An asymptotic preserving method for linear systems of balance laws based on Galerkin's method

We apply the concept of Asymptotic Preserving (AP) schemes to the linearized p-system and discretize the resulting elliptic equation using standard continuous Finite Elements instead of Finite Differences. The fully discrete method is analyzed with respect to consistency, and we compare it numerically with more traditional methods such as Implicit Euler's method. Numerical results indicate that the AP method is indeed superior to more traditional methods.Comment: Journal of Scientific Computing, 201

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation $A+A\to 0$ and (on-site) fusion $A+A\to A$ which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent $n$-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most $2n$ particles initially. By reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.Comment: 27 pages, Latex, to appear in Z. Phys.

Dynamic Matrix Ansatz for Integrable Reaction-Diffusion Processes

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Generalizing earlier work \cite{Stin95a,Stin95b} we present an alternative description of these processes in terms of a time-dependent operator algebra with quadratic relations. These relations generate the Bethe ansatz equations for the spectrum and turn the calculation of time-dependent expectation values into the problem of either finding representations of this algebra or of solving functional equations for the initial values of the operators. We use both strategies for the study of two specific models: (i) We construct a two-dimensional time-dependent representation of the algebra for the symmetric exclusion process with open boundary conditions. In this way we obtain new results on the dynamics of this system and on the eigenvectors and eigenvalues of the corresponding quantum spin chain, which is the isotropic Heisenberg ferromagnet with non-diagonal, symmetry-breaking boundary fields. (ii) We consider the non-equilibrium spin relaxation of Ising spins with zero-temperature Glauber dynamics and an additional coupling to an infinite-temperature heat bath with Kawasaki dynamics. We solve the functional equations arising from the algebraic description and show non-perturbatively on the level of all finite-order correlation functions that the coupling to the infinite-temperature heat bath does not change the late-time behaviour of the zero-temperature process. The associated quantum chain is a non-hermitian anisotropic Heisenberg chain related to the seven-vertex model.Comment: Latex, 23 pages, to appear in European Physical Journal

Motion transparency : depth ordering and smooth pursuit eye movements

When two overlapping, transparent surfaces move in different directions, there is ambiguity with respect to the depth ordering of the surfaces. Little is known about the surface features that are used to resolve this ambiguity. Here, we investigated the influence of different surface features on the perceived depth order and the direction of smooth pursuit eye movements. Surfaces containing more dots, moving opposite to an adapted direction, moving at a slower speed, or moving in the same direction as the eyes were more likely to be seen in the back. Smooth pursuit eye movements showed an initial preference for surfaces containing more dots, moving in a non-adapted direction, moving at a faster speed, and being composed of larger dots. After 300 to 500 ms, smooth pursuit eye movements adjusted to perception and followed the surface whose direction had to be indicated. The differences between perceived depth order and initial pursuit preferences and the slow adjustment of pursuit indicate that perceived depth order is not determined solely by the eye movements. The common effect of dot number and motion adaptation suggests that global motion strength can induce a bias to perceive the stronger motion in the back

An exactly solvable lattice model for inhomogeneous interface growth

We study the dynamics of an exactly solvable lattice model for inhomogeneous interface growth. The interface grows deterministically with constant velocity except along a defect line where the growth process is random. We obtain exact expressions for the average height and height fluctuations as functions of space and time for an initially flat interface. For a given defect strength there is a critical angle between the defect line and the growth direction above which a cusp in the interface develops. In the mapping to polymers in random media this is an example for the transverse Meissner effect. Fluctuations around the mean shape of the interface are Gaussian.Comment: 10 pages, late

Totally asymmetric exclusion process with long-range hopping

Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump $l$ sites ahead with the probability $p_l\sim 1/l^{\sigma+1}$ is studied by Monte Carlo simulations and the domain-wall approach. For $\sigma>1$ the standard TASEP phase diagram is recovered, but the density profiles near the transition lines display new features when $1<\sigma<2$. At the first-order transition line, the domain-wall is localized and phase separation is observed. In the maximum-current phase the profile has an algebraic decay with a $\sigma$-dependent exponent. Within the $\sigma \leq 1$ regime, where the transitions are found to be absent, analytical results in the continuum mean-field approximation are derived in the limit $\sigma=-1$.Comment: 10 pages, 9 figure