48,766 research outputs found
Singular Cucker-Smale Dynamics
The existing state of the art for singular models of flocking is overviewed,
starting from microscopic model of Cucker and Smale with singular communication
weight, through its mesoscopic mean-filed limit, up to the corresponding
macroscopic regime. For the microscopic Cucker-Smale (CS) model, the
collision-avoidance phenomenon is discussed, also in the presence of bonding
forces and the decentralized control. For the kinetic mean-field model, the
existence of global-in-time measure-valued solutions, with a special emphasis
on a weak atomic uniqueness of solutions is sketched. Ultimately, for the
macroscopic singular model, the summary of the existence results for the
Euler-type alignment system is provided, including existence of strong
solutions on one-dimensional torus, and the extension of this result to higher
dimensions upon restriction on the smallness of initial data. Additionally, the
pressureless Navier-Stokes-type system corresponding to particular choice of
alignment kernel is presented, and compared - analytically and numerically - to
the porous medium equation
Increased breast tissue receptor activator of nuclear factor- κB ligand (RANKL) gene expression is associated with higher mammographic density in premenopausal women
Size dependent line broadening in the emission spectra of single GaAs quantum dots: Impact of surface charges on spectral diffusion
Making use of droplet epitaxy, we systematically controlled the height of
self-assembled GaAs quantum dots by more than one order of magnitude. The
photoluminescence spectra of single quantum dots revealed the strong dependence
of the spectral linewidth on the dot height. Tall dots with a height of ~30 nm
showed broad spectral peaks with an average width as large as ~5 meV, but
shallow dots with a height of ~2 nm showed resolution-limited spectral lines
(<120 micro eV). The measured height dependence of the linewidths is in good
agreement with Stark coefficients calculated for the experimental shape
variation. We attribute the microscopic source of fluctuating electric fields
to the random motion of surface charges at the vacuum-semiconductor interface.
Our results offer guidelines for creating frequency-locked photon sources,
which will serve as key devices for long-distance quantum key distribution.Comment: 6 pages, 6 figures; updated figs and their description
Exclusion Statistics in a trapped two-dimensional Bose gas
We study the statistical mechanics of a two-dimensional gas with a repulsive
delta function interaction, using a mean field approximation. By a direct
counting of states we establish that this model obeys exclusion statistics and
is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte
Stiff polymer in monomer ensemble
We make use of the previously developed formalism for a monomer ensemble and
include angular dependence of the segments of the polymer chains thus
described. In particular we show how to deal with stiffness when the polymer
chain is confined to certain regions. We investigate the stiffness from the
perspectives of a differential equation, integral equations, or recursive
relations for both continuum and lattice models. Exact analytical solutions are
presented for two cases, whereas numerical results are shown for a third case.Comment: 10 pages, including 6 figure
Facial structures for various notions of positivity and applications to the theory of entanglement
In this expository note, we explain facial structures for the convex cones
consisting of positive linear maps, completely positive linear maps,
decomposable positive linear maps between matrix algebras, respectively. These
will be applied to study the notions of entangled edge states with positive
partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge
Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section
This paper focuses on the study of existence and uniqueness of distributional
and classical solutions to the Cauchy Boltzmann problem for the soft potential
case assuming integrability of the angular part of the collision
kernel (Grad cut-off assumption). For this purpose we revisit the
Kaniel--Shinbrot iteration technique to present an elementary proof of
existence and uniqueness results that includes large data near a local
Maxwellian regime with possibly infinite initial mass. We study the propagation
of regularity using a recent estimate for the positive collision operator given
in [3], by E. Carneiro and the authors, that permits to study such propagation
without additional conditions on the collision kernel. Finally, an
-stability result (with ) is presented assuming the
aforementioned condition.Comment: 19 page
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