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Generalized Hydrodynamics is a recent theory that describes large scale transport properties of one dimensional integrable models. It is built on the (typically infinitely many) local conservation laws present in these systems, and leads to…
We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After…
We address several concerns related to the derivation of drift-ordered fluid equations. Starting from a fully Galilean invariant fluid system, we show how consistent sets of perturbative drift-fluid equations in the case of a isothermal…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of a scalar hyperbolic conservation law. We begin with sufficient conditions for a space discretization to be bound…
A self-consistent quadratic theory is presented to account for nonlinear contributions in quantum dynamics. Evolution equations are shown to depend on higher-order gradients of the Hamiltonian, which are incorporated via their equations of…
We present emergent dynamics of continuous and discrete thermomechanical Cucker-Smale(TCS) models equipped with temperature as an extra observable on general digraph. In previous literature, the emergent behaviors of the TCS models were…
Systems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out of equilibrium systems. The evolution of coarse-grained variables is governed…
We study the connection between Lagrangian and Hamiltonian descriptions of closed/open dynamics, for a collection of particles with quadratic interaction (closed system) and a sub-collection of particles with linear damping (open system).…
We present the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. Given a system of differential equations possessing conservation laws, our approach is based on…
Standard quantum mechanics relies on two distinct dynamical principles: unitary evolution and collapse. A mathematically self-contained variational framework is presented that replaces this dualism with a single principle, in which…
We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advection are treated by method-of-characteristics integration,…
We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover…
The paper provides results for the stabilization of a spatially uniform equilibrium profile for a scalar conservation law that arises in the study of traffic dynamics under variable speed limit control. Two different control problems are…
Contact-rich robot dynamics are hybrid: a single observation can match several latent states and contact regimes (free, impact, stick--slip). A standard amortized filter that places no probability on a feasible contact transition will…
This paper develops a family of fast, structure-preserving numerical algorithms for the nonlinear Maxwell-Ampere Nernst-Planck equations. For the first-order scheme, the Slotboom transformation rewrites the Nernst-Planck equation to enable…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact time integration when coupled with a mimetic horizontal…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed…