmon dispersion. The maximal plasmon frequency we observed is 6580 cm−1 (λ = 1.52 μm) for a plasmonic device on BaF2 substrates . Therefore, the plasmon in TaSe2 films covers the terahertz to the telecom range, which promises broad applications in photonics and optoelectronics. Note that, according to Eq.  firstly becomes sharper and the peak height increases when the temperature decreases from 300 to 120 K. Then, on the contrary, as the temperature drops below the CDW phase transition temperature TC1, the plasmon peak becomes wider and asymmetric, and the peak height decreases. This is in sharp contrast to 2H-NbSe2, the plasmon peak of which  continually becomes sharper as the temperature decreases, as shown in Fig. 2 are generally similar to those of 2H-TaSe2 except for the temperature dependence. The detailed study for NbSe2 plasmons is presented in Supplementary note In general, the carrier scattering in metals is suppressed as the temperature decreases. As a consequence, the linewidth of the plasmon resonance reduces. For example, the WTe2 plasmons, we measured its intrinsic optical response with incident light polarized along the ribbon direction. As shown in Fig. TC1, while only Drude response is observed at higher temperature. The frequency of the absorption peak is 2180 cm−1 (270 meV) and the peak width is ~1000 cm−1 (124 meV) at 15 K, as determined from a Lorentz fitting 39, and scanning tunneling microscopy (STM)40. Furthermore, our electrical transport measurements on a TaSe2 thin film also corroborate the appearance of CDW phase transition: the slope of the resistivity changes at TC1 = 122 K as illustrated in the inset of Fig. 42, and for flakes thicker than 10 nm the phase transition temperature remains almost the same as that of the bulk43, which is the case in our study. For 2H-NbSe2, no clear CDW excitation is observed in previous reflection measurements28, presumably due to the competition between the superconductivity (TS = 7.2 K) and CDW orders (TC = 33 K)17. This is consistent with our measurements on the intrinsic optical response of 2H-NbSe2, as detailed in Supplementary note To understand the underlying mechanism of the abnormal temperature dependence of TaSe80 cm−1 20 meV and44 . Above TC1, the peak width of the first-order TaSe2 plasmons decreases from 1500 cm−1 (300 K) to 1280 cm−1 (120 K). However, when the temperature drops below TC1, the linewidth of the plasmon peak increases as the temperature decreases and eventually reaches 1620 cm−1 at 15 K, in sharp contrast to the behavior of NbSe2 plasmons. The temperature dependence of the peak width of 2H-TaSe2 plasmons deviates from that of its Drude scattering rate, which continually reduces as the temperature decreases26.The first-order plasmon of TaSed by Eq. . While fd by Eq. , becauseW = 900–400 nm, d = 20 nm). Figure 2 in uncoupled situations.To reveal the coupling effect further, we fabricated multiple plasmonic devices with plasmon resonance frequency sweeping across the CDW excitation 53, and Rabi splitting58. The coupling between two subsystems can enhance light–matter interactions and play an important role in applications, such as nanolasers59, sensors60, and quantum information processing61. The coupling effect between TaSe2 plasmonic and CDW excitations is originated from the interference effect between two different excitation pathways. Figure ω1 can be directly excited, which corresponds to the plasmon excitation. Whereas the transition between energy level 45. The energy detuning between the two transitions is ω1) and the CDW excitations (ω2) as a function of wave vectors  are depicted in Supplementary Fig. γ1 is enhanced compared to the uncoupled conditions. Meanwhile, the damping rate of the CDW excitation γ2 is also enhanced from 1000 cm−1 in the uncoupled case to 1300–1400 cm−1. The coupling rate Ω increases as the energy detuning increases from negative to positive. It presumably suggests an increase of the effective density of CDW excitations62 coupled to the plasmonic field as the size of nanostructures decreases.Depending on the coupling strength, the coupling effects between plasmons and other excitations can behave in different forms such as Purcell effectγ1, γ2, and Ω are 1618, 1375, and 1114 cm−1, respectively. With these parameters in hand, we can make a comparison between the coupling effect in 2H-TaSe2 and two typical coupling phenomena in plasmonic systems. The first is the classical analog of EIT51. In plasmonic EIT systems, the damping rate of the dark mode γ2 is significantly smaller than that of the bright mode γ1, such as the non-radiative quadrupole mode versus radiative dipole mode in metamaterials50 and the plasmon–phonon coupled systems52. In our case, γ2 of the quasi-“dark” CDW excitation is comparatively large. Consequently, only modification of the lineshape instead of a sharp dip is observed in extinction spectra. However, if we can effectively reduce γ2, a dip can emerge, as simulated in Supplementary Fig. 2 and EIT plasmonic systems share the same physics origin. The second is the strong Rabi splitting in exciton–plasmon systems58. In those systems, the coupling rate Ω is larger than the damping rates of the two excitations, which results in the formation of half-matter, half-light exciton–plasmon polaritons. Meanwhile, the hybridized polariton dispersion typically exhibits pronounced anti-crossing behavior, with large splitting in the dispersion intersection area. Here, the coupling rate Ω between TaSe2 plasmonic and CDW excitations is less than their damping rates and no clear anti-crossing scenario can be observed.The minimal energy detuning is realized for the plasmonic device with ribbon width of 700 nm. In that case, 64, phonons52, excitations in correlated materials65, and non-local quantum response of neighboring metals66. However, the coupling effect in 2H-TaSe2 have something unique. Plasmonic and CDW excitations are both internal excitations, while in many other coupled plasmonic systems, the coupling depends on excitations in different materials or structures, such as excitons in semiconductor layers and plasmons in metal nanostructures58. Therefore, TaSe2 plasmons can in return effectively manifest its intrinsic excitations. Once the plasmon peak becomes damped or asymmetric, it indicates there might exist intrinsic excitations at nearby frequency. This can open an avenue in probing weak excitations in other phase transition or correlated systems67.In light of the coupling effects, plasmons can be utilized in probing and manipulating other polaritons like excitons2 thin films, which covers a broad spectral range from the terahertz to the near-infrared region. The plasmon dispersion flattens at large wave vectors due to the screening of interband transitions. TaSe2 plasmons are tunable by varying the film thickness and dielectric environments. In addition, the coupling effect between TaSe2 plasmonic and CDW excitations is observed. The interplay between them is well interpreted by the coupled-oscillator model. 2H-TaSe2, along with other metallic TMDCs, has been demonstrated as a competitive building block in photonics. Our study can stimulate further endeavors on the plasmon in atomically thin TMDCs, given that the CDW phase transition temperature of monolayer and few-layer metallic TMDCs are dramatically different than that of their relatively thick or bulk counterparts41. Moreover, large-scale atomically thin TMDCs are available from controllable synthesis by chemical vapor deposition (CVD)69 or molecular beam epitaxy (MBE)42 methods, which can render more tunabilities such as electrical gating1 or chemical doping5.In summary, we experimentally demonstrated plasmons in 2H-TaSe2 were grown by a chemical vapor transport (CVT) method18. The 2H-NbSe2 single crystals were bought from 2D Semiconductors Inc. We checked the crystal quality by Raman spectroscopy70 . The lateral size of one thin film with uniform thickness is at most 200–300 μm. For mid-infrared (mid-IR) measurements, we can fabricate 6–12 plasmonic arrays with different ribbon widths in one homogeneous thin film. As such, the thickness uncertainty can be excluded in the determination of the plasmon dispersion. For far-IR measurements, one thin film is only large enough for one plasmonic array, because the beam size of the focused far-IR light is larger. We used electron beam lithography and reactive ion etching (the reaction gas is CF4) to fabricate ribbon arrays. Scanning electron microscope (Zeiss Sigma SEM) was used to finally determine the ribbon width. In general, the lateral etching is on the same order of magnitude of film thickness. No notable oxidation and degradation were found during the process of device fabrications and optical measurements, for the relatively thick TMDC films studied in this work  in conjunction with a Hyperion 2000 microscope to measure the extinction spectra. The incident light was focused on samples with a ×15 IR objective. A liquid-nitrogen-cooled Mercury–Cadmium–Telluride (MCT) detector and a ZnSe grid polarizer were used for mid-IR measurements, while a liquid-helium-cooled silicon bolometer and a terahertz polarizer were applied in far-IR measurements. The low-temperature measurements were carried out with a helium-flow cryostat (Janis Research ST-300).5Z0 is the vacuum impedance, nsub is the refractive index of the substrate, which is 2.38 for diamond substrates in the mid-IR range (1.46 for BaF2 and 3.44 for Si substrates), and ω is the light frequency. The optical conductivity contributed from the plasmon  is5Sp, ωp, and γp are the spectral weight, the frequency, and the damping rate of plasmon resonance, respectively, and f is the filling factor . The designed filling factor of our plasmonic devices is 0.4–0.5, but the lateral etching in fabrication process usually reduces the actual filling factor. Therefore, it is determined by the real ribbon width measured by SEM.The relation between the extinction spectrum and the sheet optical conductivity 2 and NbSe2 flakes were mechanically exfoliated onto Si/SiO2 substrates. The electrical devices were fabricated by electron-beam lithography technique and wet-etched by standard buffered HF solution for 5 s in the electrode regime. We deposited 5 nm-thick Cr and 80 nm-thick Au electrodes using magnetic sputtering. Four-terminal temperature-dependent transport measurements were carried out in a physical property measurement system  which achieved a base temperature of 1.8 K, in conjunction with lock-in amplifiers (SR830).The TaSeSupplementary Information


The study aims at evaluating the time-course changes of pre-corneal tear film after simultaneous phacoemulsification and limbal relaxing incisions (LRIs) performed in 2 groups of patients; group-A had vertical and group-B had horizontal LRIs.Fourty-two eyes of 28 patients with co-existing cataract and corneal astigmatism were studied before and after simultaneous cataract surgery and LRIs , patients were classified into 2 groups according to the orientation of LRIs; vertical (A) and horizontal (B) groups. Pre-corneal tear film stability was assessed by measuring the tear break-up time (TBUT) and the tear volume was determined using Schirmer’s I test , both preoperatively and postoperatively.P = 0.001) without significant reduction regarding basic Schirmer’s test values except for the first postoperative week in the horizontal LRI group-B (P = 0.04).TBUT was significantly reduced in both the study groups (Precorneal tear film stability is altered in the early postoperative period after simultaneous cataract and LRI incisions shown by TBUT measurement values. These changes do not appear to differ significantly depending on the orientation of LRI incisions. Microscopic damage to the ocular surface during cataract surgery is a widely established theory of postoperative dry eye syndrome resulting in ocular discomfort and dissatisfaction .Corneal astigmatism of variable degree; ranging between 1and 3 diopters; has been found to be coexistent in up to 29% of patients who are complaining of lenticular opacities and probably would undergo cataract surgery .Phacoemulsification; the modern cataract surgery; with intraocular lens implantation has been considered the gold standard treatment of cataract. The standard cataract procedure was simply targeting to correct spherical equivalent refractive error without considering a coexisting corneal astigmatism. Cataract surgery could be an aggravating factor of a pre-existing corneal astigmatism for the incisional nature of the procedure or a precipitating factor for a de novo surgical-induced astigmatism of a variable degree. Postoperative patient’s satisfaction after cataract surgery is basically related to achieving optimal postoperative distant visual acuity without the need to be spectacle or being contact lens-dependent. Despite recent improvements in surgical techniques, biometric measuring tools, and IOL power calculation formula; uncorrected corneal astigmatism still could be a source of postoperative residual refractive error –8. PatieProspective observational case series.Forty-two eyes of 28 patients were prospectively examined; patients were further classified according to the orientation of the LRIs into 2 groups; group-A who had LRIs performed along the vertical meridian  and Group-B who had the LRIs performed along the horizontal meridian . Inclusion criteria for the current study were: patients of both genders palnned to undergo cataract surgery with preoperatively documented mild to moderate corneal astigmatism (0.50–1.75 D) excluding those with severe corneal astigmatism (> 1.75 D) whom planned to have toric IOL implantation for correcting the pre-existing corneal astigmatism or not preferring to have the LRI procedure, patients with evident dry eye syndrome, severe ocular surface disorders, or systemic disease compromising the quality of the ocular surface , autoimmune disorders or corneal degenerative conditions associated with peripheral corneal thinning such as rheumatoid arthritis and pellucid marginal degeneration that render LRI to be unsafe procedure with unpredicted outcomes.Table The study protocol was approved by the institutional review board of Minia Faculty of Medicine Research Ethics Committee (FMREC) and compiled with the tenets of the Declaration of Helsinki. All study participants signed a written informed consent to participate in the study and for publication of data before being enrolled in the study; after explaining the nature and details of the study procedures.All participants had the standard cataract surgery (phacoemulsification) performed simultaneously with LRIs. The horizontal axis (0–180°) was marked at the slit-lamp preoperatively while the patient was in sitting position to compensate for potential cyclotorsion when shifting to the supine position. The incisions were performed in the steepest corneal axis at the limbus just anterior to the palisades of Vogt for correcting preoperative corneal astigmatism which was documented preoperatively by the corneal topographer . LRIs were performed according to the modified Gills’ nomogram at the commencement of surgery using a guarded micrometer diamond blade set at 500 μm as paired arcuate incisions. At the end; the incisions were irrigated with a balanced salt solution (BSS). A standard phacoemulsification technique was performed thereafter through a clear corneal temporal 2.8 mm incision; consisted of anterior continuous curvilinear capsulorrhexis (CCC), nucleus emulsification, and cortex irrigation-aspiration and implantation of an acrylic IOL implant. Postoperatively, topical antibiotic (Ofloxacin 0.3%) and steroid (Prednisolone acetate 1%) medications were administered four times daily for 2 weeks and the dose was steadily reduced thereafter. As these medications were used temporarily only, we assumed that they were not a confounding factor contributing to the postoperative ocular surface changes; moreover topical steroids have been recently considered a main line in treating meibomian gland dysfunction and dry eye syndrome.Tear film stability was assessed by the tear break-up time test which measures the interval between instillation of a sterile fluorescein strip moistened with saline applied to the inferior cul-de-sac and appearance of the first dry spots on the cornea; examination done using the cobalt-blue filter of the slit-lamp counting time in seconds needed for the first break of the precorneal tear film in a steady maintained gaze.Tear volume was determined using basic Schirmer’s test in which sterile graded Schirmer’s paper strips placed in the lower fornix while the patient is asked to close his eyes for 5 min after which the paper is removed and amount of wetting is measured.We quantitatively assessed the tear film stability and production by TBUT and basic Schirmer’s test respectively both preoperatively; at 1, 4 and 12 weeks postoperatively.The Statistical Package of Social Sciences  was adopted for tabulation and analysis the obtained data. Quantitative data were presented as mean ± standard deviation while qualitative data were expressed as number (n) and percentage (%). Kolmogorov- Smirnov for normality test was used to differentiate between parametric data and non-parametric data.P value less than 0.05 was considered statistically significant.Paired Samples Student T-test was used to compare preoperative and postoperative values. Repeated measures analysis of variance (ANOVA) was used to evaluate the changes over time. A The sample size in the study provided 95.6% statistical power at the 5% level to detect a 1-s difference in tear break-up time (TBUT), when the standard deviation (SD) of the mean difference was 1 s. Results.P = 0.001). No statistically significant differences regarding Schirmer’s test except in the first postoperative week in Group-B (P = 0.04).We have compared 21 eyes of 15 patients who had vertical LRIs (Group-A) to age-matched 21 eyes of 13 patients who had horizontal LRIs (Group-B) simultaneously with phacoemulsification; we found statistically significant reduction in the tear film stability measured by TBUT preoperatively; at 1, 4 and 12 weeks postoperatively (p = 0.01). the preoperative Schirmer’s test value was 14.71 ± 8.86 s; 12.88 ± 8.05, 13.53 ± 8.97 and 12.35 ± 8.20 s, 1, 4 and 12 weeks postoperatively, .In group-A who had vertically-oriented LRIs; the preoperative TBUT was 7.41 ± 2.48 s; 4.94 ± 2.36, 4.82 ± 1.94 and 5.59 ± 1.77 s, 1, 4 and 12 weeks postoperatively, . the preoperative Schirmer’s test value was 16.13 ± 9.32 s; 10.56 ± 5.16, 10.63 ± 4.77 and 9.75 ± 6.57 s, 1, 4 and 12 weeks postoperatively, .In group-B who had horizontally-oriented LRIs; the preoperative TBUT was 8.81 ± 5.59 s; 6.38 ± 3.79, 7.19 ± 6.45 and 4.50 ± 3.48 s, 1, 4 and 12 weeks postoperatively,  but not for tear volume production (P = 0.88 and 0.05 respectively).To analyze the course of changes over time, we used the multiple comparison test which was found to be significant for TBUT in both groups A and B ; a study conducted by Ju et al. reported that dry eye still could develop immediately after that procedure with a peak severity on day 7 postoperatively, most signs could return to basic preoperative levels within 3 months after surgery. They measured the tear film stability using OCULUS Keratograph which was not used in the current study .In a similar way; ocular surface changes after corneal laser-assisted refractive procedures have been found to be due to cutting of corneal nerves during refractive surgeries that subsequently result in suppression of the aqueous component secretion from the lacrimal gland, mucin expression on the corneal epithelial surface, and frequent blinking, previously mentioned cascade occurs because these homeostasis-maintaining mechanisms are driven by a neuronal feedback loop that is mediated by corneal sensitivity , 21.Introducing the confocal microscopy technology has helped better understanding of the dry eye pathophysiology after such incisional surgeries like LRIs as it has been proved that regeneration of the intrastromal corneal nerves usually occur within 3 to 6 months which occurs in concurrence with the recovery of corneal sensitivity and restoration of the ocular surface basic preoperative levels .In a previous study, we reported reduced quality of the ocular surface profile in terms of reduced tear film BUT and tear volume production after simultaneous cataract surgery with LRIs without largely affecting the corneal sensation; however, we did not consider for selective changes according to different location of the LRIs .Limitations of the current study are the relatively small sample size, the uncontrolled non-randomized design, the relatively short follow-up time and the lack of a control group that consist of patients undergoing cataract surgery without LRIs. The aforementioned limitations raised the need for future longitudinal controlled cohort studies with larger sample size and a longer follow-up time is highly recommended.In conclusion, the current study indicated that simultaneous LRIs with cataract surgery could result in dry eye symptoms and reduced tear film stability which probably would be transient during the early postoperative period and then recover to around the basic preoperative levels soon; those changes differ; however slightly; according to the LRIs orientation. Adequate preoperative assessment of the ocular surface quality parameters should be considered to optimize the postoperative outcome so not to compromise the patient’s life style.


Fault slip speeds range from steady plate boundary creep through to earthquake slip. Geological descriptions of faults range from localized displacement on one or more discrete planes, through to distributed shearing flow in tabular zones of finite thickness, indicating a large range of possible strain rates in natural faults. We review geological observations and analyse numerical models of two-phase shear zones to discuss the degree and distribution of fault zone heterogeneity and effects on active fault slip style. There must be certain conditions that produce earthquakes, creep and slip at intermediate velocities. Because intermediate slip styles occur over large ranges in temperature, the controlling conditions must be effects of fault properties and/or other dynamic variables. We suggest that the ratio of bulk driving stress to frictional yield strength, and viscosity contrasts within the fault zone, are critical factors. While earthquake nucleation requires the frictional yield to be reached, steady viscous flow requires conditions far from the frictional yield. Intermediate slip speeds may arise when driving stress is sufficient to nucleate local frictional failure by stress amplification, or local frictional yield is lowered by fluid pressure, but such failure is spatially limited by surrounding shear zone stress heterogeneity.This article is part of a discussion meeting issue ‘Understanding earthquakes using the geological record’. It is2.a,b). Geologically, the upper, frictional regime is characterized by brittle fault rocks, including gouges, cataclasites and pseudotachylytes (lithified friction melt), where one or more discrete fault cores are surrounded by a fractured damage zone [τ) driving frictional and viscous deformation are equal for some given strain-rate, composition, stress regime and thermal gradient. In reality, this depth is going to be a broad zone where both frictional and viscous deformation mechanisms are active [A now classic model of fault zone structure describes an upper brittle zone governed by pressure-dependent frictional sliding above a deeper ductile zone with grain-size and/or temperature-dependent viscous rheology –8 figura,b. Geolage zone ,10. The age zone –13. The age zone . The frie active ,15. Notea − b), defined by c). Here, σn′ is effective normal stress and V is slip velocity. In this framework, velocity-strengthening faults (where (a − b) > 0) accommodate displacement by stable, steady sliding, because slip does not accelerate after nucleation. Note that (a − b) can vary with velocity [a − b) < 0) are unstable if the critical stiffness (kc), a threshold that depends on material properties and effective normal stress, exceeds the system stiffness (k), determined by the wallrock stiffness. Unstable fault patches can generate earthquakes under static loading. Conditional stability occurs when (a − b) < 0 and 0 < kc < k. Note that k decreases as a slipping region grows, such that conditionally stable fault patches can be destabilized as they reach a critical length scale known as the nucleation length [c).The geological and mechanical observations outlined above for a homogeneous fault zone relate to, but do not fully describe, the fault’s depth-dependent seismic behaviour. This is further described by velocity-dependence of friction, denoted by the parameter  or T regime associated with slow earthquakes, but they do seem associated with conditional stability at or close to the seismic–aseismic transition [In transitional, conditionally stable regimes, slip speeds intermediate between steady creep and earthquakes have now been observed globally in ‘slow earthquakes’, a term that includes slow slip and low frequency earthquakes. ‘Slow slip events’ (SSEs) have been observed geodetically in well-instrumented plate boundary zones across the globe over the last two decades, and represent episodes of transient creep that repeat near-periodically at rates of mm to cm per day ,37. Low ansition ,46,47.3.a–c) assume a single composition with a single depth-dependent rheology. Our aim here is to analyse the effect of rheological heterogeneity on the bulk behaviour of fault and shear zones—with focus on how strength contrasts between coexisting materials determine the depth range of the frictional–viscous transition, and potential consequences for seismic, aseismic, and intermediate behaviours.Generalized, 1-D homogeneous fault models a–c assum(a)a). A common interpretation is therefore that subduction plate interface deformation style progressively changes from near-trench distributed, ductile deformation of unconsolidated sediments to localized, frictional sliding along faults in sedimentary rocks as the strata consolidate and lithify with progressive displacement and burial [b). There is therefore a depth range, between shallow unconsolidated sediments and deeper consolidated rocks, where variable states of consolidation is an important source of heterogeneity.Subduction-related mélanges commonly preserve evidence for early, soft sediment deformation structures overprinted by later faults and fractures ,49 figua. A commd burial ,54–56. Ad burial ,58. The a,b), the geophysical observations in active faults question the model of uniformly velocity-strengthening, unconsolidated sediments (c). An adaptation of the conceptual model is that shallow instabilities can be generated by one or more layers of frictionally unstable material within the frictionally stable zone (e). Such layers have been inferred to generate episodic creep in southern California, where relatively strong shallow intrusions and more lithified strata are inferred within otherwise unconsolidated or clay-rich velocity-strengthening fault rocks [d,e). Similarly, in the Hikurangi subduction margin, highly variable input sediments are hypothesized to play a part in shallow SSEs [Both strike-slip faults and subduction-related thrusts show variable sliding characteristics and heterogeneous interseismic accumulation of elastic strain at shallow depths ,44,59–61figure 2ediments c. An adable zone e. Such llt rocks   implies that the brittle yield is not met on both sides of the bimaterial interface. Lack of fracture propagation from one material to another also implies that the static stress drop in the ductilely deformed matrix  was insufficent to overcome frictional resistance, such that unstable slip was limited in dimension by the extent of relatively rigid materials. Fractures may also have been arrested prior to reaching instability if they are constrained to blocks that are smaller than a critical length scale [That fractures are limited to a single material as in b impliesth scale . Where sth scale –68, alsoth scale . Thus, lth scale –72.(b)c), where slip is well approximated by lateral interaction between segments of a single continuous fault. However, many fault zones are volumetric features [The earthquake cycle has long been recognized as resulting from elastic rebound , where afigure 2features , where fd). In this scenario, viscous creep accommodates finite strain at slow strain rates over long time scales, whereas frictional failure typically occurs at episodically high strain rates over short time scales once a critical level of stress has been reached [Tabular faults that contain one or more discrete fault planes in a broad zone of foliated, viscously deforming matrix can, on the other hand, deform by a combination of distributed viscous flow of the matrix and localized frictional failure along or within more competent lenses ,78 e.g.d. In thi reached ,80, alth reached . The vis reached –84, and  reached . Consequc) and creep or mixed behaviour to be common in thicker heterogeneous fault zones with scattered rigid inclusions (e.g. figure 2d). The bulk fault strength of the latter will depend on the volume fractions and geometry of two (or more) rheological components [d). For fault patches where interseismic creep is too slow to accommodate tectonically imposed displacement rates, elastic strain will accumulate until failure occurs—at a strength determined by the frictional yield of locked or partially locked areas, and potentially highly influenced by fluid pressure.In two dimensions (map-view) the seismogenic zone of a rheologically heterogeneous fault may be best represented by locked patches, which creep inefficiently, in a dominantly creeping fault zone ,3. One mfigure 2mponents  (figure (c)e). Some relatively rigid lenses and/or layers may remain in a frictional regime while adjacent rocks deform by diffusion or dislocation creep [f ), potentially leading to an intermingling of velocity-weakening and velocity-strengthening rocks [Mylonites formed deeper than the seismogenic zone are typically characterized by structures formed by distributed flow in polyphase materials, where variable viscosity is commonly illustrated by pinch-and-swell or boudinage of relatively competent layers –90 figue. Some ron creep ,92 . Although, local variations in metamorphic reaction progress may also increase heterogeneity at depth, either by producing stronger products along a prograde path, for example in eclogitisation, [Progressive shear in a dominantly viscous shear zone may gradually increase stress in and around rigid bodies embedded within it, allowing a frictional yield to be reached locally and transiently ,95. Suchfigure 1isation, , or by risation, ,99.Whereas viscosity contrasts are likely to exist throughout shear zones accommodating dominantly stable sliding below the seismogenic zone, there are areas where the contrasts are larger. These are regions where matrix viscosity is low, creep in competent materials is slow and bulk shear stress is well below the frictional yield strength of the stronger components. Locally, however, frictional failure may occur within more competent rocks because yield strength is lowered by high fluid pressures , or beca4.ηw) and high (ηs) viscosities at a steady creep rate, and an effective bulk viscosity describing the combined visco-brittle deformation, defined by v/w).Our review so far highlights various sources and degrees of rheological heterogeneity as a function of depth . From heWe consider a low viscosity, phyllosilicate-rich fault zone containing rigid lenses , as typi(a)a); however, one can think more generally of stronger layers dismembered in a weaker matrix, where strength is defined as the frictional yield τy = C0 + μ(σn − Pf). Here, C0 is cohesion and μ is static coefficient of friction, such that both level of consolidation/cementation and frictional properties determine relative strengths. This means that both composition and consolidation state is important, and relative strength may vary, and locally invert, as sedimentary layers undergo diagenesis at different rates [At the shallowest depths the rheology is granular flow and/or frictional sliding, with possible effect of pressure solution. In sheared sedimentary sequences, the typical observation is dismembered sandy layers in a muddier matrix a; howevent rates . Frictiont rates ,31,106.(b)b. The highest degree of visco-frictional interaction is predicted at depths just below the competent material’s frictional–viscous transition, where both the frictional yield (τy) and the viscous strength of component material at the imposed strain rate c).Deeper than the frictional–viscous transition of the more competent phase, the flow strengths of both materials are less than the frictional yield of the more rigid fault rocks at the steady-state strain rate. Therefore, below the frictional–viscous transition in the competent phase, the bulk flow stress departs significantly from the frictional yield curve. For shear stress to locally reach frictional yield strength at these depths, one of two things must happen; either the stress increases  5.To further analyse the effects and importance of rheological heterogeneities as described above from the geological record, we take a conceptual approach to modelling two-phase shear zones. Previous numerical studies have also considered effects of heterogeneity on fault zone behaviour. For example, by considering brittle asperities in a viscous matrix representing the seismic–aseismic transition at the base of the subduction megathrust seismogenic zone , by alte(a)τy dictated by the Mohr–Coulomb failure criterion. This set-up is analogous to matrix deformation by pressure solution, with embedded, higher viscosity clasts that may flow slower than the matrix, or episodically fracture in response to locally amplified stresses or a low frictional yield strength [ηs/ηw, and the ratio of driving stress to frictional yield τ/τy. Periodic boundary conditions are applied to the left- and right-hand boundaries, the base is kept stationary and a constant driving shear stress, τ, is applied to the top boundary. The model domain has a 4 : 1 aspect ratio and a high mesh resolution of 2048 × 512 is used to resolve the anastomosing matrix. The shear zone contains 61% competent clasts, to simulate an anastomosing shear zone system, and these clasts have a power-law size distribution with a constant aspect ratio of 1 : 3 and a maximum long axis of 84% shear zone thickness. We explore how clast fracturing and shear zone strain-rate hetereogeneity depend on varying ηs/ηw and τ/τy. Note that because stresses are amplified by the stronger clasts, local stresses will exceed the applied driving stress [ηs/ηw = 103 have been described in [ηs/ηw = 10 and 102 were run for this study.Using the particle-in-cell finite element code Underworld , we compstrength . Dynamicstrength , such thg stress . Models ribed in , where mηs/ηw and τ/τy influence the likelihood that a chain of adjacent clasts will have stress states at frictional failure, which is assumed to be analogous to bulk shear zone frictional failure. The former ratio represents the degree of viscous heterogeneity. The latter ratio is also a measure of heterogeneity, because τ/τy → 1 will mean that the fault zone is essentially at brittle failure, τ/τy ≪ 1 represents a bulk viscous shear zone, but 0 < τ/τy < 1 can lead to intermediate behaviours. Considering the ratio τ/τy is not new—it is an inverse form of the engineering safety factor for slope stability [The aim here is not to model specific faults, conditions, scales or settings, but to consider a fault system where interconnected weak zones between more competent lenses may allow strain localization, while we can also assess how deformation is distributed between the two phases and how the fault zone behaves as a bulk aggregate. We are interested in how the ratios tability , analogotability , and simtability . Note th(b)3 . Because fracturing is now essentially occurring throughout the competent clasts, while the matrix is flowing easily, the aggregate is deforming at a more or less constant strain rate (b). Though dynamic frictional slip is not modelled, we can hypothesize how such slip would be affected by the static stress state calculated here, by considering that earthquake ruptures can potentially propagate through velocity-strengthening patches of similar length scale [a).The large viscosity contrast will lead to local strain rate gradients that induce amplified shear stresses in the competent clasts , as also failure a. Becausain rate b. Thoughth scale , or thatth scale , but wilth scale . In thisτ/τy of 0.66, 63% of clast material is at frictional yield (c). Under these conditions, the strain rate in the competent clasts covers a broad range, with a peak deforming at a slow strain rate controlled by their viscosity, and others deforming faster as fractures allow them to reach matrix strain rates (d). Though much of the clast stress distribution is lower than the frictional yield, depicted by low strain-rates, hypothesized rupture pathways could still be connected between clasts that are at frictional failure (c) as fractures dynamically overcome shear resistance and velocity-strengthening friction in the matrix. This stress field may therefore be conducive to earthquake nucleation. Note that these potential rupture planes are slightly oblique to shear zone margins and will be limited in length by the shear zone thickness. If τ/τy is lower still, 0.44, then only 34% of clasts are at frictional failure, and the fault zone is dominated by viscous flow (e); the strain rate distribution is bimodal, with clearly different strain rates in fast flowing matrix and much slower flow in competent clasts (f ). The driving stress is too low, or frictional yield strength too high, for much clast material to be at frictional failure, and the hypothesized failure planes are limited to short segments that rarely connect between multiple clasts without passing through material far from frictional failure (c). Thus, fault lengths are likely to remain shorter than the nucleation length scale for instabilities.At an intermediate al yield c. Under in rates d. Though failure c as fracous flow e; the stt clasts f . The d failure c. Thus, 3 in summary gives a range from nearly fully frictional clast deformation if τ/τy is 0.88, through to dominantly viscous flow at τ/τy of 0.44, although about 1/3 of clast volume still fails frictionally at this stress ratio, albeit at very limited length scales. Reducing the viscosity ratio to 10 changes the picture to largely remove the intermediate frictional–viscous behaviour . However, with τ/τy = 0.66, only 34% of clast material is failing (b), as with τ/τy = 0.44 if the viscosity ratio is 103. This implies a relatively sharp change from frictional–viscous behaviour with τ/τy = 0.66 to frictional at τ/τy = 0.88 , as also indicated by a steepening of the % frictional deformation vs τ/τy curve in figure 5d. Reducing τ/τy to 0.44 with a viscosity ratio of 10 leaves only 1% of clast material fracturing, i.e. the shear zone is basically entirely viscous (figure 5c).A viscosity ratio of 10ehaviour . In thisl domain a. Howeve failing b, as wity = 0.88 a,b, as aτ/τy < 1. For a viscosity ratio of 10 the behaviour is uniformly viscous for τ/τy < 0.4, whereas for viscosity contrasts of 102 and 103, some very minor frictional behaviour is seen at τ/τy = 0.22 (d). As ηs/ηw increases, the transition zone covers a greater range of τ/τy values (e), because stress concentration in the competent bodies brings them closer to frictional yield [τ/τy at which frictional deformation ceases to dominate decreases. The transitions between the deformation regimes also occur at lower τ/τy ratios if ηs/ηw increases, because of this stress concentration. The transitions are likely similar at viscosity ratios >103, based on the decreasing spacing of the curves in figure 5d.Overall, clast fracturing and therefore visco-frictional interplay increases with increasing viscosity contrast, when 0 < y = 0.22 d. As ηs/y values e, becausal yield ,101, ande and 5b); 63% clast failure leads to fractures connecting across the bulk or all of the model domain (c). Accordingly, we consider the bulk deformation viscous, and frictional deformation restricted to rare and very local, short length-scale deformation if less than 30% of clast material is yielding. On the other hand, if more than 60% of the clast material is yielding, then through-going fractures accommodating frictional sliding would not need to overcome barriers of clast and/or matrix material far from failure. The intermediate case, 30–60% clast material yielding, can be considered a transitional state where local fractures develop, can link between clasts and clusters of clasts, but are limited in length-scale and rarely span the model domain. These values clearly depend on geometry and clast shape; however, we plot types of deformation in figure 5e to demonstrate the shape of the viscous, frictional and frictional–viscous fields that arise from the models in τ/τy versus ηs/ηw space. For the end-member where ηs/ηw = 1, the change from frictional to viscous deformation occurs when τ/τy < 1 and there is no transition zone, because there is no static stress concentration.Deformation style can be characterized by proportion of clast failure, as across the models 34% frictional failure appears to allow local fracturing that can only link between a few clasts ηs/ηw and τ/τy. These ratios will both change with depth, depending on the depth-dependence of material properties and effective stress state. We will calculate how these ratios are expected to vary for a particular tectonic profile and subsequently map the visco-frictional regimes to depth ranges.We can use our two-phase numerical models figures  and 5 toa, where the solid, grey curves will always have same shape but will be translated shallower or deeper depending on τ/τy. Deeper than a uniformly frictional regime, a transitional zone occurs where the volume fraction of frictional failure decreases with depth. This decrease in fracturing is a result of frictional strength increasing whereas increasingly efficient viscous flow occurs in interconnected incompetent material. As depth increases, viscosity becomes progressively lower relative to a higher frictional yield strength, and at some depth shear is entirely viscous, and any competent material is too frictionally strong relative to bulk strength for any frictional failure to occur. This line of argument, however, assumes a uniform fluid overpressure—it is important to remember that at any depth, if frictional yield can be reduced sufficiently, the proportion of material undergoing frictional failure will increase markedly. Note that this depth variation in deformation is comparable to that well established from geological observations a), based on extrapolating between models as those shown in figures τ/τy; figure 5d) is based on subduction-like conditions, including a near-lithostatic pore fluid factor  of 0.9, clast friction μ = 0.6, low driving stress of 10 MPa, and thermal gradient of 15°C km−1. As the bulk rheology changes with depth, the constant driving stress is a simplification that implies a varying strain-rate at depth if tectonic slip is approximately uniform. If viscosity decreases with increasing temperature, as expected in a purely viscous regime, then the constant stress assumption implies strain localization and decreasing shear zone width with depth. On the other hand, shear zone width may be buffered by the yield strength of the undeformed wall rocks [figure 1a. Such widening would also occur in a visco-frictional shear zone if increasing frictional strength has a greater effect on bulk strength than decreasing viscosity. Separating these models and further assessing the validity of the constant stress assumption could be a subject of future study. We assume the weakest component can deform by pressure solution, with a constant viscosity of 1019 Pa s, where T ≥ 100°C and pressure solution is efficient in quartz; at this temperature, frictional resistance is still less than 10 MPa at the given conditions, and a sharp frictional–viscous transition occurs somewhat deeper for ηs/ηw = 1 where τy drops below τ. The onset of pressure solution will be more gradual than this T-dependent onset of a constant, low viscosity implies, leading to a broader transition zone in reality than in our models. For ηs/ηw > 1, total clast failure can occur when τ/τy < 1, such that the onset of some viscous deformation is seen a few kilometres deeper. Below this, as illustrated also in figures ηs/ηw = 10. For greater ηs/ηw, however, local stress amplification leads to a mixed frictional–viscous behaviour over a substantial depth range of up to tens of kilometres.We now calculate a specific viscosity contrast profile example, and plot the fraction of competent material undergoing frictional failure against depth a, based ll rocks , which cb). Consider this weak component mixed with a quartz-dominated rheology, also plotted in (figure 6b). This competent quartz rheology is derived based on crystal plastic flow in quartz [−13 s−1, such that the clast viscous strength is conservatively underestimated. Then a viscosity ratio can be extracted from these two lithologies and shown as a function of depth .In a simplified view, the likely heterogeneous subduction thrust comprises weak, phyllosilicate-rich materials representing pelitic sediment and/or altered, hydrated oceanic crust , mixed wfigure 6n quartz , assumina,b). In other words, τ/τy = 1, and therefore all deformation is frictional independently of viscosity contrast. With increasing depth, frictional yield becomes more difficult, but for ηs/ηw > 102, and as long as τ/τy > ∼0.6 there is likely to still be through-going frictional failure . By comparison to figures The viscosity contrast is greatest at the onset of pressure solution, but at this depth, frictional yield is still relatively easy and a major proportion of deformation is therefore frictional a,b. In o failure . Howeveracturing a,c. By c1 to 103, and 0.3 < τ/τy < 0.6, in the transition zone from frictional to viscous deformation (e.g. c) as is commonly observed. Below this zone, which is likely a very narrow depth range if ηs/ηw is 10 or less, ηs/ηw approaches one and τ/τy approaches zero, such that viscous creep dominates unless local conditions, likely very high fluid pressures, allows very local frictional failure. Such local, potential instabilities will be dampened by surrounding viscous material and suppressed by a large nucleation length scale; however, unstable slip may occur if fault weakening by fluid pressurization overcomes velocity strengthening [The exact depth range where we predict a mixed behaviour with decreasing brittle behaviour with depth depends critically on parameters such as driving stress, fluid pressure and strain rate, but is consistently where the viscosity ratio is at least on the order of 10ion e.g. c as is cgthening —and thisgthening .T-dependent onset of pressure solution at 100°C hides any shallower, near-trench effects of mixed frictional–viscous or seismic–aseismic deformation. Such shallow, visco-frictional deformation may occur in some subduction zones, particularly where carbonates make up a considerable proportion of the incoming sediment sequence [We focused here on the base of the subduction interface seismogenic zone. If aseismic slip at the updip end of the seismogenic zone also involves some component of viscous deformation, then our assumption of a sharp, sequence ,138. We sequence . We high7.e). There is also the case of a competent phase close to failure, but in low volumetric proportions. Rupture propagation is then limited if the volume of matrix in between blocks is too large and experiencing a background stress far below its frictional yield [τ/τy are analogous to frictional variation providing barriers in dynamic rupture models of rough faults [τ/τy → 1), as also occurs in the rupture models.There appears to be a broad agreement among structural geologists that fault zone heterogeneity gives rise to a range of deformation styles, and a common co-existence of brittle and ductile structures ,98,128. figure 5al yield ,96,115. al yield , and thuh faults ,140—in tτ/τy ratios are high and frictional and viscous deformation modes co-occur as a result of stress amplification in the stronger phase, independently of the source of heterogeneity. This depth range of visco-frictional behaviour can be shifted up/down dynamically, depending on τ and/or fluid pressure, which may both vary substantially. Observed variations in depths of SSEs and LFEs, deemed representative of a transitional regime, may be determined by these stress and fluid pressure variations, without having to invoke variation in rheology or geothermal gradient.Our models in figures 8.τ/τy, of bulk driving stress to frictional yield strength.Although geological and rheological heterogeneity is pointed out in an increasing array of fault zones in several tectonic settings, the magnitude and length scale of such heterogeneity varies. To what extent can ’heterogeneity’ in material properties be measured, quantified and tied to heterogeneity in fault zone deformation? We propose that, at the first order, fault slip style in a heterogeneous tabular fault zone is controlled by a combination of viscosity contrast and the ratio, τ/τy at greater viscosity contrast.In this conceptual model, earthquakes require the frictional yield to be reached, and steady viscous flow requires conditions far from the frictional yield, independently of fault zone viscosity contrasts. Intermediate slip speeds may arise when driving stress is sufficient to arise local frictional failure by stress amplification, but this failure is limited in length-scale by surrounding viscously deforming media and heterogeneity of clast stresses (and/or strengths). The conditions where this is likely cover a larger range of Frictional deformation is more difficult and reliant upon local stress concentrations near the frictional–viscous transition, and this is consequently also where the models presented here predict a zone of intermediate and mixed deformation style. At greater depths, viscosity ratios are small and driving stress far from frictional yield, such that frictional sliding and mixed transitional behaviour is unlikely, but possible in the presence of high to extreme local fluid overpressures.τ/τy ratios that are intermediate between low values suppressing frictional yield and high values allowing through-going frictional failure. The exact values depend on viscosity contrast, but lead to fractures limited by viscous, weak matrix but locally allowed to nucleate by an ability for more competent lenses to flow or fracture. This is easier over a larger depth range at higher viscosity contrast, as otherwise, the bulk rheology will tend towards either fracture or viscous flow.Considering the variation in fault slip style with depth in some subduction and strike slip zones, and the numerical models presented here, intermediate fault slip speeds as seen in tremor and slow slip may correspond to slip in highly heterogeneous stress fields that may arise from