Related papers: Approximation of potential function in the problem…
We study two broad classes of physically dissimilar problems, each corresponding to stochastically driven escape from a potential well. The first class, often used to model noise-induced order parameter reversal, comprises…
We study deterministic escape dynamics in the framework of the discrete Klein-Gordon modelwith a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and…
The general, multidimensional barrier crossing problem for diffusive processes under the action of conservative forces is studied with the goal of developing tractable approximations. Particular attention is given to the effect of different…
The dynamics of a quantum particle bound by an accelerating delta-functional potential is investigated. Three cases are considered, using the reference frame moving along with the {\delta}-function, in which the acceleration is converted…
The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from…
We show how the exact renormalization group for the effective action with a sharp momentum cutoff, may be organised by expanding one-particle irreducible parts in terms of homogeneous functions of momenta of integer degree (Taylor…
The escape rate of a Brownian particle over a potential barrier is accurately described by the Kramers theory. A quantitative theory explicitly taking the activity of Brownian particles into account has been lacking due to the inherently…
Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to…
The problem of locating the global optimum of functions is studied in a dynamic setting. The dynamics of simple multistable systems under the influence of chaotic forcing is investigated. When the magnitude of the forcing signal decays…
We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum-space harmonic-oscillator potential is solved in a…
Maxwell-Amp\`{e}re-Nernst-Planck (MANP) equations were recently proposed to model the dynamics of charged particles. In this study, we enhance a numerical algorithm of this system with deep learning tools. The proposed hybrid algorithm…
The process of activation out a one-dimensional potential is investigated systematically in zero and nonzero temperature conditions. The features of the potential are traced through statistical escape out of its wells whose depths are tuned…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We consider approximating analytic functions on the interval $[-1,1]$ from their values at a set of $m+1$ equispaced nodes. A result of Platte, Trefethen \& Kuijlaars states that fast and stable approximation from equispaced samples is…
A method for approximate solution of initial value and spectral problems for one dimensional Dirac equation based on an analytic approximation of the transmutation operator is presented. In fact the problem of numerical approximation of…
We study the escape problem for interacting, self-propelled particles confined to a disc, where particles can exit through one open slot on the circumference. Within a minimal 2D Vicsek model, we numerically study the statistics of escape…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In…