In the studied catchment, the dynamics of pH is a result of both cations and anions through mainly synergistic effects of the two and their individual influences as well. This example demonstrates the potentially broad applicability of the approach, establishing the foundation to study the interaction between groups of variables in a range of complex systems.Complex systems arise as a result of the nonlinear interactions between components. In particular, the evolutionary dynamics of a multivariate system encodes the ways in which different variables interact with each other individually or in groups. One fundamental question that remains unanswered is: How do two non-overlapping multivariate subsets of variables interact to causally determine the outcome of a specific variable? Here, we provide an information-based approach to address this problem. We delineate the temporal interactions between the bundles in a probabilistic graphical model. The strength of the interactions, captured by partial information decomposition, then exposes complex behavior of dependencies and memory within the system. The proposed approach successfully illustrated complex dependence between cations and anions as determinants of  For instance, in the study of connectivity between different regions of the brain, one may be interested in how a specific reaction pulse is jointly induced by different groups of incoming signals . In stre cations . AddressAt the most elementary level, this approach calls upon investigating whether and in what way two variables interact with each other a. This tWhile the original Granger causality only assesses the change of the second-order moment to determine the reduced uncertainty, recent studies extend it to capture the change of the entire probability space by using information measures ,8. For eHere, we propose new information measures to quantify and characterize the interactive strength among two bundled variable sets in affecting the present state of a target variable c. This aThe main contribution of this study is that it is the first time to delineate the overall effect of multiple interacting grouped sources to a target using information theory. It should be noted that the proposed method is fundamentally different from existing information measures. Information theory has been extensively employed to assess pairwise interactions   between iven by: Tmn=I(XttTo characterize the information contents in on (PID) , which aBefore we develop quantitative estimation, we ask another related question: Do all the historical states in the bundled sets provide information to e of CMI , we can ponents:  a recentNote that information flow from the two partitioned histories, Equation , are fundled set .Partitioning iven by: aJmn=RJ+SComputing information flows in Equations –4) is i is i4) iStage 1: From infinite to finite cardinality—a probabilistic graphical model approach.E and a set of nodes E. Every state in E connecting from an earlier node Estimation of the quantities in Equations  and 3),,3), and quations  and (3) quations b: 5a)TmaTmXt is The usage of the Markov property successfully reduces the infinite nodes in immediate  estimator [kNN estimator was employed in this study because of its better estimation performance in using short dataset compared with other methods  [k values, such as the significant drop of kNN estimator under different data lengths and k values. Here, we chose We next computed the information flow from the entire . To quations  with k=[=5,6,7,8,,10,15 fopH on the selected cation and anion groups, which consist of both unique information (pH), pH in both histories. This is because cations consists of three of the overall four nodes in pH. Nevertheless, there still exists a certain amount of redundant information from recent dynamics, pH, that is, pH, through conditioning on pH. Meanwhile, the synergistic effect from recent dynamics, pH due to the chemical interactions between cations and anions. This analysis, which illustrates a quantitative way to characterize the information guiding the current state of the stream pH level transferred from the selected cations and anions in the stream, can be generalized to other multivariate systems.The estimated information components from immediate (low rate ), diminipH.We present an information flow-based framework to characterize the joint influence from the evolutionary dynamics of two groups of variables on the present state of a target variable. Partitioning the total information into synergistic, redundant, and unique components helps delineate different information characteristics due to the two bundled sets. This framework was applied to observed stream chemistry datasets, and successfully showed the joint impacts of cations and anions on stream The proposed information measures are fundamentally different from the causal detection analysis and other existing information measures see . The cauOne key issue associated with most multivariate analysis is the curse of dimensionality, which impairs reliable estimations on the corresponding measures. Here, we propose a two-stage approach to reduce the dimensions of the information measures. Based on the DAG for time-series, the Markov property is first assumed to reduce the dimensions from infinite in Equation  to finitpH in the studied catchment are mainly from their synergistic effect and also from their individual impacts through unique information. Such phenomenon is masked  are not conditioned in the computation of the information measures in Equation (The proposed two orders of approximation of the influence from the rest of the system further illustrate such characterization under varying impacts from the remaining variables. Characterizing such information in both immediate and distant bundled causal histories, on the other hand, details the delineation of the influence due to a recent and the complementary earlier dynamics. In the stream chemistry application, the analysis shows that the influences of cations and anions on determining the dynamics of Equation  (for theWith the increasing availability of observed time-series data, such multivariate analysis framework opens new avenues for understanding the role of different groups of components in controlling the dynamics of a complex system.


With the quick development of sensor technology in recent years, online detection of early fault without system halt has received much attention in the field of bearing prognostics and health management. While lacking representative samples of the online data, one can try to adapt the previously-learned detection rule to the online detection task instead of training a new rule merely using online data. As one may come across a change of the data distribution between offline and online working conditions, it is challenging to utilize the data from different working conditions to improve detection accuracy and robustness. To solve this problem, a new online detection method of bearing early fault is proposed in this paper based on deep transfer learning. The proposed method contains an offline stage and an online stage. In the offline stage, a new state assessment method is proposed to determine the period of the normal state and the degradation state for whole-life degradation sequences. Moreover, a new deep dual temporal domain adaptation (DTDA) model is proposed. By adopting a dual adaptation strategy on the time convolutional network and domain adversarial neural network, the DTDA model can effectively extract domain-invariant temporal feature representation. In the online stage, each sequentially-arrived data batch is directly fed into the trained DTDA model to recognize whether an early fault occurs. Furthermore, a health indicator of target bearing is also built based on the DTDA features to intuitively evaluate the detection results. Experiments are conducted on the IEEE Prognostics and Health Management (PHM) Challenge 2012 bearing dataset. The results show that, compared with nine state-of-the-art fault detection and diagnosis methods, the proposed method can get an earlier detection location and lower false alarm rate. Early fault detection always plays a key role in the field of bearing prognostics and health management (PHM). In most recent years, the quick development of sensor techniques and artificial intelligence gave rise to a new problem: early fault online detection . CompareThis paper mainly tackles early fault online detection in unsupervised mode, i.e., with no available state information for whole-life degradation data. For online scenarios, a straightforward solution is using the initial part of online data  to construct a one-class classification model. However, a trustful model can usually be built waiting for a long enough time to get sufficient data for model training, especially for a deep neural network. One can certainly accumulate enough whole-life degradation data in an offline environment, e.g., a laboratory. However, the distribution drift between offline data and online data is inevitable due to the change of working conditions. In this scenario, the offline trained model cannot be directly applied to the online task. Therefore, how to transfer fault information  between different working conditions has become a key issue to improve the accuracy and robustness of early fault online detection.Presently, most traditional fault detection methods heavily rely on the fault features  extracteFrom the discussion above, the most vital challenge to improve the performance of online detection is the effective transfer of fault knowledge between offline and online working conditions. As one of the research hotspots in machine learning, transfer learning aims to improve the predictive performance in one domain  by using the prior information contained in the data of another related, but different domain  . As a kiTo solve such shortcomings, this paper proposes a new online detection method of bearing early fault based on deep transfer learning techniques. Specifically, this method contains an offline stage and an online stage. In the offline stage, a new state assessment method is firstly proposed by integrating the Hilbert–Huang transform (HHT) and support vector data description (SVDD) to determine the period of the normal state and the degradation state. The assessment results can provide the corrected data label for further domain adaptation. Furthermore, a new deep dual temporal domain adaptation (DTDA) model is proposed to extract temporal common fault information between different working conditions. In the online stage, the sequentially collected monitoring signals are directly fed into the DTDA model to recognize if a fault occurs. This process does not need a re-training model, since the domain-invariant feature representation has been extracted by the DTDA model. Finally, a set of comparative experiments is conducted on the IEEE PHM Challenge 2012 bearing dataset, and the results demonstrate the effectiveness of the proposed method.(1)This paper proposes a new dual temporal domain adaptation model with a dual adaptation strategy. Different from most current deep transfer learning techniques, this model can transfer temporal information of degradation sequences by integrating the time convolutional network (TCN)  and the (2)This paper presents a new online health indicator (HI) construction method of bearings. This method adopts the temporal common features extracted by the DTDA model and uses principal component analysis (PCA)  to get aThe main contributions of this paper can be summarized as follows:This paper is organized as follows. In Rooted in the convolutional neural network (CNN) , the TCNt of the upper layer only depends on the value at time t and before time t of the next layer , and the size of the sliding window was set to 100. Benefiting from the sliding window, this method had no false alarm, but the detection location was a bit delayed. The main reason is that this method is not a transfer learning method and heavily relies on the amount of offline training data. If the amount of training data is insufficient, the early fault information could not be extracted completely. In contrast, the proposed method can borrow data from offline working conditions to supplement early fault information for online detection.(6)Comparison with S4VM-SODRMB:This method is also a state-of-the-art online detection method for bearing early fault. This method only needs online data to update model training in an unsupervised learning architecture. In this experiment, the first 100 samples of online data were accumulated to extract the DAE features and then train an initial SVM model. The sequentially collected data batch was used to update the SVM model successively. The radius-margin upper bound of leave-one-out error was then utilized to calculate an index for online detection. In (7)Comparison with TCA + SVDD:Transfer component analysis (TCA) is a widely used transfer learning algorithm by minimizing the MMD distance between different domains. In this experiment, TCA was first run to conduct domain adaptation between the available data from offline and online working conditions. Then, the common features were used to train an SVDD model by using the available training data from the online working condition. This SVDD model was used to recognize anomalies in the online stage. In this experiment, the regularization parameter and kernel parameter were set to 10 and one, respectively. From (8)Comparison with RD-DTL and OD-DTL:RD-DTL and OD-DTL are both the newest state-of-the-art early fault online detection methods based on deep transfer learning. RD-DTL first uses a robust auto-encoder to determine the periods of different degradation states and then constructs an MMD-based DAE network to extract common features for the normal state, followed by an SVM model for recognition. This method focuses on the robustness of the online detection model. OD-DTL utilizes a pre-trained VGG-16 network on the ImageNet dataset to fine-tune a deep neural network for bearing online detection. This method only conducts model-level domain adaptation, not considering the feature transfer. Therefore, the performance of fault detection is limited. From Here, a detailed analysis of the comparative results is listed as follows:In summary, the proposed DTDA model can achieve dual domain adaptation at the feature level, which can facilitate the transfer of fault information between different working conditions. Moreover, the DTDA utilizes the TCN as the feature extractor to extract the temporal information of the degradation process, which can improve the representative ability of the online features for early fault. Therefore, the proposed method is more applicable to the online detection of bearing early fault.Another problem of online detection is computational time. The proposed method needs to train the DTDA model in the offline stage and then directly inputs the sequentially collected online data into the model to recognize the fault occurrence. The dual domain adaptation by the DTDA provides a domain-invariant feature representation with a better discriminative ability for the online task. The offline model training is computationally expensive, since the adversarial training of the DTDA is an iteration process. However, no additional training time is required in the online stage. The classification on an online sample by the trained DTDA model is almost a linear operation, so the time for recognizing an online sample is very short. For this reason, the corresponding time data are not provided in Online detection of bearing early fault is an application-oriented fault detection method with significant practical meaning. This paper proposes a new online detection method of early fault based on deep dual temporal domain adaptation. This method adopts deep domain adaptation with temporal information to extract domain-invariant feature representation with stronger discriminative ability. Employing this representation as the channel of information transfer, the proposed method can improve the detection robustness and accuracy in the online scenario with fewer false alarms as well. This method can directly tackle whole-life degradation data, with no need to manually mark fault data in advance. Therefore, this method is more applicable for the online detection of early fault, and the idea of this paper can be widely expanded for different objects.In the next work, an attention mechanism will be introduced into domain adversarial training to improve the effect of domain adaptation for time series data. Besides, this paper focuses on the anomaly detection problem for a bearing across different working conditions. How to achieve online transfer learning across different machinery and extract common features from multiple sources is an interesting problem.


For many countries a plain-eye inspection of the COVID-19 infection curves reveals a remarkable linear growth over extended time periods. This observation is practically impossible to understand with traditional epidemiological models. These, to make them expressible in compact mathematical form, typically ignore the structure of real contact networks that are essential in the characteristic spreading dynamics of COVID-19. Here we show that by properly taking some relevant network features into account, linear growth can be naturally explained. Further, the effect of nonpharmaceutical interventions (NPIs), like national lockdowns, can be modeled with a remarkable degree of precision without fitting or fine-tuning of parameters. Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of nonpharmaceutical interventions pushing the growth rate below the recovery rate. In this phase of the pandemic many countries showed an almost linear growth of confirmed cases for extended time periods. This new containment regime is hard to explain by traditional models where either infection numbers grow explosively until herd immunity is reached or the epidemic is completely suppressed. Here we offer an explanation of this puzzling observation based on the structure of contact networks. We show that for any given transmission rate there exists a critical number of social contacts,  Textbook knowledge of epidemiology has it that an epidemic event comes to a halt when herd immunity in a population is reached , 2. HerdThe COVID-19 outbreak shows a very different picture, however. Several countries have clearly passed a first maximum of the epidemic and are converging toward zero new cases per day. None of these countries are even close to herd immunity. In Austria at the first peak of the pandemic so far, a population-wide representative PCR study showed that only about 0.3% of the population tested positive . SimilarSI Appendix, Fig. 1). According to basic epidemiological concepts, growth patterns with extended linear regions are not to be expected. They can be observed only if the infection growth rate equals the recovery rate, giving an effective reproduction number, Maybe the most striking observation in the COVID-19 infection curves is that they exhibit linear growth for an extended time interval quite in contrast to the S-shaped curves expected from epidemiological models. For a wide range of countries regardless of size, demographic and ethnic composition, or geolocation, this linear growth pattern is apparent even by a plain-eye inspection of the number of positive cases, e.g., ref. SI Appendix). A simple explanation could be a limiting capacity of availability of test kits. If the daily number of tests is limited and assuming a fixed ratio of confirmed cases per test, linear growth in the number of positively tested would be the consequence. However, most European countries, even though experiencing initial difficulty with testing capacity, have, by now, enough tests available.The basic question of this paper is to clarify the mechanism that keeps ed (SIR)  models tThe rationale underlying social distancing efforts is that they lead to a reduction of contacts which essentially makes the social network sparser . InfectiSI Appendix). However, that fact that networks matter in epidemiology has been recognized for almost two decades and has led to extremely relevant contributions, such as the dependence of vaccination thresholds on network topology , the small-world aspect, the fact that people tend to live in small groups (families), that these groups overlap, and that work and leisure relations can link distant groups , on empiWe assume that there are bility ϵ . As in aing rate . Once a SI Appendix) by At every timestep (day), We demonstrate the model schematically in The infection curve, he same) E. ClearlThe change of the infection curve from the S-shaped to a linear behavior is clearly a network effect and indicates that the mean-field assumptions might be violated. To understand this better we next study the parameter dependence more systematically.SI Appendix, Fig. 2. The asterisks in We are interested to see whether there is a critical degree, settings A, arrowsSI Appendix, Fig. 3).We checked that the position of the critical degrees is relatively robust under the size of the network and variations in topology. We find that for SI Appendix, Text S6. This result slightly overestimates the simulation results . Also finite size effects in the simulation may add to the observed deviations.For the Poissonian small-world network we are able to estimate the critical degree analytically by a “fuse model” results . HoweverThe existence of critical degrees signals the presence of a hitherto overlooked transition between linear and S-shaped growth that is most likely due to the fact that the well-mixed or mean-field assumption breaks down below SI Appendix, Fig. 7.We confirm that the mechanism to obtain linear infection curves is present also for more realistic social contact networks , 24, 25,We calibrate the model to the COVID-19 infection curves of two countries, the United States and Austria, to demonstrate its potential applicability for estimating the effects of NPIs. For this we have to make the following assumptions on the model parameters:The viral dynamics of COVID-19 are highly heterogenous . MotivatSI Appendix, Text S7.In 2019 the average household size in the European Union was 2.3 people . If we aWe use 100,000 nodes and 40 and 100 initially infected for the United States and Austria, respectively. Since it is not possible to compute every individual in the simulation, we decided to initiate the simulation at the point where 0.1% of the population tested positive, that is, 7 April for the United States and 3 April for Austria. For the respective population sizes we use United Nations data from 2019 .In SI Appendix, Fig. 4. Both types of superspreaders do shift the critical degree toward lower levels, as expected.We discuss the role of superspreaders in two additional simulations, one where we introduce superspreaders defined as individuals with a much higher degree than the population average and the other where superspreading comes from individuals which are much more contagious but have similar degrees to the rest of the population. Results are presented and discussed in SI Appendix, Figs. 9 and 10. We can exclude the a priori possibility  transition from a linear growth regime to the expected S-shaped curves.We showed that for any given transmission rate there exists a critical degree of contact networks below which linear infection curves must occur and above which the classical S-shaped curves appear that are known from epidemiological models. The model proposed here is based on a simple toy contact network that mimics features of a heterogenous degree, the small-world property, the fact that people tend to live in small groups that overlap, and the fact that distant groups are linked through work and leisure activities. We showed how the model can be used to simulate the effects of NPIs in response to the crisis by simply switching to low-degree networks that do not allow for linking of distant groups.The model not only allows us to understand the emergence of the linear growth regime, but also explains why the epidemic halts much below the levels of herd immunity (given no in-flow of infected). Further, it allows us to explain the fact that in countries which are beyond the (first) maximum of the epidemic, a relatively small number of daily cases persist for a long time. This is because small alterations and rearrangements in the contact networks will allow for a very limited spread of infections.We find that for the empirically motivated parameters used here, the critical degree is The linear growth phase appears to be dominated by cluster transmission of the disease, meaning that new infections primarily appear in the “small-worlds” or local network neighborhood  of infected individuals. In the superlinear  phase, sustained community transmission sets in where new cases cannot be traced to already known cases in their neighborhood. In this regime, transmission across the shortcuts in the network becomes more prevalent. This effective mixing of the population gives a dynamic that approaches the mean-field case of SIR-like models.SI Appendix, Fig. 6. In SI Appendix, Text S7 we discuss the impact on the Austrian infection curve if the same NPI would have been implemented 10 d later . An increase of about 30% of cases is observed. In the same spirit, in SI Appendix, Fig. 6A we demonstrate what could have happened if NPIs, with similar effects to those that were implemented in Austria, had been installed in the United States. The results indicate that about half of the cases could have been avoided (at the beginning of May 2020).Finally, we calibrated the model to realistic network parameters, transmission rates, and the time of being contagious and showed that realistic infection curves (examples of the United States and Austria are shown) emerge without any fine-tuning of parameters. The onset of the NPI (lockdown)—and the associated reduction of the degree in the contact networks—determines the final size of the outbreak which is well below the levels of herd immunity. We demonstrate the importance of timing of the interventions in SI Appendix, Text S7. In SI Appendix, Text S8 we discuss three additional case studies of the infection curves of China (Hubei), Singapore, and South Korea. We implement temporal sequences of changes in the model parameters that roughly resemble the effects of the NPIs implemented in reality. We recover the basic features of the actual infection curves to a remarkable extent, at least qualitatively .For a more detailed discussion of the applicability of the presented model in terms of modeling the effects of NPIs, refer to The two types of superspreading, the network based and transmission based, both lead to a clear finding that the presence of superspreaders shifts the critical degree toward lower levels. However, the presented mechanism to obtain linear infection curves remains fully intact. The message for Austria and the United States is that in both countries the density of superspreaders is not high enough in the considered observation period to shift the critical degree toward exponential growth, given the effective degrees in the populations.Given the number of countries that entered linear growth phases, our results raise serious concerns regarding the applicability of standard compartmental models to describe the containment phase achieved by means of NPIs. SIR-like models show linear growth only after fine-tuning parameters and linear growth would be a mere statistical fluke. We argue that network effects must be taken into account to understand postintervention epidemic dynamics.For the network preaders . Note thTo distinguish the linear from the sigmoidal growth, we propose a simple “order parameter” as the standard deviation (SD) of all new daily cases ,Supplementary File


The increased incidence of improvised explosives in military conflicts has brought about an increase in the number of traumatic brain injuries (TBIs) observed. Although physical injuries are caused by shrapnel and the immediate blast, encountering the blast wave associated with improvised explosive devices (IEDs) may be the cause of traumatic brain injuries experienced by warfighters. Assessment of the effectiveness of personal protective equipment (PPE) to mitigate TBI requires understanding the interaction between blast waves and human bodies and the ability to replicate the pressure signatures caused by blast waves. Prior research has validated compression-driven shock tube designs as a laboratory method of generating representative pressure signatures, or Friedlander-shaped blast profiles; however, shock tubes can vary depending on their design parameters and not all shock tube designs generate acceptable pressure signatures. This paper presents a comprehensive numerical study of the effects of driver gas, driver (breech) length, and membrane burst pressure of a constant-area shock tube. Discrete locations in the shock tube were probed, and the blast wave evolution in time at these points was analyzed to determine the effect of location on the pressure signature. The results of these simulations are used as a basis for suggesting guidelines for obtaining desired blast profiles. Detonation of explosive devices is typically associated with shrapnel and fire, both of which lead to visible injuries. Improvised explosive devices (IEDs) may primarily produce blast waves and shocks, which can lead to injuries that are superficially undetectable. The increased incidence of IEDs in military conflicts has been associated with a major increase in the number of traumatic brain injuries (TBIs) . The incAlthough compression-driven shock tubes have been validated as a method of generating representative blast waves , blast w0 is the peak pressure, td is the duration of the positive phase, and b is the exponential constant that controls the rate of decay  have conducted studies to improve their ability to replicate blast wave scenarios that cause injuries . They usThe objective of the work described in this paper is to use computational fluid dynamics (CFD) simulations to characterize the primary overpressure blast environment and how it changes based on the design of a laboratory shock tube. Studies were conducted to understand the effects of varying the membrane driver length, burst pressure, and driver gas. These studies focused on how the pressure-time history varies within a shock tube and do not include how the environment changes the wave after the shock tube's exit. Conducting CFD simulations is less expensive, faster, and therefore better suited for the parametric studies than building an array of modular shock tubes to conduct laboratory experiments. The results from these analyses can be used by experimentalists to ensure that the shock tube design and test article placement are conducive to producing the desired blast exposure.The shock tube in this study consists of a high-pressure region (the driver section), separated by a diaphragm from a low-pressure region (the driven section). Depending on the application, the driver section may be at a different temperature and filled with a different gas than the driven section. When the diaphragm ruptures, a normal shock travels into the driven section and an expansion wave travels into the driver section . For theThe shock tube geometry for these studies was a 6 inch constant-diameter shock tube with a 6 inch long driver section and a 192 inch long driven section. The computational mesh was generated in 2D using the commercial mesh generation software, PointwiseCFD++For the work described in this report, all simulations were set up to solve the two-dimensional (2-D) axisymmetric, unsteady, compressible fluid equations. For each time-step and grid cell, the code solves four 2-D conservation equations: mass, x-momentum, y-momentum, and energy. One or more additional equations are solved when a turbulence model is used and no additional equations are solved when the flow is modeled as inviscid.When solving for flows with multiple species, additional N-1 equations are required, where N is the number of species. The study described in section Driver Gas Study was conducted to understand the effect of the driver gas on the pressures. At most, two species (air and helium) were modeled as one driver gas mixture, so one additional equation was solved for those simulations.The flow through a shock tube is unsteady. The implicit (backward Euler), dual time-stepping algorithm was used to advance the solution from one physical time-step to another. At each global iteration (or time-step) the dual time-stepping algorithm iteratively solves the governing equations for a predefined number of inner iterations or until a predefined convergence criterion is satisfied. For simulating unsteady flows, the selection of the physical time-step is critical and depends on the velocities in the flow and the size of the smallest grid cell. If the time-step chosen is too large, the flow solution could become unstable and unphysical. If the time-step is too small, then the overall simulation  time can become very large. These issues are exacerbated when dealing with complex flows because of the need to have computational grids with many computational cells. A time-step study (results not shown here for brevity) was conducted for each candidate grid and is described later. Most simulations were conducted to achieve at least 15 ms of flow time. The maximum number of inner iterations were set to 20 to achieve a convergence of two orders of magnitude. Note that order of convergence in this context refers to the magnitude of the change between the answer at an inner-iteration relative to the magnitude of the initial guess. Early in the simulations, the code required 15–20 inner iterations to reach convergence; however, after the initial high-gradient transient flow decays, only 6–7 inner iterations were required for convergence.Prior to conducting simulations with the shock tube geometry and conditions of interest, the numerical schemes in CFD++ used for this work were validated against the Sod shock tube problem to ensure that the physics were being captured accurately . Figure Each CFD simulation requires initial conditions (ICs) and boundary conditions (BCs). Here, the driver section was initialized with the driver gas at a given gauge pressure (gauge burst pressure) of either 100, 150, or 200 psig. The remaining ICs are shown in At all solid surfaces , boundaries were assumed isothermal. At the farfield boundaries, characteristic inflow/outflow conditions were applied with pressure and temperature set at 14.7 psi and 295 K, respectively. Simulations were conducted assuming a symmetry in the Z = 0 plane. A symmetry BC was used, which acts as an inviscid wall BC where only tangential flow is allowed and the normal (to the symmetry plane) component of velocity is zero. All simulations were conducted using a 6 inch long driver section, a gauge burst pressure of 150 psig, and Helium driver gas unless otherwise noted.pmax, was also recorded. Flow-field contours of the symmetry plane were saved every 100 time-steps.Selected locations, as a function of driver length, along the shock tube centerline were used to probe the flow. Data at these locations were taken at every time-step in order to find the pressure history at each probe location, and the maximum pressure at each location was calculated. The time at which this peak pressure occurs, tMesh and time-step resolution studies were conducted to ensure that all results were mesh and time-step independent. An under-resolved mesh would artificially dissipate the shock, and a time-step that is too large could reduce the stability of the simulations leading to spurious oscillations, particularly near discontinuities such as shocks (Gibbs phenomena) –17. SimiA study was conducted to examine the effect of different driver lengths  on the shock evolution. Pressure traces were compared for this study at multiple probe locations based on non-dimensionalizing the probe's distance from the driver/driven interface to the driver length, hereafter referred to as λ. These pressure traces allow us to compare the shocks at a variety of locations and understand where a Friedlander profile can be achieved based on driver length.As the waves approach the shock tube exit, the resulting pressure signature is once again less representative of a Friedlander wave. The point at which this occurs appears not to be a function of driver length, but instead a function of proximity to the shock tube exit. Yu et al. found that this critical distance was based on the shock tube diameter . For theIn a laboratory experiment, a burst pressure study is one that tests the effect of the choice of the membrane on the pressure history. Different types of membranes burst at different pressures and, thus, the relation between the burst pressure and test-section peak pressure is observed. For our studies, it is necessary to understand the effect of membrane burst pressure on the positive phase duration of the wave. If the positive phase duration increases with the peak pressure, the overall impulse may increase significantly compared to a situation where the peak pressure increased and the positive phase duration did not.The results of the burst pressure study, The final study conducted as part of this work was to look at the effect of using air, helium, or an equal parts mixture as the driver gas. The driver gas is an important facet of the experimental setup because IEDs and explosives may release other gases, which may alter the shock properties. In a laboratory setting, it may be less desirable to use explosive nitroanimes, including RDX, due to licensing requirements and the need for specialized equipment for storage and transport . BecauseThe purpose of this paper was to provide design guidelines for shock tubes such that they can be used to generate blast waves. Parametric studies were conducted using CFD to characterize the primary overpressure blast environment created by a variety of laboratory shock tube designs. CFD was used to characterize changes in the flow that resulted from varying specific design features, such as: driver length, burst pressure, and driver gas. These studies demonstrated that a shock tube can be used to generate a Friedlander-like blast profile under specific conditions. The test section must be placed far enough from the driver/driven interface that there is no flat-top wave profile, and this distance depends on the driving gas. In addition, the test section must be placed some distance away from the shock tube exit such that the complex flow phenomena near the tube exit do not influence the blast profile. The chosen driving gas has a significant impact on the wave profile and can result in a wave that only looks like the Friedlander wave profile for a portion of the positive-phase duration.Experimentalists using shock tubes to test the impact of overpressure on the brain will have to balance two major goals—to generate both a Friedlander-shaped blast profile and a sufficiently high peak pressure in the test section to correlate the results of free-field testing for a corresponding amount of explosive. Regardless of driving gas, experimentalists may be able to meet peak pressure requirements by selecting a diaphragm material that will not burst until higher pressures. Higher burst pressures did not change the rate of decay of the waves and so the peak pressure to impulse relationship should remain the same. If this option is utilized, the sublinear relationship between burst pressure and the resultant peak pressure of the wave is important to keep in mind. In the absence of being able to change the shock tube diaphragm material, a test section closer to the driver/driven interface (minimum λ = 4) and helium as the driving gas will result in the highest peak pressures. However, this will be at the cost of not matching the Friedlander profile as well and higher impulses due to the longer positive phase duration. This option could result in incorrect assumptions about how injuries occur in the field. However, for an already-built shock tube with a test section at least 16 driver lengths downstream, air as the driving gas is more likely to result in both a more representative wave and a higher peak pressure due to the higher rate of decay in peak pressure as the wave travels downstream when helium is the driving gas. An optimized air-helium mixture for the driver gas may provide both a Friedlander shock profile and required peak pressures in the test section.A finding of the driver length study was that testing near the end of the shock tube will result in waves that are not representative of a Friedlander wave. Furthermore, the shock tube diameter, not the driver length, appears to be the key parameter related to how far the test section should be placed from the end of the shock tube. For the simulations conducted, two shock tube diameters from the exit plane is when end-jet effects began to change the wave profile. It is possible that asymmetries in the 3D environment outside of the shock tube such as the ground or floor may also impact end-jet effects and could change the conclusions of this study. CFD could be used to check for end-jet effects and analysts should look for oscillations during the decay of the wave.In conclusion, the studies demonstrated that shock tubes are a viable method of generating Friedlander-shaped blast profiles. However, careful attention must be paid to the shock tube and experimental design to ensure this profile is achieved while meeting minimum peak pressure requirements in a test section. Experimentalists will need to balance placing the test section sufficiently far from the driver/driven interface such that a Friedlander-like wave profile is formed, which will depend on the driving gas, while placing the test section far enough from the exit of the shock tube such that end-jet effects do not influence the wave. CFD can be used to help design the shock tube and provide pre-test predictions to verify that all requirements will be met.The datasets generated for this study are available on request to the corresponding author.RK conducted the analysis, analyzed the results, and wrote the manuscript. AN provided technical guidance and developed the process for conducting the analysis.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The rapid spread of the SARS-CoV-2 epidemic has simultaneous time and space dynamics. This behaviour results from a complex combination of factors, including social ones, which lead to significant differences in the evolution of the spatiotemporal pattern between and within countries. Usually, spatial smoothing techniques are used to map health outcomes, and rarely uncertainty of the spatial predictions are assessed. As an alternative, we propose to apply direct block sequential simulation to model the spatial distribution of the COVID-19 infection risk in mainland Portugal. Given the daily number of infection data provided by the Portuguese Directorate-General for Health, the daily updates of infection rates are calculated by municipality and used as experimental data in the geostatistical simulation. The model considers the uncertainty/error associated with the size of each municipality’s population. The calculation of daily updates of the infection risk maps results from the median model of one ensemble of 100 geostatistical realizations of daily updates of the infection risk. The ensemble of geostatistical realizations is also used to calculate the associated spatial uncertainty of the spatial prediction using the interquartile distance. The risk maps are updated daily and show the regions with greater risks of infection and the critical dynamics related to its development over time. When the first case of human infection by the SARS-CoV-2 virus was reported in Wuhan city, Hubei Province, China, on 31 December 2019 . The epihttps://covidmap.aledade.com/) are needed.During the early stages of the spread of a virus—when there are few infected people—environmental epidemiology using contagion risk models  is esseOne of the traditional ways to map the risk of disease is through choropleth maps, which are usually available as rates (counts or proportions) of aggregated data by region or area . However, risks by area may change if the same data are aggregated using different spatial boundaries. One of the main contributions of geostatistics for the analysis of public health data is that it addresses the improvement of methods used to map the risk of disease. Geostatistical models have found ways to accommodate count data (or rates) attached to areal spatial supports that contribute to reducing the biased visual perception produced by choropleth maps and to facilitate the analysis of the relationships between risks measured over different spatial supports. The choropleth maps would have constant rates per municipalities and sharp discontinuities at the boundary of each municipality. On the other hand, geostatistical maps, as those proposed herein, do show spatial variability within each municipality and do not exhibit sharp discontinuities at the limits of each municipality as the spatial continuity pattern is imposed by the geostatistical method used.In this context, an infection risk spatial model for COVID-19, which is based on a geostatistical framework, was proposed and implemented in mainland Portugal, considering the infection rate by municipality. The novelty of this approach is that the daily map is calculated from the number of confirmed positive tested cases reported by the Portuguese Directorate-General for Health  and made available publicly online.Next, we detail the geostatistical background related to the spatial modelling tool, direct block sequential simulation , used toThe proposed model for mapping the COVID-19 infection risk in Portugal builds upon the Poisson model for rare diseases proposed by Waller and Gotway  and exteTo predict the spatial distribution of the COVID-19 infection risk for a specific period and the associated uncertainty in mainland Portugal, we use a geostatistical model based on direct block sequential simulation , which Consider One can assume that  problem  is achieIn the Poisson kriging model , the disThe purpose of this model for the COVID-19 risk map is to access the uncertainty of infection risk through a stochastic simulation methodology capable of integrating the different demographic size of each municipality and the uncertainty attached to the infection rate by population size.The aim of this model is to generate high-resolution maps of infection risk based on recorded infection rates, and the associated spatial uncertainty. As the data are recorded in municipalities of different sizes and populations, they are interpreted as block support data. Block data refers to a non-point support data, which is generally referred to a volume but in this case of aggregated health data it refers to an area. In the application examples shown herein the spatial area refers to a municipality. The block sequential simulation algorithm gives the framework to deal with data with varying spatial support  and to make predictions with change of support. Thus, point and block support can be interpreted as two different support scales, in this case the scale related to the map cells can be referred as point support, because it denotes a small area when compared with the municipality areas. For sake of simplicity, we will refer to map cells as “point support” from this point forward.In this sense, this means the resulting high-resolution risk maps are point support based. The stochastic simulation model is based on the work of Liu and Jounel  and SoarLα is a known linear averaging function. The simple kriging estimator, At each step of the proposed stochastic simulation methodology , local mock data , where tck–block  data supAs there is noise/uncertainty attached to infection rates, resulting from population size , 16, thences Eq. , which cAssuming block errors, say Considering blocks i)Define a random path that visits each node, ii)For each node, iii)Calculate the local covariance values: block-to-block, block-to-point, point-to-block and point-to-point; build and solve the block kriging system and obtain the local mean and variance kriging estimate at location iv)Draw a value from the global probability distribution function centered at the local mean and bounded by the local variance obtained in (iii);v)Add the simulated value to the data set and repeat steps (i) to (iv) until all grid nodes are simulated for one realization;vi)Repeat steps (i) to (v) until a given pre-defined number of realizations are generated.Block sequential simulation  is the eAs previously described, the block sequential simulation is based on a stationary spatial covariance model that reveals the main spatial continuity patterns of daily infection rates. These models are usually inferred from available experimental data: from the daily official infection rates.As the experimental infection rates refer to different population sizes, these must be weighted differently when calculating the experimental variogram. In other words, municipalities with large populations should have greater weighting in the experimental variogram calculation. Here we applied an adaptation of the semivariogram proposed by , 20, whih, of each pair of municipality value was calculated with their centroids.The experimental semivariogram is calculated as follows :10\documThe number of daily infections is provided for each municipality each day by the DGS. This number of confirmed tested COV 19 cases is then converted into infection rates, mentclasspt{minimaInfection rates are assigned as point experimental data to the centroid of the municipality area Fig. a. Each mThe experimental infection rate variograms, weighted for each population, were calculated according to Eqs. The main output of the model presented here is a set of realizations of the spatial dispersion of COVID-19 infection risk in a regular grid of points (2 × 2 km) covering the whole country. Each realization .The set of median models and uncertainty COVID-19 infection risk maps for a seven-day period are available in an interactive web-based application  can eventually skew the municipality’s infection rate, particularly when the municipality has a small population.One of the most innovative components introduced by this model is its ability to be updated in the short-term. Thus, risk maps are produced using information provided daily by the DGS. Eventual sampling errors of the infected people in daily reports will be reflected in the maps.The proposed model for characterizing the COVID-19 infection risk, based on stochastic simulations, produced consistent results for risk and associated uncertainty. The daily update of risk and uncertainty maps enable a regional analysis of the dynamics of the phenomenon over time through, for example, the use of simple statistics, such as the slope of a short-term linear regression or a more comprehensive methodology such as functional data analysis . The spa


Interestingly, the model correctly retrieves the variation in The Darcy-scale properties of reservoir rocks, such as capillary pressure and relative permeability, are controlled by multiphase flow properties at the pore scale. In the present paper, we implement a volume of fluid (VOF) method coupled with a physically based dynamic contact angle to perform pore-scale simulation of two-phase flow within a porous medium. The numerical model is based on the resolution of the Navier–Stokes equations as well as a phase fraction equation incorporating a dynamic contact angle model with wetting hysteresis effect. After the model is validated for a single phase, a two-phase flow simulation is performed on both a Newtonian and a non-Newtonian fluid; the latter consists of a polymer solution displaying a shear-thinning power law viscosity. To investigate the effects of contact angle hysteresis and the non-Newtonian nature of the fluid, simulations of both drainage and imbibition are carried out in order to analyze water and oil saturation—particularly critical parameters such as initial water saturation ( Despite the large body of existing research, very few publications address the crucial role played by the wettability, quantified by the contact angle and its hysteresis, at the pore scale on the properties of both Newtonian and non-Newtonian fluids, which ultimately control fluid flow behavior at the Darcy scale. While the prediction of petrophysical properties by digital rock physics (DRP) [Predicting multiphase properties of porous media is critical in many applications including the oil and gas industry, COcs (DRP) ,2,3,4 haUnderstanding the effects of wettability in porous media is the subject of ongoing research. It is still very challenging to experimentally characterize the wettability of an oil/water/rock system in which the fluid distribution cannot be visualized and assessed accurately ,6. To ovIn , a PNM iMost of the two-phase flow models in the literature focus primarily on Newtonian fluid flow, assuming the contact angle to be static and not considering either its dynamics or hysteresis ,19. WhilIn addition, fluid flow through porous media becomes even more complex if one of the fluids is non-Newtonian, as is the case in situations such as polymer flooding or heavy oil production. The goal of the present work is two-fold: (i) the development of an accurate model for simulating wettability at the pore scale with wetting hysteresis effect, which depends on the displacement direction (drainage or imbibition), and (ii) extension to non-Newtonian fluid flow through porous media, where the effect of fluid rheology on the two-phase flow properties can be assessed.The novel contribution of this work is the development of a new simulator capable of computing the dynamics of two-phase Newtonian and non-Newtonian fluids and their interactions with rock using a dynamic contact angle model. The simulator, which can be used for different rock types at the pore scale, can provide valuable insight into the prediction of multiphase flow behavior in subsurface flow, such as in soil remediation, and can also provide better strategies for EOR.The paper is organized as follows: A numerical method based on the volume of fluid (VOF) method is adopted to accurately describe the fluid flow behavior within a porous medium at pore scale. The continuity and momentum equations to be numerically solved within VOF framework are expressed as follows:mass conservationp is the pressure, momentum conservationapproach , where t∂(ρV)∂t+∇The two phases, oil and water, are defined through the phase fraction (The compression velocity given by :5)Vc=nfpression ,24. UnliVc=nfpresFinally, the physical properties in any numerical cell of the domain can be expressed through the liquid phase fraction θd=fopted in  where itrelation ,25. Sincθd=foptedTo model the contact angle hysteresis occurring when the fluid is moving on chemically or topologically heterogenous surfaces, the equilibrium or static contact angle given in Equation  is implei et al. , contacti et al. ,30,34. Ffound in ,26.The governing equations for the two-phase flow simulation accounting for wetting hysteresis and fluid rheology are solved using Open-source Field Operation And Manipulation (OpenFOAM), a C++ toolbox for the implementation of numerical solvers. The Equations –14) are are14) aThe convergence of the iterative solver for the velocity and pressure fields are fixed at 10t papers ,24,30. BTo validate the approach based on FVM in porous media, numerical simulations to estimate the permeability are performed using a 3D micro-CT image of rock samples. The results obtained by FVM are subsequently compared to the values computed by both PNM and LBM. We consider two rock samples from the literature, the Fontainebleau sandstone and Grosmont carbonate , for theThe numerical simulation is performed on the two samples using the three numerical techniques. For illustration purposes, we show the approach for PNM, FVM and LBM simulations in z-axis in We summarize the results of the simulation of the permeability on the The accuracy of the two-phase flow modeling is highly related to the accurate description of the contact (or triple) line motion. Many studies use a static contact angle model instead of a dynamic model due to its simplicity. To validate and assess the relevance of our dynamic contact angle implementation, we analyzed the droplet dynamics upon impact on surfaces exhibiting contact angle hysteresis (CAH), which represent the difference between the advancing and receding contact angles, CAH=ct angle . The resIn addition to the effect of the contact angle, we simulate the impact of the non-Newtonian droplet following a shear thinning power law as detailed in Equation . The evoIn the following, the developed VOF model will be employed to perform the simulations of both drainage and imbibition to gain a better physical insight into two-phase flow dynamics through porous media.The approach followed in the present work attempts to imitate the experimental setup for the characterization of two-phase, water and oil saturation through the steady-state method. For convenience, the two-phase flow simulation is performed here using a 2D geometry, and the liquids (oil and water) are considered to be Newtonian.In While the dynamic contact angle model is more physically grounded than the static one, this approach assumes the substrate to be ideal. In reality, substrates exhibit a wetting hysteresis effect, making the substrate prone to retain the liquid. This wetting effect will be detailed next.We will focus on water saturation variation through a drainage test consisting of displacing the water phase by the oil to investigate the wettability effect on the fluid flow through porous media. Initially, the porous medium is 100% saturated with water  and consistency factor (We developed a volume of fluid (VOF) method to simulate a pore-scale model that takes into account the dynamic contact angle and its hysteresis. The two-phase modeling is based on the flow of both Newtonian and non-Newtonian fluids through a porous medium. The simulations are performed for drainage, in which water is displaced by oil until steady state is reached, followed by imbibition, in which oil is displaced by water or a polymer solution, leading to


Endoscopic autofluorescence lifetime imaging is a promising technique for making quantitative and non-invasive diagnoses of abnormal tissue. However, motion artifacts caused by vibration in the direction perpendicular to the tissue surface in a body makes clinical diagnosis difficult. Thus, this paper proposes a robust autofluorescence lifetime sensing technique with a lens tracking system based on a laser beam spot analysis. Our optical setup can be easily mounted on the head of an endoscope. The variation in distance between the optical system and the target surface is tracked by the change in the spot size of the laser beam captured by the camera, and the lens actuator is feedback-controlled to suppress motion artifacts. The experimental results show that, when using a lens tracking system, the standard deviation of fluorescence lifetime is dramatically reduced. Furthermore, the validity of the proposed method is experimentally confirmed by using a bio-mimicking phantom that replicates the shape, optical parameters, and chemical component distribution of the cancerous tissue. Autofluorescence lifetime measurement has significant potential for providing quantitative diagnosis and analysis because autofluorescence lifetime, which is the time constant of autofluorescence intensity decay, facilitates the acquisition of biochemical information without the influence of optical conditions in sensing devices ,2. AutofHowever, in non-contact endoscopic fluorescence lifetime measurements in digestive organs, organic motions induce strong motion artifacts distorting the fluorescence lifetime image, resulting in misdiagnosis. Motion artifacts arise from the contraction and dilatation of organs due to gastric motility, heart beating, breathing, and peristalsis. Several studies observed motion artifacts appearing in endoscopic fluorescence lifetime imaging ,14,15. GVibration in a direction perpendicular to the tissue surface is a dominant source of noise in fluorescence lifetime imaging. Some studies have attempted to reduce motion artifacts by bringing the probe into contact with the sample ,16 and dIn this study, a robust fluorescence lifetime measurement system with the focus tracking method based on the laser spot imaging is proposed. In our previous study, a motion tracking method for a blood perfusion sensor had been developed. The proposed sensor was based on laser Doppler flowmetry with a confocal optical configuration . The conIt is the fluorescence signal intensity, I0 is the initial fluorescence intensity, t is the time, and τ is the decay time constant (fluorescence lifetime). In fluorescence lifetime imaging with TCSPC, motions that are perpendicular to the tissue surface should be suppressed to achieve highly sensitive measurements of fluorescence lifetime. The detected signal is strongly affected by body motions such as heartbeats and gastro peristalsis. Therefore, a motion tracking method is necessary to maintain the distance between the target tissue and the optical system of the endoscope by controlling the lens actuator, as shown in The excitation laser for autofluorescence is focused on the tissue surface, and the focal position of the tracking laser is at a point far from that of the excitation laser. Hence, motion artifacts due to body motion can be compensated for by shifting the lens position synchronously using the feedback control of the actuator driver.To verify the proposed motion tracking fluorescence lifetime imaging system, a bench-top apparatus that replicates the endoscopic configuration is constructed, as shown in TM program  in a computer connected with the TCSPC module. The experimental apparatus is composed of a fluorescence lifetime measurement system and a motion tracking system. The excitation light source of a pulsed laser head  emitted a 70 ps pulsed laser beam at λ = 450 nm, controlled by a driver  with a repetition rate of 5 MHz. To shape a pulsed laser beam suitable for sensing, two cylindrical lenses are used. Moreover, the Gaussian laser profile can be obtained using a spatial filter. The laser beam focused with a planoconvex lens excites the tissue surface, and the emitted photons are collected by the same lens. The fluorescence photons are detected by the avalanche photo diode  with a 100 µm active sensing area on the detector through the short pass dichroic mirror , the band pass filter , and a focusing lens. The TCSPC module  counted a fluorescence photon each second and calculated the lifetime using the NIM signal from the laser driver. All these processes are controlled by a LabVIEWThe tracking laser  projects a laser spot onto the sample surface. The beam is expanded four times by the objective lens and the planoconvex lens to increase the beam diameter, and this high-NA condition gains tracking accuracy owing to the increase in the spot size variation during the movement of the tissue surface. The tracking laser beam is combined with the excitation laser beam by a polarized beam splitter  and a half wave plate . The CCD Camera  captured the laser spot color images at 30 fps through the objective lens  to analyze the spot diameter.A high-speed image analysis and low-delay feedback of the lens actuator is conducted using PC2 connected with the field-programmable gate array (FPGA) module . For the preliminary experiment to verify the proposed technique, a phantom mimicking the shape, optical characteristics, and flavin adenine dinucleotide (FAD) concentration distribution of the cancerous tissue  is prepaThe fabricated bio-mimicking phantom is mounted on the shaft type linear motor and actuated sinusoidally  and randomly  to simulate the gastric and esophagus motility ,24.The concentration dependence of the fluorescence lifetime of the fibrin matrix was measured in the static condition. In First, the homogeneous FAD gel phantom was measured with and without motion tracking to verify the proposed system. The gel phantom (thickness of 2 mm) was mounted on the stage and actuated sinusoidally a and ranred2 = 0.87, therefore, the autofluorescence lifetime was adequately detected. As shown in Finally, the bio-mimicking phantom with concentration distribution, as shown in In conclusion, we proposed a robust autofluorescence lifetime sensing method for use in an endoscopic application. To suppress the motion artifacts arising in the endoscopic autofluorescence lifetime diagnosis, the motion tracking method was implemented in the autofluorescence lifetime measurement method. The sample vibration, which replicated the body motion, was monitored via image analysis of the irradiated laser spot, and feedback control of the lens actuator was successfully conducted. To validate the proposed method, a bio-mimicking phantom imitating the cancerous tissue was fabricated using a 3D-printed mold and FAD chromophore. The autofluorescence lifetimes of the normal and abnormal areas were distinguishable under the vibration condition using the motion tracking method. Thus, the robustness and applicability of the proposed method for the optical biopsy were experimentally confirmed.