A fluid system with coupled input and output,and its application to bottlenecks in ad hoc networks

This paper studies a fluid queue with coupled input and output. Flows arrive according to a Poisson process, and when n flows are present, each of them transmits traffic into the queue at a rate c/(n+1), where the remaining c/(n+1) is used to serve the queue. We assume exponentially distributed flow sizes, so that the queue under consideration can be regarded as a system with Markov fluid input. The rationale behind studying this queue lies in ad hoc networks: bottleneck links have roughly this type of sharing policy. We consider four performance metrics: (i) the stationary workload of the queue, (ii) the queueing delay, i.e., the delay of a ‘packet’ (a fluid particle) that arrives at the queue at an arbitrary point in time, (iii) the flow transfer delay, i.e., the time elapsed between arrival of a flow and the epoch that all its traffic has been put into the queue, and (iv) the sojourn time, i.e., the flow transfer time increased by the time it takes before the last fluid particle of the flow is served. For each of these random variables we compute the Laplace transform. The corresponding tail probabilities decay exponentially, as is shown by a large-deviations analysis. F. Roijers’ work has been carried out partly in the SENTER-NOVEM funded project Easy Wireless.     

On Certain Perturbations of the Erdös–Renyi Random Graph

We study perturbations of the Erdös–Renyi model for which the statistical weight of a graph depends on the abundance of certain geometrical patterns. Using the formal correspondance with an exactly solvable effective model, we show the existence of a percolation transition in the thermodynamical limit and derive perturbatively the expression of the threshold. The free energy and the moments of the degree distribution are also computed perturbatively in that limit and the percolation criterion is compared with the Molloy–Reed criterion.     

On Guerra's broken replica-symmetry bound

Consider a random Hamiltonian $\text{H}{}_{\mathrm{N}}\text{(}\text{σ}\text{→}\text{)}$ for $\text{σ}\text{→}\text{∈Σ}{}_{\mathrm{N}}\text{={0,1}}{}^{\mathrm{<mtext>N</mtext>}}\text{.}$ We assume that the family $\text{(H}{}_{\mathrm{N}}\text{(}\text{σ}\text{→}\text{))}$ is jointly Gaussian centered and that for $\text{σ}\text{→}{}^1\text{,}\text{σ}\text{→}{}^2\text{∈Σ}{}_{\mathrm{N}}\text{,}$$\text{N}{}^{\mathrm{?1}}\text{EH}{}_{\mathrm{N}}\text{(}\text{σ}\text{→}{}^1\text{)H}{}_{\mathrm{N}}\text{(}\text{σ}\text{→}{}^2\text{)}$ =ξ(N^?1∑_i?Nσ¹_iσ²_i) for a certain function ξ on $\text{R}$. F. Guerra proved the remarkable fact that the free energy of the system with Hamiltonian $\text{H}{}_{\mathrm{N}}\text{(}\text{σ}\text{→}\text{)+h∑}{}_{\mathrm{i?N}}\text{σ}{}_{\mathrm{i}}$ is bounded below by the free energy of the Parisi solution provided that ξ is convex on $\text{R}$. We prove that this fact remains (asymptotically) true when the function ξ is only assumed to be convex on $\text{R}{}^{\mathrm{+}}$. This covers in particular the case of the p-spin interaction model for any p. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.     

Towards the synthesis of MAX-phase functional coatings by pulsed laser deposition

Pulsed laser deposition with a Nd:YAG laser was used to grow thin films from a pre-synthesized Ti₃SiC₂ MAX-phase formulated ablation target on oxidized Si(1 0 0) and MgO(1 0 0) substrates. The depositions were carried out in a substrate temperature range from 300 to 900 K, and the pressure in the deposition chamber ranged from vacuum (10⁻⁵ Pa) to 0.05 Pa Argon background pressure. The properties of the films have been investigated by Rutherford backscattering spectrometry for film thickness and stoichiometric composition and X-ray diffraction for the crystallinity of the films. The silicon content of the films varied with the energy density of the laser beam. To suppress especially the silicon re-sputtering from the substrate, the energy of the incoming particles must be below a threshold of 20 eV. Therefore, the energy density of the laser beam must not be too high. At constant deposition energy density the film thickness depends strongly on the background pressure. The X-ray diffraction measurements show patterns that are typical of amorphous films, i.e. no Ti₃SiC₂ related reflections were found. Only a very weak TiC(2 0 0) reflection was seen, indicating the presence of a small amount of crystalline TiC.     

Perron's method for second order hyperbolic PDE. Part I

In parts I, II, and III combined of this paper, we define a notion of viscosity solution for these equations and existence is proved by a Perron-like method. Here, in part I, we prove useful identities, and a maximum-like principle for smooth sub(super) solutions of the standard wave equation. We define a new potential theoretic (P) notion of solution, subsolution and supersolution, and a related potential type (P) Cauchy problem for semilinear second order hyperbolic equations.     

Electron-stimulated desorption of D (H) from condensed D2O (H2O) films

The electron-stimulated desorption (ESD) of D⁻ and H⁻ ions from condensed D₂O and H₂O films is investigated. Three low-energy peaks are observed in the ESD anion yield, which are identified as arising from excitation of ²B₁, ²A₁ and ²B₂ dissociative electron attachment (DEA) resonances. Additional structure is observed between 18 and 32 eV, which may be due to ion pair formation or to DEA resonances involving the 2a₁ orbital. The ion yield resulting from excitation of the ²B₁ resonance increases as the film is heated. We attribute the increase in the ion yield to thermally induced hydrogen bond breaking near the surface, which enhances the lifetimes of the excited states that lead to desorption.