We discuss the general link between mode-coupling like equations (which serve as the basis of some recent theories of supercooled liquids) and the dynamical equations governing mean-field spin-glass models, or the dynamics of a particle in a random potential. The physical consequences of this interrelation are underlined. It suggests to extend the mode-coupling approximation to temperatures wel...

In the present paper an embedded-boundary formulation that is applicable to fluid structure interaction problems is presented. The Navier-Stokes equations for incompressible flow are solved on a fixed grid which is not aligned with the body. A corotational formulation is used to describe the dynamics of a body that moves through the fixed grid undergoing large-angle/large-displacement rigid bod...

Extending the previous 2-gender dioecious biploid gene-mating evolution model, we attempt to answer “whether the Hardy-Weinberg global stability and the exact analytic dynamical solutions can be found in the generalized N-gender polyploid gene-mating system?” For a 2-gender gene-mating evolution model, a pair of male and female determines the trait of their offspring. Each of the pair contribut...

The recognition that fluid-dynamical models can yield solutions with less symmetry than the governing equations is not new. Jacobi's discovery that a rotating fluid mass could have equilibrium configurations lacking rotational symmetry is a famous nineteenth-century example. In modern terminology, Jacobi's asymmetric equilibria appear through a symmetry­ breaking bifurcation from a family of sy...

Visualisation of complex nonlinear equation solutions is a useful analysis tool for various scientific and engineering applications. We have re-examined the geometrical interpretation of the classical nonlinear four-wave mixing equations for the specific scheme of a phase sensitive one-pump fiber optical parametric amplification, which has recently attracted revived interest in the optical comm...

Here we review a hybrid lattice Boltzmann algorithm to solve the equations of motion of cholesteric liquid crystals. The method consists in coupling a lattice Boltzmann solver for the Navier-Stokes equation to a finite difference method to solve the dynamical equations governing the evolution of the liquid crystalline order parameter. We apply this method to study the growth of cholesteric blue...

In this paper, we present three second-order finite element methods solving Maxwell’s equations when metamaterials are involved. The first method is based on integral-differential equations transformed from the governing equations; the other two methods solve the original governing differential equations. Numerical results are presented for the last two methods.

impact responses of rectangular composite plates with embedded shape memory alloy (sma) wires are investigated in the present research. the plate is assumed to be placed in a thermal environment; so that in contrast to the available researches in the field, the shape memory and ferroelasticity effects have to be considered also in addition to the superelasticity. the governing equations are der...

This paper presents the governing equations on the rectangular plate with the variation of material stiffness through their thick using higher order shear deformation theory (HSDT). The governing equations are obtained by using Hamilton's principle with regard to variation of Young's modulus in through their thick with regard sinusoidal variation of the displacement field across the thickness. ...