20,640 research outputs found
A note on the Boltzmann distribution and the linear ordering problem
The Boltzmann distribution plays a key role in the field of optimization as it directly connects this field with that of probability. Basically, given a function to optimize, the Boltzmann distribution associated to this function assigns higher probability to the candidate solutions with better quality. Therefore, an efficient sampling of the Boltzmann distribution would turn optimization into an easy task. However, inference tasks on this distribution imply performing operations over an exponential number of terms, which hinders its applicability. As a result, the scientific community has investigated how the structure of objective functions is translated to probabilistic properties in order to simplify the corresponding Boltzmann distribution. In this paper, we elaborate on the properties induced in the Boltzmann distribution associated to permutation-based combinatorial optimization problems. Particularly, we prove that certain characteristics of the linear ordering problem are translated as conditional independence relations to the Boltzmann distribution in the form of L â decomposability
Phase Ordering in Nematic Liquid Crystals
We study the kinetics of the nematic-isotropic transition in a
two-dimensional liquid crystal by using a lattice Boltzmann scheme that couples
the tensor order parameter and the flow consistently. Unlike in previous
studies, we find the time dependences of the correlation function, energy
density, and the number of topological defects obey dynamic scaling laws with
growth exponents that, within the numerical uncertainties, agree with the value
1/2 expected from simple dimensional analysis. We find that these values are
not altered by the hydrodynamic flow. In addition, by examining shallow
quenches, we find that the presence of orientational disorder can inhibit
amplitude ordering.Comment: 21 pages, 14 eps figures, revte
Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
This article studies Markovian stochastic motion of a particle on a graph
with finite number of nodes and periodically time-dependent transition rates
that satisfy the detailed balance condition at any time. We show that under
general conditions, the currents in the system on average become quantized or
fractionally quantized for adiabatic driving at sufficiently low temperature.
We develop the quantitative theory of this quantization and interpret it in
terms of topological invariants. By implementing the celebrated Kirchhoff
theorem we derive a general and explicit formula for the average generated
current that plays a role of an efficient tool for treating the current
quantization effects.Comment: 22 pages, 7 figure
Symmetry, complexity and multicritical point of the two-dimensional spin glass
We analyze models of spin glasses on the two-dimensional square lattice by
exploiting symmetry arguments. The replicated partition functions of the Ising
and related spin glasses are shown to have many remarkable symmetry properties
as functions of the edge Boltzmann factors. It is shown that the applications
of homogeneous and Hadamard inverses to the edge Boltzmann matrix indicate
reduced complexities when the elements of the matrix satisfy certain
conditions, suggesting that the system has special simplicities under such
conditions. Using these duality and symmetry arguments we present a conjecture
on the exact location of the multicritical point in the phase diagram.Comment: 32 pages, 6 figures; a few typos corrected. To be published in J.
Phys.
Influence of carrier lifetime on quantum criticality and superconducting Tc of (TMTSF)_2ClO_4
This work presents and analyzes electrical resistivity data on the organic
superconductor (TMTSF)ClO and their anion substituted alloys
(TMTSF)(ClO)(ReO) along the least conducting
axis. Nonmagnetic disorder introduced by finite size domains of anion ordering
on non Fermi liquid character of resistivity is investigated near the
conditions of quantum criticality. The evolution of the -linear resistivity
term with anion disorder shows a limited decrease in contrast with the complete
suppression of the critical temperature as expected for unconventional
superconductivity beyond a threshold value of . The resulting breakdown of
scaling between both quantities is compared to the theoretical predictions of a
linearized Boltzmann equation combined to the scaling theory of umklapp
scattering in the presence of disorder induced pair-breaking for the carriers.Comment: 13 pages, 8 figure
Correlations and Renormalization in Lattice Gases
A complete formulation is given of an exact kinetic theory for lattice gases.
This kinetic theory makes possible the calculation of corrections to the usual
Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of
correlations. It is shown that renormalized transport coefficients can be
calculated perturbatively by summing terms in an infinite series. A
diagrammatic notation for the terms in this series is given, in analogy with
the diagrammatic expansions of continuum kinetic theory and quantum field
theory. A closed-form expression for the coefficients associated with the
vertices of these diagrams is given. This method is applied to several standard
lattice gases, and the results are shown to correctly predict experimentally
observed deviations from the Boltzmann analysis.Comment: 94 pages, pure LaTeX including all figure
Role of particle conservation in self-propelled particle systems
Actively propelled particles undergoing dissipative collisions are
known to develop a state of spatially distributed coherently moving clusters.
For densities larger than a characteristic value, clusters grow in time and form
a stationary well-ordered state of coherent macroscopic motion. In this work
we address two questions. (i) What is the role of the particlesâ aspect ratio in
the context of cluster formation, and does the particle shape affect the systemâs
behavior on hydrodynamic scales? (ii) To what extent does particle conservation
influence pattern formation? To answer these questions we suggest a simple
kinetic model permitting us to depict some of the interaction properties between
freely moving particles and particles integrated in clusters. To this end, we
introduce two particle species: single and cluster particles. Specifically, we
account for coalescence of clusters from single particles, assembly of single
particles on existing clusters, collisions between clusters and cluster disassembly.
Coarse graining our kinetic model, (i) we demonstrate that particle shape (i.e.
aspect ratio) shifts the scale of the transition density, but does not impact the
instabilities at the ordering threshold and (ii) we show that the validity of particle
conservation determines the existence of a longitudinal instability, which tends to amplify density heterogeneities locally, and in turn triggers a wave pattern
with wave vectors parallel to the axis of macroscopic order. If the system is in
contact with a particle reservoir, this instability vanishes due to a compensation
of density heterogeneities
Astrophysical Gyrokinetics: Basic Equations and Linear Theory
Magnetohydrodynamic (MHD) turbulence is encountered in a wide variety of
astrophysical plasmas, including accretion disks, the solar wind, and the
interstellar and intracluster medium. On small scales, this turbulence is often
expected to consist of highly anisotropic fluctuations with frequencies small
compared to the ion cyclotron frequency. For a number of applications, the
small scales are also collisionless, so a kinetic treatment of the turbulence
is necessary. We show that this anisotropic turbulence is well described by a
low frequency expansion of the kinetic theory called gyrokinetics. This paper
is the first in a series to examine turbulent astrophysical plasmas in the
gyrokinetic limit. We derive and explain the nonlinear gyrokinetic equations
and explore the linear properties of gyrokinetics as a prelude to nonlinear
simulations. The linear dispersion relation for gyrokinetics is obtained and
its solutions are compared to those of hot-plasma kinetic theory. These results
are used to validate the performance of the gyrokinetic simulation code {\tt
GS2} in the parameter regimes relevant for astrophysical plasmas. New results
on global energy conservation in gyrokinetics are also derived. We briefly
outline several of the problems to be addressed by future nonlinear
simulations, including particle heating by turbulence in hot accretion flows
and in the solar wind, the magnetic and electric field power spectra in the
solar wind, and the origin of small-scale density fluctuations in the
interstellar medium.Comment: emulateapj, 24 pages, 10 figures, revised submission to ApJ:
references added, typos corrected, reorganized and streamline
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