402,602 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

### Fast orthogonal least squares algorithm for efficient subset model selection

Abstract-An efficient implementation of the orthogonal least squares algorithm for subset model selection is derived in this correspondence. Computational complexity of the algorithm is examined and the result shows that this new fast orthogonal least squares algorithm significantly reduces computational requirements. This error reduction ratio provides a criterion for forward subset selection. At the beginning of the 11th stage of the selection procedure, X has been transformed into Xâ€ťâ€™- â€ť = [WI... wI,- I xj,â€™-â€™)... x::;-â€™)] and y into y(/â€™-â€™), The 11th stage consists of i) For p 5 j 5.If, compute ii) 1

### Mapping class group and U(1) Chern-Simons theory on closed orientable surfaces

U(1) Chern-Simons theory is quantized canonically on manifolds of the form
$M=\mathbb{R}\times\Sigma$, where $\Sigma$ is a closed orientable surface. In
particular, we investigate the role of mapping class group of $\Sigma$ in the
process of quantization. We show that, by requiring the quantum states to form
representation of the holonomy group and the large gauge transformation group,
both of which are deformed by quantum effect, the mapping class group can be
consistently represented, provided the Chern-Simons parameter $k$ satisfies an
interesting quantization condition. The representations of all the discrete
groups are unique, up to an arbitrary sub-representation of the mapping class
group. Also, we find a $k\leftrightarrow1/k$ duality of the representations.Comment: 17 pages, 3 figure

### Ground state energy of unitary fermion gas with the Thomson Problem approach

The dimensionless universal coefficient $\xi$ defines the ratio of the
unitary fermions energy density to that for the ideal non-interacting ones in
the non-relativistic limit with T=0. The classical Thomson Problem is taken as
a nonperturbative quantum many-body arm to address the ground state energy
including the low energy nonlinear quantum fluctuation/correlation effects.
With the relativistic Dirac continuum field theory formalism, the concise
expression for the energy density functional of the strongly interacting limit
fermions at both finite temperature and density is obtained. Analytically, the
universal factor is calculated to be $\xi={4/9}$. The energy gap is
\Delta=\frac{{5}{18}{k_f^2}/(2m).Comment: Identical to published version with revisions according to comment

### Forced sloshing of inviscid fluids

Forced sloshing motion of inviscid fluids in rigid cylinder

### Online Matrix Completion Through Nuclear Norm Regularisation

It is the main goal of this paper to propose a novel method to perform matrix
completion on-line. Motivated by a wide variety of applications, ranging from
the design of recommender systems to sensor network localization through
seismic data reconstruction, we consider the matrix completion problem when
entries of the matrix of interest are observed gradually. Precisely, we place
ourselves in the situation where the predictive rule should be refined
incrementally, rather than recomputed from scratch each time the sample of
observed entries increases. The extension of existing matrix completion methods
to the sequential prediction context is indeed a major issue in the Big Data
era, and yet little addressed in the literature. The algorithm promoted in this
article builds upon the Soft Impute approach introduced in Mazumder et al.
(2010). The major novelty essentially arises from the use of a randomised
technique for both computing and updating the Singular Value Decomposition
(SVD) involved in the algorithm. Though of disarming simplicity, the method
proposed turns out to be very efficient, while requiring reduced computations.
Several numerical experiments based on real datasets illustrating its
performance are displayed, together with preliminary results giving it a
theoretical basis.Comment: Corrected a typo in the affiliatio

### Searching for radiative pumping lines of OH masers: II. The 53.3um absorption line towards 1612MHz OH maser sources

This paper analyzes the 53.3um line in the ISO LWS spectra towards a similar
sample of OH/IR sources. We find 137 LWS spectra covering 53.3um and associated
with 47 galactic OH/IR sources. Ten of these galactic OH/IR sources are found
to show and another 5 ones tentatively show the 53.3um absorption while another
7 sources highly probably do not show this line. The source class is found to
be correlated with the type of spectral profile: red supergiants (RSGs) and AGB
stars tend to show strong blue-shifted filling emission in their 53.3um
absorption line profiles while HII regions tend to show a weak red-shifted
filling emission in the line profile. GC sources and megamasers do not show
filling emission feature. It is argued that the filling emission might be the
manifestation of an unresolved half emission half absorption profile of the
53.3um doublet. The 53.3 to 34.6um equivalent width (EW) ratio is close to
unity for RSGs but much larger than unity for GC sources and megamasers while H
II regions only show the 53.3um line. The pump rate defined as maser to IR
photon flux ratio is approximately 5% for RSGs. The pump rates of GC sources
are three order of magnitude smaller. Both the large 53.3 to 34.6um EW ratio
and the small pump rate of the GC OH masers reflect that the two detected
`pumping lines' in these sources are actually of interstellar origin. The pump
rate of Arp 220 is 32%--much larger than that of RSGs, which indicates that the
contribution of other pumping mechanisms to this megamaser is important.Comment: 34 pages, 12 figures, 4 table

- â€¦