Related papers: Optimal barrier subdivision for Kramers' escape ra…
The transmission of fermions of mass m and energy E through an electrostatic potential barrier of rectangular shape (i.e. supporting an infinite electric field), of height U> E + m - due to the many-body nature of the Dirac equation…
Time-dependent analytical solutions to Schr\"{o}dinger's equation with quantum shutter initial conditions are used to investigate the issue of the tunneling time of forerunners in rectangular potential barriers. By using a time-frequency…
We consider the survival probability of a particle in the presence of a finite number of diffusing traps in one dimension. Since the general solution for this quantity is not known when the number of traps is greater than two, we devise a…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
We consider a potential scattering of Bose-Hubbard dimer in 1D optical lattice. A numerical approach based on effective non-Hermitian Hamiltonian has been developed for solving the scattering problem. It allows to compute the tunneling and…
The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the…
Energy barriers for different moves of a single Rh adatom in the vicinity of steps on Rh(111) surface are studied with molecular statics. Interatomic interactions are modeled by the semi-empirical many-body Rosato-Guillope-Legrand…
Consider the problem on sequential change-point detection on multiple data streams. We provide the asymptotic lower bounds of the detection delays at all levels of change-point sparsity and we derive a smaller asymptotic lower bound of the…
Quantum mechanics predicts an exponentially small probability that a particle with energy greater than the height of a potential barrier will nevertheless reflect from the barrier in violation of classical expectations. This process can be…
The relationship between the threshold energy for a deep sub-barrier fusion hindrance phenomenon and the energy at which the regime of interaction changes (the turning-off of the nuclear forces and friction) in the sub-barrier capture…
Quantum mechanical motion of a particle in a periodic asymmetric potential is studied theoretically at zero temperature. It is shown based on semi-classical approximation that the tunneling probability from one local minimum to the next…
Kakutani's random interval-splitting process iteratively divides, via a uniformly random splitting point, the largest sub-interval in a partition of the unit interval. The length of the longest sub-interval after $n$ steps, suitably centred…
We study the escape rate for the Farey map, an infinite measure preserving system, with a hole including the indifferent fixed point. Due to the ergodic properties of the map, the standard theoretical approaches to this problem cannot be…
The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing--free dividing surface. We show here that it is possible to define such optimal dividing surface in…
We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…
Quantum tunnelling phenomenon allows a particle in Schr\"odinger mechanics tunnels through a barrier that it classically could not overcome. Even the infinite potentials do not always form impenetrable barriers. We discuss an answer to the…
The dynamics of mechanical systems such as turbomachinery with multiple blades are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and…
Break of radial symmetry for interaction energy minimizers is a phenomenon where a radial interaction potential whose associated energy minimizers are never radially symmetric. Numerically, it has been frequently observed for various types…
We consider the optimal dividend problem for the insurance risk process in a general Levy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give…
We present a mathematical model for optimizing breakaway strategies in competitive cycling, balancing power expenditure, aerodynamic drag, and crashing. Our framework incorporates probabilistic crash dynamics, allowing a cyclist's risk…