A non-stationary problem coupling PDEs and ODEs modelizing an automotive catalytic converter

In this article we prove the existence and uniqueness of the solution of a non-stationary problem that modelizes the behavior of the concentrations and the temperature of gases going through a cylindrical passage of an automotive catalytic converter. This problem couples parabolic partial differential equations (PDEs) in a domain with one parabolic partial differential equation and some ordinary differential equations (ODEs) on a part of its boundary.     

Mathematical aspects of the Maxwell problem

We study the large-time behaviour of global smooth solutions to the Cauchy problem for hyperbolic regularization of conservation laws. An attracting manifold of special smooth global solutions is determined by the Chapman projection onto the phase space of consolidated variables. For small initial data we construct the Chapman projection and describe its properties in the case of the Cauchy problem for moment approximations of kinetic equations. The existence conditions for the Chapman projection are expressed in terms of the solvability of the Riccati matrix equations with parameter.     

On fractional integro-differential inclusions with state-dependent delay in Banach spaces

In this article we investigate the existence of solutions on a compact interval for the fractional integro-differential inclusions with state-dependent delay in Banach spaces when the delay is infinite. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values.     

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.     

利用GEANT4和FLUKA研究质子诱发散裂反应出射中子双微分截面

在中高能质子诱发散裂反应相关核工程设计中,可靠的蒙特卡罗模拟程序结合核反应理论模型具有较好的理论指导意义。本工作中,利用GEANT4耦合INCL4和ABLA理论模型以及FLUKA耦合PEANUT模型模拟计算了几百MeV至几个GeV质子轰击Be,Al,Fe,W,U等靶后30°,60°,120°,150°出射角产生的散裂中子双微分截面,并与现有实验数据进行了比较。结果发现,FLUKA和GEANT4模拟计算较好地再现了Al,Fe,W,U等靶实验测量数据。然而,模拟结果明显低估了Be靶出射中子能量小于10 MeV能区的实验数据。For the design of nuclear engineering related with medium-high energy proton induced spallation reaction,the reliable Monte Carlo simulation codes coupled with nuclear reaction models have a good theoretical guidance.In this work,the production spallation neutron double differential cross sections at 30°,60°,120°,150°emission angle for Be,Al,Fe,W,U target materials at incident proton energies between several hundred MeV and GeV are theoretically calculated by using the GEANT4 coupled INCL4 and ABLA,and the FLUKA coupled PEANUT.The calculated results were compared with the available experimental data.It is found that the GEANT4 and FLUKA calculations well reproduced the experimental measurement of Al,Fe,W,U target materials.However,calculations obviously underestimated the emission neutrons of Be target for lower than 10 MeV energy range.     

Asymptotics of the 1/2-dimension,Discrete Airy Equation and its Approximating Differential Equation

A discrete finite difference model is constructed for the Airy equation using a nonstandard scheme formulated by Mickens and Ramadhani. The method of dominant balance is then applied to obtain a first-order difference equation for the solution that increases sufficiently fast as k→∞. We then calculate the corresponding approximating differential equation and obtain its exact solution as well as its “exact” discrete finite difference representation. The application of various symmetry operations allows the determination of the related rapidly decreasing solution and the oscillatory solutions for negative values of x k>=hk, where h=?x.     

Global periodicity and complete integrability of discrete dynamical systems

Consider the discrete dynamical system generated by a map F. It is said that it is globally periodic if there exists a natural number p such that F ^p (x)=x for all x in the phase space. On the other hand, it is called completely integrable if it has as many functionally independent first integrals as the dimension of the phase space. In this paper, we relate both concepts. We also give a large list of globally periodic dynamical systems together with a complete set of their first integrals, emphasizing the ones coming from difference equations.     

Complete set of periodic solutions of a discontinuous recurrence equation

A nonlinear three-term recurrence relation arising from seeking the steady states of a cellular neural network with bang‐bang control is studied. We show that each solution is periodic and its prime period can be determined by three of its consecutive terms. By means of this periodicity property, we may then solve the steady state problem which to our knowledge is not solved by other means.     

An efficient and robust numerical algorithm for estimating parameters in Turing systems

We present a new algorithm for estimating parameters in reaction–diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer–Meinhardt reaction–diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available.