Related papers: Finding Transition Pathways on Manifolds

The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…

Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…

We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular…

The sliding mode approach is recognized as an efficient tool for treating the chattering behavior in hybrid systems. However, the amplitude of chattering, by its nature, is proportional to magnitude of discontinuous control. A possible…

This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…

A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…

Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…

We develop a discrete Boltzmann-type model that uses dynamics in phase space to describe the behavior of traffic flows. Firstly, we model the traffic flow at mesoscopic scale using dynamics in phase space, which is considered as an…

Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of…

Polarity reversals are a key feature of Earth's magnetic field, yet the processes governing them are still poorly understood. Dipole reversals have been found in many numerical dynamo simulations and often occur close to the transition…

For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect trajectories with prescribed itineraries: the scattering map, the…

We study forced oscillations on differentiable manifolds which are globally defined as the zero set of appropriate smooth maps in some Euclidean spaces. Given a T-periodic perturbative forcing field, we consider the two different scenarios…

We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is…

I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…

Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the…

There is a reasonable possibility that the present-day Atlantic Meridional Overturning Circulation is in a bi-stable regime and hence it is relevant to compute probabilities and pathways of noise-induced transitions between the stable…

We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…

Many processes in chemistry, physics, and biology involve rare events in which the system escapes from a metastable state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation events…