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Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…

We study the thermal escape problem in the moderate-to-high and high damping regime of a system with a parabolic barrier. We present a formula that matches our numerical results accounting for finite barrier effects, and compare it with…

The thermal decay of linear chains from a metastable state is investigated. A crossover from rigid to elastic decay occurs when the number of particles, the single particle energy barrier or the coupling strength between the particles is…

Kinetic traps are a notorious problem in equilibrium statistical mechanics, where temperature quenches ultimately fail to bring the system to low energy configurations. Using multifarious self-assembly as a model system, we introduce a…

We numerically investigate bouncing and non-bouncing of droplets during isothermal impact on superhydrophobic surfaces. An in-house, experimentally-validated, finite-element method based computational model is employed to simulate the…

We describe a model for the thermodynamics and dynamics of glass-forming liquids in terms of excitations from an ideal glass state to a Gaussian manifold of configurationally excited states. The quantitative fit of this three parameter…

Stochastic gradient descent (SGD) is central to deep learning, yet the dynamical origin of its preference for flatter, more generalizable solutions remains unclear. Here, by analyzing SGD learning dynamics, we identify a nonequilibrium…

Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems…

Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present…

Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…

Throughout computational science, there is a growing need to utilize the continual improvements in raw computational horsepower to achieve greater physical fidelity through scale-bridging over brute-force increases in the number of mesh…

Saddle points play important roles as the transition states of activated process in gradient system driven by energy functional. However, for the same energy functional, the saddle points, as well as other stationary points, are different…

A framework for performing event-driven, adaptive time step simulations of systems of rigid bodies interacting under stepped or terraced potentials in which the potential energy is only allowed to have discrete values is outlined. The…

This paper presents a molecular dynamics simulation of an inelastic gas, where collisions between molecules are characterized by a coefficient of restitution less than unity. The simulation employs an event-driven algorithm to efficiently…

In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for…

Thermally activated escape over a potential barrier in the presence of periodic driving is considered. By means of novel time-dependent path-integral methods we derive asymptotically exact weak-noise expressions for both the instantaneous…

A fundamental objective of materials modeling is identifying atomic structures that align with experimental observables. Conventional approaches for disordered materials involve sampling from thermodynamic ensembles and hoping for an…

Gradient descent dynamics in complex energy landscapes, i.e. featuring multiple minima, finds application in many different problems, from soft matter to machine learning. Here, we analyze one of the simplest examples, namely that of soft…

Accelerated molecular dynamics (MD) simulations are implemented to model the sliding process of AFM experiments at speeds close to those found in experiment. In this study the hyperdynamics method, originally devised to extend MD time…

Slow relaxation and glassiness have been the focus of extensive research attention, along with popular and technological interest, for many decades. While much understanding has been attained through mean-field and mode-coupling models,…