Stochastic modeling and analysis of hepatitis and tuberculosis co-infection dynamics

Several mathematical models have been developed to investigate the dynamics of tuberculosis(TB)and hepatitis B virus(HBV).Numerous current models for TB,HBV,and their co-dynamics fall short in capturing the important and practical aspect of unpredictability.It is crucial to take into account a stochastic co-infection HBV–TB epidemic model since different random elements have a substantial impact on the overall dynamics of these diseases.We provide a novel stochastic co-model for TB and HBV in this study,and we establish criteria on the uniqueness and existence of a nonnegative global solution.We also looked at the persistence of the infections as long its dynamics are governable by the proposed model.To verify the theoretical conclusions,numerical simulations are presented keeping in view the associated analytical results.The infections are found to finally die out and go extinct with certainty when L´evy intensities surpass the specified thresholds and the related stochastic thresholds fall below unity.The findings also demonstrate the impact of noise on the decline in the co-circulation of HBV and TB in a given population.Our results provide insights into effective intervention strategies,ultimately aiming to improve the management and control of TB and HBV co-infections.

Thermoelastic analysis of multiple defects with the extended finite element method

In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.

Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

This paper reports a multiscale analysis method to predict the thermomechanical coupling performance of composite structures with quasi-periodic properties.In these material structures,the configurations are periodic,and the material coefficients are quasi-periodic,i.e.,they depend not only on the microscale information but also on the macro location.Also,a mutual interaction between displacement and temperature fields is considered in the problem,which is our particular interest in this study.The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented.Then,a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail.Finally,some numerical examples are given.And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasiperiodic properties.

The Numerical Accuracy Analysis of Asymptotic Homogenization Method and Multiscale Finite Element Method for Periodic Composite Materials

In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.

Compact finite difference schemes for the backward fractional Feynman–Kac equation with fractional substantial derivative

The fractional Feynman-Kac equations describe the distributions of functionals of non-Brownian motion, or anomalous diffusion, including two types called the forward and backward fractional Feynman-Kac equations, where the nonlocal time-space coupled fractional substantial derivative is involved. This paper focuses on the more widely used backward version. Based on the newly proposed approximation operators for fractional substantial derivative, we establish compact finite difference schemes for the backward fractional Feynman-Kac equation. The proposed difference schemes have the q-th(q = 1, 2, 3, 4) order accuracy in temporal direction and fourth order accuracy in spatial direction, respectively. The numerical stability and convergence in the maximum norm are proved for the first order time discretization scheme by the discrete energy method, where an inner product in complex space is introduced. Finally, extensive numerical experiments are carried out to verify the availability and superiority of the algorithms. Also, simulations of the backward fractional Feynman-Kac equation with Dirac delta function as the initial condition are performed to further confirm the effectiveness of the proposed methods.

Statistical Multiscale Analysis of Transient Conduction and Radiation Heat Transfer Problem in Random Inhomogeneous Porous Materials

This paper is devoted to the homogenization and statistical multiscale analysis of a transient heat conduction problem in random porous materials with a nonlinear radiation boundary condition.A novel statistical multiscale analysis method based on the two-scale asymptotic expansion is proposed.In the statistical multiscale formulations,a unified linear homogenization procedure is established and the second-order correctors are introduced for modeling the nonlinear radiative heat transfer in random perforations,which are our main contributions.Besides,a numerical algorithm based on the statistical multiscale method is given in details.Numerical results prove the accuracy and efficiency of our method for multiscale simulation of transient nonlinear conduction and radiation heat transfer problem in random porous materials.

Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure

The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon- dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale （SOTS） computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu- lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap- proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure.

Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous materials.For this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all considered.Firstly,the repre.sentation for the microscopic configuration of the statistically inhomogeneous materials is described.Secondly,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and stresses.And then the algorithm procedure corresponding to the SSOTS method is brought forward.The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods.In addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case.It demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very distinct.The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

Constructing reduced model for complex physical systems via interpolation and neural networks

The work studies model reduction method for nonlinear systems based on proper orthogonal decomposition (POD)and discrete empirical interpolation method (DEIM). Instead of using the classical DEIM to directly approximate thenonlinear term of a system, our approach extracts the main part of the nonlinear term with a linear approximation beforeapproximating the residual with the DEIM. We construct the linear term by Taylor series expansion and dynamic modedecomposition (DMD), respectively, so as to obtain a more accurate reconstruction of the nonlinear term. In addition, anovel error prediction model is devised for the POD-DEIM reduced systems by employing neural networks with the aid oferror data. The error model is cheaply computable and can be adopted as a remedy model to enhance the reduction accuracy.Finally, numerical experiments are performed on two nonlinear problems to show the performance of the proposed method.

Microstructural Modeling and Multiscale Mechanical Properties Analysis of Cancellous Bone

This paper is devoted to the microstructure geometric modeling and mechanical properties computation of cancellous bone.The microstructure of the cancellous bone determines its mechanical properties and a precise geometric modeling of this structure is important to predict the material properties.Based on the microscopic observation,a new microstructural unit cell model is established by introducing the Schwarz surface in this paper.And this model is very close to the real microstructure and satisfies the main biological characteristics of cancellous bone.By using the unit cell model,the multiscale analysis method is newly applied to predict the mechanical properties of cancellous bone.The effective stiffness parameters are calculated by the up-scaling multi-scale analysis.And the distribution of microscopic stress in cancellous bone is determined through the down-scaling procedure.In addition,the effect of porosity on the stiffness parameters is also investigated.The predictive mechanical properties are in good agreement with the available experimental results,which verifies the applicability of the proposed unit cell model and the validness of the multiscale analysis method to predict the mechanical properties of cancellous bone.

Chemical vapor deposition growth of large-scale hexagonal boron nitride with controllable orientation

Chemical vapor deposition （CVD） synthesis of large-domain hexagonal boron nitride （h-BN） with a uniform thickness is very challenging, mainly due to the extremely high nucleation density of this material. Herein, we report the successful growth of wafer-scale, high-quality h-BN monolayer films that have large single-crystalline domain sizes, up to -72 μm in edge length, prepared using a folded Cu-foil enclosure. The highly confined growth space and the smooth Cu surface inside the enclosure effectively reduced the precursor feeding rate together and induced a drastic decrease in the nucleation density. The orientation of the as-grown h-BN monolayer was found to be strongly correlated to the crystallographic orientation of the Cu substrate： the Cu （111） face being the best substrate for growing aligned h-BN domains and even single-crystalline monolayers. This is consistent with our density functional theory calculations. The present study offers a practical pathway for growing high-quality h-BN films by deepening our fundamental understanding of the process of their growth by CVD.

Oxygen-assisted direct growth of large-domain and high-quality graphene on glass targeting advanced optical filter applications

Growing high quality graphene films directly on glass by chemical vapor deposition(CVD)meets a growing demand for constructing high-performance electronic and optoelectronic devices.However,the graphene synthesized by prevailing methodologies is normally of polycrystalline nature with high nucleation density and limited domain size,which significantly handicaps its overall properties and device performances.Herein,we report an oxygen-assisted CVD strategy to allow the direct synthesis of 6-inch-scale graphene glass harvesting markedly increased graphene domain size(from 0.2 to 1.8μm).Significantly,as-produced graphene glass attains record high electrical conductivity(realizing a sheet resistance of 900Ω·sq^(-1)at a visible-light transmittance of 92%)amongst the state-of-the-art counterparts,readily serving as transparent electrodes for fabricating high-performance optical filter devices.This work might open a new avenue for the scalable production and application of emerging graphene glass materials with high quality and low cost.

Precise orbit determination for a large LEO constellation with inter-satellite links and the measurements from different ground networks:a simulation study

Geodetic applications of Low Earth Orbit(LEO)satellites requires accurate satellite orbits.Instead of using onboard Global Navigation Satellite System observations,this contribution treats the LEO satellite constellation independently,using Inter-Satellite Links and the measurements of different ground networks.Due to geopolitical and geographical reasons,a ground station network cannot be well distributed.We compute the impact of different ground networks(i.e.,global networks with different numbers of stations and regional networks in different areas and latitudes)on LEO satellite orbit determination with and without the inter-satellite links.The results are based on a simulated constellation of 90 LEO satellites.We find that the orbits determined using a high latitude network is worse than using a middle or low latitude network.This is because the high latitude network has a poorer geometry even if the availability of satellite measurements is higher than for the other two cases.Also,adding more stations in a regional network shows almost no improvements on the satellite orbits if the number of stations is more than 16.With the help of ISL observations,however,the satellite orbits determined with a small regional network can reach the same accuracy as that with the global network of 60 stations.Furthermore,satellite biases can be well estimated(less than 0.6 mm)and have nearly no impact on satellite orbits.It does thus not matter if they are not physically calibrated for estimating precise orbits.

XFEM for Fracture Analysis in 2D Anisotropic Elasticity

In this paper,a method is proposed for extracting fracture parameters in anisotropic thermoelasticity cracking via interaction integral method within the framework of extended finite element method(XFEM).The proposed method is applied to linear thermoelastic crack problems.The numerical results of the stress intensity factors(SIFs)are presented and compared with those reported in related references.The good agreement of the results obtained by the developed method with those obtained by other numerical solutions proves the applicability of the proposed approach and confirms its capability of efficiently extracting thermoelasticity fracture parameters in anisotropic materials.

Acceleration Strategies Based on an Improved Bubble Packing Method

The bubble packing method can generate high-quality node sets in simple and complex domains.However,its efficiency remains to be improved.This study is a part of an ongoing effort to introduce several acceleration schemes to reduce the cost of simulation.Firstly,allow the viscosity coefficient c in the bubble governing equations to change according the coordinate of the bubble which are defined separately as odd and normal bubbles,and meanwhile with the saw-shape relationship with time or iterations.Then,in order to relieve the over crowded initial bubble placement,two coefficients w1 and w2 are introduced to modify the insertion criterion.The range of those two coefficients are discussed to be w1=1,w2∈[0.5,0.8].Finally,a self-adaptive termination condition is logically set when the stable system equilibrium is achieved.Numerical examples illustrate that the computing cost can significantly decrease by roughly 80%via adopting various combination of proper schemes(except the uniform placement example),and the average qualities of corresponding Delaunay triangulation substantially exceed 0.9.It shows that those strategies are efficient and can generate a node set with high quality.

A FULLY DISCRETE IMPLICIT-EXPLICIT FINITE ELEMENT METHOD FOR SOLVING THE FITZHUGH-NAGUMO MODEL

This work develops a fully discrete implicit-explicit finite element scheme for a parabolicordinary system with a nonlinear reaction term which is known as the FitzHugh-Nagumo model from physiology.The first-order backward Euler discretization for the time derivative,and an implicit-explicit discretization for the nonlinear reaction term are employed for the model,with a simple linearization technique used to make the process of solving equations more efficient.The stability and convergence of the fully discrete implicit-explicit finite element method are proved,which shows that the FitzHugh-Nagumo model is accurately solved and the trajectory of potential transmission is obtained.The numerical results are also reported to verify the convergence results and the st ability of the proposed method.

Fracture Analysis in Orthotropic Thermoelasticity Using Extended Finite Element Method

In this paper,a method for extracting stress intensity factors(SIFs)in orthotropic thermoelasticity fracture by the extended finite element method(XFEM)and interaction integral method is present.The proposed method is utilized in linear elastic crack problems.The numerical results of the SIFs are presented and compared with those obtained using boundary element method(BEM).The good accordance among these two methods proves the applicability of the proposed approach and conforms its capability of efficiently extracting thermoelasticity fracture parameters in orthotropic material.