Directing Brownian motion on a periodic surface

We consider an overdamped Brownian particle, exposed to a two-dimensional, square lattice potential and a rectangular ac-drive. Depending on the driving amplitude, the linear response to a weak dc-force along a lattice symmetry axis consist in a mobility in basically any direction. In particular, motion exactly opposite to the applied dc-force may arise. Upon changing the angle of the dc-force relatively to the square lattice, the particle motion remains predominantly opposite to the dc-force. The basic physical mechanism consists in a spontaneous symmetry breaking of the unbiased deterministic particle dynamics.Comment: 4 Pages, 4 figures, accepted for Phys. Rev. Let

Algebraic Aspects of Abelian Sandpile Models

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G, and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of toppling matrix. We construct scalar functions, linear in height variables of the pile, that are invariant toppling at any site. These invariants provide convenient coordinates to label the recurrent configurations of the sandpile. For an L X L square lattice, we show that g = L. In this case, we observe that the system has nontrivial symmetries coming from the action of the cyclotomic Galois group of the (2L+2)th roots of unity which operates on the set of eigenvalues of the toppling matrix. These eigenvalues are algebraic integers, whose product is the order |G|. With the help of this Galois group, we obtain an explicit factorizaration of |G|. We also use it to define other simpler, though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3

Research Notes : Australia : Designation of a core collection of perennial Glycine

Over the last decade, a large germplasm collection of the 12 currently recognized perennial species of Glycine has been assembled. This collection, now numbering more than 1400 accessions, is held in Canberra, Australia, and is recognized by the International Board of Plant Genetic Resources as the world base collection for perennial Glycine. The 12 species include five that have been described recently

The grand canonical ABC model: a reflection asymmetric mean field Potts model

We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean field interactions. The three types of particles are designated as $A$, $B$, and $C$. The system is described by a grand canonical ensemble with temperature $T$ and chemical potentials $T\lambda_A$, $T\lambda_B$, and $T\lambda_C$. We find that for $\lambda_A=\lambda_B=\lambda_C$ the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature $\hat T_c=(2\pi/\sqrt3)^{-1}$. For other values of the chemical potentials the system has a unique equilibrium state. As is the case for the canonical ensemble for this $ABC$ model, the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics. We note that $\hat T_c=3T_c$, where $T_c$ is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities $r_A=r_B=r_C=1/3$.Comment: 24 pages, 3 figure

Exact solutions for a mean-field Abelian sandpile

We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe

Analysis of conductor impedances accounting for skin effect and nonlinear permeability

It is often necessary to protect sensitive electrical equipment from pulsed electric and magnetic fields. To accomplish this electromagnetic shielding structures similar to Faraday Cages are often implemented. If the equipment is inside a facility that has been reinforced with rebar, the rebar can be used as part of a lighting protection system. Unfortunately, such shields are not perfect and allow electromagnetic fields to be created inside due to discontinuities in the structure, penetrations, and finite conductivity of the shield. In order to perform an analysis of such a structure it is important to first determine the effect of the finite impedance of the conductors used in the shield. In this paper we will discuss the impedances of different cylindrical conductors in the time domain. For a time varying pulse the currents created in the conductor will have different spectral components, which will affect the current density due to skin effects. Many construction materials use iron and different types of steels that have a nonlinear permeability. The nonlinear material can have an effect on the impedance of the conductor depending on the B-H curve. Although closed form solutions exist for the impedances of cylindrical conductors made of linear materials, computational techniques are needed for nonlinear materials. Simulations of such impedances are often technically challenging due to the need for a computational mesh to be able to resolve the skin depths for the different spectral components in the pulse. The results of such simulations in the time domain will be shown and used to determine the impedances of cylindrical conductors for lightning current pulses that have low frequency content

Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process

It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is manifested by the existence of a phase in which the densities of the two species are not equal. In order to provide a more rigorous basis to these observations we consider the limit of the process when the rate at which particles leave the system goes to zero. In this limit the process reduces to a biased random walk in the positive quarter plane, with specific boundary conditions. The stationary probability measure of the position of the walker in the plane is shown to be concentrated around two symmetrically located points, one on each axis, corresponding to the fact that the system is typically in one of the two states of broken symmetry in the exclusion process. We compute the average time for the walker to traverse the quarter plane from one axis to the other, which corresponds to the average time separating two flips between states of broken symmetry in the exclusion process. This time is shown to diverge exponentially with the size of the chain.Comment: 42 page

Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz

We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this Matrix Product Ansatz, the components of the eigenvectors of the ASEP Markov matrix can be expressed as traces of products of non-commuting operators. We derive the relations between the operators involved and show that they generate a quadratic algebra. Our construction provides explicit finite dimensional representations for the generators of this algebra.Comment: 16 page

Physically meaningful and not so meaningful symmetries in Chern-Simons theory

We explicitly show that the Landau gauge supersymmetry of Chern-Simons theory does not have any physical significance. In fact, the difference between an effective action both BRS invariant and Landau supersymmetric and an effective action only BRS invariant is a finite field redefinition. Having established this, we use a BRS invariant regulator that defines CS theory as the large mass limit of topologically massive Yang-Mills theory to discuss the shift k \to k+\cv of the bare Chern-Simons parameter $k$ in conncection with the Landau supersymmetry. Finally, to convince ourselves that the shift above is not an accident of our regularization method, we comment on the fact that all BRS invariant regulators used as yet yield the same value for the shift.Comment: phyzzx, 21 pages, 2 figures in one PS fil