Simulation of large deviation functions using population dynamics

In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation functions and their simulations, we review the method of Giardin\`a \emph{et al.} for discrete time processes and that of Lecomte \emph{et al.} for the continuous time counterpart. Last we explain how these methods can be modified to handle static observables and extract information about intermediate times.Comment: Proceedings of the 10th Granada Seminar on Computational and Statistical Physic

On the Role of Interfacial Reactions, Dissolution and Secondary Precipitation During the Laser Additive Manufacturing of Metal Matrix Composites: A Review

Since current trends in the transportation, energy or mechanical industries impose increasingly demanding service conditions for metallic parts, metal matrix composites (MMCs) are the object of a growing interest. Powder-based laser additive manufacturing, which allows making parts with complex shapes, appears particularly adapted for the production of MMCs. This paper reviews the current state-of-the-art in the production of MMCs by additive processes, with the aim of assessing the potentials and difficulties offered by these techniques. Two main processing routes are envisaged, i.e. (1) the processing of ex situ composites in which the reinforcing phase as a powder—often of ceramic particles—is directly mixed with the powder of the matrix alloy, and both powders are simultaneously processed by the laser. (2) Alternatively, the reinforcing phase can be produced in situ by a chemical reaction during the fabrication of the composite. For both processing routes, a careful control is needed to overcome challenges brought, e.g. by the behaviour of the reinforcement particles in the laser beam, by changes in laser absorptivity or by the dissolution of the reinforcing particles in the molten metal, in order to produce MMCs with enhanced usage properties

Using geophysics on a terminal moraine damming a glacial lake: the Flatbre debris flow case, Western Norway

A debris flow occurred on 8 May 2004, in Fjǽrland, Western Norway, due to a Glacial Lake Outburst Flood and a natural terminal moraine failure. The site was investigated in 2004 and 2005, using pre- and post-flow aerial photos, airborne laser scanning, and extensive field work investigations, resulting in a good understanding of the mechanics of the debris flow, with quantification of the entrainment and determination of the final volume involved. However, though the moraine had a clear weak point, with lower elevation and erosion due to overflowing in the melting season, the sudden rupture of the moraine still needs to be explained. As moraines often contain an ice core, a possible cause could be the melting of the ice, inducing a progressive weakening of the structure. Geophysical investigations were therefore carried out in September 2006, including seismic refraction, GPR and resistivity. All methods worked well, but none revealed the presence of ice, though the depth to bedrock was determined. On the contrary, the moraine appeared to be highly saturated in water, especially in one area, away from the actual breach and corresponding to observed water seepage at the foot of the moraine. To estimate future hazard, water circulation through the moraine should be monitored over time

Temperature-induced crossovers in the static roughness of a one-dimensional interface

At finite temperature and in presence of disorder, a one-dimensional elastic interface displays different scaling regimes at small and large lengthscales. Using a replica approach and a Gaussian Variational Method (GVM), we explore the consequences of a finite interface width $\xi$ on the small-lengthscale fluctuations. We compute analytically the static roughness $B(r)$ of the interface as a function of the distance $r$ between two points on the interface. We focus on the case of short-range elasticity and random-bond disorder. We show that for a finite width $\xi$ two temperature regimes exist. At low temperature, the expected thermal and random-manifold regimes, respectively for small and large scales, connect via an intermediate `modified' Larkin regime, that we determine. This regime ends at a temperature-independent characteristic `Larkin' length. Above a certain `critical' temperature that we identify, this intermediate regime disappears. The thermal and random-manifold regimes connect at a single crossover lengthscale, that we compute. This is also the expected behavior for zero width. Using a directed polymer description, we also study via a second GVM procedure and generic scaling arguments, a modified toy model that provides further insights on this crossover. We discuss the relevance of the two GVM procedures for the roughness at large lengthscale in those regimes. In particular we analyze the scaling of the temperature-dependent prefactor in the roughness B(r)\sim T^{2 \text{\thorn}} r^{2 \zeta} and its corresponding exponent \text{\thorn}. We briefly discuss the consequences of those results for the quasistatic creep law of a driven interface, in connection with previous experimental and numerical studies

Natural and projectively equivariant quantizations by means of Cartan Connections

The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas-Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an \sl(m+1,\R)-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.Comment: 13 page

Observation of resonance trapping in an open microwave cavity

The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. In this letter, the first direct experimental verification of this effect, known as resonance trapping, is presented. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.Comment: to be published in Phys. Rev. Let

Thermodynamics of histories for the one-dimensional contact process

The dynamical activity K(t) of a stochastic process is the number of times it changes configuration up to time t. It was recently argued that (spin) glasses are at a first order dynamical transition where histories of low and high activity coexist. We study this transition in the one-dimensional contact process by weighting its histories by exp(sK(t)). We determine the phase diagram and the critical exponents of this model using a recently developed approach to the thermodynamics of histories that is based on the density matrix renormalisation group. We find that for every value of the infection rate, there is a phase transition at a critical value of s. Near the absorbing state phase transition of the contact process, the generating function of the activity shows a scaling behavior similar to that of the free energy in an equilibrium system near criticality.Comment: 16 pages, 7 figure

Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems

Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional points are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. In the present paper this parameter is the coupling strength to the continuum. It is shown that the positions of the exceptional points (their accumulation point in the thermodynamical limit) depend on the particular type and energy dependence of the coupling to the continuum in the same way as the transition point of the corresponding phase transition.Comment: 22 pages, 4 figure