Phase diagram of the ABC model on an interval

The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here the latter model is studied on a one-dimensional lattice of N sites with closed (zero flux) boundaries. In this geometry the local particle conserving dynamics satisfies detailed balance with respect to a canonical Gibbs measure with long range asymmetric pair interactions. This generalizes results for the ring case, where detailed balance holds, and in fact the steady state measure is known only for the case of equal densities of the different species: in the latter case the stationary states of the system on a ring and on an interval are the same. We prove that in the N to infinity limit the scaled density profiles are given by (pieces of) the periodic trajectory of a particle moving in a quartic confining potential. We further prove uniqueness of the profiles, i.e., the existence of a single phase, in all regions of the parameter space (of average densities and temperature) except at low temperature with all densities equal; in this case a continuum of phases, differing by translation, coexist. The results for the equal density case apply also to the system on the ring, and there extend results of Clincy et al.Comment: 52 pages, AMS-LaTeX, 8 figures from 10 eps figure files. Revision: minor changes in response to referee reports; paper to appear in J. Stat. Phy

From Vicious Walkers to TASEP

We propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for $m$ particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-dissipation relation allowing us to reinterpret the result as the particle current generating function in the totally asymmetric simple exclusion process. Thus we obtain the particle current distribution asymptotically in the large time limit as the number of particles is fixed. The results apply to the large deviation scale as well as to the diffusive scale. In the latter we obtain a new universal distribution, which has a skew non-Gaussian form. For $m$ particles its asymptotic behavior is shown to be $e^{-\frac{y^{2}}{2m^{2}}}$ as $y\to -\infty$ and $e^{-\frac{y^{2}}{2m}}y^{-\frac{m(m-1)}{2}}$ as $y\to \infty$.Comment: 37 pages, 4 figures, Corrected reference

Multi-Level Analysis and Optimization of Design

This paper discusses a knowledge-based computer-aided design system, that provides multi-level analysis capabilities, and that automatically propagates constraints on design variables from level to level. It also Supports formulation and solution of optimization problems at different levels, so that a solution can be approached by solving a sequence of appropriately constrained sub-optimization problems. Theory and implementation are discussed, and a detailed case study of application to the design of small house plans is provide

Top-Down Knowledge-Based Design

Traditional computer drafting systems and three- dimensional geometric modelling systems work in bottom-up fashion. They provide a range of graphic primitives, such as vectors, arcs, and splines, together with operators for inserting, deleting, combining, and transforming instances of these. Thus they are conceptually very similar to word processors, with the difference that they operate on two- dimensional or three-dimensional patterns of graphic primitives rather than one-dimensional strings of characters. This sort of system is effective for input and editing of drawings or models that represent existing designs, but provides little more help than a pencil when you want to construct from scratch a drawing of some complex object such as a human figure, an automobile, or a classical column: you must depend on your own knowledge of what the pieces are and how to shape them and put them together. If you already know how to draw something then a computer drafting system will help you to do so efficiently, but if you do not know how to begin, or how to develop and refine the drawing, then the efficiency that you gain is of little practical consequence. And accelerated performance, flashier color graphics, or futuristic three-dimensional modes of interaction will not help with this problem at all. By contrast, experienced expert graphic artists and designers usually work in top-down fashion-beginning with a very schematic sketch of the whole object, then refining this, in step-by-step fashion, till the requisite level of precision and completeness is reached. For example, a figure drawing might begin as a “stick figurei schema showing lengths and angles of limbs, then be developed to show the general blocking of masses, and finally be resolved down to the finest details of contour and surface. Similarly, an architectural drawing might begin as a parti showing just a skeleton of construction lines, then be developed into a single-line floor plan, then a plan showing accurate wall thicknesses and openings, and finally a fully developed and detailed drawing

Discontinuous condensation transition and nonequivalence of ensembles in a zero-range process

We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of a condensation transition. In contrast to previous results, the phase transition is discontinuous and the system exhibits ergodicity breaking and metastable phases. This leads to a richer phase diagram, including nonequivalence of ensembles in certain phase regions. The paper is motivated by results from granular clustering, where these features have been observed experimentally