相关论文: Continuous-time link-based kinematic wave model: f…

Whitham modulation theory describes the zero dispersion limit of nonlinear waves by a system of conservation laws for the parameters of modulated periodic traveling waves. Here, admissible, discontinuous, weak solutions of the Whitham…

We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…

We develop a class of C1-continuous time integration methods that are applicable to conservative problems in elastodynamics. These methods are based on Hamilton's law of varying action. From the action of the continuous system we derive a…

Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a…

The theory of dynamical Coulomb blockade is extended to tunneling elements driven by a time-dependent voltage. It is shown that for standard set-ups where an external voltage is applied to a tunnel junction via an impedance, time-dependent…

In this paper we give a general account of Wave Interaction Theory which by now consists of two parts: kinetic wave turbulence theory (WTT), using a statistical description of wave interactions, and the D-model recently introduced in…

The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…

Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…

We review recent advances regarding the long-time dynamics of space-periodic water waves, focusing on 1) bifurcation of quasi-periodic solutions, both standing and traveling; 2) long-time well-posedness results; 3) modulational instability…

In this paper, we are concerned with the local-in-time well-posedness of a fluid-kinetic model in which the BGK model with density dependent collision frequency is coupled with the inhomogeneous Navier-Stokes equation through drag forces.…

Recently, Koopman operator theory has become a powerful tool for developing linear representations of non-linear dynamical systems. However, existing data-driven applications of Koopman operator theory, including both traditional and deep…

We derive a modular fluid-flow network congestion control model based on a law of fundamental nature in networks: the conservation of information. Network elements such as queues, users, and transmission channels and network performance…

A formulation of quantum electrodynamics is proposed, in which the local law of conservation of electric charge serves as the source of the gauge condition. The equations of motion of the gauge variable and the density of the charge…

We investigate the stability of plane wave solutions of equations describing quantum particles interacting with a complex environment. The models take the form of PDE systems with a non local (in space or in space and time) self-consistent…

We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the…

In this paper, we study the nonlinear dispersive waves including the rarefaction and dispersive shock waves in the discrete modified KdV equation through the numerical simulations of the dispersive Riemann problems. In particular, we…

This paper proposes high-order accurate well-balanced (WB) energy stable (ES) adaptive moving mesh finite difference schemes for the shallow water equations (SWEs) with non-flat bottom topography. To enable the construction of the ES…

Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…

We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions…

We derive a collisionless kinetic theory for an ensemble of molecules undergoing nonholonomic rolling dynamics. We demonstrate that the existence of nonholonomic constraints leads to problems in generalizing the standard methods of…