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We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic…
Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as…
We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system…
Reservoir computing provides a time and cost-efficient alternative to traditional learning methods.Critical regimes, known as the "edge of chaos," have been found to optimize computational performance in binary neural networks. However,…
The flow field in a two-dimensional three-ramp hypersonic mixed-compression inlet in a freestream Mach number of $M_\infty=5$ is numerically solved to understand the unsteady throttling dynamics. Throttling conditions are simulated by…
Compressed Sensing algorithms often make use of the hard thresholding operator to pass from dense vectors to their best s-sparse approximations. However, the output of the hard thresholding operator does not depend on any information from a…
The collision of a gravitationally-driven horizontal current with a barrier following release from a confining lock is investigated using a shallow water model of the motion, together with a sophisticated boundary condition capturing the…
We extend flow matching to ensembles of linear systems in both deterministic and stochastic settings. Averaging over system parameters induces memory leading to a non-Markovian interpolation problem for the stochastic case. In this setting,…
In various models and systems involving the escape of periodically forced particle from the potential well, a common pattern is observed. Namely, the minimal forcing amplitude required for the escape exhibits sharp minimum for the…
We propose a one-dimensional nonlocal stochastic model of adsorption and desorption depending on one parameter, the adsorption rate. At a special value of this parameter, the model has some interesting features. For example, the spectrum is…
In this paper we develop an encounter-based model of a run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ with partially absorbing, sticky boundaries at both ends. We assume that the particle switches between two constant…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
We introduce the voter model on the infinite lattice with a slow membrane and investigate its hydrodynamic behavior and nonequilibrium fluctuations. The model is defined as follows: a voter adopts one of its neighbors' opinion at rate one…
This paper provides an exponential stability result for the adaptive anti-unwinding attitude tracking control problem of a rigid body with uncertain but constant inertia parameters, without requiring the satisfaction of persistent…
Safety-critical applications require controllers/policies that can guarantee safety with high confidence. The control barrier function is a useful tool to guarantee safety if we have access to the ground-truth system dynamics. In practice,…
This paper addresses the problem of obtaining low-order models of fluid flows for the purpose of designing robust feedback controllers. This is challenging since whilst many flows are governed by a set of nonlinear, partial…
We analyze numerically the critical behavior of an absorbing phase transition in the conserved transfer threshold process. We determined the steady state scaling behavior of the order parameter as a function of both, the control parameter…
Asymmetric damping is widely used in passive vehicle suspensions, with rebound damping often recommended to exceed compression damping by a factor of two to three. Despite its prevalence, this guideline remains largely empirical and lacks a…
The two-dimensional backward-facing step flow is a canonical example of noise amplifier flow: global linear stability analysis predicts that it is stable, but perturbations can undergo large amplification in space and time as a result of…