Hydrodynamic Limit of Gradient Exclusion Processes with Conductances

Fix a strictly increasing right continuous with left limits function ${W: \mathbb{R} \to \mathbb{R}}Fix a strictly increasing right continuous with left limits function W: \mathbbR ? \mathbbR{W: \mathbb{R} \to \mathbb{R}} and a smooth function F: [l,r] ? \mathbb R{\Phi : [l,r] \to \mathbb R}, defined on some interval [l, r] of \mathbb R{\mathbb R}, such that 0 < b\leqq F￠\leqq b^-1{0 < b\leqq \Phi'\leqq b^{-1}}. On the diffusive time scale, the evolution of the empirical density of exclusion processes with conductances given by W is described by the unique weak solution of the non-linear differential equation ?_t r = (d/dx)(d/dW) F(r){\partial_t \rho = ({\rm d}/{\rm d}x)({\rm d}/{\rm d}W) \Phi(\rho)}. We also present some properties of the operator (d/dx)(d/dW).     

Study of Frozen Waves’ theory through a continuous superposition of Bessel beams

This paper presents a study of a recent solution to Maxwell's equation, the so-called “Frozen Waves”, whose main characteristics are to remain static in space, and to keep an arbitrary longitudinal field pattern previously chosen. These waves could be obtained by an adequate, but discrete, superposition of monochromatic Bessel beams. Contrary to that, we have here proposed a new way to get these waves through a continuous superposition of Bessel beams, and discussed some physical aspects and then exemplified for both loss and lossless media.     

Occupation Time of Exclusion Processes with Conductances

We obtain the fluctuations for the occupation time of one-dimensional symmetric exclusion processes with speed change, where the transition rates (conductances) are driven by a general function \(W\) . The approach does not require sharp bounds on the spectral gap of the system nor the jump rates to be bounded from above or below. We present some examples and for one of them, we observe that the fluctuations of the current are trivial, but the fluctuations of the occupation time are given by a fractional Brownian Motion. This shows that, in general, the fluctuations of the current and of the occupation time are not of same order.     

A Particle System with Explosions: Law of Large Numbers for the Density of Particles and the Blow-Up Time

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a strong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation ? _t u=? _xx u+f(u). If f(u)=u ^p , 1<p??3, we also obtain a law of large numbers for the explosion time.     

A simple model for maser action obtained through a magnetic tunnel junction placed inside a resonant cavity

Magnetic tunnel junctions are currently being used in magnetoresistive reading heads, magnetic field sensors and MRAMs, due to its giant magnetoresistance effect whose roots are linked to strong spin-dependent scattering mechanisms. The existence of spin-polarized currents in such devices posed us the question over the possibility to generate coherent microwave radiation in a spin inverted population medium, maintained through a spin-polarized current. In this paper we investigate the possibility of obtaining a maser effect considering a magnetic tunnel junction placed inside a resonant cavity. We put forward a simple model based on phenomenological rate equations, being the spin-polarized currents determined by the physics of the magnetic tunnel junction.     

Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion

We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $\alpha ∕n$ or $(1?\alpha )∕n$ (resp. $\beta ∕n$ or $(1?\beta )∕n$) where $\alpha ,\beta >0$ and $n$ is a scaling parameter. We obtain the non-equilibrium fluctuations and from the latter we obtain also the non-equilibrium stationary fluctuations.     

Instrumented Indentation of Carbides in a Martensitic Matrix and in a Sintered Sample

Niobium carbide (NbC) has high wear and corrosion resistance and retains these characteristics at high temperatures. In industrial applications, as well as in academia, NbC can be found in various configurations, such as carbides dispersed in the microstructure of steel or as sintered components. The aim of this study is to use the instrumented indentation (nanoindentation) technique to evaluate the properties of carbides present in the martensitic matrix of a cast steel or as a sintered specimen. In the case of the cast alloy, the sample had an MC-type carbide volume fraction of approximately 5%. In the second case, the NbC specimen was sintered using spark-plasma sintering (SPS). Additional specimen characterization was conducted using X-ray diffraction (XRD) and scanning electron microscopy (SEM) with energy-dispersive X-ray spectroscopy (EDX). Nanoindentation analyses were conducted with loads up to 10 mN, allowing hardness impressions with dimensions significantly smaller than the size of the carbides in the cast specimens. The results indicated relatively uniform values of 22 GPa and 348 GPa for the hardness and reduced elastic modulus of the sintered specimen, respectively. The EDX analysis results of the cast specimen indicated that the MC-type carbides had regions with different chemical compositions. Differences in the carbide chemical compositions were also observed when different regions of the cast specimen were compared. Nevertheless, similar properties were obtained in all regions, with a trend for the carbides in the cast specimen to present a higher hardness and lower modulus than those in the sintered specimen.     

Phase transition in equilibrium fluctuations of symmetric slowed exclusion

We analyze the equilibrium fluctuations of density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow bond where it is αn^−β$\alpha n^{-\beta }$, with α>0$\alpha >0$, β∈[0,+∞]$\beta \in [0,+\infty ]$ and n$n$ is the scaling parameter. Depending on the regime of β$\beta$, we find three different behaviors for the limiting fluctuations whose covariances are explicitly computed. In particular, for the critical value β=1$\beta =1$, starting a tagged particle near the slow bond, we obtain a family of Gaussian processes indexed in α$\alpha$, interpolating a fractional Brownian motion of Hurst exponent 1/4$1/4$ and the degenerate process equal to zero.     

Crossover to the Stochastic Burgers Equation for the WASEP with a Slow Bond

We consider the weakly asymmetric simple exclusion process in the presence of a slow bond and starting from the invariant state, namely the Bernoulli product measure of parameter \({\rho \in (0,1)}\). The rate of passage of particles to the right (resp. left) is \({\frac{1}{2} + \frac{a}{2n^{\gamma}}}\) (resp. \({\frac{1}{2} - \frac{a}{2n^{\gamma}}}\)) except at the bond of vertices \({\{-1,0\}}\) where the rate to the right (resp. left) is given by \({\frac{\alpha}{2n^\beta} + \frac{a}{2n^{\gamma}}}\) (resp. \({\frac{\alpha}{2n^\beta}-\frac{a}{2n^{\gamma}}}\)). Above, \({\alpha > 0}\), \({\gamma \geq \beta \geq 0}\), \({a\geq 0}\). For \({\beta < 1}\), we show that the limit density fluctuation field is an Ornstein–Uhlenbeck process defined on the Schwartz space if \({\gamma > \frac{1}{2}}\), while for \({\gamma = \frac{1}{2}}\) it is an energy solution of the stochastic Burgers equation. For \({\gamma \geq \beta =1}\), it is an Ornstein–Uhlenbeck process associated to the heat equation with Robin’s boundary conditions. For \({\gamma \geq \beta > 1}\), the limit density fluctuation field is an Ornstein–Uhlenbeck process associated to the heat equation with Neumann’s boundary conditions.