Related papers: Transport in partially hyperbolic fast-slow system…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…
Hyperbolic partial differential equations on a one-dimensional spatial domain are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of non-homogeneous transmission lines. The…
The optimization of the conversion of thermal energy into work and the minimization of dissipation for nano- and mesoscopic systems is a complex challenge because of the important role fluctuations play on the dynamics of small systems. We…
This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
We analyze the dynamics of multi-agent collective behavior models and their control theoretical properties. We first derive a large population limit to parabolic diffusive equations. We also show that the non-local transport equations…
This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
In the present thesis, we study the heat flow in mesoscopic one-dimensional transport systems. Using the analysis of full counting statistics, we calculate the cumulant generating function of the particle and heat flows and prove its…
We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the…
Energy-transport equations for the transport of fermions in optical lattices are formally derived from a Boltzmann transport equation with a periodic lattice potential in the diffusive limit. The limit model possesses a formal gradient-flow…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
We investigate energy transport in several two-level atom or spin-1/2 models by a direct coupling to heat baths of different temperatures. The analysis is carried out on the basis of a recently derived quantum master equation which…
We study a message passing model, applicable also to traffic problems. The model is implemented in a discrete lattice, where particles move towards their destination, with fluctuations around the minimal distance path. A repulsive…
In this article we study a class of hyperbolic partial differential equations of order one on the semi-axis. The so-called port-Hamiltonian systems cover for instance the wave equation and the transport equation, but also networks of the…
Having driven a large part of the decade's progress in physics, nanoelectronics is now passing from today's realm of the extraordinary to tomorrow's commonplace. This carries the problem of turning proofs of concept into practical…