Search results for "Partial"

On the Multipeakon Dissipative Behavior of the Modified Coupled Camassa-Holm Model for Shallow Water System

2013

Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/107450 Open Access This paper investigates the multipeakon dissipative behavior of the modified coupled two-component Camassa-Holm system arisen from shallow water waves moving. To tackle this problem, we convert the original partial differential equations into a set of new differential equations by using skillfully defined characteristic and variables. Such treatment allows for the construction of the multipeakon solutions for the system. The peakon-antipeakon collisions as well as the dissipative behavior (energy loss) after wave breaki…

Return to Equilibrium, Non-self-adjointness and Symmetries, Recent Results with M. Hitrik and F. Hérau

2014

In this talk we review some old and new results about the use of supersymmetric structures in semi-classical problems. Necessary and sufficient conditions are obtained for a real semiclassical partial differential operator of order two to possess a supersymmetric structure. For operators coming from a chain of oscillators, coupled to two heat baths, we show the non-existence of a smooth supersymmetric structure. The recent and new results all come from joint works with Michael Hitrik and Frederic Herau.

Importance of torsion and invariant volumes in Palatini theories of gravity

2013

We study the field equations of extensions of general relativity formulated within a metric-affine formalism setting torsion to zero (Palatini approach). We find that different (second-order) dynamical equations arise depending on whether torsion is set to zero (i) a priori or (ii) a posteriori, i.e., before or after considering variations of the action. Considering a generic family of Ricci-squared theories, we show that in both cases the connection can be decomposed as the sum of a Levi-Civita connection and terms depending on a vector field. However, while in case (i) this vector field is related to the symmetric part of the connection, in (ii) it comes from the torsion part and, therefo…

Matrix solutions of diffusion equation

2002

On the local existence of maximal slicings in spherically symmetric spacetimes

2010

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution may be accomplished analytical or numerically. We provide a general procedure to construct such maximal slicings.

2018

We have performed the most comprehensive resonance-model fit of π-π-π+ states using the results of our previously published partial-wave analysis (PWA) of a large data set of diffractive-dissociation events from the reaction π-+p→π-π-π++precoil with a 190  GeV/c pion beam. The PWA results, which were obtained in 100 bins of three-pion mass, 0.5<m3π<2.5  GeV/c2, and simultaneously in 11 bins of the reduced four-momentum transfer squared, 0.1<t′<1.0  (GeV/c)2, are subjected to a resonance-model fit using Breit-Wigner amplitudes to simultaneously describe a subset of 14 selected waves using 11 isovector light-meson states with JPC=0-+, 1++, 2++, 2-+, 4++, and spin-exotic 1-+ quantum numbers. T…

Parabolic equations with natural growth approximated by nonlocal equations

2017

In this paper we study several aspects related with solutions of nonlocal problems whose prototype is $$ u_t =\displaystyle \int_{\mathbb{R}^N} J(x-y) \big( u(y,t) -u(x,t) \big) \mathcal G\big( u(y,t) -u(x,t) \big) dy \qquad \mbox{ in } \, \Omega \times (0,T)\,, $$ being $ u (x,t)=0 \mbox{ in } (\mathbb{R}^N\setminus \Omega )\times (0,T)\,$ and $ u(x,0)=u_0 (x) \mbox{ in } \Omega$. We take, as the most important instance, $\mathcal G (s) \sim 1+ \frac{\mu}{2} \frac{s}{1+\mu^2 s^2 }$ with $\mu\in \mathbb{R}$ as well as $u_0 \in L^1 (\Omega)$, $J$ is a smooth symmetric function with compact support and $\Omega$ is either a bounded smooth subset of $\mathbb{R}^N$, with nonlocal Dirichlet bound…

The effective diffusion coefficient in a one-dimensional discrete lattice with the inclusions

2015

Abstract The expression for the effective diffusion coefficient in one-dimensional discrete lattice model of random walks in matrix with inclusions and unequal hopping lengths is derived. This allowed us to suggest a physical interpretation to the concentration jump – ad hoc parameter commonly used in extended effective medium theory for accounting particle partial reflection on the boundary matrix–inclusion. The analytical results obtained are in excellent agreement with computer simulations.

Numerical study of a multiscale expansion of the Korteweg de Vries equation and Painlev\'e-II equation

2007

The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by the elliptic solution of KdV where the amplitude, wave-number and frequency are not constant but evolve according to the Whitham equations. Whereas the difference between the KdV and the asymptotic solution decreases as $\epsilon$ in the interior of the Whitham oscillatory zone, it is known to be only of order $\epsilon^{1/3}$ near the leading edge of this zone. To obtain a more accurate description near the leading edge of the oscillatory zone we present a…

Partial wave analysis inK-matrix formalism

1995

A description is given of the K-matrix formalism. The formalism, which is normally applied to two-body scattering processes, is generalized to production of two-body channels with finalstate interactions. A multi-channel treatment of production of resonances has been worked out in the P-vector approach of Aitchison. An alternative approach, derived from the P-vector, gives the production amplitude as a product of the T-matrix for a two-body system and a vector Q specifying its production. This formulation, called Q-vector approach here, has also been worked out. Examples of practical importance are given.