43 research outputs found
Tzitzeica solitons versus relativistic CalogeroâMoser three-body clusters
We establish a connection between the hyperbolic relativistic CalogeroâMoser systems and a class of soliton solutions to the Tzitzeica equation (also called the DoddâBulloughâZhiberâShabatâMikhailov equation). In the 6N-dimensional phase space Omega of the relativistic systems with 2N particles and N antiparticles, there exists a 2N-dimensional PoincarĂŠ-invariant submanifold OmegaP corresponding to N free particles and N bound particle-antiparticle pairs in their ground state. The Tzitzeica N-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of OmegaP. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state
Multiphysics simulation of corona discharge induced ionic wind
Ionic wind devices or electrostatic fluid accelerators are becoming of
increasing interest as tools for thermal management, in particular for
semiconductor devices. In this work, we present a numerical model for
predicting the performance of such devices, whose main benefit is the ability
to accurately predict the amount of charge injected at the corona electrode.
Our multiphysics numerical model consists of a highly nonlinear strongly
coupled set of PDEs including the Navier-Stokes equations for fluid flow,
Poisson's equation for electrostatic potential, charge continuity and heat
transfer equations. To solve this system we employ a staggered solution
algorithm that generalizes Gummel's algorithm for charge transport in
semiconductors. Predictions of our simulations are validated by comparison with
experimental measurements and are shown to closely match. Finally, our
simulation tool is used to estimate the effectiveness of the design of an
electrohydrodynamic cooling apparatus for power electronics applications.Comment: 24 pages, 17 figure
Differential constraints and exact solutions of nonlinear diffusion equations
The differential constraints are applied to obtain explicit solutions of
nonlinear diffusion equations. Certain linear determining equations with
parameters are used to find such differential constraints. They generalize the
determining equations used in the search for classical Lie symmetries
A List of 1 + 1 Dimensional Integrable Equations and Their Properties
This paper contains a list of known integrable systems. It gives their recursion-, Hamiltonian-, symplectic- and cosymplectic operator, roots of their symmetries and their scaling symmetry