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"Small worlds" are large systems in which any given node has only a few connections to other points, but possessing the property that all pairs of points are connected by a short path, typically logarithmic in the number of nodes. The use…
We consider the skew product $F: (x,u) \mapsto (f(x), u + \tau(x))$, where the base map $f : \mathbb{T}^{1} \to \mathbb{T}^{1}$ is piecewise $\mathcal{C}^{2}$, covering and uniformly expanding, and the fibre map $\tau : \mathbb{T}^{1} \to…
Like other critical phenomena, the jamming transition accompanies the divergence of the relaxation time $\tau$. A recent numerical study of frictionless spherical particles proves that $\tau$ is inversely proportional to the lowest non-zero…
We analyze the dynamics of desorption of a polymer molecule which is pulled at one of its ends with force $f$, trying to desorb it. We assume a monomer to desorb when the pulling force on it exceeds a critical value $f_{c}$. We formulate an…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
We show that for planar dispersing billiards the return times distribution is, in the limit, Poisson for metric balls almost everywhere w.r.t. the SRB measure. Since the Poincar\'e return map is piecewise smooth but becomes singular at the…
A time dependent generalization of the Ginzburg -Landau Lagrangian is proposed. It contains two terms determining the time dependence and the four arbitrary scalar functions. Relevant equations, which coincide with equations following from…
This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results…
We obtain improved local well-posedness results for the Lorentzian timelike minimal surface equation. In dimension $d=3$, for a surface of arbitrary co-dimension, we show a gain of $1/3$ derivative regularity compared to a generic equation…
In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to…
We study sublinear-time algorithms for solving linear systems $Sz = b$, where $S$ is a diagonally dominant matrix, i.e., $|S_{ii}| \geq \delta + \sum_{j \ne i} |S_{ij}|$ for all $i \in [n]$, for some $\delta \geq 0$. We present randomized…
We analyze the waiting time distribution of time distances $\tau$ between two nearest-neighbor flares. This analysis is based on the joint use of two distinct techniques. The first is the direct evaluation of the distribution function…
This paper proposes an adaptive time-stepping mothods for stochastic diffusion systems whose drift and diffusion coefficients are locally Lipschitz continuous and may exhibit polynomial growth. By controlling the growth of both the drift…
Consider the set of functions $f_{\theta}(x)=|\theta -x|$ on $\mathbb{R}$. Define a Markov process that starts with a point $x_0 \in \mathbb{R}$ and continues with $x_{k+1}=f_{\theta_{k+1}}(x_{k})$ with each $\theta _{k+1}$ picked from a…
We consider the mass-supercritical, defocusing, nonlinear Schr{\"o}dinger equation. We prove loss of regularity in arbitrarily short times for regularized initial data belonging to a dense set of any fixed Sobolev space for which the…
In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…
We consider the problem of computing the Lebesgue volume of compact basic semi-algebraic sets. In full generality, it can be approximated as closely as desired by a converging hierarchy of upper bounds obtained by applying the Moment-SOS…
We study the pulsar timing properties and the data analysis methods during glitch recoveries. In some cases one first fits the time-of-arrivals (TOAs) to obtain the "time-averaged" frequency $\nu$ and its first derivative $\dot\nu$, and…
The formulation of the time-dependent Schrodinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced,…
We present a theoretical argument to derive a scaling law between the mean translocation time $\tau$ and the chain length $N$ for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions,…