116,015 research outputs found
Stochastic comparisons of series and parallel systems with randomized independent components
Consider a series or parallel system of independent components and assume that the components are randomly chosen from two different batches, with the components of the first batch being more reliable than those of the second. In this note it is shown that the reliability of the system increases, in usual stochastic order sense, as the random number of components chosen from the first batch increases in increasing convex order. As a consequence, we establish a result analogous to the Parrondo's paradox, which shows that randomness in the number of components extracted from the two batches improves the reliability of the series syste
Computational and Mathematical Modelling of the EGF Receptor System
This chapter gives an overview of computational and mathematical modelling of the EGF receptor system. It begins with a survey of motivations for producing such models, then describes the main approaches that are taken to carrying out such modelling, viz. differential equations and individual-based modelling. Finally, a number of projects that applying modelling and simulation techniques to various aspects of the EGF receptor system are described
Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems
In "equation-free" multiscale computation a dynamic model is given at a fine,
microscopic level; yet we believe that its coarse-grained, macroscopic dynamics
can be described by closed equations involving only coarse variables. These
variables are typically various low-order moments of the distributions evolved
through the microscopic model. We consider the problem of integrating these
unavailable equations by acting directly on kinetic Monte Carlo microscopic
simulators, thus circumventing their derivation in closed form. In particular,
we use projective multi-step integration to solve the coarse initial value
problem forward in time as well as backward in time (under certain conditions).
Macroscopic trajectories are thus traced back to unstable, source-type, and
even sometimes saddle-like stationary points, even though the microscopic
simulator only evolves forward in time. We also demonstrate the use of such
projective integrators in a shooting boundary value problem formulation for the
computation of "coarse limit cycles" of the macroscopic behavior, and the
approximation of their stability through estimates of the leading "coarse
Floquet multipliers".Comment: Submitted to Journal of Computational Physic
Disagreement between correlations of quantum mechanics and stochastic electrodynamics in the damped parametric oscillator
Intracavity and external third order correlations in the damped nondegenerate
parametric oscillator are calculated for quantum mechanics and stochastic
electrodynamics (SED), a semiclassical theory. The two theories yield greatly
different results, with the correlations of quantum mechanics being cubic in
the system's nonlinear coupling constant and those of SED being linear in the
same constant. In particular, differences between the two theories are present
in at least a mesoscopic regime. They also exist when realistic damping is
included. Such differences illustrate distinctions between quantum mechanics
and a hidden variable theory for continuous variables.Comment: accepted by PR
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