A discrete model is introduced to account for the time-periodic oscillations of the photocurrent in a superlattice observed by Kwok et al, in an undoped 40 period AlAs/GaAs superlattice. Basic ingredients are an effective negative differential resistance due to the sequential resonant tunneling of the photoexcited carriers through the potential barriers, and a rate equation for the holes that incorporates photogeneration and recombination. The photoexciting laser acts as a damping factor ending the oscillations when its power is large enough. The model explains: (i) the known oscillatory static I-V characteristic curve through the formation of a domain wall connecting high and low electric field domains, and (ii) the photocurrent and photoluminescence time-dependent oscillations after the domain wall is formed. In our model, they arise from the combined motion of the wall and the shift of the values of the electric field at the domains. Up to a certain value of the photoexcitation, the non-uniform field profile with two domains turns out to be metastable: after the photocurrent oscillations have ceased, the field profile slowly relaxes toward the uniform stationary solution (which is reached on a much longer time scale). Multiple stability of stationary states and hysteresis are also found. An interpretation of the oscillations in the photoluminescence spectrum is also given.

We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit. Ms. number

We prove that the Jacobi algorithm applied implicitly on a decomposition A = X D X T of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. The relative error in every eigenvalue is bounded by O( κ(X )), where is the machine precision and κ(X ) ≡ X 2 · X −1 2 is the spectral condition number of X . The eigenvectors are also computed accurately in the appropriate sense. We believe that this is the first algorithm to compute accurate eigenvalues of symmetric (indefinite) matrices that respects and preserves the symmetry of the problem and uses only orthogonal transformations.

We report on time-resolved studies of electric-field domains in weakly coupled GaAs quantum-well structures. Photoluminescence and photocurrent experiments probe the motion of charged domain walls triggered by steplike changes in the illumination. Results reveal complex oscillations with frequencies in the range 4 -8 MHz. These findings are discussed in terms of a discrete drift model relying on negative-differential conductance due to resonant tunneling. Calculations give a global phase diagram and time behavior consistent with experiments.

Deterministic and stochastic cellular automata models available to study two-dimensional traffic fIow are compared in this paper. It is shown that a connection between them can be made only when the infinite time and infinite system limits are taken in the appropriate order. We also stress the crucial importance of the choice of boundary conditions in the deterministic model to obtain bulk properties. PACS number(s): 64.60.Cn, 05.20.Dd, 47.90.+a, 89.40.+k In the last few years there has been a growing interest in the study of cellular automata (CA) models which try to mimic, with simple rules, the features of traffic in highways [1]. Recently some work has also been focused on the behavior of traffic in cities. Along this line two CA models have been proposed [2,3]. Both describe two equal populations of cars moving in perpendicular directions from node to node of a square-lattice-like city with streets pointing only up and right and periodic boundary conditions (BC's). Movement occurs in discrete time steps and traffic lights rule it so that they allow horizontal and vertical movements alternately. The interaction between cars forbids a car to jump to a node if it is occupied by another car at the same time step.The model of Ref. [3] includes the ability of cars to turn with probability y e [0,1/2]. When y=0 this model reduces to that of Ref. [2]. In both models a phase transition from a freely moving phase to a jammed one occurs above a certain density of cars. Whereas the jammed phase is characterized in both models by a low value of the average velocity U (which approaches 0 as y goes to 0), there is a drastically different behavior of the average velocity as a function of the density of cars n in the freely moving phase. The deterministic model [2] shows that U remains constant and equal to its maximum value up to the transition density, while the stochastic model [3] exhibits an almost linear decrease with slope -1/2 which appears not to depend on y. A recent mean-field-like study of the latter model [4] confirms this fact. It is the purpose of this paper to make clear the connection between these two models and the origin of this discontinuity of the behavior of v(n) in the parameter 7.In Ref.[4] a microscopic description of these models was achieved by introducing a set of Boolean variables, namely (i) occupation numbers of site r and time step t for vertical and horizontal cars, p, ', and v'", respectively, (ii)