Abstract In the supermarket model there are n queues, each with a unit rate server. Customers arrive in a Poisson process at rate λn, where 0 < λ < 1. Each customer chooses d ≥ 2 queues uniformly at random, and joins a shortest one. It is known that the equilibrium distribution of a typical queue length converges to a certain explicit limiting distribution as n→∞. We quantify the rate of conver...

Sharp temporal decay estimates are established for the gradient and time derivative of solutions to the Hamilton-Jacobi equation ∂tvε + H(|∇xvε|) = ε ∆vε in R × (0,∞), the parameter ε being either positive or zero. Special care is given to the dependence of the estimates on ε. As a by-product, we obtain convergence of the sequence (vε) as ε → 0 to a viscosity solution, the initial condition bei...

In this appendix we collect and describe mathematical results for first passage, boundaryless, and reflecting-boundary drift diffusion problems. We consider both diffusion and OrnsteinUhlenbeck (O-U) models. The main tools are drawn from applied probability, the theory of stochastic ordinary differential equations, and classical perturbation and asymptotic methods. Here we focus on continuous m...

A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipat...

An experiment for measuring self-filtration in terms of change in volume fraction downstream of a constriction compared to volume fraction upstream of said constriction was designed and tested. The user has the ability to control a variety of parameters including constriction geometry, flow rate, and initial volume fraction in order to evaluate their impact on downstream volume fraction. The re...

Abstract. A combined method for the simultaneous inclusion of complex zeros of a polynomial, composed of two circular arithmetic methods, is presented. This method does not use polynomial derivatives and has the order of convergence equals four. Computationally verifiable initial conditions that guarantee the convergence are also stated. Two numerical example are included to demonstrate the con...

Consider a difference equation which takes the k-th largest output of m functions of the previousm terms of the sequence. If the functions are also allowed to change periodically as the difference equation evolves, this is analogous to a differential equation with periodic forcing. A large class of such non-autonomous difference equations are shown to converge to a periodic limit, which is inde...

We establish rates of convergence of solutions to scaling (or similarity) profiles in a coagulation type system modelling submonolayer deposition. We prove that, although all memory of the initial condition is lost in the similarity limit, information about the large cluster tail of the initial condition is preserved in the rate of approach to the similarity profile. The proof relies in a chang...

This paper reports the results of experimentally removing ammonia from synthetically prepared ammonia solution using a micro scale mixing loop air stripper. Effects of various operational parameters (such as: pH, air flow rate, wastewater flow rate and initial ammonia concentration) were evaluated. By increasing the pH from 10 to 12.25 the amount of KLa increased from 0.26 to 0.73 hr-1. A consi...

The three-point correlation function of cosmological fluctuations is a sensitive probe of the physics of inflation. We calculate the bispectrum, Bg(k1, k2, k3), Fourier transform of the three-point function of density peaks (e.g., galaxies), using the Matarrese-Lucchin-Bonometto formula. The bispectrum of peaks is not only sensitive to that of the underlying matter density fluctuations, but als...