A non-uniform basis order for the discontinuous Galerkin method of the 3D dissipative wave equation with perfectly matched layer

In this study a discontinuous Galerkin method (DG) for solving the three-dimensional time-dependent dissipative wave equation is investigated. In the case of unbounded problems, the perfectly matching layer (PML) is used to truncate the computational domain. The aim of this work is to investigate a simple selection method for choosing the basis order for elements in the computational mesh in order to obtain a predetermined error level. The selection method studied here relies on the error estimates provided by Ainsworth [M. Ainsworth, Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods, Journal of Computational Physics 198(1) (2004) 106–130]. The performance of the non-uniform basis is examined using numerical experiments. In the simulated model problems, a feasible method choosing the basis order for arbitrary sized elements is achieved. In simulations, the effect of dissipation and the choices of the PML parameters on the performance of the DG method are also investigated.     

Communication modes in vector diffraction

The communication modes, which mathematically correspond to singular value decomposition, have proven a useful concept in optical scalar-field diffraction, with applications in resolution studies, image synthesis, and wave propagation. For optical near-field geometries the communication modes have to be extended to electromagnetic field accounting for the polarization properties. In this paper we present the vector-valued communication modes method based on the rigorous electric-field diffraction integral. As a special case the transverse-electric scalar field modes are obtained. The intensity and polarization properties of the leading electromagnetic communication modes in near-field arrangements with rectangular apertures are discussed in terms of the Stokes parameters. For small separations between the transmitting and receiving apertures the fundamental mode possesses a ring-shaped hollow structure. The polarization properties of the near-field modes show features on spatial scales smaller than the wavelength of light. The system symmetries lead to degenerate communication modes.     

From low-momentum interactions to nuclear structure

We present an overview of low-momentum two-nucleon and many-body interactions and their use in calculations of nuclei and infinite matter. The softening of phenomenological and effective field theory (EFT) potentials by renormalization group (RG) transformations that decouple low and high momenta leads to greatly enhanced convergence in few- and many-body systems, while maintaining a decreasing hierarchy of many-body forces. This review surveys the RG-based technology and results, discusses the connections to chiral EFT, and clarifies various misconceptions.     

Wave train selection behind invasion fronts in reaction-diffusion predator-prey models

Wave trains, or periodic travelling waves, can evolve behind invasion fronts in oscillatory reaction-diffusion models for predator-prey systems. Although there is a one-parameter family of possible wave train solutions, in a particular predator invasion a single member of this family is selected. Sherratt (1998) [13] has predicted this wave train selection, using a λ-ω system that is a valid approximation near a supercritical Hopf bifurcation in the corresponding kinetics and when the predator and prey diffusion coefficients are nearly equal. Away from a Hopf bifurcation, or if the diffusion coefficients differ somewhat, these predictions lose accuracy. We develop a more general wave train selection prediction for a two-component reaction-diffusion predator-prey system that depends on linearizations at the unstable homogeneous steady states involved in the invasion front. This prediction retains accuracy farther away from a Hopf bifurcation, and can also be applied when the predator and prey diffusion coefficients are unequal. We illustrate the selection prediction with its application to three models of predator invasions.     

Mixed-mode solutions in an air-filled differentially heated rotating annulus

We present an analysis of the primary bifurcations that occur in a mathematical model that uses the (three-dimensional) Navier-Stokes equations in the Boussinesq approximation to describe the flows of a near unity Prandtl number fluid (i.e. air) in the differentially heated rotating annulus. In particular, we investigate the double Hopf (Hopf-Hopf) bifurcations that occur along the axisymmetric to non-axisymmetric flow transition. Parameter-dependent centre manifold reduction and normal forms are used to show that in certain regions in parameter space, stable quasiperiodic mixed-azimuthal mode solutions result as a nonlinear interaction of two bifurcating waves with different azimuthal wave numbers. These flows have been called wave dispersion and interference vacillation. The results differ from similar studies of the annulus with a higher Prandtl number fluid (i.e. water). In particular, we show that a decrease in Prandtl number can stabilize these mixed-mode solutions.     

基于联合作战兵力配置的非合作博弈研究

基于联合作战实体定量分析的作战能力指数组合期望效用,研究了联合作战任务兵力配置问题,建立了二人零和参数博弈模型,并讨论了模型构建的理论依据与算法.     

A thermoelastic system of memory type in noncylindrical domains

In this paper, we consider a hyperbolic thermoelastic system of memory type in domains with moving boundary. The problem models vibrations of an elastic bar under thermal effects according to the heat conduction law of Gurtin and Pipkin. Global existence is proved by using the penalty method of Lions.     

On the universality of the thermomechanics of forces driving singular sets

Summary It is shown that the formal expression of the driving force acting on a one- dimensional or two-dimensional singular set of material points (crack tip in fracture, phase-transition front or shock wave) and of the accompanying dissipation in an irreversible progress of the set is independent of the precise material behaviour at regular points. A four-dimensional space-time canonical formalism is introduced establishing the necessary consistency between the power expended by the driving force (spatial component) and the resulting heat source (timelike component) localized at the singular set. Possible extensions of this result are discussed. Received 8 April 1999; accepted for publication 4 May 1999     

单兵种对双兵种作战模型

本文讨论了单兵种对双兵种作战的 Lanchester模型 ,分析研究了战斗进程中各方兵力的动态变化 ,给出了单兵种方的最优兵力分配原则 .     

Elastoplastic Deformation of Flexible Cylindrical Shells With Two Circular Holes under Axial Tension

The elastoplastic state of thin cylindrical shells with two circular holes under axial tension is analyzed considering finite deflections. The distributions of stresses along the contours of the holes and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for either physical nonlinearity (plastic deformations) and geometrical nonlinearity (finite deflections) alone and with a numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between the holes and the nonlinear factors accounted for__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 5, pp. 52–57, May 2005.