In this paper, we present an explicit, unconditionally stable and accurate numerical method for the Maxwell–Dirac system (MD) and use it to study dynamics of MD. As preparatory steps, we take the three-dimensional (3D) Maxwell– Dirac system, scale it to obtain a two-parameter model and review plane wave solution of free MD. Then we present a time-splitting spectral method (TSSP) for MD. The key...

Using the maximum entropy method, spectral functions of the pseudo-scalar and vector mesons are extracted from lattice Monte Carlo data of the imaginary time Green's functions. The resonance and continuum structures as well as the ground state peaks are successfully obtained. Error analysis of the resultant spectral functions is also given on the basis of the Bayes probability theory.

Dendritic processing is now considered to be important in pre-processing of signals coming into a cell. Dendrites are involved in both propagation and backpropagation of signals 1. In a cylindrical dendrite, signals moving in either direction will be similar. However, if the dendrites taper, then this is not the case any more. The picture gets more complex if the ion channel distribution along ...

We present a numerical method for simulations of nonlinear surface water waves over variable bathymetry. It is applicable to either twoor three-dimensional flows, as well as to either static or moving bottom topography. The method is based on the reduction of the problem to a lower-dimensional Hamiltonian system involving boundary quantities alone. A key component of this formulation is the Dir...

To develop an understanding of singularity formation in vortex sheets, we consider model equations that exhibit shared characteristics with the vortex sheet equation but are slightly easier to analyze. A model equation is obtained by replacing the ux term in Burgers' equation by alternatives that contain contributions depending globally on the solution. We consider the continuum of partial diie...

A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Yin, Clercx and Montgomery, Comput. Fluid...

After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations in one horizontal dimension. The numerical discretization is validated by comparisons with analytical, experimental data or other numerical solutions obtained...

The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is...

Usually, n is larger than m. When m = 0, the DAEs reduce to the ODEs. There are many numerical methods used to solve ODEs, but only a few is used to solve DAEs [1–5]. A lot of engineering problems are modelled as a combination of ODEs and NAEs, which are abbreviated as differential algebraic equations (DAEs). The DAEs are both numerically and analytically difficult than the ODEs. Recently, ther...

We study implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into sub-determinants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple sub-determinant identity which has a non-trivial inte...