E. Levine

A study of microstrip array antennas with the feed network

The radiation and losses in microstrip antennas with a corporate feed network are studied. A surface current approach is applied in which the electrical currents in the feed lines are modeled as in ideal transmission lines. The free-space radiation and the surface-wave excitation of typical segments in printed feed networks are studied. A four-element array antenna with its printed feed network is analyzed and predicted radiation patterns, directivity, and gain are presented and compared with experimental results. The gain and directivity of large arrays of 16, 64, 256 and 1024 elements are calculated and measurements in the frequency range of 10 to 35 GHz are reported. >

Criterion for phase separation in one-dimensional driven systems.

A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided.

Zero-range process with open boundaries

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density ρc. In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters.

Phase-separation transition in one-dimensional driven models

A class of models of two-species driven diffusive systems which is shown to exhibit phase separation in d=1 dimensions is introduced. Unlike previously studied models exhibiting similar phenomena, here the relative density of the two species is fluctuating within the macroscopic domain of the phase separtated state. The nature of the phase transition from the homogeneous to the phase-separated state is discussed in view of a recently introduced criterion for phase separation in one-dimensional driven systems.

Long-range attraction between probe particles mediated by a driven fluid

The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven fluid mediates an effective long-range attraction between the two probes, with a force that decays at large distances x as ? b/x, where b is a function of the interaction parameters. Depending on the amplitude b, the two probes may form one of three states: a) an unbound state, where the distance grows diffusively with time; b) a weakly bound state, in which the distance grows sub-diffusively; and c) a strongly bound state, where the average distance stays finite in the long-time limit. Similar results are found for the behavior of any finite number of probes.

Spontaneous symmetry breaking in a non-conserving two-species driven model

A two-species particle model on an open chain with dynamics which is non-conserving in the bulk is introduced. The dynamical rules which define the model obey a symmetry between the two species. The model exhibits a rich behaviour which includes spontaneous symmetry breaking and localized shocks. The phase diagram in several regions of parameter space is calculated within the mean-field approximation, and compared with Monte Carlo simulations. In the limit where fluctuations in the number of particles in the system are taken to be zero, an exact solution is obtained. We present and analyse a physical picture which serves to explain the different phases of the model.

Sharp crossover and anomalously large correlation length in driven systems

Models of one-dimensional driven diffusive systems sometimes exhibit an abrupt increase in the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behaviour may be misinterpreted as a genuine phase transition. A simple mechanism for this sharp increase is presented. The mechanism is introduced within the framework of a recently suggested correspondence between driven diffusive systems and zero-range processes. It is shown that when the dynamics of the model is such that small domains are suppressed in the steady-state distribution, anomalously large correlation lengths may build up. The mechanism is examined in detail in two models.

Modelling one-dimensional driven diffusive systems by the Zero-Range Process

Abstract.The recently introduced correspondence between one-dimensional two-species driven models and the Zero-Range Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated through the length dependence of the current emitted from a particle domain. A direct numerical method for evaluating this current is introduced, and used to test the assumptions underlying this approach. In addition, a model for isolated domain dynamics is introduced, which provides a simple way to calculate the current also for the non-equal density case. This approach is demonstrated and applied to a particular two-species model, where a phase separation transition line is calculated.

Phase transition in a non-conserving driven diffusive system

An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and show that it can exhibit a continuous phase transition in which the density of vacancies decreases to zero. The model has no absorbing state and furnishes an example of a one-dimensional phase transition in a homogeneous non-conserving system which does not belong to the absorbing state universality classes.

Phase Transitions in Traffic Models

It is suggested that the question of existence of a jamming phase transition in a broad class of single-lane cellular-automaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between free-flow and jammed states, as the car density is increased.