Related papers: Reduction of periodic one-dimensional hopping mode…

The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…

Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new…

We address some open questions regarding the phase diagram of the one-dimensional Hubbard model with asymmetric hopping coefficients and balanced species. In the attractive regime we present a numerical study of the passage from on-site…

We constructed a model that evolved from a non-equilibrium state to an equilibrium state. The model only needs two basic coefficients, including self-similar coefficients and non-equilibrium coefficients. The coefficients of the model can…

We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the…

Analytic solution is given in the steady state limit for the system of Master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile, directional impurity (defect bond).…

Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…

A new model is proposed for the purpose of modelling the ``wave function collapse'' of a two-state quantum system. The collapse to a classical state is driven by a nonlinear evolution equation with an extreme sensitivity to absolute phase.…

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…

We study a model for the movement of surfaces, namely the conserved, restricted solid-on-solid model. The surface configurations are restricted such that the difference between the heights at adjacent sites is no more than one. In addition…

In the first part of this thesis, we present our efforts on experimental validation of the predictive performance of mechanics-based mathematical models on a physical one-legged hopping robot platform. We extend upon a recently proposed…

Large-scale three dimensional molecular dynamics simulations of hopper flow are presented. The flow rate of the system is controlled by the width of the aperture at the bottom. As the steady-state flow rate is reduced, the force…

Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…

A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with…

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Dephasing of one-particle states in closed quantum dots is analyzed within the framework of random matrix theory and Master equation. Combination of this analysis with recent experiments on the magnetoconductance allows for the first time…

This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…

In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…