Related papers: Metadynamics for transition paths in irreversible …
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
We study the metastable dynamics of a discretised version of the mass-conserving stochastic Allen-Cahn equation. Consider a periodic one-dimensional lattice with $N$ sites, and attach to each site a real-valued variable, which can be…
Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…
Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic…
We propose a new geometric approach to describe the qualitative dynamics of chemical reactions networks. By this method we identify metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with applications of transition path sampling to classical dynamics, the method does not rely…
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian L\'evy noise. Among these complex phenomena, the most…
Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal…
We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of…
Metastability, characterized by a variability of regimes in time, is a ubiquitous type of neural dynamics. It has been formulated in many different ways in the neuroscience literature, however, which may cause some confusion. In this…
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…
Metastability appears when a thermodynamic system, such as supercooled water (which is liquid below freezing temperature), lands on the "wrong" side of a phase transition, and remains for a very long time in a state different from its…
A switching dynamical system by means of piecewise linear systems in R^3 that presents multistability is presented. The flow of the system displays multiple scroll attractors due to the unstable hyperbolic focus-saddle equilibria with…
We present a molecular simulation method to simultaneously find multiple transition pathways, and their associated free-energy profiles. The scheme extends path-metadynamics (PMD) [Phys. Rev. Lett. 109, 020601 (2012)] with multiple paths…
Statistical Mechanics deals with ensembles of microstates that are compatible with fixed constraints and that on average define a thermodynamic macrostate. The evolution of a small system is normally subjected to changing constraints and…
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…