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We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
We present a dynamical description of slow relaxation processes based on the extension of Onsager's fluctuation theory to systems in local quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional probability density is…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of…
In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter $\epsilon$ such that, for every fixed value of the slow variable, the fast dynamics are sufficiently chaotic with…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay value. Finding a formula for the…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
The behavior of active matter under confinement poses significant challenges due to the intricate coupling between dynamics near boundaries and those in the bulk. A defining feature of active matter systems is that a substantial portion of…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the…
A basic result in synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their outputs and neutrally stable, it is shown that a linear output feedback law…
We perform numerical simulations of the sandpile model for non-vanishing driving fields $h$ and dissipation rates $\epsilon$. Unlike simulations performed in the slow driving limit, the unique time scale present in our system allows us to…
There has been much success in describing the limiting spatial fluctuations of growth models in the Kardar-Parisi-Zhang (KPZ) universality class. A proper rescaling of time should introduce a non-trivial temporal dimension to these limiting…