Dynamics of virus infection models with density‐dependent diffusion and Beddington–DeAngelis functional response

In this work, we integrate both density‐dependent diffusion process and Beddington–DeAngelis functional response into virus infection models to consider their combined effects on viral infection and its control. We perform global analysis by constructing Lyapunov functions and prove that the system is well posed. We investigated the viral dynamics for scenarios of single‐strain and multi‐strain viruses and find that, for the multi‐strain model, if the basic reproduction number for all viral strains is greater than 1, then each strain persists in the host. Our investigation indicates that treating a patient using only a single type of therapy may cause competitive exclusion, which is disadvantageous to the patient's health. For patients infected with several viral strains, the combination of several therapies is a better choice. Copyright © 2017 John Wiley & Sons, Ltd.     

Modelling and numerical approach to a class of metal‐forming problems—Quasi‐steady case

A class of quasi‐steady metal‐forming problems, with rigid‐plastic, incompressible, strain and strain‐rate dependent material model and with unilateral frictionless and nonlinear, nonlocal Coulomb's frictional contact conditions is considered. A coupled variational formulation, constituted of a variational inequality, with nonlinear and nondifferentiable terms, and a strain evolution equation, is derived and under a restriction on the material characteristics and using a variable stiffness parameters method with time retardation, existence, uniqueness and convergence results are obtained and presented. An algorithm, combining this method and the finite element method, is proposed and applied for solving an example strip drawing problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Analytical and numerical solutions of a two‐dimensional multi‐term time‐fractional Oldroyd‐B model

In this paper, we consider a two‐dimensional multi‐term time‐fractional Oldroyd‐B equation on a rectangular domain. Its analytical solution is obtained by the method of separation of variables. We employ the finite difference method with a discretization of the Caputo time‐fractional derivative to obtain an implicit difference approximation for the equation. Stability and convergence of the approximation scheme are established in the L_∞ ‐norm. Two examples are given to illustrate the theoretical analysis and analytical solution. The results indicate that the present numerical method is effective for this general two‐dimensional multi‐term time‐fractional Oldroyd‐B model.     

The micromechanics of three‐dimensional collagen‐I gels

We study the micromechanics of collagen‐I gel with the goal of bridging the gap between theory and experiment in the study of biopolymer networks. Three‐dimensional images of fluorescently labeled collagen are obtained by confocal microscopy, and the network geometry is extracted using a 3D network skeletonization algorithm. Each fiber is modeled as an elastic beam that resists stretching and bending, and each crosslink is modeled as torsional spring. The stress–strain curves of networks at three different densities are compared with rheology measurements. The model shows good agreement with experiment, confirming that strain stiffening of collagen can be explained entirely by geometric realignment of the network, as opposed to entropic stiffening of individual fibers. The model also suggests that at small strains, crosslink deformation is the main contributer to network stiffness, whereas at large strains, fiber stretching dominates. As this modeling effort uses networks with realistic geometries, this analysis can ultimately serve as a tool for understanding how the mechanics of fibers and crosslinks at the microscopic level produce the macroscopic properties of the network. © 2010 Wiley Periodicals, Inc. Complexity 16: 22‐28, 2011     

Comparison of hyperelastic 2‐D and 3‐D model foams at large deformations

The influence of the modeling dimension on the determination of effective properties for hyperelastic foams is investigated by means of regular 2‐D and 3‐D model foams. For calculating the effective stress‐strain relationships of both microstructures, a strain energy based homogenization procedure is employed. The results from numerical analyses show that with a 2‐D model foam the basic deformation mechanisms of the 3‐D model can be captured. Nevertheless, due to the distinct quantitative deviations found from the homogenization analyses, 3‐D modeling approaches should be used if quantitative predictions for the effective material properties are required. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.     

TOWARDS A STANDARD FOR THE INDIVIDUAL‐BASED MODELING OF PLANT POPULATIONS: SELF‐THINNING AND THE FIELD‐OF‐NEIGHBORHOOD APPROACH

ABSTRACT. In classical theoretical ecology there are numerous standard models which are simple, generally applicable, and have well‐known properties. These standard models are widely used as building blocks for all kinds of theoretical and applied models. In contrast, there is a total lack of standard individual‐based models (IBM's), even though they are badly needed if the advantages of the individual‐based approach are to be exploited more efficiently. We discuss the recently developed ‘field‐of‐neighborhood’ approach as a possible standard for modeling plant populations. In this approach, a plant is characterized by a circular zone of influence that grows with the plant, and a field of neighborhood that for each point within the zone of influence describes the strength of competition, i.e., growth reduction, on neighboring plants. Local competition is thus described phenomenologically. We show that a model of mangrove forest dynamics, KiWi, which is based on the FON approach, is capable of reproducing self‐thinning trajectories in an almost textbook‐like manner. In addition, we show that the entire biomass‐density trajectory (bdt) can be divided into four sections which are related to the skewness of the stem diameter distributions of the cohort. The skewness shows two zero crossings during the complete development of the population. These zero crossings indicate the beginning and the end of the self‐thinning process. A characteristic decay of the positive skewness accompanies the occurrence of a linear bdt section, the well‐known self‐thinning line. Although the slope of this line is not fixed, it is confined in two directions, with morphological constraints determining the lower limit and the strength of neighborhood competition exerted by the individuals marking the upper limit.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Sub‐linear capacity scaling for multi‐path channel models

The theoretic capacity of a communication system constituted of several transmitting/receiving elements is determined by the singular values of its transfer matrix. Results based on an independent identically distributed channel model, representing an idealized rich propagation environment, state that the capacity is directly proportional to the number of antennas. Nevertheless there is growing experimental evidence that the capacity gain can be at best scaled at a sub‐linear rate with the system size. In this paper, we show under appropriate assumptions on the transfer matrix of the system that the theoretic information‐capacity of multi‐antenna systems is upper bounded by a sub‐linear function of the number of transmitting/receiving links. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical and asymptotic study of non‐axisymmetric magnetohydrodynamic boundary layer stagnation‐point flows

Both numerical and asymptotic analyses are performed to study the similarity solutions of three‐dimensional boundary‐layer viscous stagnation point flow in the presence of a uniform magnetic field. The three‐dimensional boundary‐layer is analyzed in a non‐axisymmetric stagnation point flow, in which the flow is developed because of influence of both applied magnetic field and external mainstream flow. Two approaches for the governing equations are employed: the Keller‐box numerical simulations solving full nonlinear coupled system and a corresponding linearized system that is obtained under a far‐field behavior and in the limit of large shear‐to‐strain‐rate parameter (λ). From these two approaches, the flow phenomena reveals a rich structure of new family of solutions for various values of the magnetic number and λ. The various results for the wall stresses and the displacement thicknesses are presented along with some velocity profiles in both directions. The analysis discovered that the flow separation occurs in the secondary flow direction in the absence of magnetic field, and the flow separation disappears when the applied magnetic field is increased. The flow field is divided into a near‐field (due to viscous forces) and far‐field (due to mainstream flows), and the velocity profiles form because of an interaction between two regions. The magnetic field plays an important role in reducing the thickness of the boundary‐layer. A physical explanation for all observed phenomena is discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.     

A TWO‐STAGE INFORMATION‐THEORETIC APPROACH TO MODELING LANDSCAPE‐LEVEL ATTRIBUTES AND MAXIMUM RECRUITMENT OF CHINOOK SALMON IN THE COLUMBIA RIVER BASIN

ABSTRACT. Many anadromous salmonid stocks in the Pacific Northwest are at their lowest recorded levels, which has raised questions regarding their long‐term persistence under current conditions. There are a number of factors, such as freshwater spawning and rearing habitat, that could potentially influence their numbers. Therefore, we used the latest advances in information‐theoretic methods in a two‐stage modeling process to investigate relationships between landscape‐level habitat attributes and maximum recruitment of 25 index stocks of chinook salmon (Onocorhynchus tshawy‐tscha) in the Columbia River basin. Our first‐stage model selection results indicated that the Ricker‐type, stock recruitment model with a constant Ricker a, i.e., recruits‐per‐spawner at low numbers of fish) across stocks was the only plausible one given these data, which contrasted with previous unpublished findings. Our second‐stage results revealed that maximum recruitment of chinook salmon had a strongly negative relationship with percentage of surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and private moderate‐high impact managed forest. That is, our model predicted that average maximum recruitment of chinook salmon would decrease by at least 247 fish for every increase of 33% in surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and privately managed forest. Conversely, mean annual air temperature had a positive relationship with salmon maximum recruitment, with an average increase of at least 179 fish for every increase in 2°C mean annual air temperature.     

Existence of global solutions for a three‐species predator‐prey model with cross‐diffusion

In this short note, we study a strongly coupled system of partial differential equations which models the dynamics of a two‐predator‐one‐prey ecosystem in which the prey exercises defense switching and the predators collaboratively take advantage of the prey's strategy. We prove the existence of global strong solutions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A geometric‐based algebraic multigrid method for higher‐order finite element equations in two‐dimensional linear elasticity

In this paper, we will discuss the geometric‐based algebraic multigrid (AMG) method for two‐dimensional linear elasticity problems discretized using quadratic and cubic elements. First, a two‐level method is proposed by analyzing the relationship between the linear finite element space and higher‐order finite element space. And then a geometric‐based AMG method is obtained with the existing solver used as a solver on the first coarse level. The resulting AMG method is applied to some typical elasticity problems including the plane strain problem with jumps in Young's modulus. The results of various numerical experiments show that the proposed AMG method is much more robust and efficient than a classical AMG solver that is applied directly to the high‐order systems alone. Moreover, we present the corresponding theoretical analysis for the convergence of the proposed AMG algorithms. These theoretical results are also confirmed by some numerical tests. Copyright © 2008 John Wiley & Sons, Ltd.     

Static output‐feedback control for interval type‐2 discrete‐time fuzzy systems

This article investigates the problem of reliable mixed control for discrete‐time interval type‐2 (IT2) fuzzy model‐based systems via static output‐feedback (SOF) control method. The number of fuzzy rules and the membership functions for the SOF controller are different from those for the plant. A sufficient criterion of reliable stability with mixed performance is derived for the closed‐loop system with sensor failure. The SOF controller is designed for two different cases (known sensor failure case and unknown sensor failure case) to guarantee the reliable stability with mixed performance. Moreover, novel criteria are presented to obtain the optical performance for the closed‐loop system. Finally, an example is used to verify the effectiveness of the proposed design scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 74–88, 2016     

Corrigendum to “Kripke‐style semantics for many‐valued logics”

This note contains a correct proof of the fact that the set of all first‐order formulas which are valid in all predicate Kripke frames for Hájek's many‐valued logic BL is not arithmetical. The result was claimed in [5], but the proof given there was incorrect. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of a thermo‐viscoplastic model with Lipschitz continuous constitutive equations

We study a thermo‐mechanical model, where the mechanical inelastic model with a Lipschitz–continuous constitutive relation for the plastic strain is coupled with a heat equation. The main results are the local‐in‐time existence and uniqueness of the solution to the considered model and the existence of the solution for an arbitrarily long time interval for the sufficiently small given data. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamical transition for S‐K‐T biological competing model with cross‐diffusion

The main objective of this paper is to study the dynamical transition for the S‐K‐T biological competition system with cross‐diffusion. Based on the spectral analysis, the principle of exchange of stabilities conditions for eigenvalues are obtained. By using the dynamical transition theory, 2 different types of dynamical transition for the S‐K‐T model are also derived. In addition, an example is given to illustrate our main results.