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Our motivation is a mathematical model describing the spatial propagation of an epidemic disease through a population. In this model, the pathogen diversity is structured into two clusters and then the population is divided into eight classes which permits to distinguish between the infected/uninfected population with respect to clusters. In this paper, we prove the weak and the global existence results of the solutions for the considered reaction-diffusion system with Neumann boundary. Next, mathematical Turing formulation and numerical simulations are introduced to show the pattern formation for such systems. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid model for opinion formation in a large group of agents exposed to the persuasive action of a small number of strong opinion leaders. The model is defined by coupling a finite difference equation for the dynamics of leaders opinion with a continuous integro-differential equation for the dynamics of the others. Such a definition stems from the idea that the leaders are few and tend to retain original opinions, so that their dynamics occur on a longer time scale with respect to the one of the other agents. A general well-posedness result is established for the initial value problem linked to the model. The asymptotic behavior in time of the related solution is characterized for some general parameter settings, which mimic distinct social scenarios, where different emerging behaviors can be observed. Analytical results are illustrated and extended through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper deals with a diffusive logistic equation on one dimensional isotropically growing domain. The model equation on growing domains is first presented, and the comparison principle is then proved. The asymptotic behavior of temporal solutions to the reaction-diffusion problem is given by constructing upper and lower solutions. Our result shows that when the domain grows slowly, the species successfully spreads to the whole habitat and stabilizes at a positive steady state, while it dies out in the long run if the domain grows fast. Numerical simulations are also presented to illustrate the analytical result. [ABSTRACT FROM AUTHOR]

This paper is concerned with a two-species predator-prey reaction-diffusion system with Beddington-DeAngelis functional response and subject to homogeneous Neumann boundary conditions. By linearizing the system at the positive constant steady-state solution and analyzing the associated characteristic equation in detail, the asymptotic stability of the positive constant steady-state solution and the existence of local Hopf bifurcations are investigated. Also, it is shown that the appearance of the diffusion and homogeneous Neumann boundary conditions can lead to the appearance of codimension two Bagdanov-Takens bifurcation. Moreover, by applying the normal form theory and the center manifold reduction for partial differential equations (PDEs), the explicit algorithm determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions is given. Finally, numerical simulations supporting the theoretical analysis are also included. [ABSTRACT FROM AUTHOR]

This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has been shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents computer simulation of the forging process using the finite volume method (FVM). The process of forging is highly non-linear, where both large deformations and continuously changing boundary conditions occur. In most practical cases, the initial billet shape is relatively simple, but the final shape of the end product is often geometrically complex, to the extent that it is commonly obtained using multiple forming stages. Examples of the numerical simulation of the forged pieces provided were created using Msc/SuperForge computer code. The main results of the analysis are deformed shape, temperature, pressure, effective plastic strain, effective stress and forces acting on the die. [ABSTRACT FROM AUTHOR]

We present effective methods for the numerical simulation of high-power-pumped continuous-wave (CW) and pulsed erbium-ytterbium-codoped fiber amplifiers (EYDFAs). For CW EYDFAs, a novel initial guess method and a robust algorithm are proposed to ensure the convergence of the boundary-value problems involved in the solution of the numerical model. For pulsed EYDFAs, an efficient finite-difference method based on the Lax-Wendroff scheme is developed. With these methods, high-power CW or pulsed EYDFAs can be simulated. As an example, a high-power pulse-pumped low repetition rate EYDFA is analyzed. Besides demonstrating the proposed methods, the simulation results show that the optimal pulse width of the pump can be determined by the power of the backward Yb-ASE, and the time delay between the signal and pump pulses play an important role in optimizing the performance of a high power pulse-pumped EYDFA. [ABSTRACT FROM AUTHOR]

The application of the wavelet method to vortex motion prediction is investigated. First, the wavelet method is used to solve two initial boundary problems so as to verify its abilities of controlling numerical errors and capturing local structures. Then, the adaptive wavelet method is used to simulate the vortex emerging process. The results show that the wavelet method can control numerical errors easily, can capture local structures adaptively, and can predict the vortex fluctuation evolution. Therefore, the application of the wavelet method to turbulence is suggested. [ABSTRACT FROM AUTHOR]

An efficient local extrapolation of the exponential operator splitting scheme is introduced to solve the multi-dimensional space-fractional nonlinear Schrödinger equations. Stability of the scheme is examined by investigating its amplification factor and by plotting the boundaries of the stability regions. Empirical convergence analysis and calculation of the local truncation error exhibit the second-order accuracy of the proposed scheme. The performance and reliability of the proposed scheme are tested by implementing it on two- and three-dimensional space-fractional nonlinear Schrödinger equations including the space-fractional Gross-Pitaevskii equation, which is used to model optical solitons in graded-index fibers. [ABSTRACT FROM AUTHOR]