Related papers: Stability of the Minimum Energy Path
In this paper, we revisit asymptotic stability for the two-dimensional incompressible porous media equation and the Stokes transport system in a periodic channel. It is well-known that a stratified density, which strictly decreases in the…
Empirical force fields employed in molecular dynamics simulations of complex systems can be optimised to reproduce experimentally determined structural and thermodynamic properties. In contrast, experimental knowledge about the rates of…
The Minimum Eccentricity Shortest Path (MESP) Problem consists in determining a shortest path (a path whose length is the distance between its extremities) of minimum eccentricity in a graph. It was introduced by Dragan and Leitert [9] who…
The probability of trajectories of weakly diffusive processes to remain in the tubular neighbourhood of a smooth path is given by the Freidlin-Wentzell-Graham theory of large deviations. The most probable path between two states (the…
Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling…
In finite systems, such as nanoparticles and gas-phase molecules, calculations of minimum energy paths (MEPs) connecting initial and final states of transitions as well as searches for saddle points are complicated by the presence of…
The free energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path…
The solution of the shortest path problem on a surface is not only a theoretical problem to be solved in the field of mathematics, but also problems that need to be solved in very different fields such as medicine, defense and construction…
Gene expression patterns (GEPs) are established by cross-regulating target genes that interpret morphogen gradients. However, as development progresses, morphogen activity is reduced, leaving the emergent GEP without stabilizing positional…
The rapid adoption of electric vehicles (EVs) in modern transport systems has made energy-aware routing a critical task in their successful integration, especially within large-scale transport networks. In cases where an EV's remaining…
A central feature of quantum mechanics is that a measurement is intrinsically probabilistic. As a result, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system…
Transition path sampling (TPS) is a powerful technique for investigating rare transitions, especially when the mechanism is unknown and one does not have access to the reaction coordinate. Straightforward application of TPS does not…
This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize…
The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima…
Message propagation is fundamental in constructing distributed systems upon sparsely connected communication networks. For providing easy message propagation primitives, the mutual-exclusive propagation (MEP) of one-bit messages is…
Employing physically-consistent numerical methods is an important step towards attaining robust and accurate numerical simulations. When addressing compressible flows, in addition to preserving kinetic energy at a discrete level, as done in…
The modern theory of rare events is grounded in near equilibrium ideas, however many systems of modern interest are sufficiently far from equilibrium that traditional approaches do not apply. Using the recently developed variational path…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
In a coherent monoenergetic beam of non-interacting particles, the phase velocity and the particle transport velocity are functions of position, with the strongest variation being in the focal region. These velocities are everywhere…