This work presents a new user-friendly lyophilization simulation and process optimization tool, freely available under the name LyoPRONTO. This tool comprises freezing and primary drying calculators, a design-space generator, and a primary drying optimizer. The freezing calculator performs 0D lumped capacitance modeling to predict the product temperature variation with time which shows reasonably good agreement with experimental measurements. The primary drying calculator performs 1D heat and mass transfer analysis in a vial and predicts the drying time with an average deviation of 3% from experiments. The calculator is also extended to generate a design space over a range of chamber pressures and shelf temperatures to predict the most optimal setpoints for operation. This optimal setpoint varies with time due to the continuously varying product resistance and is taken into account by the optimizer which provides varying chamber pressure and shelf temperature profiles as a function of time to minimize the primary drying time and thereby, the operational cost. The optimization results in 62% faster primary drying for 5% mannitol and 50% faster primary drying for 5% sucrose solutions when compared with typical cycle conditions. This optimization paves the way for the design of the next generation of lyophilizers which when coupled with accurate sensor networks and control systems can result in self-driving freeze dryers. INTRODUCTIONLyophilization refers to the energy and time intensive process of solvent  removal used to improve the long-term storage stability of perishable materials ,2. A typTn) is reached and nucleation begins. Due to the latent heat generated by nucleation, the product temperature increases to the freezing temperature (Tf). Beyond this point, the ice crystallization occurs while heat is released till the entire sample is frozen. The temperature decreases continuously during the crystallization process and during the final step of solid cooling.Developing a better understanding of the freezing process is crucial to lyophilization understanding and optimization because the sublimation rate of ice during primary drying is strongly influenced by the ice crystal morphology. A typical profile of the product temperature during freezing is shown in Fig. et al.  is ~ 0.6, and during crystallization and solid cooling is ~ 0.1. Since these values are slightly greater than the cut-off value, the lumped capacitance method leads to a higher error, but the agreement is taken to be satisfactory owing to the stochastic nature of the nucleation process which leads to a significant error even when the time-intensive finite-element method is used. This can be seen in the work of Nakagawa et al.  lumped capacitance heat transfer, (ii) constant product temperature during ice crystallization, and (iii) heat is transferred to the product only from the shelf. Lumped capacitance method refers to the assumption of low resistance to conduction within the product when compared with the heat transfer between the product and its surroundings and thereby, of a spatially uniform temperature within the product. The temperature gradient within the product is small when the Biot number, r Bi ≫ 1 . Biot nuBi < 0.1 . During a et al. , where aThe 0D transient equation for heat transfer used is given by:ρ is the product density in the liquid form, Cp is its specific heat capacity, V is the product volume, Tpr is the product temperature, t is the time, h is the heat transfer coefficient between the shelf and the product, Av is the vial area, and Tsh is the shelf temperature. The negative sign indicated that the product temperature decreases with time. In our model we estimate the heat transfer coefficient based on the experimental cooling rate of the product using Eq. Tn to Tf is used to determine the crystallization time Δt, as:where, Hf is the latent heat of fusion of ice. The temperature is assumed to be constant and equal to Tf during the crystallization. It is significant to note that this method neglects the heat transfer between the ambient air and the product and only considers heat transfer between the shelf, the vial, and the product. Solid cooling occurs once the crystallization is complete and is modeled using Eq. where, A limitation of this model is that experimentally measured nucleation and freezing temperatures must be provided as inputs to the model. Ice nucleation is spontaneous and random, and the nucleation temperature depends on the solution properties, process parameters, environmental factors, container characteristics, and the presence of particulate matter . One metLyoPRONTO performs heat and mass transfer modeling to determine primary drying time as well as the sublimation flux and maximum product temperature as functions of time during primary drying. The model assumptions are (i) 1D quasi steady state heat and mass transfer, (ii) center vial is representative of the entire batch, and (iii) convective heat transfer can be neglected. The lyophilization calculator and design-space generator are based on previously published 1D models ,20–23. WKv), which is a function of the chamber pressure (Pch), as given by , is a function of the cake length , which is determined as , which is typically taken to be 2 to 3°C below the critical temperature. In this case, the chamber pressure is fixed, but the shelf temperature is not. The sublimation front temperature, and thereby the sublimation rate, at every time step are determined based on the fixed Tbot. It is worth noting that LyoPRONTO accounts for the shelf temperature ramping from the freezing to the primary drying stages based on the ramping rate and freezing shelf temperature provided.where, ow tests , minimumow tests , or usinow tests ,31,32. TTbot ≤ Tpr, max where, Pch, opt and Tsh, opt are the ones that result in this maximum possible sublimation flux which are determined iteratively at each time step till the drying is complete. Figure Pch and Tsh, while keeping the other fixed at specified setpoints. The effect of varying and optimizing both or just one of the two cycle parameters is explored in the optimization section.The key new feature of LyoPRONTO is the optimizer tool which determines the optimal chamber pressure and shelf temperature at each time step such that the total drying time is minimized. For given vial, lyophilizer, product, and load parameters, the maximum possible sublimation flux is determined based on Eq. We perform experiments at constant chamber pressure and shelf temperature setpoints for comparison with the modeling results in order to evaluate the performance of LyoPRONTO. We use the laboratory-scale freeze-dryer REVO by Millrock Technology, Kingston, NY for our experiments. One of the four loadable shelves of the lyophilizer is loaded fully with 398 Schott 6R vials filled with 2 mL of 5% mannitol solution each. For the freezing step, we ramp the shelf temperature from room temperature to − 20°C at a rate of 1°C/min and hold for 2 h. Next, we ramp the shelf temperature to − 5°C and hold for 1 h. The primary drying is carried out at a shelf temperature of − 5°C with the chamber pressure in the 100 to 1500 mTorr range. The experiment at 300 mTorr is repeated for the same conditions using pure water as the product in order to evaluate the performance of the lumped capacitance freezing model.The convergence of the Pirani gauge measurement with the capacitance manometer (CM) reading marks the end of primary drying for the center vials . SeparatFigure Tf and Tn values are known based on previous experiments, the freezing model can predict a range of times required for the completion of the freezing process. Since the model overpredicts the crystallization time when compared with the experiments, it is safe to use these values to predict the total time required for the freezing step. Since the uncontrolled nucleation process is stochastic, the agreement between the model and experiments can be taken to be satisfactory when designing a freezing cycle where a factor of safety can be incorporated. This model has the added advantage of being user friendly, computationally less expensive than a multi-dimensional finite element model, and fast.The crystallization and solid cooling steps can be clearly distinguished in the product temperature profiles. The simulated crystallization time is about twice the experimental value for both cases due to the assumption of lumped capacitance. The product temperature profiles during solid cooling obtained using LyoPRONTO and thermocouples display similar trends and converge to the shelf temperature by the end of the solid cooling process. The fluctuation in the measured product temperature profile near the shelf temperature setpoint value towards the end of solid cooling is expected to be due to the variation in the shelf surface temperature itself as shown by the measured shelf temperature profile. While setting up a freezing process during a freeze-drying cycle, it is required to specify the time for which the shelf temperature must be maintained at the value corresponding to the freezing step. Beyond this time, the setpoints are changed to the annealing or primary drying step values. If a range of expected Kv values to obtain the best agreement between the experimental and simulated drying times. An example of this corresponding to the 300 mTorr case is shown in Fig. Kv of 5.1 × 10−4 cal/s K cm2 which gives a simulated drying time of 11.62 h. Thus, the heat transfer coefficient at a chamber pressure of 300 mTorr for the vial and lyophilizer combination is 5.1 × 10−4 cal/s K cm2 (21.34 W/m2 K). Similarly, the values of Kv that best match the experimental drying time based on Pirani gauge and manometer convergence are found at 100 and 1500 mTorr. Table Kv values at all three chamber pressures and compares the resulting drying time with the experimental value. This provides us with three values of Pch and three values of Kv and the three parameters, KC, KP , and KD in Eq. We perform experimental lyophilization runs at chamber pressures of 100, 300, and 1500 mTorr and a shelf temperature of − 5°C as described in the “KC, KP , and KD, to determine the Kv at 150 mTorr. The results modeled using this Kv are compared with experimental measurements at a chamber pressure of 150 mTorr and shelf temperature of − 5°C in Fig. KC, KP , and KD are used in LyoPRONTO along with the shelf temperature and chamber pressure setpoints as inputs and the outputs of the simulation are the product temperatures at the vial bottom and sublimation front, and the sublimation flux. The time step used for all the simulations is 3 min. The effect of the time step size is explored in a subsequent section of this paper. The simulated drying time of 12.36 h agrees within 2% of the experimental drying time of 12.62 h. The experimental product temperature at the vial bottom is averaged over three center vials and shows good agreement with the simulated temperature at the same location. The sublimation flux displays the expected trend of decreasing with time due to increasing cake resistance as the drying progresses.We use the fit heat transfer parameters, Kv and Rp based on Eqs. Pikal’s seminal paper in 1985  on simulKv and consequently, the product temperatures, are lower. The inclusion of the tray reduces the heat transferred from the shelf to the vials, and increases the drying time. The cause for the dip in Pikal’s  and aggressive (Tsh = 25°C) cycle conditions are provided in the paper and summarized in Table Kv value for the vial at 57 mTorr from the drying time values based on the two aforementioned methods. This is done for the lysozyme-drying time data, and since the vial heat transfer characteristics are independent of the product, we use these values for other protein formulations. Since the radiative heat transfer from the bottom and top shelves to the vials vary significantly at − 25 and 25°C, we obtain two sets of vial heat transfer coefficients based on the shelf temperature and their values are given in Table Kv values determined from PG and TC drying times produce product temperature measurements that do not differ significantly from each other, and both consistently overpredict the values at 25°C shelf temperature.Lewis et al.  experimeKv values determined for 0.5% protein concentration are used for these cases. The predicted and experimental drying times show good agreement once again, with an average deviation of 2%. The modeled product temperatures deviate lesser from the experimental measurements showing an average deviation of 4%. Thus, LyoPRONTO displays the ability to simulate well the primary drying parameters for various products at a wide variety of input conditions.Figure The popular iterative method among a majority of the existing lyophilization calculators in the pharmaceutical community is to divide the product length equally into a fixed number of divisions, and perform calculations from a product length of zero to the maximum. In general, the number of divisions used is 5 or 10, and in some rare cases goes up to 100. On the other hand, LyoPRONTO uses the time stepping method to proceed through the primary drying process. The time starts at 0 and proceeds till the entire length of the product is dried in steps which can be specified as an input.Figure For the faster cycle shown in Fig. et al. (We generate the design space for a range of chamber pressure and shelf temperature setpoints for the lyophilizer, product, and fill and load conditions in Fig. et al.  and maxiWhen the drying begins, and the cake length is 0, the most optimal chamber pressure at the maximum shelf temperature of 120°C is 480 mTorr. This value falls to 120 mTorr when half the drying is complete, and the cake length is equal to half the initial product length. Towards the end of drying, the inputs are purely limited by the maximum product temperature and the most optimal values are the minimum chamber pressure of 50 mTorr beyond which leakage may occur in the chamber, and a shelf temperature of 110°C. This shows that the optimal primary drying parameters varies significantly and continuously throughout the process and that it is imperative to optimize them in real time in order to improve the process time and energy efficiency.et al. (In this section, we compare traditional single setpoint cycles for chamber pressure and shelf temperature to optimized cycles with variable chamber pressure and/or shelf temperature. For the 2 mL of 5% mannitol solution in Schott 6R vials used in the experiments presented earlier, a typical cycle is simulated at the chamber pressure and shelf temperature setpoint values of 150 mTorr and 30°C respectively, as provided by Sane et al.  for 5% mTbot at the limiting product temperature of − 5°C, Tsh at 30°C, and determining the chamber pressure to obtain the highest sublimation rate possible under the given conditions.The constraints imposed for the optimized cycle are the maximum product temperature of − 5°C and equipment capability as described in the previous subsection. The maximum shelf temperature and minimum chamber pressure are limited to 120°C and 50 mTorr, respectively. The primary drying time for the typical cycle is 5.11 h. As seen in Fig. Tpr,   max increases continuously till it reaches the limiting value, and beyond this point, the cycle parameters become product temperature limited. The shelf temperature decreases continuously to ensure the − 5°C limit for the product is not exceeded.Figure Pch, opt reduces continuously till the minimum chamber pressure limit is reached when 83% of the product is dried. For the rest of the cycle, this minimum Pch is the limiting factor. The total drying time is 1.96 h and the optimization leads to 62% reduction in the primary drying time when compared with the typical cycle.Figure 15dshows the most optimal primary drying process possible for the given conditions and constraints. Both the chamber pressure and shelf temperature are variable. The figure shows that for most of the cycle, the maximum shelf temperature and maximum product temperature are both limiting factors. In other words, the most optimal chamber pressure is the one that produces the maximum sublimation flux when the shelf temperature and product bottom temperature are fixed at their maximum limiting values. The driving force for sublimation is the pressure difference between the sublimation front and the chamber. As the drying progresses, the product resistance increases, and a greater pressure difference is required to sustain the maximum sublimation flux. Consequently, the Pch and Tsh reduces the primary drying time by half. Low chamber pressures are more suitable for sucrose cycles and the optimal value stays at its minimum value of 50 mTorr. Since the limiting product temperature is much lower than that for 5% mannitol, the shelf temperature never reaches its maximum value of 120°C. The sublimation rate is limited by the low shelf temperature and is not high enough to exceed the equipment capability. The optimal shelf temperature is the one that produces the highest sublimation flux for a product bottom temperature of − 35°C and chamber pressure of 50 mTorr.Figure In order to demonstrate the behavior of the optimizer when the equipment capability is the limiting factor, we perform a simulation for product and fill conditions similar to that in Fig. In all these simulations, we do not consider the effects of heat transfer non-uniformity encountered in the lyophilization chamber. We assume that the vial heat transfer coefficient and drying time are the same for all the vials loaded in the chamber and equal to those of the center vials on account of their longer drying time. A simple way for incorporating this in the simulations is to divide the total number of vials into center and edge vials and use different vial heat transfer coefficients for each set. With more accurate process monitoring using sensor networks, the measurements could be coupled with the code to determine the most optimal conditions that not only minimize the total drying time within the constraints, but also minimize the non-uniformity in the chamber. The maximum shelf temperature that can be used without product lift-off or vial blow-out must be characterized experimentally and this must be imposed as the limiting value. Analysis of the residual moisture content and specific surface area tests to evaluate cake shrinkage in addition to the experimental demonstration of variable process parameter optimization are to be included in future work.The Lyophilization Process Optimization Tool or LyoPRONTO is an open-source application that can be used to model various aspects of the lyophilization process for a given cycle and to design more efficient cycles. The existing freezing models require 2D or 3D finite element analysis of the product in the vial which is time consuming and computationally expensive. LyoPRONTO presents a novel method of applying a 0D lumped capacitance heat transfer model to predict the crystallization time and product temperature profile during the freezing process. The overprediction of the ice crystallization time when compared with experiments can be attributed to the stochastic nature of the nucleation process and the assumption of a 0D model. The results are qualitatively accurate and can quantitatively be used to design freezing cycles provided a factor of safety is included to account for the stochasticity. The 1D quasi-steady heat and mass transfer analysis of primary drying is based on existing models but using time steps instead of steps of product length. The modeling results deviate on average by 3% from experimental measurements. The tool is also capable of determining the vial heat transfer characteristics and product resistance parameters based on the experimental drying time and product temperature profile respectively which reduces the number of overall experiments required for the complete characterization of a lyophilization cycle.LyoPRONTO can generate the primary drying design space for a given product, vial, load, and lyophilizer combination, with the most optimal setpoint of operation being the point of intersection of the equipment capability curve and the maximum allowable product temperature isotherm. Since this optimal point varies at each instant of time during a cycle, the most efficient cycle is one with variable time-dependent chamber pressure and shelf temperature profiles set at their optimal values at all times. The optimizer tool in LyoPRONTO is designed to determine such a variable profile for chamber pressure and/or shelf temperature within the constraints of the equipment, product, and practical limitations. The time interval for the variation can also be changed as an input parameter. Optimal cycles with 3 min variations in chamber pressure and shelf temperature result in a 62% reduction in the primary drying time for a 5% mannitol cycle in a laboratory scale when compared with a typical single setpoint cycle. This reduction is 50% for 5% sucrose solution and the optimization results in a significant primary drying time reduction under both partial and full load conditions.


The goals of palliative care are to relieve suffering and promote quality of life. Palliative care for older persons has been less prioritised than palliative care for younger people with cancer, which may lead to unnecessary suffering and decreased quality of life at the final stage of life.To evaluate whether a palliative care intervention had any influence on the perceived quality of life of older persons (≥65 years).This study was conducted as a complex intervention performed with an experimental crossover design. The intervention was implemented in 20 nursing homes, with a six‐month intervention period in each nursing home. Twenty‐three older persons (≥65 years) in the intervention group and 29 in the control group were interviewed using the WHOQOL‐BREF and WHOQOL‐OLD questionnaires at both baseline and follow‐up. The collected data were analysed using the Wilcoxon signed‐rank test to compare paired data between baseline and follow‐up.In the intervention group, no statistically significant increases in quality of life were found. This result contrasted with the control group, which revealed statistically significant declines in quality of life at both the dimension and item levels. Accordingly, this study showed a trend of decreased health after nine months in both the intervention and control groups.It is reasonable to believe that quality of life decreases with age as part of the natural course of the ageing process. However, it seems that the palliative care approach of the intervention prevented unnecessary quality of life decline by supporting sensory abilities, autonomy and social participation among older persons in nursing homes. From the ageing perspective, it may not be realistic to strive for an increased quality of life in older people living in nursing homes; maybe the goal should be to delay or prevent reduced quality of life. Based on this perspective, the intervention prevented decline in quality of life in nursing home residents.The high number of deaths shows the importance to identify palliative care needs in older persons at an early stage to prevent or delay deterioration of quality of life. It seems that the palliative care approach in this intervention prevented unnecessary QoL decline by supporting sensory abilities, autonomy and social participation among older persons living in nursing homes.Frail older persons are often excluded from research; this study is one of few intervention studies on palliative care in nursing homes reporting outcomes of the residents.There is an urgent need to continue testing different models to identify effective implementation strategies for palliative care due to the increased number of older persons in many countries.This intervention model reduces the gap in the limited knowledge regarding how palliative care can be implemented in nursing homes.The high number of deaths shows that it is important that staff are able to identify older persons in nursing homes who are in need of palliative care in the early stage.Due to the progression of multi‐morbidity in frail older persons living in nursing homes, a realistic QoL goal is to delay or prevent its deterioration.This intervention recommends that staff and manager seminars are held more frequently than every five weeks.The dropout rate due to death or insufficient energy was considerably high, so a narrower follow‐up period is recommended when frail older persons are included in experimental studies.Education regarding evidence‐based high‐quality palliative care is a promising model that can be performed in nursing homes; therefore, this palliative care approach can be easily disseminated to all staff.1The palliative care approach is used to promote quality of life (QoL), reduce symptoms and relieve suffering in persons with progressive, life‐threatening illnesses or injuries, despite the age, diagnosis and context of care  and front‐line leaders over a 6‐month period in 20 nursing homes in two different counties in the south of Sweden (County A and County B). Firstly, the intervention was implemented in ten nursing homes in County A, while ten nursing homes in County B served as a control group. Then, the ten control nursing homes in County B implemented the intervention, and ten new nursing homes in County A, which had not received the intervention, were chosen as a control group  dropouts were related to death, not enough energy, and/or lack of interest in participating in the follow‐up interview. Altogether, 23 older persons in the intervention group and 29 in the control group were interviewed at both baseline and follow‐up and were included in this study. The demographic variables of the two groups were similar, with a median age of 87 years, and most of the included older persons were female, widowers or widows Table .2.4A contact person was designated at each of the included nursing homes and informed the older persons who met the inclusion criteria about the aim and design of the study. If the older person responded positively regarding participation in the study, their oral informed consent was requested. Then, the contact person passed the personal data of the older persons to the researchers, and the time and place for the interview were determined. Before the interview, the information about the study was repeated, and the older person had the opportunity to ask questions before signing the written informed consent. With the intention of obtaining reliable data, the older persons answered the two questionnaires in the form of a structured interview. The four interviewers who asked the older persons the questions from the questionnaires were all Registered Nurses and had experience interviewing older persons. The response options were printed in large text on a separate paper to assist the older persons in answering the questions  physical health, containing seven items; (b) psychological, containing six items; (c) social relationships, containing three items; and (d) environment, containing eight items. The older persons were asked to respond on a five‐point positively rated Likert scale. The total score of the scale ranges from 26 to 130, with higher values indicating a better quality of life , the project leader of KUPA. Thus, the total score in this study ranged from 25 to 125. 0.66, 0.73, 0.38, 0.60.The WHOQOL‐OLD questionnaire consists of a total of 24 questions and is used to assess QoL in older adults. The questionnaire consists of six domains containing four items each: (a) sensory abilities; (b) autonomy; (c) past, present and future abilities; (d) social participation; (e) death and dying; and (f) intimacy. Respondents are asked to respond on a five‐point positively rated Likert scale. The total score of the scale ranges from 24 to 120, with higher values indicating a better perceived QoL . The selection of the statistical tests to analyse data other than the descriptive statistics was based on whether the data were distributed normally and the scale level of the instruments. A Wilcoxon signed‐rank test was used to compare paired data from after the intervention period to the data from before the intervention period. Subgroup analysis, using the Mann–Whitney U test and the Kruskal–Wallis test, was applied to compare baseline characteristics of the intervention group and the control group. The same analyses were applied for the dropouts in the intervention group with the participants in the intervention group and the dropouts within the control group with the participants in the control group. Either Pearson's chi‐square test or Fisher's exact test was used when the expected value was <5. Analyses were performed using IBM SPSS Statistics version 24. A two‐tailed 2.7The Regional Ethics Review Board in Lund approved the KUPA project (reference number: 2015/4). The project is also registered under trial registration NCT02708498. The ethical research principles for medical research guided this study in accordance with the ethical standards of the Declaration of Helsinki  of the intervention and control groups as well as the dropouts in the intervention group with the participants in the intervention group and the dropouts within the control group with the participants in the control group. The total median score from the QOL‐BREF questionnaire for the intervention group at baseline was 84 (first quartile (Q1)‐third quartile (Q3) = 77–97). The corresponding score for the control group was 85 (Q1–Q3 = 77–92.5). Three months after the knowledge‐based palliative care intervention was completed, a non‐significant increase was reported in the intervention group, with a median score of 86 (Q1–Q3 = 74–95), while the control group reported a non‐significant decrease, with a median score of 82 (Q1–Q3 = 77.5–90)  and “negative feelings”   Table . The quesensory abilities dimension decreased from 16 to 13 , the median score in the autonomy dimension decreased from 15 to 12 , and the median score in the social participation dimension decreased from 15 to 13 . In the intervention group, no statistically significant changes were found for any of the dimensions  and the item “received the recognition you deserve in life” decreased from a median score of 4 at baseline to a median score of 3 at follow‐up . Furthermore, an increase was found in the control group for “loss of sensory abilities that affect participation in activities” from a median score of 3 to a median score of 4   for all nursing home residents. ACP is a discussion with the resident or a representative of the resident about the goals and desired direction of the patient's care. One RCT study using ACP for 309 older persons aged 80 and over found that when using ACP, end‐of‐life wishes were much more likely to be known , which also decreased the generalisation of the results, even though the recruiting procedure was carried out in both small and large nursing homes as well as in both urban and rural areas. It should be noted that no statistically significant differences regarding background variables were detected between the dropouts and the included older persons. Including a larger number of nursing homes was not justifiable from a resource point of view but poses a threat to the effectiveness of the intervention. In fact, the residents in nursing homes represent the frailest older population in Sweden, with a median survival time of six to nine months ; interviews with the older persons: LB. All authors contributed to the content of the manuscript text and critically reviewed, discussed, and approved the final version of the manuscript.


The nature and characteristics of this family of complexes involving π coordination between the fullerene and a metal centre have been studied from a theoretical point of view. We are particularly interested in complexes where η6 coordination is present, this being the strangest manifestation of known coordinations, and thus we have studied several known and simulated compounds of this kind in order to understand the lack of examples. The presence of other η6 or η5 ligands on the opposite side seems to be an important element aiding the stabilization of these complexes, also inducing the conductive and semiconductive behaviour of the studied species.Novel organometallic complexes of fullerene C The extensive family of fullerene compounds has attracted considerable interest in several different fields of chemistry and physics due to their particular intrinsic characteristics ,2. One o2 fashion on a 6,6 junction of the fullerene [5 mode is found [6 complex [There are several examples of coordination compounds where a fullerene is joined to a metal atom, but the large majority are compounds where the coordination occurs in ηullerene ,6, althois found  and an e complex ,9.60 or a C70 unit, but there is also a very interesting possibility [60 or C70 mentioned above, therefore there is a greater possibility for η6 coordination to take place. The pyramidalization angle is defined as the angle between the projection of a specific C-C bond and a plane containing one of the designed carbons and its two adjacent atoms and it is useful to measure the sphericity of the fullerene molecules.All the references mentioned above concern experimental or theoretical works where the substituting fullerene is a Csibility ,11,12,136 with a C74 or larger ligand [All the known metallic complexes consisting of larger fullerenes are endohedral, but there are no experimental reports describing an exo complex ηr ligand ,4,5, but80 fullerene isomers [6 fashion with a transition metal atom, with an oxidation state of zero and complemented by a benzene ring, in order to have a coordination sphere which matches the 18 electron rule [The main goal in this work is to examine the family of all C isomers ,15,16 coron rule . This stAll calculations were carried out by applying a pure DFT method for energy evaluations, applying Becke’s gradient corrections  for exch80 fullerene family consists of several members, and seven possible isomers have been identified [5d, D2, Ih, C2v (two isomers), D3 and D5h. We have simulated the possible coordination compounds of six of these and in the case of the fullerene C2v, we have found almost the same energy behaviour, as well as frontier molecular orbital behaviour. Therefore we have decided to include only the results from one of the two analogs. All the corresponding structures are presented in The Centified . They beIt is obvious that cases exist where it is possible to find several isomers for the complexes because the metals have different coordination possibilities. To simulate all possibilities represents an enormous task and will be undertaken in a future study. However in this study, we present the results for only one structure from each fullerene isomer and we have chosen those instances where the structure was easier to optimize and where the six-member ring presents the most planar shape. We have adopted a nomenclature where each complex is named according to the point group of the fullerene that is coordinated with the metal, although in all cases the symmetry of the complexes is less than that of the isolated fullerenes.The first important question is; can these complexes exist? If the answer is yes, can all isomers have complexes? In this respect, the entire family has been studied. The first analysis only consists of a comparison between the frequency calculations.i.e., the isomers Ih and D5h have negative frequencies, which was to a certain degree anticipated in both cases because these C80 isomers are not stable molecules [2 and D5d. However it is very common to find that a compound becomes stable when it forms a complex with a metal centre, indeed both isomers can be stabilized by the formation of an endohedral complex with two atoms of a lanthanid metal [The results show that two species, olecules ,21 due tid metal ,22, theri.e., the C2v). Thus the result is very interesting because again only the large symmetry isomers (Ih and D5h) seem to be difficult to prepare (in terms of thermodynamics). All present reasonable stability values, however there are other criteria which may be useful indicators.The total energy of the six compounds can be compared; the relative values are presented  manifests the strongest bond between the fullerene ligand and the metal.The definitive results are presented in 2 emanating from the atomic centre of the Cr-benzene fragment localized in the HOMO of all configurations, considering the narrow difference between HOMO and LUMO in all cases the back bonding depicted is possible, however the effect is stronger in the case in which the pyramidalization angle is the larger.The strength of this bond must be a consequence of improved overlapp between the orbitals of the metal and the six-member ring from the fullerene ligand, which participates in the coordination. A better interaction can be found for this isomer which has a larger pyramidalization angle, because the spheroidal shape of the body compels the pz orbitals of the six member rings on the fullerenes to become outside to the centre of the hexagone, this interaction can be found in the LUMO of all cases causing improved overlapping with the toroidal ring of the molecular orbitals dz2. In the case of the fullerenes from the C80 family, the corresponding values are presented in 5d and D2 isomers have large pyramidalization angles. The same angle in the case of the fullerene C60 is 31°, a value which was obtained in both theoretical and experimental works [Therefore in the present cases a larger pyramidalization angle helps to have a better bonding between the fullerene and the metal atom. The shape of the resultant molecular orbitals for the complex is shown in al works ,24.h are able to have a five folded degenerated set for the HOMO and a four folded degenerated set for the LUMO [The nature of the bond can be surmised as a consequence of the electronic behaviour of the fragments involved. First, all fullerenes and their derivatives are well known as electronic acceptors . The symthe LUMO . Thus inh belongs to the point group C2 and the D3d belongs to the Cs point group, therefore there are no cases with degenerated sets for their frontier orbitals, but in all cases the HOMO-LUMO gap is very short. These values are also presented in 5d structure, where the value of the HOMO-LUMO gap for these species is ~0.2 eV, representing a conductor with a similar value to that of the grapheme [The analysis of the molecular orbital scheme for all the isomers being studied is very important if a stable complex is to be proposed. All the frontier molecular orbitals are shown in grapheme . This re6 coordination has been analyzed theoretically. The family presents four cases of complexes which yield promising results with the respect of thermodynamic stability, they are the complexes with fullerenes with symmetry C2v, D3, D2 and D5d whereas the two remaining isomers coming from the more symmetrical fullerenes, i.e., Ih and D5h, seems to be unstable species. All of them can have strong π bonds between the fullerene and the chromium atom, but the interaction is ruled by two factors, one is the narrow energy gap between HOMO and LUMO in all cases  that allow a back bond interaction that reinforce the bond and the pyramidalization angle that allow this back bond between the pz orbitals coming from the six membered ring of the fullerene that contributes to the bond  and the dz2 orbital from the metal in the fragment CrC6H6 . All species show interesting electronic features and if they are prepared will be useful for electronic devices application.The ability of the family of C80 fullerenes to generate organometallic complexes with a metal in oxidation state zero and η


Hammers provide most powerful general purpose automation for proof assistants based on HOL and set theory today. Despite the gaining popularity of the more advanced versions of type theory, such as those based on the Calculus of Inductive Constructions, the construction of hammers for such foundations has been hindered so far by the lack of translation and reconstruction components. In this paper, we present an architecture of a full hammer for dependent type theory together with its implementation for the Coq proof assistant. A key component of the hammer is a proposed translation from the Calculus of Inductive Constructions, with certain extensions introduced by Coq, to untyped first-order logic. The translation is “sufficiently” sound and complete to be of practical use for automated theorem provers. We also introduce a proof reconstruction mechanism based on an eauto-type algorithm combined with limited rewriting, congruence closure and some forward reasoning. The algorithm is able to re-prove in the Coq logic most of the theorems established by the ATPs. Together with machine-learning based selection of relevant premises this constitutes a full hammer system. The performance of the whole procedure is evaluated in a bootstrapping scenario emulating the development of the Coq standard library. For each theorem in the library only the previous theorems and proofs can be used. We show that 40.8% of the theorems can be proved in a push-button mode in about 40 s of real time on a 8-CPU system. Interactive Theorem Proving (ITP) systems  we denote an occurrence of a term t in a term context C.We now describe a simplification of our proof search procedure. We will treat the current proof state as a collection of judgements of the form A) to the judgement A is inserted is implicitly assumed to be the same as the position at which The proof search procedure applies the rules from Fig. e denote fresh existential metavariables of appropriate types. These metavariables need to be instantiated later by Coq’s unification algorithm. In the rules k ranges over all k are premises of the rule, not just a single one. Moreover, in these rules for any term T by P is an atomic proposition, i.e., a proposition which is not a dependent product, an existential, a disjunction or a conjunction. In the T is not a proposition.In Fig. The tactic yapply in rule f Matita , but ourThe tactic yrewrite in rule The rules in Fig. The above description is only a readable approximation of what is actually implemented. Some further heuristics are used and more complex restrictions are put on what rules may be applied when. In particular, some loop checking (checking whether a judgement repeats) is implemented, the number of times a hypothesis may be used for rewriting is limited, and we also use heuristic rewriting in hypotheses and heuristic instantiation of universal hypotheses. Some heuristics we use are inspired by the crush tactic of Adam Chlipala .As mentioned before, our proof search procedure could be seen as an extension of a search for lgorithm , 75. As The proof reconstruction phase in the hammer tactic uses a number of tactics derived from the procedure described above, with different depth limits, a bit different heuristics and rule application restrictions; plus a few other tactics, including Coq’s intuition, simpl, subst, and heuristic constant unfolding. Various reconstruction tactics are tried in order with a time limit for each, until one of them succeeds (or none succeed—then the proof cannot be reconstructed).It is important to note that no time limits are supposed to be present in the final proof scripts. The CoqHammer plugin shows which of the tactics succeeded, and the user is supposed to copy this tactic, replacing the hammer tactic invocation. The final reconstruction tactic does not rely on any time limits or make any calls to external ATPs. Its results are therefore completely reproducible on different machines, in contrast to the main hammer tactic itself.In this section we present the technique used to select the combination of strategies included in the integrated hammer and present an evaluation of the components as well as the final offered strategy.The evaluation in this section will perform a push-button re-proving of Coq problems without using their proofs. In order for the evaluation of the system to be fair, we need ensure that no information from a proof is used in its re-proving, as well as that the actual strategy that is used by the whole system has been developed without the knowledge of the proofs being evaluated.The system will be evaluated on the problems generated from all theorems in the Coq standard library of Coq version 8.5 (a version of the plugin works with Coq 8.6 and 8.7 as well). The problems were generated from the source code of the library, counting as theorems all definitions  that were followed by the Proof keyword. The source code of the library was then modified to insert a hook to our hammer plugin after each Proof keyword. The plugin tries to re-prove the theorem using the Coq theorems accessible at the point when the statement of the theorem is introduced, using the three phases of premise selection, ATP invocation and proof reconstruction as described above.This simulates how a hammer would be used in the development of the Coq standard library. In particular, when trying to re-prove a given theorem we use only the objects accessible in the Coq kernel at the moment the theorem statement is encountered by Coq. Of course, neither the re-proved theorem itself nor any theorems or definitions that depend on it are used. The number of problems obtained by automatically analysing the Coq standard library source code in the way described above is 9276. This differs significantly from the number of problems reported in . There tFurthermore, the problems are divided in a training set consisting of about 10% of the problems in the standard library and a validation set containing the remaining 90% of the problems. The training set is used to find a set of complementary strategies. Just like for the hammers for higher-order logic based systems and for Mizar a single best combination of the premise-selection algorithm, number of selected premises, and ATP run for a longer time is much weaker than running a few such combinations even for a shorter time. Contrary to existing hammer constructions , 55, we and they could be reconstructed by the proof reconstruction procedure described in Sect. In our evaluation we used the following ATPs: E Prover version 1.9 , VampireThe results of the hammer strategies including the premise selection are very good in comparison with the results on the dependencies. Evaluating the translation with hrecon reconstruction is presented in Table Given the common hardware configuration of computers today, we consider as the integrated system a combination of eight complementary strategies. The final results of the hammer including reconstruction on the validation set are presented in Table The intended use of a hammer is to prove relatively simple goals using available lemmas. The main problem a hammer system tries to solve is that of finding appropriate lemmas in a large collection and combining them to prove the goal. The advantage of a hammer over specialised domain-specific tactics is that it is a general system not depending on any domain knowledge. The hammer plugin may use all currently accessible lemmas, which includes lemmas proven earlier in a given formalization, not only the lemmas from the standard library or other predefined libraries.It sometimes happens that the ATPs find proofs with fewer dependencies than the proofs in the standard library. One example is the Coq lemma isometric_rotation:Its current proof in the Coq standard library uses 6 auxiliary facts and is performed using the following 7 line script: Multiple ATPs found a shorter proof which uses only two of the dependencies: the definition of euclidean distance and the lemma isometric_rotation_0. This suggests that the proof using the injectivity of square root is a detour, and indeed it is possible to write a much simpler valid Coq proof of the lemma using just the two facts used by the ATPs: The proof may also be reconstructed from the found dependencies inside Coq. This is also the case for all other examples presented in this section. The proof of this lemma in the standard library uses 6 auxiliary lemmas and is performed by the following proof script (two lemmas not visible in the script were added by the tactic prove_sup0):  ATPs found a proof of le_double using only 3 lemmas: Arith.PeanoNat.Nat.le_0 _l, Arith.Mult.mult_S_le_reg_l and Init.Peano.le_n. None of these lemmas appear among the original dependencies.Also for some theorems the ATPs found proofs which use premises not present in the dependencies extracted from the proof of the theorems in the standard library. An example is the lemma le_double from Reals.ArithProp:  This cannot be proven using the omega tactic because of the presence of multiplication. The tactic invocations eauto with arith or firstorder with arith do not work either. The hammer tool finds a proof using two lemmas from Arith.PeanoNat.Nat: add_comm and mul_comm.Another example of hammer usage is a proof of the following fact:  This goal cannot be solved using standard Coq tactics, including the tactic omega. Z3 with 128 preselected premises found a proof using the following lemmas from Arith.PeanoNat.Nat: add_succ_r, le_0_l, pow_succ_r, add_0_r. The proof may be reconstructed using hexhaustive 0 or hyelles 5 tactic invocations.A similar example is the goal  This goal cannot be solved (in reasonable time) using either eauto with datatypes or firstorder with datatypes. The hammer solves this goal using just one lemma: Lists.List.in_app_iff.The next example of a goal solvable by the hammer involves operations on lists. This goal cannot be solved using standard Coq tactics. Eprover with 512 preselected premises found a proof using two lemmas from Lists.List: in_cons and in_or_app.A similar example is This goal can be solved neither by standard Coq tactics nor by the hammer. However, it suffices to issue the ltac command induction l and the hammer can solve the resulting two subgoals, none of which could be solved by standard Coq tactics. The subgoal for induction base is:  The hammer solves this goal using the lemma Forall_cons from Lists.List and the definition of ++ (Datatypes.app). The subgoal for the induction step is:The hammer solves this goal using the lemma Forall_cons, the inductive hypothesis (IHl) and the definition of ++. Note that to reconstruct the ATP proof for this goal it is crucial that our reconstruction tactics can do inversion on inductive predicates in the context.The hammer is currently not capable of reasoning by induction, except in some very simple cases. Here is an example of a goal where induction is needed. In this section we briefly discuss the limitations of the current implementation of the CoqHammer tool. We also compare the hammer with the automation tactics already available in Coq.The intended use of a hammer is to prove relatively simple goals using accessible lemmas. Currently, the hammer works best with lemmas from the Coq standard library. Testing with other libraries has been as yet very limited and the hammer tool may need some adjustments to achieve comparable success rates.The hammer works best when the goal and the needed lemmas are “close to” first-order logic, as some more sophisticated features of the Coq logic are not translated adequately. In particular, when dependent types are heavily used in a development then the effectiveness of the hammer tool is limited. Specifically, case analysis over inhabitants of small propositional inductive types is not translated properly, and the fact that in Coq all inhabitants of A small propositional inductive type is an inductive type in In Coq all propositions  of the proofs founds by the ATPs, which is lower than that in other systems. The premise selection algorithms are not as precise as those involving machine learning algorithms tailored for particular logics. In particular, for similar size parts of the libraries almost the same premise selection algorithms used in HOLyHammer  or IsabeThe core of the hammer—the translation to FOL—could be improved to make use of more knowledge available in the prover in order to offer a higher success rate. It could also be modified to make it more effective on developments heavily using dependent types, and to more properly handle the advanced features of the Coq logic, possibly basing on some of the ideas in . FinallyIn our work we have focused on the Coq standard library. Evaluations on a proof assistant standard library were common in many hammer comparisons, however this is rarely the level at which users are actually working, and looking at more advanced Coq libraries could give interesting insights for all components of a hammer. Since we focused on the standard library during development, it is likely that the effectiveness of the hammer is lower on libraries not similar to the standard library.In particular, the Mathematical Components Library based on SSReflect  would be


Simulation data are presented for identifying and analysing the dynamic properties of the rainbow metamaterials as presented in the articles “Rainbow metamaterials for broadband multi-frequency vibration attenuation: numerical analysis and experimental validation”  and “Optimal design of rainbow elastic metamaterials” . In this data article, the frequency response functions and mode shapes of the rainbow metamaterials are numerically calculated by Finite Element models set up in Ansys Mechanical APDL. Harmonic analysis was performed to figure out the receptance function values of the rainbow metamaterials within the frequency regime 0–500 Hz. Modal analysis was applied to estimate the mode shapes, which could be used to explain the critical peaks and dips in the receptance function curve. Source files of Finite Element models are provided in the data. The Finite Element simulation is not only an effective alternative way to estimate the dynamic properties of the rainbow metamaterials, the mode shape analysis, which is unlikely to be achieved with the analytical model, provides direct insights into the underlying vibration mechanism of the rainbow metamaterials. The receptance function values of the rainbow metamaterial are obtained as shown in Typical mode shapes of the rainbow metamaterials with corresponding natural frequencies equal to the critical peak and dip frequencies marked in the receptance function curve of Raw simulation data for the receptance functions and mode shapes are shared respectively as supplemental files “FRFcal.db” and “Modeshape cal.db”.2In the FE model, the modelling assumptions are as follows: the Π-shaped beam and parallel plate insertions are modelled by Shell181 element, the cantilever beams Beam188 element, and the spatially varying mass21 element. All the boundaries of the rainbow metamaterial beam are unconstrained.For the receptance function simulation, a load force F = 1 N in Z-direction is exerted on one end of the beam as shown in The obtained mode shapes could explain the critical points in receptance function curve, which also reveals the vibration mechanism of the rainbow metamaterial. As can be seen from


Haloxylon ammodendron, a plant widely distributed in arid lands, as an example, we used a consumer‐grade handheld camera to take a series of overlapping images of this plant. Computer vision and photogrammetric software were used to reconstruct highly detailed three‐dimensional data of the plant surface. This surface data was compared to the point cloud of the plant acquired from concomitant terrestrial laser scanning. We demonstrated that the accuracy and degree of completeness of the image‐derived point clouds are comparable to that of laser scanning. Plant structural parameters (such as tree height and crown width) and three‐dimensional models extracted from the point clouds also agree well with a relative difference of less than 5%. Our case study shows that a common camera and image processing software can be an affordable, highly portable, and viable option for acquiring accurate and detailed high‐density and high‐resolution three‐dimensional information about plant structure in the environment. This digitization technique can record the plant and its surrounding environment effectively and efficiently, and it can be applied to many ecological fields and studies.Plant structural parameters are important for ecological studies and for monitoring the environment. Terrestrial laser scanning has become a widely accepted technique for acquiring accurate high‐density three‐dimensional information about plant surfaces; however, this instrument is expensive, technically challenging to operate, heavy, and difficult to transport to hard‐to‐reach areas such as dense forests and undeveloped areas without easy vehicle access. Using  Obtaining accurate plant structural parameters  is important for a wide variety of applications within the fields of forestry and ecology and for environmental studies  surface information of the scene can be reconstructed from overlapping images taken by the camera from different viewpoints. Some examples of recent applications include single‐tree and plot‐level 3D modeling  is a drought‐resistant plant species distributed widely in the arid lands of the Middle East and Central Asia. Its size ranges from a large shrub to a small tree . Specifically, we would like to answer the following questions. (1) Can 3D surface points be obtained using computer vision and photogrammetry to process overlapping photographs taken from around the plant with an off‐the‐shelf consumer‐grade camera? (2) How does this image‐derived point cloud data compare to point clouds derived from the established laser scanning technique in terms of accuracy and completeness? (3) How does the plant structural information derived from the point clouds produced using the two techniques compare?The main goal of this study is to determine whether a computer vision‐based technique can be used to obtain accurate high‐resolution 3D information from saxaul  at the Fukang Desert Ecological Research Station  laser scanner on 8 August 2015 to obtain detailed information about plants in the plot. The transmitted laser pulse is in the near‐infrared spectrum , and the scanner is accurate to 3 mm at a 100 m distance. The normal working measurement range is dependent on the target reflectivity; for example, at 90% reflectivity, the range can be up to 600 m; with 20% reflectivity, it is 280 m. The scanner weighs approximately 10 kg (excluding the battery).There are seven saxaul plants growing in this plot that are being continuously monitored for stem sap flow along with other long‐term ecological observations. Each individual plant is protected within a cage‐like structure made of steel pipes Figure . The stuThe weather was cloudy with some wind. For each full‐view laser scan at 0.04 degrees, more than 10 million data points were acquired. Scan time in the field was around 10 min per station .Reflective disks being scanned were identified in the resulting point cloud and used as tie points for scan‐to‐scan registration; registration results of better than 1 cm were achieved for all of the scans. After registration, all of the scan data were put into the same project coordinate system, and data from all scan positions were combined to get full coverage of the study objects. The data were registered and combined using the RiscanPRO software that was supplied with the laser scanner. Furthermore, outliers and noise were also removed using the software tool. Basic data processing was usually finished in half an hour. The TLS point cloud served as a reference for evaluating the image‐based point cloud.2.3Image data were acquired the day after laser scanning. The sky was overcast when photographs were taken. A Nikon D600 digital camera and AF‐S Nikkor 24‐85 mm f/3.5‐4.5G ED VR lens  were used. The total weight  was 1.2 kg.A series of images were acquired of tree 1. The operator took a picture of the plant from a specific position and then moved to the next position by a small step. Care was taken to make sure that there were many overlaps (at least 60%) between two consecutive photographs. The camera was held by an operator at approximately eye level (170 cm above ground) and pointed toward the tree, and the focus was manually adjusted. A schematic showing the camera trajectories around the plant is shown in Figure The camera was not calibrated beforehand. It was set to program mode, which causes the camera to automatically change its shutter speed and aperture to achieve the optimal exposure. The typical parameters were as follows: F10 aperture, 1/500 s shutter speed, and an ISO value of 640. The camera was manually focused before taking the photographs. The image size was 6,016 × 4,016 pixels, and a total of 37 pictures were taken along the camera trajectory. The photography took less than 5 min and produced a total of 389 MB of image data.Pix4DMapper  and PhotoScan  were used to process photographs for computer vision and photogrammetry. These are two commercial photogrammetry programs frequently used in many research applications. The image processing steps are similar in the two programs. The first step uses a structure from motion (SfM) technique to reconstruct both camera positions and 3D points. More specifically, unique features were extracted from the images and then matched with features extracted from other images. A self‐calibrating bundle block adjustment is then applied to calibrate the cameras and derive a sparse set of feature coordinates  to transform the image's 3D data to the TLS project coordinate system. This facilitated the comparison between the image‐derived and TLS point clouds by giving both sets the same coordinate system. Five points were used as control points; four of them were at the center of the bolts that fasten the iron pipes at the four corners of the cage, and the last one was located at the upper left corner of the solar panel near the ground Figure . The XYZImage processing time and the number of points generated are summarized in Table Irrelevant data points such as those corresponding to the ground and cage were manually removed from both TLS and image‐derived point cloud data, and only the points corresponding to the tree were kept . Only data with similar densities were compared . Figure 33.1From Figure The major components of the plant (its branches and leaves) are visible in the image‐derived point cloud, but some of the finer branches and leaves are missing, particularly in the lower and the furthest parts of the tree, making it difficult to compare those regions in the image‐derived point cloud with the reference TLS data. Additionally, there are some false data points indicated in the figure by the presence of blue and green points where there are no corresponding TLS points. Noise is also noticeable in some regions; for example, at the higher part of the plant, there is a thick patch of white points. These white points can be reduced in the image preprocessing step by applying a mask to the background. A mask delineates the area of the image that will be used for 3D modeling, and the background is therefore excluded. Manual masking is a time‐consuming process and it was not implemented in this study.We looked at the point spatial distribution pattern in different scene configurations. After deleting the apparent noise and unrelated objects from the scene, we obtained a point cloud of tree 1 along with the cage and the ground. Next, the ground and the steel pipes were manually removed. The spatial point density also changed after this process as shown in Table It can be inferred from the table that the points in the image are not evenly distributed spatially; they are concentrated in the ground and the pipes. After extracting the points corresponding to the plant, the density drops to nearly half of its original value (relative difference of approximately 45%). In the TLS data, the distribution is more even, as the point density before and after removing the ground and the pipes changes very little (a relative difference of approximately 13%).3.2To quantify the spatial distribution of the points, we computed the cloud‐to‐cloud distance in CloudCompare using TLS data as a reference. CloudCompare is an open source 3D point cloud and mesh processing program  of 2 cm thickness were cut through the point cloud at different heights. Figure A closer look at the point clouds revealed more detailed information about their similarities and differences. Horizontal slices  direction, and crown width was defined as the maximum difference in the horizontal (XY) plane. The parameters derived from TLS point clouds were used as reference values. Due to its protected status, we did not enter the cage to measure the plant height and crown width directly. As the TLS data were acquired from multiple positions with fine resolution, it can capture surface information of the whole plant and the plant height and crown width derived from these TLS data can be regarded as accurate. Table We also compared the plant parameters that could be conveniently extracted and the tree models that could be reconstructed from the different point clouds. Tree heights and crown widths were measured manually from the noise‐removed point cloud. Tree height was defined as the maximum difference in the vertical . Manually carrying the heavy instrument  over a long distance to a hard‐to‐reach survey site would be burdensome. It also takes some training and experience to learn how to set up scan positions and operate scan controls. In contrast, consumer‐grade handheld cameras are widely available, cheap, lightweight, and easy to use; the image processing program is also very easy to use.To apply a computer vision (SfM) algorithm, images need to be taken with enough overlap and from different viewing angles. Following this guideline, we were successfully able to reconstruct dense surface points from the saxaul plant from 37 photographs taken with a consumer‐grade camera. Although it is easy and safe to take as many photographs as one wishes to guarantee a successful 3D reconstruction, having to process so many photographs may not always be desirable because of the additional time and computing resources required. Taking just enough photographs for 3D reconstruction remains an art as the composition of each scene is different and the number of features varies. It seems that a minimum of 60% overlap between the images is highly recommended for 3D reconstruction. Some researcher . Unlike the plants being protected for long‐term ecological observation, it was not enclosed in a cage. Surface points of its stem and main branches were reconstructed from 20 photographs. We suspected that the regularly shaped steel pipe cage actually helped 3D reconstruction by providing more feature cues; however, even without this additional aid, saxaul plants were still effectively modeled. It will be interesting to determine whether this image‐based reconstruction also works for other desert plants such as We processed these photographs with two leading commercial photogrammetry software packages using the default settings. The point clouds obtained from image processing had medium quality and density. It is possible to achieve points with better quality and density; however, the results thus far prove that these medium‐quality point clouds are comparable to the data points acquired from TLS in terms of data quantity and accuracy. The price of the software is a few thousand dollars Table , which rIn our study, as well as in other similar studies , this GCP procedure is not required. It would be easier to make a few distance measurements of some of the objects in the scene while one is out in the field taking photographs and later assign dimensions to these objects in the reconstructed point cloud.In this study, we sought to recover the 3D structure of a single plant using overlapping images taken with a camera from the ground. This technique can easily be extended to wider areas covering many plants .Image‐derived points are unevenly distributed spatially; the density of a point is related to the plant structure and image frame configuration among other things. Different software and parameter settings also generate somewhat different results. More studies are needed to fully understand the advantages and disadvantages of these software programs. In addition to the In addition to the commercial software, there are some open source computer vision programs such as Bundler Snavely, , VisualS5The purpose of this study was to determine whether detailed and accurate 3D desert plant surface data could be obtained from overlapping images taken with an off‐the‐shelf consumer‐grade handheld camera. By comparing the point clouds derived from different sources , as well as plant structural information extracted from the point clouds, we found that the image‐derived points were dense and accurate enough to represent the detailed major branching structure of the plant. However, there were missing points in some of the finer branches and leaves, and noise was present in areas with significant background interference. Compared to the reference terrestrial laser scanning data, the average accuracy of image‐derived point data was within 2 cm using point‐to‐point comparisons. The relative differences of the extracted plant heights and crown widths were below 5%. Thus, we have definite answers to the questions we posed.Computer vision and photogrammetry software offer an easy, low‐cost, and accurate approach for 3D plant reconstruction. Terrestrial laser scanning produces accurate and complete data, but this technique is limited by its heavy and relatively expensive hardware and its more technically demanding operation. Both TLS and computer vision technology are developing fast, as lighter and more affordable LIDAR sensors are emerging. By no means will one technique totally replace the other; we just have more tools in our toolbox to choose from. We anticipate computer vision techniques will complement TLS and find more applications in ecology and environmental monitoring and research.We expect that future research and development will focus on the automation of some parts of the processing, such as masking or scaling, plant structural parameter extraction, and the integration of the whole process into a single software package. Following in this direction, a low‐cost photogrammetric analysis toolbox could be very helpful for assessing plant growth and monitoring the environment.The authors claim no conflict of interest.CC and HH designed the experiment; HH and HZ acquired the data and performed the analysis; HH wrote the manuscript; CC and TL revised the manuscript.


Here, we follow the stable propagation of a roughening crack using simultaneously Digital Image Correlation and Infra-Red imaging. In a quasi-two-dimensional paper sample, the crack tip and ahead of that the fracture process zone follow the slowly, diffusively moving “hot spot” ahead of the tip. This also holds when the crack starts to roughen during propagation. The well-established intermittency of the crack advancement and the roughening of the crack in paper are thus subject to the dissipation and decohesion in the hot spot zone. They are therefore not only a result of the depinning of the crack in a heterogeneous material. The sample response to loading is not smooth but intermittent, and cracks move likewise by avalanches and leave rough trails or crack surfaces. Understanding why and how is important both for fracture mechanics and for the fundamental reasons that give rise to such behavior. The complexity seen means that ordinary Linear Elastic Fracture Mechanics (LEFM) or the minimal theoretical approach needs to be considered with care, and the understanding of how strong materials are, and why, is quite challenging.Fracture as a physics problem is a challenge since many of the features seen in an experiment on failure exhibit complex phenomena5. The addition of disorder in the material combines with the driving external stress and the self-elasticity of the crack front to create a critical point: precisely at the disorder-dependent external stress value the crack velocity is zero excluding creep propagation. From this follows a number of important consequences like the critical strength and its dependence on sample size, the (in- and out-of-plane) self-affine roughness exponents measuring the rough cracks, the fluctuating character of the crack propagation velocity due to avalanches, and the sub-critical response or creep. Such theories have been applied with success to planar crack fronts2, to account for crack surface roughening1, and to explain the stress-dependence of the creep rate7, to mention a few.One recently found and developed paradigm to explain avalanches and such is the depinning of cracks, as an application of a general non-equilibrium phase transition in statistical mechanics3. In reality, cracks exist in an environment where several coupled phenomena may take place. Plastic deformation ahead of the crack and material weakening or “damage mechanics” due to the overloading of the material in the proximity are both often simply summarized by the presence of a Fracture Process Zone (FPZ)9. It is an open question to which degree the generalization of LEFM by depinning is applicable, and what other scenarios may be found.However, fracture is a multi-scale phenomenon. Critical crack propagation describes materials with a few key extra parameters like the strength of the elastic coupling of fluctuations along the crack front, the average fracture toughness and the standard deviation as a measure of disorder11. Paper is known to exhibit crack roughening11, a fact that can be checked by tearing a piece by hand and lead to self-affine roughness (see e.g. ref.13) and intermittent crack propagation16. Less known is that the energy dissipation is also detectable by Infra-Red (IR) imaging, as the material heats up under loading and in the presence of a defect the localized heating creates noticeable or easily measurable “hot spots”, with a clear temperature difference to the rest of the sample18. We combine the sample stress-strain curve with IR observations, and perform simultaneous Digital Image Correlation (DIC) analyses of the sample strain fields21 to look at the causality of the crack propagation or its relation to the maximum dissipation and to the peaks of the tensile stresses (as measured by the strain fields) during crack propagation and simultaneous roughening.Here, we study the failure of a notched material sample in the context of an elasto-plastic material (copy paper) with a FPZε, temperature change) decay to the background values.In what follows, we discuss a typical experiment. The simultaneous measurement of the sample surface temperature fields and local displacements (see Methods section) allows to superimpose the measured fields on the top of each other and look for their simultaneous development with time in a tensile test. This is illustrated in Fig. 11. For small enough strains the behavior is roughly linearly elastic. The bending of the stress-strain curve around t = 20 s is a signature of the development of plastic deformation and irreversible strain. During this phase, the “hot spot” appears in the IR images and becomes a feature with details we discuss below. At around 60 seconds (corresponding to a strain of 2.3%) the peak stress σc is reached, and beyond that peak the hot spot is detectable until the final sample failure, which occurs at around 90 seconds. The last part of the stress-strain curve corresponds to stable crack propagation with the elastic compliance of the sample changing (decreasing) in a linear manner.We use here and in what follows seconds instead of strain to underline the timescale of the hot spot development. The sample stress-strain curve in Fig. t = 37 s there is a clear evidence that the crack has advanced. The effect of the crack propagation to the carried load of the sample is small compared to the propagation after t = 60 s.However, the crack already propagates slightly before this. Starting around t > 30 s) of the stress-strain curve of Fig. x−) direction of the crack propagation are shown, the maximum tensile strain εyy from DIC, the instantaneous position of the hot spot, and a running average of its location. Up to about 37 seconds the spot stays slightly ahead of the maximum of the strain, and after that they start to move in unison  of the FPZ and the actual crack tip. This in turn is crucial in considering the roughening of the crack surfaces and the role of interface depinning in understanding crack dynamics. Our results show that there is a case in which cracks roughen, but via a different mechanism.2 copy paper, with pencil marks to facilitate the DIC computations  of an experiment.The experimental setup consists of Instron E1000 tensile testing machine, Flir A320 thermal camera and Dalsa Genie HM1024 grayscale digital camera. The sample is standard 80 g/mons Fig. . The temv = 0.04 mm s−1 which corresponds to a strain rate of −4 s−1. The tensile testing machine measures the force that is then converted to stress by dividing by the initial sample cross sectional area.The loading protocol is displacement controlled so that the velocity of the top clamp is 23 using a region of interest of 32 × 32 pixels.The thermal camera operates with a frequency of 20 Hz and an image area of 320 × 240 pixels and can detect temperature differences of 0.05 °C which corresponds to the noise level in the thermal data. The digital grayscale images are obtained with an image area of 1024 × 768 pixels and a frequency of 10 Hz. The grayscale images are processed with a Digital Image Correlation algorithmThe spatial accuracy is set in a way where a pixel in thermal imaging corresponds to 0.1 mm, which is eventually the same accuracy we obtain for strain fields. One region of interest in DIC is 32 × 32 pixels leading to 0.1 × 0.1 mm in spatial accuracy.