Related papers: Exploring Isomerization Dynamics on a Potential En…
The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the…
Isomorphs are curves in the thermodynamic phase diagram along which structure and dynamics are invariant to a good approximation. There are two main ways to trace out isomorphs, the configurational-adiabat method and the…
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…
Lagrangian coherent structures (LCSs) are material surfaces that shape finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from…
Surface-induced liquid crystalline phase transitions evoke fundamental interest and can provide deeper insight into the nature of low-dimensional phase transitions. Board-like conjugated polymers are particularly interesting because they…
We introduce and analyze numerical companion matrix methods for the reconstruction of hypersurfaces with crossings from smooth interpolants given unordered or, without loss of generality, value-sorted data. The problem is motivated by the…
Chesnavich's model Hamiltonian for the reaction CH$_4^+ \rightarrow$ CH$_3^+$ is known to exhibit a range of interesting dynamical phenomena including roaming. The model system consists of two parts: a rigid, symmetric top representing the…
Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different…
We apply a recently proposed criterion for the existence of phase transitions, which is based on the properties of the saddles of the energy landscape, to a simplified model of a system with gravitational interactions, referred to as the…
We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but…
An asymmetrical 2D Ising model with a zigzag surface, created by diagonally cutting a regular square lattice, has been developed to investigate the thermodynamics and phase transitions on surface by the methodology of recursive lattice,…
Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and shells, as well as molecular reconfigurations in chemical…
We review recent results on the potential energy landscape (PES) of model liquids. The role of saddle-points in the PES in connecting dynamics to statics is investigated, confirming that a change between minima-dominated and…
We examined theory for force-induced unbinding on a two-dimensional free energy surface where the internal dynamics of biomolecules is coupled with the rupture process under constant tension f. We show that only if the transition state…
The method of controlled Lagrangians for discrete mechanical systems is extended to include potential shaping in order to achieve complete state-space asymptotic stabilization. New terms in the controlled shape equation that are necessary…
This work introduces a novel Lagrangian-based framework to analyze forced convective heat transfer in the unsteady wake of a heated elliptical cylinder inclined at angles ranging from $\theta = 0^\circ$ to $90^\circ$, in $15^\circ$…
We establish the Lagrangian nature of the discrete isospectral and isomonodromic dynamical systems corresponding to the re-factorization transformations of the rational matrix functions on the Riemann sphere. Specifically, in the…
We numerically study the interplay between heterogeneous dynamics and properties of negatively curved regions of the potential energy surface in a model glassy system. We find that the unstable modes of saddles and quasi-saddles undergo a…
This paper compares the advantages, limitations, and computational considerations of using Finite-Time Lyapunov Exponents (FTLEs) and Lagrangian Descriptors (LDs) as tools for identifying barriers and mechanisms of fluid transport in…
The potential energy landscape (PEL) formalism is a statistical mechanical approach to describe supercooled liquids and glasses. Here we use the PEL formalism to study the pressure-induced transformations between low-density amorphous ice…