Random walks in Dirichlet environment: an overview

Random Walks in Dirichlet Environment (RWDE) correspond to Random Walks in Random Environment (RWRE) on $\Bbb{Z}^d$ where the transition probabilities are i.i.d. at each site with a Dirichlet distribution. Hence, the model is parametrized by a family of positive weights $(\alpha_i)_{i=1, \ldots, 2d}$, one for each direction of $\Bbb{Z}^d$. In this case, the annealed law is that of a reinforced random walk, with linear reinforcement on directed edges. RWDE have a remarkable property of statistical invariance by time reversal from which can be inferred several properties that are still inaccessible for general environments, such as the equivalence of static and dynamic points of view and a description of the directionally transient and ballistic regimes. In this paper we give a state of the art on this model and several sketches of proofs presenting the core of the arguments. We also present new computation of the large deviation rate function for one dimensional RWDE.Comment: 35 page

Catalytic CVD Synthesis of Double and Triple-walled Carbon Nanotubes by the Control of the Catalyst Preparation

We report the influence of catalyst preparation conditions for the synthesis of carbon nanotubes (CNTs) by catalytic chemical vapour deposition (CCVD). Catalysts were prepared by the combustion route using either urea or citric acid as the fuel. We found that the milder combustion conditions obtained in the case of citric acid can either limit the formation of carbon nanofibres (defined as carbon structures not composed of perfectly co-axial walls or only partially tubular) or increase the selectivity of the CCVD synthesis towards CNTs with fewer walls, depending on the catalyst composition. It is thus for example possible in the same CCVD conditions to prepare (with a catalyst of identical chemical composition) either a sample containing more than 90% double- and triple-walled CNTs, or a sample containing almost 80% double-walled CNTs

The weight and density of carbon nanotubes versus the number of walls and diameter

The weight and density of carbon nanotubes are calculated as a function of their characteristics (inner diameter, outer diameter, and number of walls). The results are reported in the form of diagrams which may be useful to other researchers, in particular in the fields of synthesis/production, materials and composites, health/toxicity studies

Curvature singularity and film-skating during drop impact

We study the influence of the surrounding gas in the dynamics of drop impact on a smooth surface. We use an axisymmetric 3D model for which both the gas and the liquid are incompressible; lubrication regime applies for the gas film dynamics and the liquid viscosity is neglected. In the absence of surface tension a finite time singularity whose properties are analysed is formed and the liquid touches the solid on a circle. When surface tension is taken into account, a thin jet emerges from the zone of impact, skating above a thin gas layer. The thickness of the air film underneath this jet is always smaller than the mean free path in the gas suggesting that the liquid film eventually wets the surface. We finally suggest an aerodynamical instability mechanism for the splash.Comment: 5 figure

Collateral and Adverse Selection in Transition Countries

This paper tackles the question of knowing whether collateral helps solve adverse selection problems in transition countries. We use a unique dataset of about 400 bank loans from 16 transition countries. Our findings support the view of a positive link between the presence of collateral and the risk premium, which is in accordance with the observed-risk hypothesis. This suggests that collateral does not mitigate adverse selection problems in transition countries.Bank, collateral, transition economies.

Lanthanides extraction processes in molten fluoride media. Application to nuclear spent fuel reprocessing

This paper describes four techniques of extraction of lanthanides elements (Ln) from molten salts in the general frame of reprocessing nuclear wastes; One of them is chemical: the precipitation of Ln ions in insoluble compounds (oxides or oxifluorides); the others use electrochemical methodology in molten fluorides for extraction and measurement of the progress of the processes: first electrodeposition of pure Ln metals on an inert cathode material was proved to be incomplete and cause problems for recovering the metal; electrodeposition of Ln in the form of alloys seems to be far more promising because on one hand the low activity of Ln shifts the electrodeposition potential in a more anodic range avoiding any overlapping with the solvent reduction and furthermore exhibit rapid process kinetics; two ways were examined: (i) obtention of alloys by reaction of the electroreducing Ln and the cathode in Ni or preferably in Cu, because in this case we obtain easily liquid compounds, that enhances sensibly the process kinetics; (ii) codeposition of Ln ions with aluminium ions on an inert cathode giving a well defined composition of the alloy. Each way was proved to give extraction efficiency close to unity in a moderate time

Building self-optimized communication systems based on applicative cross-layer information

This article proposes the Implicit Packet Meta Header(IPMH) as a standard method to compute and represent common QoS properties of the Application Data Units (ADU) of multimedia streams using legacy and proprietary streams’ headers (e.g. Real-time Transport Protocol headers). The use of IPMH by mechanisms located at different layers of the communication architecture will allow implementing fine per-packet selfoptimization of communication services regarding the actual application requirements. A case study showing how IPMH is used by error control mechanisms in the context of wireless networks is presented in order to demonstrate the feasibility and advantages of this approach

Stable fluctuations for ballistic random walks in random environment on Z

We consider transient random walks in random environment on Z in the positive speed (ballistic) and critical zero speed regimes. A classical result of Kesten, Kozlov and Spitzer proves that the hitting time of level $n$, after proper centering and normalization, converges to a completely asymmetric stable distribution, but does not describe its scale parameter. Following a previous article by three of the authors, where the (non-critical) zero speed case was dealt with, we give a new proof of this result in the subdiffusive case that provides a complete description of the limit law. The case of Dirichlet environment turns out to be remarkably explicit

Mechanical behavior of entangled fibers and entangled cross-linked fibers during compression

Entangled fibrous materials have been manufactured from different fibers: metallic fibers, glass fibers, and carbon fibers. Specimens have been produced with and without cross links between fibers. Cross-links have been achieved using epoxy spraying. The scope of this article is to analyze the mechanical behavior of these materials and to compare it with available models. The first part of this article deals with entangled fibrous materials without crosslink between fibers. Compression tests are detailed and test reproducibility is checked. In the second part, compression tests were performed on materials manufactured with cross-linked fibers. The specific mechanical behavior obtained is discussed