Chapman-Enskog-maximum entropy method on time-dependent neutron transport equation

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman-Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity R_f. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.     

Regularity results for evolutionary nonlinear variational and quasi-variational inequalities with applications to dynamic equilibrium problems

The aim of this paper is to obtain the continuity of solutions to time-dependent nonlinear variational and quasi-variational inequalities which express many dynamic equilibrium problems. To prove our results, we make use of Minty’s Lemma and of the notion of the Mosco’s convergence.     

Hydrogenation of acetylene–ethylene mixtures on Pd catalysts: study of the surface mechanism by computational approaches. Metal dispersion and catalytic activity

The hydrogenation mechanism of acetylene–ethylene mixtures on Pd catalysts under different experimental conditions was studied by employing a time-dependent Monte Carlo approach set to use a fixed series of event probabilities. The dependence of the catalyst activity and selectivity on the sizes of the metal particles was simulated at microscopic level and the results, also refined by fitting procedures, suggested proper explanations for the apparent nonuniformity of the related experimental findings. The use of the steric hindrance parameter of the surface species and the available surface energy on the metallic catalyst sites was decisive for reproducing the experimental results. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

An application of bilinear integration to quantum scattering

Scattering theory has its origin in Quantum Mechanics. From the mathematical point of view it can be considered as a part of perturbation theory of self-adjoint operators on the absolutely continuous spectrum. In this work we deal with the passage from the time-dependent formalism to the stationary state scattering theory. This problem involves applying Fubini's Theorem to a spectral measure integral and a Lebesgue integral of functions that take values in spaces of operators. In our approach, we use bilinear integration in a tensor product of spaces of operators with suitable topologies and generalize the results previously stated in the literature.     

SBA splitting for approximation of invariants in time-dependent Hamiltonian systems

Most physical phenomena are described by time-dependent Hamiltonian systems with qualitative features that should be preserved by numerical integrators used for approximating their dynamics. The initial energy of the system together with the energy added or subtracted by the outside forces, represent a conserved quantity of the motion. For a class of time-dependent Hamiltonian systems [8] this invariant can be defined by means of an auxiliary function whose dynamics has to be integrated simultaneously with the system’s equations. We propose splitting procedures featured by a SB³A property that allows to construct composition methods with a reduced number of determining order equations and to provide the same high accuracy for both the dynamics and the preservation of the invariant quantity.     

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.     

Error Estimates for Finite-Element Navier-Stokes Solvers without Standard Inf-Sup Conditions

The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions. The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields. The methods use C^1 elements for velocity and C^0 elements for pressure. A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag, Israeli, DeVille and Karniadakis.     

Studies on some perfectly matched layers for one-dimensional time-dependent systems

We will analyze some perfectly matched layers (PMLs) for the one-dimensional time-dependent Maxwell system, acoustic equations and hyperbolic systems in unbounded domains. The exponential decays and convergence of the PML solutions are studied. Some finite difference schemes are proposed for the PML equations and their stability and convergence are established. The work of Y. Lin was fully supported by the NSERC of Canada, of K. Zhang partially supported by a Direct Grant of CUHK (2060276) and NNSF (No. 10701039 of China), whereas the work of J. Zou was fully supported by Hong Kong RGC grants (Project 404606 and Project 404407).     

Rayleigh problem for a MHD Sisko fluid

The problem of unsteady unidirectional flow of an incompressible Sisko fluid bounded by a suddenly moved plate is studied. The fluid is magnetohydrodynamic (MHD) in the presence of a time-dependent magnetic field applied transversely to the flow. The non-linear flow problem arising from the laws of momentum, mass and suitable boundary and initial conditions is solved analytically using Lie symmetry method. The manner in which the various emerging parameters affect the structure of the velocity is delineated.     

A study on KdV and Gardner equations with time-dependent coefficients and forcing terms

In this work we study the KdV equation and the Gardner equation with time-dependent coefficients and forcing term for each equation. A generalized wave transformation is used to convert each equation to a homogeneous equation. The soliton ansatz will be applied to the homogeneous equations to obtain soliton solutions.