An innovative multistage, physiologically structured, population model to understand the European grapevine moth dynamics

We present a multistage, physiologically structured, population model for studying the dynamics of one of the most important grapevine insect pests. Growth of the population at each stage is modeled considering the climatic variations and the grape variety. A result of existence and uniqueness of solutions is presented for this original hyperbolic system as well as simulations of experimental field data.     

Parallel simulation today

This paper surveys topics that presently define the state of the art in parallel simulation. Included in the tutorial are discussions on new protocols, mathematical performance analysis, time parallelism, hardware support for parallel simulation, load balancing algorithms, and dynamic memory management for optimistic snchronization.     

Coarse-grained bifurcation analysis and detection of criticalities of an individual-based epidemiological network model with infection control

We present and discuss how the so called Equation-free approach for multi-scale computations can be used to systematically study certain aspects of the dynamics of detailed individual-based epidemiological simulators. As our illustrative example, we choose a simple individual-based stochastic epidemic model evolving on a fixed random regular network (RRN). We show how control policies based on the isolation of the infected population can dramatically influence the dynamics of the disease resulting to big-amplitude oscillations. We also address the development of a computational framework that enables detailed epidemiological simulators to converge to their coarse-grained critical points, which mark the onset of the emergent time-dependent solutions as well as to trace branches of coarse-grained unstable equilibria. Using the individual-based simulator we construct the coarse-grained bifurcation diagrams illustrating the dependence of the solutions on the disease characteristics.     

Measure-transmission metric and stability of structured population models

In Gwiazda, et al. (2012) a framework for studying cell differentiation processes based on measure-valued solutions of transport equations was introduced. Under application of the so-called measure-transmission conditions it enabled to describe processes involving both discrete and continuous transitions. This framework, however, admits solutions which lack continuity with respect to initial data. In this paper, we modify the framework from Gwiazda, et al. (2012) by replacing the flat metric, known also as bounded Lipschitz distance, by a new Wasserstein-type metric. We prove, that the new metric provides stability of solutions with respect to perturbations of initial data while preserving their continuity in time. The stability result is important for numerical applications.     

Permanence of population growth models with impulsive effects

This paper establishes criteria for permanence of populations which undergo impulsive effects at fixed times between intervals of continuous evolution governed by a differential system. It is also shown that suitable impulses may prevent the extinction or unbounded growth of populations whose evolutions are otherwise governed solely by a differential system. Examples are provided to demonstrate the application of the results obtained.     

Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks

The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be some of the major challenges nowadays. Detailed individual-based mathematical models on complex networks play an important role towards this aim. In this work, it is shown how one can exploit the Equation-Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic models with coarse-grained, system-level analysis within a pair-wise representation perspective. The proposed computational methodology provides a systematic approach for analyzing the parametric behavior of complex/multiscale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual-based SIRS epidemic model deploying on a random regular connected graph. Using the individual-based simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing I compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level.     

Method of lines for physiologically structured models with diffusion

We deal with a size-structured model with diffusion. Partial differential equations are approximated by a large system of ordinary differential equations. Due to a maximum principle for this approximation method its solutions preserve positivity and boundedness. We formulate theorems on stability of the method of lines and provide suitable numerical experiments.     

Mathematical simulation of light pulse propagating within a microring resonator system and applications

This paper presents the very fascinating simulation results of light pulse traveling within a ring resonator system that have shown the unexpected results with various applications. The design system consists of a nonlinear microring/nanoring resonator system incorporating an add/drop filter. The proposed fabricated material used is InGaAsP/InP, which can provide the required output behaviors. Three different forms of input light pulses are Gaussian pulse, dark and bright soliton, whereas the suitable simulation parameters are input power, pulse width, ring radii and the material refractive indices. Three different forms of the results have been interpreted, whereas the dominants behaviors are such as Gaussian soliton, multisoliton and tunable dark soliton are described, and the potential applications for new laser sources, new communication bands and dynamic optical tweezers have been discussed.     

A Python framework to create and simulate models with variable structure in common simulation environments

In modelling and simulation, model complexity increases with the complexity of real systems, often resulting in unfeasibly long simulation times. Variable-structure models, which can change their equation set during run-time, offer a solution. This article introduces an object-oriented approach that describes such models independent of a simulation environment. The problem of changing equations during run-time is addressed using a Python framework. Three tools are already integrated, namely, Dymola, OpenModelica and Matlab/Simulink. With this framework, existing models can be easily reused, and the advantages of different simulation tools can be leveraged. The framework is illustrated using a simple satellite launch example, along with instructions for how to use the framework. The main aim of the framework is to simulate complex models with a few mode changes and thus save simulation time. With two real-world examples and a scalability analysis, it is shown that the framework fulfils these requirements.     

Parallel machine scheduling with additional resources: Notation,classification, models and solution methods

Majority of parallel machine scheduling studies consider machine as the only resource. However, in most real-life manufacturing environments, jobs may require additional resources, such as automated guided vehicles, machine operators, tools, pallets, dies, and industrial robots, for their handling and processing. This paper presents a review and discussion of studies on the parallel machine scheduling problems with additional resources. Papers are surveyed in five main categories: machine environment, additional resource, objective functions, complexity results and solution methods, and other important issues. The strengths and weaknesses of the literature together with open areas for future studies are also emphasized. Finally, extensions of integer programming models for two main classes of related problems are given and conclusions are drawn based on computational studies.     

Baseline models of spatial population dynamics

To understand human population dynamics fully, before considering complex human agency it may be useful to construct baseline models to see where such agency may and may not be necessary. In fact, the dynamics of human populations may be amenable to mathematical modeling with relatively parsimonious mechanisms. We review some of the more prominent of such models, namely, the spatial Galton-Watson (GW) model, modifications of the GW model that add migration and immigration, and the Bolker-Pacala model, in which mortality (or birth rate) is affected by competition. We show that change in the distribution of population density over the last century for 12 American rural states may be captured by the simplest of the models, the spatial GW model.     

Dynamics of transitions in population interactions

A two-species model with transitions between population interactions is studied. Rich dynamics is observed as the number and quality of equilibria change when model parameters and functional responses vary. Existence and stability of equilibria and nonexistence of periodic solutions are established, existence of some bifurcation phenomena are analytically and numerically studied, explicit threshold values are computed to determine the kind of interaction (mutualism, competition, host-parasite) between the species, and several numerical examples are provided to illustrate the main results in this work.     

Mathematical modeling and numerical simulation of CO2 transport through hollow-fiber membranes

Chemical absorption of carbon dioxide was studied theoretically using hollow-fiber membrane contactors in this work. A 2D mathematical model was developed to study CO₂ transport through hollow-fiber membrane contactors. The model considers axial and radial diffusion in the membrane contactor. It also considers convection in the tube and shell side with chemical reaction. The finite element method (FEM) was used to solve the model equations. Modeling predictions were validated with the experimental data obtained from literature for CO₂ absorption in amine aqueous solutions as solvent. The modeling predictions were in good agreement with the experimental data for different values of gas and liquid velocities. The liquid solvents considered for this study include aqueous solutions of monoethanolamine (MEA), diethanolamine (DEA), N-methyldiethanolamine (MDEA), 2-amino-2-methyl-1-propanol (AMP) and potassium carbonate (K₂CO₃). The simulation results indicated that amine aqueous solutions were better than K₂CO₃ aqueous solution for CO₂ absorption. Also simulation results revealed that the removal of CO₂ with aqueous solution of MEA was the highest among the amines solvents. The hollow-fiber membrane contactors showed a great potential in the area of CO₂ absorption.     

Parallel simulation by multi-instruction,longest-path algorithms

This paper presents several basic algorithms for the parallel simulation of G/G/1 queueing systems and certain networks of such systems. The coverage includes systems subject to manufacturing or communication blocking, or to loss of customer due to capacity constraints. The key idea is that the customer departure times are represented by longest-path distance in directed graphs instead of by the usual recursive equations. This representation leads to scalable algorithms with a high degree of parallelism that can be implemented on either MIMD or SIMD parallel computers. This revised version was published online in June 2006 with corrections to the Cover Date.     

Efficient automatic simulation of parallel computation on networks of workstations

Andrews et al. [Automatic method for hiding latency in high bandwidth networks, in: Proceedings of the ACM Symposium on Theory of Computing, 1996, pp. 257-265; Improved methods for hiding latency in high bandwidth networks, in: Proceedings of the Eighth Annual ACM Symposium on Parallel Algorithms and Architectures, 1996, pp. 52-61] introduced a number of techniques for automatically hiding latency when performing simulations of networks with unit delay links on networks with arbitrary unequal delay links. In their work, they assume that processors of the host network are identical in computational power to those of the guest network being simulated. They further assume that the links of the host are able to pipeline messages, i.e., they are able to deliver P packets in time O(P+d) where d is the delay on the link.In this paper we examine the effect of eliminating one or both of these assumptions. In particular, we provide an efficient simulation of a linear array of homogeneous processors connected by unit-delay links on a linear array of heterogeneous processors connected by links with arbitrary delay. We show that the slowdown achieved by our simulation is optimal. We then consider the case of simulating cliques by cliques; i.e., a clique of heterogeneous processors with arbitrary delay links is used to simulate a clique of homogeneous processors with unit delay links. We reduce the slowdown from the obvious bound of the maximum delay link to the average of the link delays. In the case of the linear array we consider both links with and without pipelining. For the clique simulation the links are not assumed to support pipelining.The main motivation of our results (as was the case with Andrews et al.) is to mitigate the degradation of performance when executing parallel programs designed for different architectures on a network of workstations (NOW). In such a setting it is unlikely that the links provided by the NOW will support pipelining and it is quite probable the processors will be heterogeneous. Combining our result on clique simulation with well-known techniques for simulating shared memory PRAMs on distributed memory machines provides an effective automatic compilation of a PRAM algorithm on a NOW.     

Periodic solutions of some models with strong Allee effects

In this paper, the authors obtain sufficient conditions for the existence of two positive periodic solutions to models representing the dynamics of a renewable resource that is subject to a strong Allee effect. The Leggett-Williams multiple fixed point theorem is used to prove the results.     

Qualitative analysis of second-order models of tumor–immune system competition

This paper deals with the qualitative analysis, existence of equilibria and asymptotic behavior of some second-order models of the competition between tumor and immune cells. The background model belongs to d’Onofrio [A. d’Onofrio, A general framework for modeling tumor–immune system competition and immunotherapy: Mathematical analysis and biomedical inferences, Physica D 208 (2005) 220–235; A. d’Onofrio, Tumor–immune system interaction: Modelig the tumor-stimulated proliferation of effectors and immunotherapy, Math. Models Methods Appl. Sci. 16 (2006) 1375–1401]. Various developments proposed in this paper are focussed on the hiding–learning dynamics, followed by the qualitative analysis.     

封闭容器中二维自然对流直接数值模拟的一个并行算法

本文对具有不同温度竖壁的封闭容器中二维自然对流问题进行了直接数值模拟,控制方程在非均匀网络上使用空间二阶精度和时间一阶精度进行离散,程序是在国家高性能计算中心（武汉）的并行计算机“曙光１０００Ａ”上实现的,使用４个结点,获得的加速比和效率分别约为２．８９和０．７２。     

Optimization of finite element bidimensional models: an approach based on genetic algorithms

This paper deals with the optimization of 2D finite element shapes using the very promising methods based on genetic algorithms. The codification of the design variables is carried out by generating series of strings in binary code. Classical genetic operators such as crossover, mutation and reproduction are used for the optimization process. A more refined operators needed to improve the performance of the process are used as well. Some illustrative examples are presented and discussed     

Two-time scales in spatially structured models of population dynamics: A semigroup approach

The aim of this work is to provide a unified approach to the treatment of a class of spatially structured population dynamics models whose evolution processes occur at two different time scales. In the setting of the C₀-semigroup theory, we will consider a general formulation of some semilinear evolution problems defined on a Banach space in which the two-time scales are represented by a parameter ε>0 small enough, that mathematically gives rise to a singular perturbation problem. Applying the so-called aggregation of variables method, a simplified model called the aggregated model is constructed. A nontrivial mathematical task consists of comparing the asymptotic behaviour of solutions to both problems when ε→₀₊, under the assumption that the aggregated model has a compact attractor. Applications of the method to a class of two-time reaction-diffusion models of spatially structured population dynamics and to models with discrete spatial structure are given.