2,084 research outputs found
The blockage problem
We investigate the totally asymmetric exclusion process on Z, with the jump
rate at site i given by r_i=1 for i nonzero, r_0=r. It is easy to see that the
maximal stationary current j(r) is nondecreasing in r and that j(r)=1/4 for
r>=1; it is a long outstanding problem to determine whether or not the critical
value r_c of r such that j(r)=1/4 for r>r_c is strictly less than 1. Here we
present a heuristic argument, based on the analysis of the first sixteen terms
in a formal power series expansion of j(r) obtained from finite volume systems,
that r_c=1 and that for r less than 1 and near 1, j(r) behaves as
1/4-\gamma\exp[-{a/(1-r)}] with a approximately equal to 2. We also give some
new exact results about this system; in particular we prove that j(r)=J_max(r),
with J_max(r) the hydrodynamic maximal current defined by Seppalainen, and thus
establish continuity of j(r). Finally we describe a related exactly solvable
model, a semi-infinite system in which the site i=0 is always occupied. For
that system, the critical r is 1/2 and the analogue j_s(r) of j(r) satisfies
j_s(r)=r(1-r) for r<=1/2; j_s(r) is the limit of finite volume currents inside
the curve |r(1-r)|=1/4 in the complex r plane and we suggest that analogous
behavior may hold for the original system.Comment: 23 pages, 6 figure
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
New procedures in estimating feed substitution rates and in determining economic efficiency in pork production II. Replacement rates of corn and soybean oilmeal in fortified rations for growing-fattening swine on pasture
A previous bulletin reported results from an experiment designed to predict substitution rates and economic optima in corn/soybean oilmeal rations for growing and fattening hogs in drylot.2 Principles and analytical models were included which illustrate that the least-cost ration depends both on (1) the marginal rate of substitution between feeds and (2) the ratio of feed prices. These basic concepts will not be repeated in this bulletin.
Since more hogs are farrowed in spring than in fall, the research reported in this study was conducted for growing and fattening hogs raised on pasture. Like the drylot study, the objectives of the pasture experiment were to estimate: (1) the production function, (2) the substitution rate between corn and soybean oilmeal at different points on the production surface, (3) the least-cost ration for different soybean oilmeal/corn price ratios, (4) the relationship between the rate of hog gains and the input of corn and soybean oilmeal and (5) the proportion of the years in which a least-cost feeding system results in greater profits than a least-time feeding system. Substitution between major classes of feed such as corn and soybean oilmeal is possible mainly where the rations are fortified with appropriate quantities of trace minerals (as well as antibiotics in the case of drylot feeding). These fortifying elements have been included in the rations of this study
Spectral Degeneracies in the Totally Asymmetric Exclusion Process
We study the spectrum of the Markov matrix of the totally asymmetric
exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY
filling. Although the system does not possess obvious symmetries except
translation invariance, the spectrum presents many multiplets with degeneracies
of high order. This behaviour is explained by a hidden symmetry property of the
Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the
corresponding number of multiplets are derived and compared with numerical
results obtained from exact diagonalisation of small size systems. This
unexpected structure of the TASEP spectrum suggests the existence of an
underlying large invariance group.
Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur
Continuity of the four-point function of massive -theory above threshold
In this paper we prove that the four-point function of massive
\vp_4^4-theory is continuous as a function of its independent external
momenta when posing the renormalization condition for the (physical) mass
on-shell. The proof is based on integral representations derived inductively
from the perturbative flow equations of the renormalization group. It closes a
longstanding loophole in rigorous renormalization theory in so far as it shows
the feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two
explanatory paragraphs adde
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 , , and . The system is
described by a grand canonical ensemble with temperature and chemical
potentials , , and . We find that for
the system undergoes a phase transition from a
uniform density to a continuum of phases at a critical temperature . For other values of the chemical potentials the system
has a unique equilibrium state. As is the case for the canonical ensemble for
this model, the grand canonical ensemble is the stationary measure
satisfying detailed balance for a natural dynamics. We note that , where is the critical temperature for a similar transition in
the canonical ensemble at fixed equal densities .Comment: 24 pages, 3 figure
Phase diagram of the ABC model with nonconserving processes
The three species ABC model of driven particles on a ring is generalized to
include vacancies and particle-nonconserving processes. The model exhibits
phase separation at high densities. For equal average densities of the three
species, it is shown that although the dynamics is {\it local}, it obeys
detailed balance with respect to a Hamiltonian with {\it long-range
interactions}, yielding a nonadditive free energy. The phase diagrams of the
conserving and nonconserving models, corresponding to the canonical and
grand-canonical ensembles, respectively, are calculated in the thermodynamic
limit. Both models exhibit a transition from a homogeneous to a phase-separated
state, although the phase diagrams are shown to differ from each other. This
conforms with the expected inequivalence of ensembles in equilibrium systems
with long-range interactions. These results are based on a stability analysis
of the homogeneous phase and exact solution of the hydrodynamic equations of
the models. They are supported by Monte-Carlo simulations. This study may serve
as a useful starting point for analyzing the phase diagram for unequal
densities, where detailed balance is not satisfied and thus a Hamiltonian
cannot be defined.Comment: 32 page, 7 figures. The paper was presented at Statphys24, held in
Cairns, Australia, July 201
Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams
It is shown how strictly four-dimensional integration by parts combined with
differential renormalization and its infrared analogue can be applied for
calculation of Feynman diagrams.Comment: 6 pages, late
The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized
at the one-loop level by multiplicative dimensional renormalization of the
coupling constant and fields of the theory. We compute the beta function of the
theory and conclude that the theory is asymptotically free. We also show that
the Weyl-Moyal matrix defining the deformed product over the space of functions
on R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and
the divergent contributions corrected accordingly. As a result the model
turns out to be asymptotically fre
Bethe Ansatz calculation of the spectral gap of the asymmetric exclusion process
We present a new derivation of the spectral gap of the totally asymmetric
exclusion process on a half-filled ring of size L by using the Bethe Ansatz. We
show that, in the large L limit, the Bethe equations reduce to a simple
transcendental equation involving the polylogarithm, a classical special
function. By solving that equation, the gap and the dynamical exponent are
readily obtained. Our method can be extended to a system with an arbitrary
density of particles.
Keywords: ASEP, Bethe Ansatz, Dynamical Exponent, Spectral Gap
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