We consider a supply chain consisting of a sequence of buffer queues and processors with certain throughput times and capacities. Based on a simple rule for releasing parts, i.e. batches of product or individual product items, from the buffers into the processors we derive a hyperbolic conservation law for the part density and flux in the supply chain. The conservation law will be asymptoticall...

We consider a fractal scalar conservation law, that is to say, a conservation law modified by a fractional power of the Laplace operator, and we propose a numerical method to approximate its solutions. We make a theoretical study of the method, proving in the case of an initial data belonging to L∞ ∩ BV that the approximate solutions converge in L∞ weak-∗ and in Lp strong for p < ∞, and we give...

This paper illustrates an algorithm to generate a complex acoustic stimulus whose statistical properties are as close as possible to the non-stationary dynamics revealed by the current analysis of the electro-encephalogram activity of the human brain. Thus, the composition is driven by crucial events, namely renewal non-Poisson events with an inter-time distribution density ψ(τ ), which is an i...

Let ug the unique solution of a parabolic variational inequality of second kind, with a given g. Using a regularization method, we prove, for all g1 and g2, a monotony property between μug1 + (1 − μ)ug2 and uμg1+(1−μ)g2 for μ ∈ [0, 1]. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over g for each heat transfer coefficient h > 0, associated...

We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. We therefore investigate a sec...

Abstract. We investigate large deviations for a family of conservative stochastic PDEs (viscous conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The associated rate functional vanishes on a wide set, the so-called set of measure-valued solutions to the limiting conservation law. We therefore...

We show that Einstein’s gravitational field has zero energy, momentum, and stress. This conclusion follows directly from the gravitational field equations, in conjunction with the differential law of energy-momentum conservation T ;ν = 0. Einstein rejected this conservation law despite the fact that it is generally covariant. We trace his rejection to a misapplication of Gauss’ divergence formu...