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Diffusion induced by Poissonian shocks: a concept inherent in a stochastic theory of wear

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  • Bezák, V.

Abstract

A class of one-dimensional diffusions is studied based on the equation q(τ) = -f0- f1(τ) where f0 > 0 is a (deterministic) constant and f1(τ) a stationary stochastic process defined by one-sided Poissonian shocks, f1(τ) = ΣQjδ(τ - τj), Qj⪰0, 0⪯τ⪯t. The amplitudes Qj are random, distributed with an arbitrary probability density S(Q). With q(t) = x, q(0) = x0, an explicit expression is derived for the probability density P(x,t¦x0). If q(τ) represents a variable characterising the quality of an object undergoing wear, the lifetime λ > 0 of the object is defined by the equation q(λ) = x. Here x < x0 is the lowest value of q still tolerable for the functioning of the object. Statistical properties of λ are studied (its mean, variance and probability density L(x, λ¦x0)). With two-sided Poissonian shocks distributed with a symmetric amplitude probability density, S(Q) = S(-Q), a new representation for the density matrix of quasiparticles with an arbitrary dispersion law E = E(k)⪰0 is indicated.

Suggested Citation

  • Bezák, V., 1994. "Diffusion induced by Poissonian shocks: a concept inherent in a stochastic theory of wear," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(1), pages 127-148.
    • Handle: RePEc:eee:phsmap:v:206:y:1994:i:1:p:127-148
    DOI: 10.1016/0378-4371(94)90121-X
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    References listed on IDEAS

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    1. van Kampen, N.G., 1979. "Composite stochastic processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 96(3), pages 435-453.
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