Related papers: Potential well in Poincar\'e recurrence
The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is…
The purpose of this work is to analyze the flow due to a potential point vortex pair in the vicinity of a symmetry line (or "wall"), in order to understand why the presence of the wall, even far from the vortices, accelerates fluid mixing…
We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions between particles are specified by means of a pairwise potential,…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hbar \omega$. A WKB wave function is constructed…
We study behaviors of scalar quantities near the possible blow-up time, which is made of smooth solutions of the Euler equations, Navier-Stokes equations and the surface quasi-geostrophic equations. Integrating the dynamical equations of…
We develop a theory describing how a convectively unstable active field in an open flow is transformed into absolutely unstable by local mixing. Presenting the mixing region as one with a locally enhanced effective diffusion allows us to…
Understanding the performance of a pool of servers is crucial for proper dimensioning. One of the main challenges is to take into account the complex interactions between servers that are pooled to process jobs. In particular, a job can…
Quantum mechanical control of the position of a particle by using a trapping potential well is an important problem for the manipulation of a quantum particle. We study the probability of successful conveyance of a particle trapping in a…
Basic peculiarities of market price fluctuations are known to be well described by a recently developed random walk model in a temporally deforming quadric potential force whose center is given by a moving average of past price traces…
Fluid queues are mathematical models frequently used in stochastic modelling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the…
This paper is a continuation of a previous work about the study of the survival probability modelizing the molecular predissociation in the Born-Oppenheimer framework. Here we consider the critical case where the reference energy…
The mixing efficiency of a flow advecting a passive scalar sustained by steady sources and sinks is naturally defined in terms of the suppression of bulk scalar variance in the presence of stirring, relative to the variance in the absence…
We investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by [Bianchi, Dommers, and Giardin\`a, Electronic Journal of Probability, 22: 1-34, 2017], which presented the…
We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal…
It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of…
For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We…
We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in…
Predicting potential and counterfactual outcomes from observational data is central to individualized decision-making, particularly in clinical settings where treatment choices must be tailored to each patient rather than guided solely by…
Understanding how annual peak flow, $Q_p$, relates to upstream basin area, $A$, and their scaling have been one of the challenges in surface hydrology. Although a power-law scaling relationship (i.e., $Q_p \propto A^\alpha$) has been widely…
In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincar\'e recurrences…