7,525 research outputs found
Fractional Operators, Dirichlet Averages, and Splines
Fractional differential and integral operators, Dirichlet averages, and
splines of complex order are three seemingly distinct mathematical subject
areas addressing different questions and employing different methodologies. It
is the purpose of this paper to show that there are deep and interesting
relationships between these three areas. First a brief introduction to
fractional differential and integral operators defined on Lizorkin spaces is
presented and some of their main properties exhibited. This particular approach
has the advantage that several definitions of fractional derivatives and
integrals coincide. We then introduce Dirichlet averages and extend their
definition to an infinite-dimensional setting that is needed to exhibit the
relationships to splines of complex order. Finally, we focus on splines of
complex order and, in particular, on cardinal B-splines of complex order. The
fundamental connections to fractional derivatives and integrals as well as
Dirichlet averages are presented
Single-particle and collective excitations in a charged Bose gas at finite temperature
The main focus of this work is on the predictions made by the dielectric
formalism in regard to the relationship between single-particle and collective
excitation spectra in a gas of point-like charged bosons at finite temperature
below the critical region of Bose-Einstein condensation. Illustrative
numerical results at weak coupling () are presented within the Random
Phase Approximation. We show that within this approach the single-particle
spectrum forms a continuum extending from the transverse to the longitudinal
plasma mode frequency and leading to a double-peak structure as increases,
whereas the density fluctuation spectrum consists of a single broadening peak.
We also discuss the momentum distribution and the superfluidity of the gas.Comment: 15 pages, 5 figure
Numerical performances of low rank stap based on different heterogeneous clutter subspace estimators
International audienceSpace time Adaptive Processing (STAP) for airborne RADAR fits the context of a disturbance composed of a Low Rank (LR) clutter, here modeled by a Compound Gaussian (CG) process, plus a white Gaussian noise (WGN). In such context, the corresponding LR adaptive filters used to detect a target require less training vectors than classical methods to reach equivalent performance. Unlike the classical filter which is based on the Covariance Matrix (CM) of the noise, the LR filter is based on the clutter subspace projector, which is usually derived from a Singular Value Decomposition (SVD) of a noise CM estimate. Regarding to the considered model of LR-CG plus WGN, recent results are providing both direct estimators of the clutter subspace [1][2] and an exact MLE of the noise CM [3]. To promote the use of these new estimation methods, this paper proposes to apply them to realistic STAP simulations
Conserved Density Fluctuation and Temporal Correlation Function in HTL Perturbation Theory
Considering recently developed Hard Thermal Loop perturbation theory that
takes into account the effect of the variation of the external field through
the fluctuations of a conserved quantity we calculate the temporal component of
the Euclidian correlation function in the vector channel. The results are found
to be in good agreement with the very recent results obtained within the
quenched approximation of QCD and small values of the quark mass ()
on improved lattices of size at (),
(), and (), where is
the temporal extent of the lattice. This suggests that the results from lattice
QCD and Hard Thermal Loop perturbation theory are in close proximity for a
quantity associated with the conserved density fluctuation.Comment: 16 pages, 4 figures; One para added in introduction, Fig 1 modified;
Accepted in Phys. Rev.
Breakdown of Hydrodynamic Transport Theory in the Ordered Phase of Helimagnets
It is shown that strong fluctuations preclude a hydrodynamic description of
transport phenomena in helimagnets, such as MnSi, at T>0. This breakdown of
hydrodynamics is analogous to the one in chiral liquid crystals. Mode-mode
coupling effects lead to infinite renormalizations of various transport
coefficients, and the actual macroscopic description is nonlocal. At T=0 these
effects are weakened due to the fluctuation-dissipation theorem, and the
renormalizations remain finite. Observable consequences of these results, as
manifested in the neutron scattering cross-section, are discussedComment: 4pp., 1 eps figur
The size-star formation relation of massive galaxies at 1.5<z<2.5
We study the relation between size and star formation activity in a complete
sample of 225 massive (M > 5 x 10^10 Msun) galaxies at 1.5<z<2.5, selected from
the FIREWORKS UV-IR catalog of the CDFS. Based on stellar population synthesis
model fits to the observed restframe UV-NIR SEDs, and independent MIPS 24
micron observations, 65% of galaxies are actively forming stars, while 35% are
quiescent. Using sizes derived from 2D surface brightness profile fits to high
resolution (FWHM_{PSF}~0.45 arcsec) groundbased ISAAC data, we confirm and
improve the significance of the relation between star formation activity and
compactness found in previous studies, using a large, complete mass-limited
sample. At z~2, massive quiescent galaxies are significantly smaller than
massive star forming galaxies, and a median factor of 0.34+/-0.02 smaller than
galaxies of similar mass in the local universe. 13% of the quiescent galaxies
are unresolved in the ISAAC data, corresponding to sizes <1 kpc, more than 5
times smaller than galaxies of similar mass locally. The quiescent galaxies
span a Kormendy relation which, compared to the relation for local early types,
is shifted to smaller sizes and brighter surface brightnesses and is
incompatible with passive evolution. The progenitors of the quiescent galaxies,
were likely dominated by highly concentrated, intense nuclear star bursts at
z~3-4, in contrast to star forming galaxies at z~2 which are extended and
dominated by distributed star formation.Comment: 6 pages, 4 figures, accepted for publication in Ap
Effects of disorder on quantum fluctuations and superfluid density of a Bose-Einstein condensate in a two-dimensional optical lattice
We investigate a Bose-Einstein condensate trapped in a 2D optical lattice in
the presence of weak disorder within the framework of the Bogoliubov theory. In
particular, we analyze the combined effects of disorder and an optical lattice
on quantum fluctuations and superfluid density of the BEC system. Accordingly,
the analytical expressions of the ground state energy and quantum depletion of
the system are obtained. Our results show that the lattice still induces a
characteristic 3D to 1D crossover in the behavior of quantum fluctuations,
despite the presence of weak disorder. Furthermore, we use the linear response
theory to calculate the normal fluid density of the condensate induced by
disorder. Our results in the 3D regime show that the combined presence of
disorder and lattice induce a normal fluid density that asymptotically
approaches 4/3 of the corresponding condensate depletion. Conditions for
possible experimental realization of our scenario are also proposed.Comment: 8 pages, 0 figure. To appear in Physical Review
Dynamic correlations in stochastic rotation dynamics
The dynamic structure factor, vorticity and entropy density dynamic
correlation functions are measured for Stochastic Rotation Dynamics (SRD), a
particle based algorithm for fluctuating fluids. This allows us to obtain
unbiased values for the longitudinal transport coefficients such as thermal
diffusivity and bulk viscosity. The results are in good agreement with earlier
numerical and theoretical results, and it is shown for the first time that the
bulk viscosity is indeed zero for this algorithm. In addition, corrections to
the self-diffusion coefficient and shear viscosity arising from the breakdown
of the molecular chaos approximation at small mean free paths are analyzed. In
addition to deriving the form of the leading correlation corrections to these
transport coefficients, the probabilities that two and three particles remain
collision partners for consecutive time steps are derived analytically in the
limit of small mean free path. The results of this paper verify that we have an
excellent understanding of the SRD algorithm at the kinetic level and that
analytic expressions for the transport coefficients derived elsewhere do indeed
provide a very accurate description of the SRD fluid.Comment: 33 pages including 16 figure
Fractional Fokker-Planck Equation for Fractal Media
We consider the fractional generalizations of equation that defines the
medium mass. We prove that the fractional integrals can be used to describe the
media with noninteger mass dimensions. Using fractional integrals, we derive
the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski
equation). In this paper fractional Fokker-Planck equation for fractal media is
derived from the fractional Chapman-Kolmogorov equation. Using the Fourier
transform, we get the Fokker-Planck-Zaslavsky equations that have fractional
coordinate derivatives. The Fokker-Planck equation for the fractal media is an
equation with fractional derivatives in the dual space.Comment: 17 page
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