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Wang F.-Y.,Beijing Normal University | Wang F.-Y.,University of Swansea | Xu L.,EURANDOM
Infinite Dimensional Analysis, Quantum Probability and Related Topics | Year: 2012

By using coupling method, a Bismut type derivative formula is established for the Markov semigroup associated to a class of hyperdissipative stochastic Navier-Stokes/Burgers equations. As applications, gradient estimates, dimension-free Harnack inequality, strong Feller property, heat kernel estimates and some properties of the invariant probability measure are derived. © 2012 World Scientific Publishing Company.


Ledovskikh A.,Eurandom | Danilov D.,TU Eindhoven | Vermeulen P.,TU Eindhoven | Notten P.H.L.,TU Eindhoven | Notten P.H.L.,Philips
Journal of the Electrochemical Society | Year: 2010

The recently presented electrochemical kinetic model, describing the electrochemical hydrogen storage in hydride-forming materials, was extended by the description of the solid/electrolyte interface, i.e., the charge-transfer kinetics and electrical double-layer charging. A complete set of equations was derived, describing the equilibrium hydrogen partial pressure, the equilibrium electrode potential, the exchange current density, and the electrical double-layer capacitance as a function of hydrogen content in both solid-solution and two-phase coexistence regions. The model was applied to simulate isotherms of Pd thin films with nominal thicknesses of 200 and 10 nm. The model demonstrates good agreement between the simulation results and experimental data. © 2010 The Electrochemical Society.


Ayesta U.,National Polytechnic Institute of Toulouse | Ayesta U.,CNRS Laboratory for Analysis and Architecture of Systems | Boxma O.J.,EURANDOM | Boxma O.J.,TU Eindhoven | And 2 more authors.
Queueing Systems | Year: 2012

We study an M/G/1 processor sharing queue with multiple vacations. The server only takes a vacation when the system has become empty. If he finds the system still empty upon return, he takes another vacation, and so on. Successive vacations are identically distributed, with a general distribution. When the service requirements are exponentially distributed we determine the sojourn time distribution of an arbitrary customer. We also show how the same approach can be used to determine the sojourn time distribution in an M/M/1-PS queue of a polling model, under the following constraints: the service discipline at that queue is exhaustive service, the service discipline at each of the other queues satisfies a so-called branching property, and the arrival processes at the various queues are independent Poisson processes. For a general service requirement distribution we investigate both the vacation queue and the polling model, restricting ourselves to the mean sojourn time. © 2012 The Author(s).


Ravid R.,Haifa University | Ravid R.,ORT Braude College | Boxma O.J.,EURANDOM | Boxma O.J.,TU Eindhoven | Perry D.,Haifa University
Queueing Systems | Year: 2013

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according to which backorders are satisfied by repaired items is the longest queue rule: At the completion of a service (repair), the repaired item is delivered to the base that has the largest number of failed items. We point out a direct relation between our model and the classical longer queue model. We obtain simple expressions for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. Finally, we derive the sojourn time distributions. © 2012 The Author(s).


den Hollander F.,Leiden University | Petrelis N.,EURANDOM
Journal of Mathematical Chemistry | Year: 2010

In this paper we review some recent results, obtained jointly with Stu Whittington, for a mathematical model describing a copolymer in an emulsion. The copolymer consists of hydrophobic and hydrophilic monomers, concatenated randomly with equal density. The emulsion consists of large blocks of oil and water, arranged in a percolation-type fashion. To make the model mathematically tractable, the copolymer is allowed to enter and exit a neighboring pair of blocks only at diagonally opposite corners. The energy of the copolymer in the emulsion is minus α times the number of hydrophobic monomers in oil minus β times the number of hydrophilic monomers in water. Without loss of generality we may assume that the interaction parameters are restricted to the cone {(α,β)∈ ℝ2: {pipe}β{pipe}≤α}. We show that the phase diagram has two regimes: (1) in the supercritical regime where the oil blocks percolate, there is a single critical curve in the cone separating a localized and a delocalized phase; (2) in the subcritical regime where the oil blocks do not percolate, there are three critical curves in the cone separating two localized phases and two delocalized phases, and meeting at two tricritical points. The different phases are characterized by different behavior of the copolymer inside the four neighboring pairs of blocks. © 2009 The Author(s).


den Hollander F.,Leiden University | Nardi F.R.,EURANDOM | Nardi F.R.,TU Eindhoven | Troiani A.,Leiden University
Journal of Statistical Physics | Year: 2012

This is the third in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature in a large finite box with an open boundary. Each pair of particles occupying neighboring sites has a negative binding energy provided their types are different, while each particle has a positive activation energy that depends on its type. There is no binding energy between particles of the same type. At the boundary of the box particles are created and annihilated in a way that represents the presence of an infinite gas reservoir. We start the dynamics from the empty box and are interested in the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box. In the first paper we identified the parameter range for which the system is metastable, showed that the first entrance distribution on the set of critical droplets is uniform, computed the expected transition time up to and including a multiplicative factor of order one, and proved that the nucleation time divided by its expectation is exponentially distributed, all in the limit of low temperature. These results were proved under three hypotheses, and involved three model-dependent quantities: the energy, the shape and the number of critical droplets. In the second paper we proved the first and the second hypothesis and identified the energy of critical droplets. In the third paper we prove the third hypothesis and identify the shape and the number of critical droplets, thereby completing our analysis. Both the second and the third paper deal with understanding the geometric properties of subcritical, critical and supercritical droplets, which are crucial in determining the metastable behavior of the system, as explained in the first paper. The geometry turns out to be considerably more complex than for Kawasaki dynamics with one type of particle, for which an extensive literature exists. The main motivation behind our work is to understand metastability of multi-type particle systems. © 2012 Springer Science+Business Media New York.


Nardi F.R.,EURANDOM | Nardi F.R.,TU Eindhoven | Spitoni C.,Leiden University
Journal of Statistical Physics | Year: 2012

In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i. e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an exponential random variable and that the rate of the exponential random variable is an exponential function of the inverse temperature β times a prefactor that does not scale with β. Our approach combines geometric and potential theoretic arguments. © 2011 Springer Science+Business Media, LLC.


Van De Ven P.M.,TU Eindhoven | Janssen A.J.E.M.,EURANDOM | Van Leeuwaarden J.S.H.,TU Eindhoven | Borst S.C.,TU Eindhoven | Borst S.C.,Alcatel - Lucent
Performance Evaluation | Year: 2011

Random-access algorithms such as CSMA provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, tractable stochastic models have been shown to yield accurate throughput estimates for CSMA networks. We consider a saturated random-access network on a general conflict graph, and prove that for every feasible combination of throughputs, there exists a unique vector of back-off rates that achieves this throughput vector. This result entails proving global invertibility of the non-linear function that describes the throughputs of all nodes in the network. We present several numerical procedures for calculating this inverse, based on fixed-point iteration and Newton's method. Finally, we provide closed-form results for several special conflict graphs using the theory of Markov random fields. © 2011 Elsevier B.V. All rights reserved.


den Hollander F.,Leiden University | Nardi F.R.,EURANDOM | Nardi F.R.,TU Eindhoven | Troiani A.,Leiden University
Journal of Statistical Physics | Year: 2011

This is the second in a series of three papers in which we study a two-dimensional lattice gas consisting of two types of particles subject to Kawasaki dynamics at low temperature in a large finite box with an open boundary. Each pair of particles occupying neighboring sites has a negative binding energy provided their types are different, while each particle has a positive activation energy that depends on its type. There is no binding energy between particles of the same type. At the boundary of the box particles are created and annihilated in a way that represents the presence of an infinite gas reservoir. We start the dynamics from the empty box and are interested in the transition time to the full box. This transition is triggered by a critical droplet appearing somewhere in the box. In the first paper we identified the parameter range for which the system is metastable, showed that the first entrance distribution on the set of critical droplets is uniform, computed the expected transition time up to and including a multiplicative factor of order one, and proved that the nucleation time divided by its expectation is exponentially distributed, all in the limit of low temperature. These results were proved under three hypotheses, and involve three model-dependent quantities: the energy, the shape and the number of critical droplets. In the second paper we prove the first and the second hypothesis and identify the energy of critical droplets. In the third paper we settle the rest. Both the second and the third paper deal with understanding the geometric properties of subcritical, critical and supercritical droplets, which are crucial in determining the metastable behavior of the system, as explained in the first paper. The geometry turns out to be considerably more complex than for Kawasaki dynamics with one type of particle, for which an extensive literature exists. The main motivation behind our work is to understand metastability of multi-type particle systems. © 2011 The Author(s).

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