66,592 research outputs found
Numerical study of a multiscale expansion of KdV and Camassa-Holm equation
We study numerically solutions to the Korteweg-de Vries and Camassa-Holm
equation close to the breakup of the corresponding solution to the
dispersionless equation. The solutions are compared with the properly rescaled
numerical solution to a fourth order ordinary differential equation, the second
member of the Painlev\'e I hierarchy. It is shown that this solution gives a
valid asymptotic description of the solutions close to breakup. We present a
detailed analysis of the situation and compare the Korteweg-de Vries solution
quantitatively with asymptotic solutions obtained via the solution of the Hopf
and the Whitham equations. We give a qualitative analysis for the Camassa-Holm
equationComment: 17 pages, 13 figure
Concentration around the mean for maxima of empirical processes
In this paper we give optimal constants in Talagrand's concentration
inequalities for maxima of empirical processes associated to independent and
eventually nonidentically distributed random variables. Our approach is based
on the entropy method introduced by Ledoux.Comment: Published at http://dx.doi.org/10.1214/009117905000000044 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The polymer mat: Arrested rebound of a compressed polymer layer
Compression of an adsorbed polymer layer distorts its relaxed structure.
Surface force measurements from different laboratories show that the return to
this relaxed structure after the compression is released can be slowed to the
scale of tens of minutes and that the recovery time grows rapidly with
molecular weight. We argue that the arrested state of the free layer before
relaxation can be described as a Guiselin brush structure1, in which the
surface excess lies at heights of the order of the layer thickness, unlike an
adsorbed layer. This brush structure predicts an exponential falloff of the
force at large distance with a decay length that varies as the initial
compression distance to the 6/5 power. This exponential falloff is consistent
with surface force measurements. We propose a relaxation mechanism that
accounts for the increase in relaxation time with chain length.Comment: 24 pages, 5 figre
Thermodynamics and quark susceptibilities: a Monte-Carlo approach to the PNJL model
The Monte-Carlo method is applied to the Polyakov-loop extended
Nambu--Jona-Lasinio (PNJL) model. This leads beyond the saddle-point
approximation in a mean-field calculation and introduces fluctuations around
the mean fields. We study the impact of fluctuations on the thermodynamics of
the model, both in the case of pure gauge theory and including two quark
flavors. In the two-flavor case, we calculate the second-order Taylor expansion
coefficients of the thermodynamic grand canonical partition function with
respect to the quark chemical potential and present a comparison with
extrapolations from lattice QCD. We show that the introduction of fluctuations
produces only small changes in the behavior of the order parameters for chiral
symmetry restoration and the deconfinement transition. On the other hand, we
find that fluctuations are necessary in order to reproduce lattice data for the
flavor non-diagonal quark susceptibilities. Of particular importance are pion
fields, the contribution of which is strictly zero in the saddle point
approximation
- …