Results 51 to 60 of about 667 (82)

Overview on uncertainty quantification in traffic models via intrusive method [PDF]

arXiv, 2022
We consider traffic flow models at different scales of observation. Starting from the well known hierarchy between microscopic, kinetic and macroscopic scales, we will investigate the propagation of uncertainties through the models using the stochastic Galerkin approach.
arxiv  

A Lipschitz metric for conservative solutions of the two-component Hunter--Saxton system [PDF]

arXiv, 2015
We establish the existence of conservative solutions of the initial value problem of the two-component Hunter--Saxton system on the line. Furthermore we investigate the stability of these solutions by constructing a Lipschitz metric.
arxiv  

The KdV hierarchy: universality and a Painleve transcendent

, 2011
We study the Cauchy problem for the Korteweg-de Vries (KdV) hierarchy in the small dispersion limit where $\e\to 0$. For negative analytic initial data with a single negative hump, we prove that for small times, the solution is approximated by the ...
Claeys, T., Grava, T.
core   +1 more source

Maximum entropy principle approach to a non-isothermal Maxwell-Stefan diffusion model [PDF]

arXiv, 2021
In this study we apply the maximum entropy principle to derive the properly scaled velocity distribution function of Boltzmann equations for mixtures, which leads to a non-isothermal Maxwell-Stefan diffusion model. We also analyze the entropy balance law and derive the kinetic entropy production from the scaled distribution function.
arxiv  

The Entropic journey of Kac's Model [PDF]

arXiv, 2023
The goal of this paper is to review the advances that were made during the last few decades in the study of the entropy, and in particular the entropy method, for Kac's many particle system.
arxiv  

Boltzmann-type models with uncertain binary interactions

, 2017
In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics.
Tosin, Andrea, Zanella, Mattia
core   +1 more source

Lipschitz metric for the Hunter-Saxton equation [PDF]

arXiv, 2009
We study stability of solutions of the Cauchy problem for the Hunter-Saxton equation $u_t+uu_x=\frac14(\int_{-\infty}^xu_x^2 dx-\int_{x}^\infty u_x^2 dx)$ with initial data $u_0$. In particular, we derive a new Lipschitz metric $d_\D$ with the property that for two solutions $u$ and $v$ of the equation we have $d_\D(u(t),v(t))\le e^{Ct} d_\D(u_0,v_0)$.
arxiv  

Price dynamics in financial markets: a kinetic approach [PDF]

arXiv, 2010
The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of agents' heterogeneity in emerging power laws for price distributions is emphasized and discussed.
arxiv  

On the Maxwell-Stefan diffusion limit for a mixture of monatomic gases [PDF]

arXiv, 2015
Multi-species Boltzmann equations for gaseous mixtures, with analytic cross sections and under Grad's angular cutoff assumption, are considered under diffusive scaling. In the limit, we formally obtain an explicit expression for the binary diffusion coefficients in the Maxwell-Stefan equations.
arxiv  

Chimera multiscale simulation of complex flowing matter [PDF]

arXiv, 2016
We discuss a unified mesoscale framework for the simulation of complex states of flowing matter across scales of motion which requires no explicit coupling between different macro-meso-micro levels. The idea is illustrated through selected examples of complex flows at the micro and nanoscale.
arxiv