Multi-patch Model Research Articles

An efficient isogeometric buckling optimization framework for multi-patch laminated shells: Leveraging 3D solid elements, lamination parameters and penalty method

Buckling is a common failure mode of laminated shell structures during service, and isogeometric analysis methods are highly suitable for the buckling analysis due to their accurate geometric modeling capability and high-order continuity. However, the isogeometric buckling analysis for a multi-patch structure and its optimal design still face challenges in computational efficiency. To address this issue, this paper proposes an integrated framework for the buckling optimization of multi-patch laminated shells, which leverages 3D solid elements, lamination parameters, and the penalty coupling method. Solid-shell elements have advantages in shell analysis due to their simplicity, absence of rotational degrees of freedom, and adaptive layering in the thickness direction. Lamination parameters simplify the optimization of fiber orientations in laminated shells by condensing the design variable space and improving the convexity of the optimization problem. The penalty method can handle the coupling in multiple patches at a relatively low cost. Nevertheless, lamination parameters are rarely applied to the case of solid-shell elements. In addition, despite using lamination parameters, the number of design variables for multi-patch structures remains significantly large. To tackle these issues, this study derives the solid-shell formulation in lamination parameters and the sensitivity analysis formulae in the reverse mode. Experiment validation is conducted to assess the accuracy of the proposed method based on lamination parameters with solid elements, the feasibility of the multi-patch optimization model, and the computational efficiency of optimization sensitivity based on the reverse mode compared to the forward counterpart common in the literature.

An effective drift-diffusion model for pandemic propagation and uncertainty prediction

Predicting pandemic evolution involves complex modeling challenges, typically involving detailed discrete mathematics executed on large volumes of epidemiological data. Making them physics based provides added intuition as well as predictive value. Differential equations have the advantage of offering smooth, well-behaved solutions that try to capture overall predictive trends and averages. In this paper, the canonical susceptible-infected-recovered model is simplified, in the process generating quasi-analytical solutions and fitting functions that agree well with the numerics, as well as infection data across multiple countries. The equations provide an elegant way to visualize the evolution of the pandemic spread, by drawing equivalents with the similar dynamics of a particle, whose location over time represents the growing fraction of the population that is infected. This particle slides down a potential whose shape is set by model epidemiological parameters such as reproduction rate. Potential sources of errors and their growth over time are identified, and the uncertainties are mapped into a diffusive jitter that tends to push the particle away from its minimum. The combined physical understanding and analytical expressions offered by such an intuitive drift-diffusion model sets the foundation for their eventual extension to a multi-patch model while offering practical error bounds and could thus be useful in making policy decisions going forward.

Mixed-mode thermo-mechanical fracture: An adaptive multi-patch isogeometric phase-field cohesive zone model

This work presents an adaptive phase-field cohesive zone model (PF-CZM) for simulating mixed-mode crack nucleation and growth in isotropic rock-like materials subjected to thermo-mechanical interactions. The proposed approach combines an adaptive multi-patch isogeometric analysis (MP-IGA) and length-scale insensitive PF-CZM. The formulation captures the distinct critical energy release rates for Mode-I and Mode-II fractures, which is crucial for predicting mixed-mode thermo-mechanical fracture behavior in isotropic rock-like materials. The PF-CZM governing equations are solved with isogeometric analysis based on locally refined non-uniform rational B-splines (LR NURBS), and the complex structural geometry is exactly described with multiple LR NURBS patches. The field variables, such as displacement, phase-field, and temperature at the interface of adjacent patches, are coupled using Nitsche’s method. To enhance the computational efficiency while maintaining accuracy, a refinement-correction adaptive scheme combined with the structured mesh refinement strategy is developed. The proposed framework is validated against recent numerical and experimental results in the literature, particularly in the context of capturing complex behavior of mixed-mode crack propagation in isotropic rock-like materials subjected to thermo-mechanical loading.

Optimal region-specific social distancing strategies in a complex multi-patch model through reinforcement learning

Although non-pharmaceutical interventions such as social distancing have proven effective in curbing outbreaks, they also carry economic consequences. This poses a dilemma for policymakers striving to find a balance between disease control and economic burden. This delicate balance varies regionally, influenced by non-epidemiological factors such as population movements, socio-demographic characteristics, and the intricacies of social distancing policies. These factors interact in intricate ways, shaping the transmission dynamics of COVID-19. To address this complexity, we propose an innovative approach utilizing deep reinforcement learning (RL). This method assists in tailoring intervention policies for diverse regions, taking into account their unique dynamics. We incorporate South Korea’s social distancing policies and their economic impact into a RL framework with a multi-region epidemic model, offering a comprehensive solution. We integrate official mobility data and GDP specific to each region, employing the proximity policy optimization algorithm to determine the most appropriate region-specific social distancing policy. The algorithm’s reward function considers both outbreak control and economic impacts, providing policymakers with the flexibility to fine-tune the balance between these two factors according to their preferences. This adjustment can be performed across three distinct cost scenarios: High, Base, and Low-cost scenarios. In scenarios with High-costs, social distancing measures are aimed at regions with extensive connectivity and higher transmission rates. When costs are moderate, policies center around the period of peak prevalence, illustrating adaptable strategies in areas characterized by high transmission rates, budget limitations, and population mobility. In situations with Low-costs, these measures encompass most regions, excluding those with low transmission rates. The study’s results support focused interventions in specific regions to balance outbreak control and economic impact mitigation.

A hybrid Lagrangian–Eulerian model for vector-borne diseases

In this paper, a multi-patch and multi-group vector-borne disease model is proposed to study the effects of host commuting (Lagrangian approach) and/or vector migration (Eulerian approach) on disease spread. We first define the basic reproduction number of the model, R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_0$$\\end{document}, which completely determines the global dynamics of the model system. Namely, if R0≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_0 \\le 1 $$\\end{document}, then the disease–free equilibrium is globally asymptotically stable, and if R0>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_0 > 1 $$\\end{document}, then there exists a unique endemic equilibrium which is globally asymptotically stable. Then, we show that the basic reproduction number has lower and upper bounds which are independent of the host residence times matrix and the vector migration matrix. In particular, nonhomogeneous mixing of hosts and vectors in a homogeneous environment generally increases disease persistence and the basic reproduction number of the model attains its minimum when the distributions of hosts and vectors are proportional. Moreover, R0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {R}_0$$\\end{document} can also be estimated by the basic reproduction numbers of disconnected patches if the environment is homogeneous. The optimal vector control strategy is obtained for a special scenario. In the two-patch and two-group case, we numerically analyze the dependence of the basic reproduction number and the total number of infected people on the host residence times matrix and illustrate the optimal vector control strategy in homogeneous and heterogeneous environments.

Spatial spread of COVID-19 during the early pandemic phase in Italy

Quantifying the potential spatial spread of an infectious pathogen is key to defining effective containment and control strategies. The aim of this study is to estimate the risk of SARS-CoV-2 transmission at different distances in Italy before the first regional lockdown was imposed, identifying important sources of national spreading. To do this, we leverage on a probabilistic model applied to daily symptomatic cases retrospectively ascertained in each Italian municipality with symptom onset between January 28 and March 7, 2020. Results are validated using a multi-patch dynamic transmission model reproducing the spatiotemporal distribution of identified cases. Our results show that the contribution of short-distance (≤10km)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\le 10 km)$$\\end{document} transmission increased from less than 40% in the last week of January to more than 80% in the first week of March 2020. On March 7, 2020, that is the day before the first regional lockdown was imposed, more than 200 local transmission foci were contributing to the spread of SARS-CoV-2 in Italy. At the time, isolation measures imposed only on municipalities with at least ten ascertained cases would have left uncontrolled more than 75% of spillover transmission from the already affected municipalities. In early March, national-wide restrictions were required to curb short-distance transmission of SARS-CoV-2 in Italy.

An adaptive multi-patch isogeometric phase-field model for fatigue fracture

Fatigue fracture is one of the main causes of structural failure under cyclic loading, so accurate evaluation of fatigue fracture is very important for the design of structures subjected to cyclic loading. In this work, we propose an adaptive fatigue phase-field model within the framework of multi-patch isogeometric analysis to simulate crack nucleation and propagation in brittle materials under cyclic loading. Multiple non-uniform rational B-splines (NURBS) patches are used to exactly represent complex structures, and the Nitsche’s method is adopted to enforce the compatibility of the displacements, stresses and phase-field variables between two patches. The coupled governing equations of fatigue phase-field model are established based on the Nitsche’s method, and the selection of Nitsche’s parameters are determined from numerical experiments. A refinement-correction adaptive approach based on locally refined non-uniform rational B-splines (LR NURBS) structured mesh refinement strategy is developed to alleviate the computational burden caused by the requirement of small element size around crack surface and the large number of fatigue loading. The proposed multi-patch isogeometric phase-field model can deal with the coupling between equal/unequal length interfaces, thus the fatigue crack propagation simulation in arbitrary complex structure can be implemented. Several numerical examples are investigated to verify the practicality of the multi-patch isogeometric phase-field model and the effectiveness of the adaptive scheme.

Vector-borne disease models with Lagrangian approach.

We develop a multi-group and multi-patch model to study the effects of population dispersal on the spatial spread of vector-borne diseases across a heterogeneous environment. The movement of host and/or vector is described by Lagrangian approach in which the origin or identity of each individual stays unchanged regardless of movement. The basic reproduction number [Formula: see text] of the model is defined and the strong connectivity of the host-vector network is succinctly characterized by the residence times matrices of hosts and vectors. Furthermore, the definition and criterion of the strong connectivity of general infectious disease networks are given and applied to establish the global stability of the disease-free equilibrium. The global dynamics of the model system are shown to be entirely determined by its basic reproduction number. We then obtain several biologically meaningful upper and lower bounds on the basic reproduction number which are independent or dependent of the residence times matrices. In particular, the heterogeneous mixing of hosts and vectors in a homogeneous environment always increases the basic reproduction number. There is a substantial difference on the upper bound of [Formula: see text] between Lagrangian and Eulerian modeling approaches. When only host movement between two patches is concerned, the subdivision of hosts (more host groups) can lead to a larger basic reproduction number. In addition, we numerically investigate the dependence of the basic reproduction number and the total number of infected hosts on the residence times matrix of hosts, and compare the impact of different vector control strategies on disease transmission.

Deep Multi-Patch Hierarchical Network-based Visibility Restoration Model for Autonomous Vehicles

Deep Multi-Patch Hierarchical Network-based Visibility Restoration Model for Autonomous Vehicles

The impact of dispersal and allee effects on tick invasion: a spatially-explicit discrete-time modelling approach

We develop a spatially-explicit discrete-time model that describes tick population dynamics and incorporates the developmental stages for an individual tick. The model allows for two types of movements across patches: (1) active tick movement and (2) movement of ticks through a host. We analyse the dynamics of the model under a nonlinear fecundity term that exhibits an Allee effect. We show that the system has bounded solutions and, under certain conditions on the parameters, is monotone. Using the next generation matrix approach, we define the net reproductive number of the multi-patch model, R ( 0 ) , and establish conditions under which R ( 0 ) determines the local and global asymptotic stability of the extinction equilibrium. We then show that the model exhibits rich dynamics including a monostable equilibrium, multi-stable equilibria, and cycles. Finally, we perform some numerical studies to further examine how dispersal and Allee effects impact tick survival and system stability.

An adaptive multi-patch isogeometric phase-field model for dynamic brittle fracture

This paper presents an adaptive multi-patch isogeometric phase-field model based on Nitsche's method for simulating dynamic brittle fracture. Complex structures are accurately represented with multiple patches, and Nitsche's method is used to link two adjacent patches to ensure the compatibility and continuity of physical quantities (such as displacements, stresses, phase-field variables) on the coupling edge. LR NURBS with the local refinement ability are used for spatial discretization, while a generalized-α method is used for temporal discretization. The staggered algorithm and hybrid PFM formulation are adopted to enhance the solution efficiency of multi-field coupled system. In addition, the local refinement is executed utilising the phase-field threshold. Several dynamic fracture examples are used to validate the proposed approach's accuracy and effectiveness. The proposed approach can effectively model dynamic fracture propagation, and numerical results demonstrate that the adaptive analysis may significantly lower the computing cost.

An Interpretable Radiomics Model Based on Two-Dimensional Shear Wave Elastography for Predicting Symptomatic Post-Hepatectomy Liver Failure in Patients with Hepatocellular Carcinoma.

The aim of this study was to develop and validate an interpretable radiomics model based on two-dimensional shear wave elastography (2D-SWE) for symptomatic post-hepatectomy liver failure (PHLF) prediction in patients undergoing liver resection for hepatocellular carcinoma (HCC). A total of 345 consecutive patients were enrolled. A five-fold cross-validation was performed during training, and the models were evaluated in the independent test cohort. A multi-patch radiomics model was established based on the 2D-SWE images for predicting symptomatic PHLF. Clinical features were incorporated into the models to train the clinical-radiomics model. The radiomics model and the clinical-radiomics model were compared with the clinical model comprising clinical variables and other clinical predictive indices, including the model for end-stage liver disease (MELD) score and albumin-bilirubin (ALBI) score. Shapley Additive exPlanations (SHAP) was used for post hoc interpretability of the radiomics model. The clinical-radiomics model achieved an AUC of 0.867 (95% CI 0.787-0.947) in the five-fold cross-validation, and this score was higher than that of the clinical model (AUC: 0.809; 95% CI: 0.715-0.902) and the radiomics model (AUC: 0.746; 95% CI: 0.681-0.811). The clinical-radiomics model showed an AUC of 0.822 in the test cohort, higher than that of the clinical model (AUC: 0.684, p = 0.007), radiomics model (AUC: 0.784, p = 0.415), MELD score (AUC: 0.529, p < 0.001), and ALBI score (AUC: 0.644, p = 0.016). The SHAP analysis showed that the first-order radiomics features, including first-order maximum 64 × 64, first-order 90th percentile 64 × 64, and first-order 10th percentile 32 × 32, were the most important features for PHLF prediction. An interpretable clinical-radiomics model based on 2D-SWE and clinical variables can help in predicting symptomatic PHLF in HCC.

An isogeometric analysis framework for ventricular cardiac mechanics

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical features many elements may be required, possibly leading to unnecessarily large computation costs. Without loss of accuracy, a reduction in computation cost can be achieved by integrating geometry representation and solution approximation into a single framework using the isogeometric analysis (IGA) paradigm. In this study, we propose an IGA framework suitable for echocardiogram data of cardiac mechanics, where we show the advantageous properties of smooth splines through the development of a multi-patch anatomical model. A nonlinear cardiac model is discretized following the IGA paradigm, meaning that the spline geometry parametrization is directly used for the discretization of the physical fields. The IGA model is benchmarked with a state-of-the-art biomechanics model based on traditional FEM. For this benchmark, the hemodynamic response predicted by the high-fidelity FEM model is accurately captured by an IGA model with only 320 elements and 4700 degrees of freedom. The study is concluded by a brief anatomy-variation analysis, which illustrates the geometric flexibility of the framework. The IGA framework can be used as a first step toward an efficient workflow for an improved understanding of, and clinical decision support for, the treatment of cardiac diseases like heart rhythm disorders.

Multi-patch multi-scale model for motion deblurring with high-frequency information

Nowadays deep learning-based models have made encouraging accomplishments in the field of image motion deblurring, but this type of algorithms does not effectively use the known prior knowledge and the physical model of motion blur. So as to settle the above disputes, this paper suggests a multi-patch multi-scale input model that fuses high-frequency information, structural self-similarity (SSS), multi-scale channel spatial attention (MSCSA), and superpixel gradient loss for motion deblurring. The multi-patch multi-scale input model can fully extract the salient information, scale information, and high-frequency information of the image to restore the sharp image. The SSS module can take full advantage of the prior information of the structure self-similarity of the image. And the MSCSA module dynamically and selectively enhances relevant features and suppresses irrelevant features by fusing spatial, scale, and channel characteristics. Moreover, this paper advises a superpixel gradient loss function, which can remove motion blur and restore sharp images more effectively. And to increase the diversity of scenes, for the first time, we propose a motion blur dataset (Underwater-Blur) specifically for underwater scenes. Massive comparative experiments conducted on three public datasets of GoPro, RealBlur, RWBI, and the Underwater-Blur dataset prove that our model outperforms the state-of-the-art in terms of comprehensive performance.

Role of immigration and emigration on the spread of COVID-19 in a multipatch environment: a case study of India

Human mobility has played a critical role in the spread of COVID-19. The understanding of mobility helps in getting information on the acceleration or control of the spread of disease. The COVID-19 virus has been spreading among several locations despite all the best efforts related to its isolation. To comprehend this, a multi-patch mathematical model of COVID-19 is proposed and analysed in this work, where-in limited medical resources, quarantining, and inhibitory behaviour of healthy individuals are incorporated into the model. Furthermore, as an example, the impact of mobility in a three-patch model is studied considering the three worst-hit states of India, i.e. Kerala, Maharashtra and Tamil Nadu, as three patches. Key parameters and the basic reproduction number are estimated from the available data. Through results and analyses, it is seen that Kerala has a higher effective contact rate and has the highest prevalence. Moreover, if Kerala is isolated from Maharashtra or Tamil Nadu, the number of active cases will increase in Kerala but reduce in the other two states. Our findings indicate that the number of active cases will decrease in the high prevalence state and increase in the lower prevalence states if the emigration rate is higher than the immigration rate in the high prevalence state. Overall, proper travel restrictions are to be implemented to reduce or control the spread of disease from the high-prevalence state to other states with lower prevalence rates.

Inference on a Multi-Patch Epidemic Model with Partial Mobility, Residency, and Demography: Case of the 2020 COVID-19 Outbreak in Hermosillo, Mexico.

Most studies modeling population mobility and the spread of infectious diseases, particularly those using meta-population multi-patch models, tend to focus on the theoretical properties and numerical simulation of such models. As such, there is relatively scant literature focused on numerical fit, inference, and uncertainty quantification of epidemic models with population mobility. In this research, we use three estimation techniques to solve an inverse problem and quantify its uncertainty for a human-mobility-based multi-patch epidemic model using mobile phone sensing data and confirmed COVID-19-positive cases in Hermosillo, Mexico. First, we utilize a Brownian bridge model using mobile phone GPS data to estimate the residence and mobility parameters of the epidemic model. In the second step, we estimate the optimal model epidemiological parameters by deterministically inverting the model using a Darwinian-inspired evolutionary algorithm (EA)-that is, a genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification in the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results demonstrate that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from the HMC method yield large credible intervals, improving their coverage for the observed and predicted daily incidences. Furthermore, we observe that the use of a multi-patch model with mobility yields improved predictions when compared to a single-patch model.

Multipatch stochastic epidemic model for the dynamics of a tick-borne disease

Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the largest patch reproduction number and for connected patches it lies between the minimum and maximum of the patch reproduction numbers. Numerical simulations for a two-patch deterministic and stochastic differential equation models are performed to illustrate the dynamics of the disease for varying migration rates. Our results show that the probability of eliminating or minimizing the disease in both patches is high when there is no migration unlike when it is present. The results imply that the probability of disease extinction can be increased if deer and tick movement are controlled or even prohibited especially when there is an outbreak in one or both patches since movement can introduce a disease in an area that was initially disease-free. Thus, screening of infectives in protected areas such as deer farms, private game parks or reserves, etc. before they migrate to other areas can be one of the intervention strategies for controlling and preventing disease spread.

Nonlinear diffusion in multi-patch logistic model.

We examine a multi-patch model of a population connected by nonlinear asymmetrical migration, where the population grows logistically on each patch. Utilizing the theory of cooperative differential systems, we prove the global stability of the model. In cases of perfect mixing, where migration rates approach infinity, the total population follows a logistic law with a carrying capacity that is distinct from the sum of carrying capacities and is influenced by migration terms. Furthermore, we establish conditions under which fragmentation and nonlinear asymmetrical migration can lead to a total equilibrium population that is either greater or smaller than the sum of carrying capacities. Finally, for the two-patch model, we classify the model parameter space to determine if nonlinear dispersal is beneficial or detrimental to the sum of two carrying capacities.

Optimal vaccination control for COVID-19 in a metapopulation model: a case of the Philippines

We investigate a contextual problem of how to distribute a limited supply of vaccines over a period of time in a country where different regions have its own vaccination capacities. Considering that daily vaccination will affect future disease progression, we aim to find a distribution strategy over time that can minimize the total infection and implementation costs. Lagrangian and Eulerian migrations connect our multi-patch COVID-19 model, and vaccination is added as a control measure. An optimal control problem with an isoperimetric constraint is formulated and solved using the Adapted Forward–Backward Sweep Method. In distributing 5 million vaccines in 50 days, simulations showed that the optimal control strategy could lead to a difference of reducing two hundred thousand infections in just one region.

IMPROVING CONTROL STRATEGIES OF INFECTIONS BY RESISTANT PATHOGENS IN A HOSPITAL NETWORK

The efficacy of infection prevention and control on several hospital networks is assessed. We tested two kinds of strategy, a network-topology-based allocation and a [Formula: see text]-based allocation, where [Formula: see text] is the basic reproduction number of the infection. For this, a multi-patch deterministic model simulates the spread of carbapenemase-producing Enterobacteriaceae in several theoretical hospital networks parametrized by data from Brazil. Our results show that: (i) the allocation methods based on the [Formula: see text] of the hospitals may work better than the network-topology-based allocations; (ii) results from control efficacy for a specific hospital network cannot be generalized to other types of networks. Putting together the global network topology with local factors that drive pathogens transmission, the [Formula: see text]-based allocation method seems to be enough to control of healthcare-associated infections. Overall, the obtained results emphasize the importance of data collection on infection transmission and patient transfers.