Metastability for the contact process on the preferential attachment graph

We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an arbitrarily small infection rate $\lambda$ with positive probability. More precisely, they showed that with probability $\lambda^{\Theta (1)}$, it survives for a time exponential in the largest degree. Here we obtain sharp bounds for the density of infected sites at a time close to exponential in the number of vertices (up to some logarithmic factor).Comment: 45 pages; accepted for publication in Internet Mathematic

Contact process on one-dimensional long-range percolation

Recently, by introducing the notion of cumulatively merged partition, M\'enard and Singh provide a sufficient condition on graphs ensuring that the critical value of the contact process is positive. In this note, we show that the one-dimensional long range percolation with high exponent satisfies their condition and thus the contact process exhibits a non-trivial phase transition.Comment: 11 p in Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 201

Super-exponential extinction time of the contact process on random geometric graphs

In this paper, we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connecting radius tending to infinity. We obtain that for any infection rate $\lambda >0$, the contact process on these graphs survives a time super-exponential in the number of vertices.Comment: Accepted for publication in Combinatorics, Probability and Computin

Metastability for the contact process on the configuration model with infinite mean degree

We study the contact process on the configuration model with a power law degree distribution, when the exponent is smaller than or equal to two. We prove that the extinction time grows exponentially fast with the size of the graph and prove two metastability results. First the extinction time divided by its mean converges in distribution toward an exponential random variable with mean one, when the size of the graph tends to infinity. Moreover, the density of infected sites taken at exponential times converges in probability to a constant. This extends previous results in the case of an exponent larger than $2$ obtained in \cite{CD,MMVY,MVY}.Comment: Proposition 6.2 replaced by a weaker version (after a gap in its proof was mentioned to us by Daniel Valesin). Does not affect the two main theorems of the pape

Nakayama automorphisms of double Ore extensions of Koszul regular algebras

Let $A$ be a Koszul Artin-Schelter regular algebra and $\sigma$ an algebra homomorphism from $A$ to $M_{2\times 2}(A)$. We compute the Nakayama automorphisms of a trimmed double Ore extension $A_P[y_1, y_2; \sigma]$ (introduced in \cite{ZZ08}). Using a similar method, we also obtain the Nakayama automorphism of a skew polynomial extension $A[t; \theta]$, where $\theta$ is a graded algebra automorphism of $A$. These lead to a characterization of the Calabi-Yau property of $A_P[y_1, y_2; \sigma]$, the skew Laurent extension $A[t^{\pm 1}; \theta]$ and $A[y_1^{\pm 1}, y_2^{\pm 1}; \sigma]$ with $\sigma$ a diagonal type.Comment: The paper has been heavily revised including the title, and will appear in Manuscripta Mathematic

Exploring the use of mobile sensors for noise and black carbon measurements in an urban environment

Mobile measurements have been collected on a bicycle equipped with a global positioning system (GPS) in a few connecting streets in Gent (Belgium). The 1-s sound pressure levels and 1-s black carbon concentrations were measured. In addition, 5 continuous monitoring fixed stations connected to building facades were used. Different processing methods are compared, based on different temporal and spatial weighting aggregations. The possibility to take profit of the fixed stations to refine estimations is tested, according to the noise levels collected at fixed stations and the distance between mobile and fixed sensors. In a last step, route selection based on travel distance, noise levels and black-carbon measurements is explored based on the data obtained

Sensitivity of combustion driven damage mechanisms to instability

A multi-disciplinary framework is developed to evaluate the damage on gas turbine engine liners including interrelated sub-domains such as combustion dynamics, stress, modal, fracture mechanics analyses and life assessment. Comparative operation conditions for the combustion dynamics have been investigated. Excessive vibrations induced by the limit cycle operation resulted in mechanical stresses and strains on the structure. The structural integrity of both the intact and damaged test specimens have been monitored by vibration-based and thermal-based techniques during the combustion operation. The progressive damage on the damaged specimen configuration has been analyzed and linked to the combustion driven mechanisms. Damage evaluation, life assessment and physical experimental approaches have been integrated and utilized to evaluate the fatigue dominant damage in combustion liner material. This study addresses a reference in ensuring the safety and reliability of gas turbine engine combustors. The outcome provides a better understanding and a quantification of the material damage progress and the component behavior in terms of life consumption and combustion dynamics

Damage evolution by using the near-tip fields of a crack in gas turbine liners

A residual lifetime prediction study has been performed on a combustion liner metallic material exposed to elevated temperatures by simulating the evolution of plastic work fields at a crack tip under monotonically loading. The strain and stress distribution has been computed by finite element analysis. The method gives a measure of the metal degradation and enables to evaluate the failure limit of a progressive damage under the operating conditions of gas turbine components. The study allows making a correlation between the progress of damage of a combustion liner and the loading conditions, the material type and the geometry of a specimen by the parametric design construction