15,016 research outputs found
A density functional theory for general hard-core lattice gases
We put forward a general procedure to obtain an approximate free energy
density functional for any hard-core lattice gas, regardless of the shape of
the particles, the underlying lattice or the dimension of the system. The
procedure is conceptually very simple and recovers effortlessly previous
results for some particular systems. Also, the obtained density functionals
belong to the class of fundamental measure functionals and, therefore, are
always consistent through dimensional reduction. We discuss possible extensions
of this method to account for attractive lattice models.Comment: 4 pages, 1 eps figure, uses RevTeX
Dynamics and Long-Run Structure in U.S. Meat Demand
�Empirical analysis, based on a general dynamic Almost Ideal Demand System, shows the commonly used autoregressive and partial adjustment processes are restrictive to meal demand data. This study derives a linear specification in levels form to investigate dynamics in a general framework. Merging a long-run steady state structure with short-run dynamics results in consistent and robust long-run demand elasticities.
Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
A key problem in making precise perturbative QCD predictions is to set the
proper renormalization scale of the running coupling. The extended
renormalization group equations, which express the invariance of physical
observables under both the renormalization scale- and scheme-parameter
transformations, provide a convenient way for estimating the scale- and
scheme-dependence of the physical process. In this paper, we present a solution
for the scale-equation of the extended renormalization group equations at the
four-loop level. Using the principle of maximum conformality (PMC) /
Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal
terms in the perturbative expansion series can be summed into the
running coupling, and the resulting scale-fixed predictions are independent of
the renormalization scheme. Different schemes lead to different effective
PMC/BLM scales, but the final results are scheme independent. Conversely, from
the requirement of scheme independence, one not only can obtain
scheme-independent commensurate scale relations among different observables,
but also determine the scale displacements among the PMC/BLM scales which are
derived under different schemes. In principle, the PMC/BLM scales can be fixed
order-by-order, and as a useful reference, we present a systematic and
scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit
application for determining the scale setting of up to four
loops is presented. By using the world average , we obtain the asymptotic scale for the 't Hooft associated
with the scheme, MeV, and
the asymptotic scale for the conventional scheme,
MeV.Comment: 9 pages, no figures. The formulas in the Appendix are correcte
Emergent bipartiteness in a society of knights and knaves
We propose a simple model of a social network based on so-called
knights-and-knaves puzzles. The model describes the formation of networks
between two classes of agents where links are formed by agents introducing
their neighbours to others of their own class. We show that if the proportion
of knights and knaves is within a certain range, the network self-organizes to
a perfectly bipartite state. However, if the excess of one of the two classes
is greater than a threshold value, bipartiteness is not observed. We offer a
detailed theoretical analysis for the behaviour of the model, investigate its
behaviou r in the thermodynamic limit, and argue that it provides a simple
example of a topology-driven model whose behaviour is strongly reminiscent of a
first-order phase transitions far from equilibrium.Comment: 12 pages, 5 figure
The Effect of Porosity on X-ray Emission Line Profiles from Hot-Star Winds
We investigate the degree to which the nearly symmetric form of X-ray
emission lines seen in Chandra spectra of early-type supergiant stars could be
explained by a possibly porous nature of their spatially structured stellar
winds. Such porosity could effectively reduce the bound-free absorption of
X-rays emitted by embedded wind shocks, and thus allow a more similar
transmission of red- vs. blue-shifted emission from the back vs. front
hemispheres. For a medium consisting of clumps of size l and volume filling
factor f, in which the `porosity length' h=l/f increases with local radius as h
= h' r, we find that a substantial reduction in wind absorption requires a
quite large porosity scale factor h' > 1, implying large porosity lengths h >
r. The associated wind structure must thus have either a relatively large scale
l~ r, or a small volume filling factor f ~ l/r << 1, or some combination of
these. The relatively small-scale, moderate compressions generated by intrinsic
instabilities in line-driving seem unlikely to give such large porosity
lengths, leaving again the prospect of instead having to invoke a substantial
(ca. factor 5) downward revision in assumed mass-loss rates.Comment: 6 pages in apj-emulate; 3 figures; submitted to Ap
Spurious trend switching phenomena in financial markets
The observation of power laws in the time to extrema of volatility, volume
and intertrade times, from milliseconds to years, are shown to result
straightforwardly from the selection of biased statistical subsets of
realizations in otherwise featureless processes such as random walks. The bias
stems from the selection of price peaks that imposes a condition on the
statistics of price change and of trade volumes that skew their distributions.
For the intertrade times, the extrema and power laws results from the format of
transaction data
Dynamics of Surface Roughening with Quenched Disorder
We study the dynamical exponent for the directed percolation depinning
(DPD) class of models for surface roughening in the presence of quenched
disorder. We argue that for dimensions is equal to the exponent
characterizing the shortest path between two sites in an
isotropic percolation cluster in dimensions. To test the argument, we
perform simulations and calculate for DPD, and for
percolation, from to .Comment: RevTex manuscript 3 pages + 6 figures (obtained upon request via
email [email protected]
Effective Invariant Theory of Permutation Groups using Representation Theory
Using the theory of representations of the symmetric group, we propose an
algorithm to compute the invariant ring of a permutation group. Our approach
have the goal to reduce the amount of linear algebra computations and exploit a
thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at
http://www.springer.com
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