37,467 research outputs found
Propagation of and Maxwellian weighted bounds for derivatives of solutions to the homogeneous elastic Boltzmann Equation
We consider the -dimensional space homogeneous Boltzmann equation for
elastic collisions for variable hard potentials with Grad (angular) cutoff. We
prove sharp moment inequalities, the propagation of -Maxwellian weighted
estimates, and consequently, the propagation -Maxwellian weighted
estimates to all derivatives of the initial value problem associated to the
afore mentioned problem.
More specifically, we extend to all derivatives of the initial value problem
associated to this class of Boltzmann equations corresponding sharp moment
(Povzner) inequalities and time propagation of -Maxwellian weighted
estimates as originally developed A.V. Bobylev in the case of hard spheres in 3
dimensions; an improved sharp moments inequalities to a larger class of angular
cross sections and -exponential bounds in the case of stationary states to
Boltzmann equations for inelastic interaction problems with `heating' sources,
by A.V. Bobylev, I.M. Gamba and V.Panferov, where high energy tail decay rates
depend on the inelasticity coefficient and the the type of `heating' source;
and more recently, extended to variable hard potentials with angular cutoff by
I.M. Gamba, V. Panferov and C. Villani in the elastic case collision case and
so -Maxwellian weighted estimated were shown to propagate if initial
states have such property. In addition, we also extend to all derivatives the
propagation of -Maxwellian weighted estimates to solutions of the
initial value problem to the Boltzmann equations for elastic collisions for
variable hard potentials with Grad (angular) cutoff.Comment: 24 page
Time relaxation of interacting single--molecule magnets
We study the relaxation of interacting single--molecule magnets (SMMs) in
both spatially ordered and disordered systems. The tunneling window is assumed
to be, as in Fe8, much narrower than the dipolar field spread. We show that
relaxation in disordered systems differs qualitatively from relaxation in fully
occupied cubic and Fe_8 lattices. We also study how line shapes that develop in
''hole--digging'' experiments evolve with time t in these fully occupied
lattices. We show (1) that the dipolar field h scales as t^p in these hole line
shapes and show (2) how p varies with lattice structure. Line shapes are not,
in general, Lorentzian. More specifically, in the lower portion of the hole,
they behave as (h/t^p)^{(1/p)-1} if h is outside the tunnel window. This is in
agreement with experiment and with our own Monte Carlo results.Comment: 21 LaTeX pages, 6 eps figures. Submitted to PRB on 15 June 2005.
Accepted on 13 August 200
Chiral low-energy constants from tau data
We analyze how the recent precise hadronic tau-decay data on the V-A spectral
function and general properties of QCD such as analyticity, the operator
product expansion and chiral perturbation theory (ChPT), can be used to improve
the knowledge of some of the low-energy constants of ChPT. In particular we
find the most precise values of L_{9,10} (or equivalently l_{5,6}) at order p^4
and p^6 and the first phenomenological determination of C_87 (c_50).Comment: Proceedings of the 6th International Workshop on Chiral Dynamics
(Bern, Switzerland, July 6-10, 2009). 9 pages, 3 figure
Studies of the nucler equation of state using numerical calculations of nuclear drop collisions
A numerical calculation for the full thermal dynamics of colliding nuclei was developed. Preliminary results are reported for the thermal fluid dynamics in such processes as Coulomb scattering, fusion, fusion-fission, bulk oscillations, compression with heating, and collisions of heated nuclei
Context-aware mobile app for the multidimensional assessment of the elderly,
Rural areas in Europe are presenting a decreasing population density and an increasing age index. These elders usually present multiple diseases that require complex tools to identify the exact cares that they need. Currently, different frameworks can evaluate their functional status and identify the required cares to maintain their Quality of Life, together with the associated cost to the health system. Nevertheless, these frameworks are usually questionnaires that have to be performed by already overloaded professionals. In this paper, we make use of mobile technologies to build a system capable of monitoring the activities of the elderly and analysing these data to assess their functional status. The experiments carried out show us that it correctly evaluates these patients and reduces the effort required by health professionals
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