3,099 research outputs found
Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System
In this article, we study the self-similar solutions of the 2-component
Degasperis-Procesi water system:% [c]{c}%
\rho_{t}+k_{2}u\rho_{x}+(k_{1}+k_{2})\rho u_{x}=0
u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\rho\rho_{x}=0. By the
separation method, we can obtain a class of self-similar solutions,% [c]{c}%
\rho(t,x)=\max(\frac{f(\eta)}{a(4t)^{(k_{1}+k_{2})/4}},\text{}0),\text{}u(t,x)=\frac{\overset{\cdot}{a}(4t)}{a(4t)}x
\overset{\cdot\cdot}{a}(s)-\frac{\xi}{4a(s)^{\kappa}}=0,\text{}a(0)=a_{0}%
\neq0,\text{}\overset{\cdot}{a}(0)=a_{1}
f(\eta)=\frac{k_{3}}{\xi}\sqrt{-\frac{\xi}{k_{3}}\eta^{2}+(\frac{\xi}{k_{3}}\alpha)
^{2}}% where with , and are constants. which the
local or global behavior can be determined by the corresponding Emden equation.
The results are very similar to the one obtained for the 2-component
Camassa-Holm equations. Our analytical solutions could provide concrete
examples for testing the validation and stabilities of numerical methods for
the systems. With the characteristic line method, blowup phenomenon for
is also studied.Comment: 13 Pages, Key Words: 2-Component Degasperis-Procesi, Shallow Water
System, Analytical Solutions, Blowup, Global, Self-Similar, Separation
Method, Construction of Solutions, Moving Boundary, 2-Component Camassa-Holm
Equation
The Finite-time Ruin Probabilities of a Bidimensional risk model with Constant Interest Force and correlated Brownian Motions
We follow some recent works to study bidimensional perturbed compound Poisson
risk models with constant interest force and correlated Brownian Motions.
Several asymptotic formulae for three different type of ruin probabilities over
a finite-time horizon are established.
Our approach appeals directly to very recent developments in the ruin theory
in the presence of heavy tails of unidimensional risk models and the dependence
theory of stochastic processes and random vectors.Comment: 25page
Molecular emission near metal interfaces: the polaritonic regime
The strong coupling of a dense layer of molecular excitons with
surface-plasmon modes in a metal gives rise to polaritons (hybrid light-matter
states) called plexcitons. Surface plasmons cannot directly emit into (or be
excited by) free-space photons due to the fact that energy and momentum
conservation cannot be simultaneously satisfied in photoluminescence. Most
plexcitons are also formally non-emissive, even though they can radiate via
molecules upon localization due to disorder and decoherence. However, a
fraction of them are bright even in the presence of such deleterious processes.
In this letter, we theoretically discuss the superradiant emission properties
of these bright plexcitons, which belong to the upper energy branch and reveal
huge photoluminescence enhancements compared to bare excitons. Our study
generalizes the well-known problem of molecular emission next to a metal
interface to collective molecular states and provides new design principles for
the control of photophysical properties of molecular aggregates using
polaritonic strategies.Comment: Replaced previous version, noticing that van Hove anomalies are only
observed in the direct and reflected contributions of photoluminescence, but
they cancel out when added up in the total photoluminescence. The correct
phenomenology is that enhancements of photoluminescence are still huge (not
infinite) and are near (not exactly at) the critical poin
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