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The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…

While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose…

We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…

This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first…

Spectral submanifolds (SSMs) have recently been shown to provide exact and unique reduced-order models for nonlinear unforced mechanical vibrations. Here we extend these results to periodically or quasiperiodically forced mechanical…

These lecture notes can be read in two ways. The first two Sections contain a review of the phenomenology of several physical systems with slow nonequilibrium dynamics. In the Conclusions we summarize the scenario derived from the solution…

This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two…

Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low…

Dynamic facilitation theory assumes short-ranged dynamic constraints to be the essential feature of supercooled liquids and draws much of its conclusions from the study of kinetically constrained models. While deceptively simple, these…

An analytic approach to phenomenological models inspired by cubic string field theory is introduced and applied to some examples. We study a class of actions for a minimally coupled, homogeneous scalar field whose energy density contains…

The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…

We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of…

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average…

Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…

Within the framework of the thermal wave model, an investigation is made of the longitudinal dynamics of high energy charged particle beams. The model includes the self-consistent interaction between the beam and its surroundings in terms…

Driven elastic manifolds in random media exhibit a depinning transition to a state with non-vanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than…

Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from…