Related papers: Validity of the Brunet-Derrida formula for the spe…
We study the effect of a cut-off on the speed of pulled fronts of the one dimensional reaction diffusion equation. We prove rigorous upper and lower bounds on the speed in terms of the cut-off parameter epsilon. From these bounds we…
We study the effect of a small cutoff $\epsilon$ on the velocity of a pulled front in one dimension by means of a variational principle. We obtain a lower bound on the speed dependent on the cutoff, and for which the two leading order terms…
We study the change in the speed of pushed and bistable fronts of the reaction diffusion equation in the presence of a small cut-off. We give explicit formulas for the shift in the speed for arbitrary reaction terms f(u). The dependence of…
The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts…
We analyze the dynamics of pattern forming fronts which propagate into an unstable state, and whose dynamics is of the pulled type, so that their asymptotic speed is equal to the linear spreading speed v^*. We discuss a method that allows…
We analyze the transition between pulled and pushed fronts both analytically and numerically from a model-independent perspective. Based on minimal conceptual assumptions, we show that pushed fronts bifurcate from a branch of pulled fronts…
We give an explicit formula for the change of speed of pushed and bistable fronts of the reaction diffusion equation when a small cutoff is applied at the unstable or metastable equilibrium point. The results are valid for arbitrary…
We establish two integral variational principles for the spreading speed of the one dimensional reaction diffusion equation with Stefan boundary conditions. The first principle is valid for monostable reaction terms and the second principle…
Fronts that start from a local perturbation and propagate into a linearly unstable state come in two classes: pulled and pushed. ``Pulled'' fronts are ``pulled along'' by the spreading of linear perturbations about the unstable state, so…
We establish an exact formula for the average number of edges appearing on the boundary of the global convex hull of n independent Brownian paths in the plane. This requires the introduction of a counting criterion which amounts to "cutting…
This article establishes cutoff convergence or abrupt convergence of three statistical quantities for multivariate (Hurwitz) stable geometric Brownian motion: the autocorrelation function, the Wasserstein distance between the current state…
We establish selection of critical pulled fronts in invasion processes. Our result shows convergence to a pulled front with a logarithmic shift for open sets of steep initial data, including one-sided compactly supported initial conditions.…
Cut-set bounds on achievable rates for network communication protocols are not in general tight. In this paper we introduce a new technique for proving converses for the problem of transmission of correlated sources in networks, that…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
Contraction properties of the Riccati operator are studied within the context of non-stationary linear-quadratic optimal control. A lifting approach is used to obtain a bound on the rate of strict contraction, with respect to the Riemannian…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this…
We consider the problem of the speed selection mechanism for the one dimensional nonlinear diffusion equation $u_t = u_{xx} + f(u)$. It has been rigorously shown by Aronson and Weinberger that for a wide class of functions $f$, sufficiently…
We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…