1,352 research outputs found
Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model
This paper deals with a one--dimensional model for granular materials, which
boils down to an inelastic version of the Kac kinetic equation, with
inelasticity parameter . In particular, the paper provides bounds for
certain distances -- such as specific weighted --distances and the
Kolmogorov distance -- between the solution of that equation and the limit. It
is assumed that the even part of the initial datum (which determines the
asymptotic properties of the solution) belongs to the domain of normal
attraction of a symmetric stable distribution with characteristic exponent
\a=2/(1+p). With such initial data, it turns out that the limit exists and is
just the aforementioned stable distribution. A necessary condition for the
relaxation to equilibrium is also proved. Some bounds are obtained without
introducing any extra--condition. Sharper bounds, of an exponential type, are
exhibited in the presence of additional assumptions concerning either the
behaviour, near to the origin, of the initial characteristic function, or the
behaviour, at infinity, of the initial probability distribution function
Antiferro-quadrupole resonance in CeB6
We report experimental observation of a new type of magnetic resonance caused
by orbital ordering in a strongly correlated electronic system. Cavity
measurements performed on CeB6 single crystals in a frequency range 60-100 GHz
show that a crossing of the phase boundary TQ(B) between the
antiferro-quadrupole and paramagnetic phases gives rise to development at T
<TQ(B) of a magnetic resonance. The observed mode is gapless and correspond to
g-factor 1.62.Comment: 2 pages, Submitted to SCES05 proceeding
Magnetic resonance in cerium hexaboride caused by quadrupolar ordering
Experimental evidence of the magnetic resonance in the antiferro-quadrupole
phase of CeB6 is reported. We have shown that below orbital ordering
temperature a new magnetic contribution from localized magnetic moments (LMM)
emerge and gives rise to observed resonant phenomenon. This behaviour is hardly
possible to expect in dense Kondo system, where LMM should vanish al low
temperatures rather than emerge. From the other hand, in the quadrupole
ordering concept, where magnetism of Ce magnetic ions is solely accounted, is
difficult to explain splitting of magnetisation into components having
different physical nature. Therefore an adequate theory explaining magnetic
properties of CeB6 including magnetic resonance and orbital ordering appears on
the agenda.Comment: 4 pages, Accepted paper for MISM05 proceeding
Proof of projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two
We prove an important partial case of the pseudo-Riemannian version of the
projective Lichnerowicz conjecture stating that a complete manifold admitting
an essential group of projective transformations is the round sphere (up to a
finite cover).Comment: 32 pages, one .eps figure. The version v1 has a misprint in Theorem
1: I forgot to write the assumption that the degree of mobility is greater
than two. The versions v3, v4 have only cosmetic changes wrt v
Soliton molecules in trapped vector Nonlinear Schrodinger systems
We study a new class of vector solitons in trapped Nonlinear Schrodinger
systems modelling the dynamics of coupled light beams in GRIN Kerr media and
atomic mixtures in Bose-Einstein condensates. These solitons exist for
different spatial dimensions, their existence is studied by means of a
systematic mathematical technique and the analysis is made for inhomogeneous
media
Landscape equivalent of the shoving model
It is shown that the shoving model expression for the average relaxation time
of viscous liquids follows largely from a classical "landscape" estimation of
barrier heights from curvature at energy minima. The activation energy involves
both instantaneous bulk and shear moduli, but the bulk modulus contributes less
than 8% to the temperature dependence of the activation energy. This reflects
the fact that the physics of the two models are closely related.Comment: 4 page
Proton-Antiproton Annihilation into a Lambda_c-Antilambda_c Pair
The process p-pbar -> Lambda_c-Antilambda_c is investigated within the
handbag approach. It is shown that the dominant dynamical mechanism,
characterized by the partonic subprocess u-ubar -> c-cbar factorizes in the
sense that only the subprocess contains highly virtual partons, a gluon to
lowest order of perturbative QCD, while the hadronic matrix elements embody
only soft scales and can be parameterized in terms of helicity flip and
non-flip generalized parton distributions. Modelling these parton distributions
by overlaps of light-cone wave functions for the involved baryons we are able
to predict cross sections and spin correlation parameters for the process of
interest.Comment: 39 pages, 7 figures, problems with printout of figures resolved, Ref.
33 and referring sentences in section 4 change
Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentials
We discuss a method to create two-dimensional traps as well as atomic shell,
or bubble, states for a Bose-Einstein condensate initially prepared in a
conventional magnetic trap. The scheme relies on the use of time-dependent,
radio frequency-induced adiabatic potentials. These are shown to form a
versatile and robust tool to generate novel trapping potentials. Our shell
states take the form of thin, highly stable matter-wave bubbles and can serve
as stepping-stones to prepare atoms in highly-excited trap eigenstates or to
study `collapse and revival phenomena'. Their creation requires gravitational
effects to be compensated by applying additional optical dipole potentials.
However, in our scheme gravitation can also be exploited to provide a route to
two-dimensional atom trapping. We demonstrate the loading process for such a
trap and examine experimental conditions under which a 2D condensate may be
prepared.Comment: 16 pages, 10 figure
Network development in biological gels: role in lymphatic vessel development
In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the collagen volume fraction, and the evolution of the proton concentration in a collagen implant; as described in experiments of Boardman and Swartz (Circ. Res. 92, 801â808, 2003). Using linear stability analysis, we find that above a critical level of proton concentration, spatial patterns form due to small perturbations in the initially uniform steady state. Using a long wavelength reduction, we can reduce the two coupled partial differential equations to one fourth order equation that is very similar to the CahnâHilliard equation; however, it has more complex nonlinearities and degeneracies. We present the results of numerical simulations and discuss the biological implications of our model
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