523,636 research outputs found
The finite-temperature thermodynamics of a trapped unitary Fermi gas within fractional exclusion statistics
We utilize a fractional exclusion statistics of Haldane and Wu hypothesis to
study the thermodynamics of a unitary Fermi gas trapped in a harmonic
oscillator potential at ultra-low finite temperature. The entropy per particle
as a function of the energy per particle and energy per particle versus
rescaled temperature are numerically compared with the experimental data. The
study shows that, except the chemical potential behavior, there exists a
reasonable consistency between the experimental measurement and theoretical
attempt for the entropy and energy per particle. In the fractional exclusion
statistics formalism, the behavior of the isochore heat capacity for a trapped
unitary Fermi gas is also analyzed.Comment: 6 pages, 6 figure
Local Regularization Assisted Orthogonal Least Squares Regression
A locally regularized orthogonal least squares (LROLS) algorithm is proposed for constructing parsimonious or sparse regression models that generalize well. By associating each orthogonal weight in the regression model with an individual regularization parameter, the ability for the orthogonal least squares (OLS) model selection to produce a very sparse model with good generalization performance is greatly enhanced. Furthermore, with the assistance of local regularization, when to terminate the model selection procedure becomes much clearer. This LROLS algorithm has computational advantages over the recently introduced relevance vector machine (RVM) method
Gibbsian Hypothesis in Turbulence
We show that Kolmogorov multipliers in turbulence cannot be statistically
independent of others at adjacent scales (or even a finite range apart) by
numerical simulation of a shell model and by theory. As the simplest
generalization of independent distributions, we suppose that the steady-state
statistics of multipliers in the shell model are given by a
translation-invariant Gibbs measure with a short-range potential, when
expressed in terms of suitable ``spin'' variables: real-valued spins that are
logarithms of multipliers and XY-spins defined by local dynamical phases.
Numerical evidence is presented in favor of the hypothesis for the shell model,
in particular novel scaling laws and derivative relations predicted by the
existence of a thermodynamic limit. The Gibbs measure appears to be in a
high-temperature, unique-phase regime with ``paramagnetic'' spin order.Comment: 19 pages, 9 figures, greatly expanded content, accepted to appear in
J. Stat. Phy
Strongly Coupled Inflaton
We continue to investigate properties of the strongly coupled inflaton in a
setup introduced in arXiv:0807.3191 through the AdS/CFT correspondence. These
properties are qualitatively different from those in conventional inflationary
models. For example, in slow-roll inflation, the inflaton velocity is not
determined by the shape of potential; the fine-tuning problem concerns the dual
infrared geometry instead of the potential; the non-Gaussianities such as the
local form can naturally become large.Comment: 12 pages; v3, minor revision, comments and reference added, JCAP
versio
Stability Of contact discontinuity for steady Euler System in infinite duct
In this paper, we prove structural stability of contact discontinuities for
full Euler system
Driving Operators Relevant: A Feature of Chern-Simons Interaction
By computing anomalous dimensions of gauge invariant composite operators
and in Chern-Simons fermion and boson
models, we address that Chern-Simons interactions make these operators more
relevant or less irrelevant in the low energy region. We obtain a critical
Chern-Simons fermion coupling, , for a phase
transition at which the leading irrelevant four-fermion operator
becomes marginal, and a critical Chern-Simons boson
coupling, , for a similar phase transition
for the leading irrelevant operator . We see this phenomenon
also in the expansion.Comment: (ten pages, latex, figures included
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