Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Antireflection of an absorbing substrate by an absorbing thin film at normal incidence

An absorbing substrate of complex refractive index n2 - jk2 at wavelength λ can be coated by an absorbing thin film of complex refractive index n1 - jk1 and thickness d to achieve zero reflection at normal incidence. For given n2,k2 multiple solutions (n1,k1,d/λ) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si substrate at two wavelengths (6328 and 4420 Å). The response of these absorbing antireflection layers to changes of the angle of incidence from 0 to 45° and to changes of thickness of ±10% is also determined and compared to the limting case of a nonabsorbing antireflection layer

Antireflection of an absorbing substrate by an absorbing thin film at normal incidence

An absorbing substrate of complex refractive index n2 - jk2 at wavelength λ can be coated by an absorbing thin film of complex refractive index n1 - jk1 and thickness d to achieve zero reflection at normal incidence. For given n2,k2 multiple solutions (n1,k1,d/λ) are found that correspond to infinitely many distinct antireflection layers. This is demonstrated for a Si substrate at two wavelengths (6328 and 4420 Å). The response of these absorbing antireflection layers to changes of the angle of incidence from 0 to 45° and to changes of thickness of ±10% is also determined and compared to the limting case of a nonabsorbing antireflection layer

Electrodeposition of In2S3 buffer layer for Cu(In,Ga)Se2 solar cells

AbstractThe electrochemical deposition of In2S3 thin films was carried out from an aqueous solution of InCl3 and Na2S2O3. The effect of the potential of deposition was studied on the cell parameters of CIGSe based solar cells. The obtained films depending on the deposition potential and thickness exhibited complete substrate coverage or nanocolumnar layers. XPS measurements detected the presence of indium sulphide and hydroxide depending on the deposition parameters. Maximum photoelectric conversion efficiency of 10.2% was obtained, limited mainly by a low fill factor (56%). Further process optimization is expected to lead to efficiencies comparable to CdS buffer layers

Tangling clustering of inertial particles in stably stratified turbulence

We have predicted theoretically and detected in laboratory experiments a new type of particle clustering (tangling clustering of inertial particles) in a stably stratified turbulence with imposed mean vertical temperature gradient. In this stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, that results in formation of a gradient of the mean particle number density, \nabla N, and generation of fluctuations of the particle number density by tangling of the gradient, \nabla N, by velocity fluctuations. The mean temperature gradient, \nabla T, produces the temperature fluctuations by tangling of the gradient, \nabla T, by velocity fluctuations. These fluctuations increase the rate of formation of the particle clusters in small scales. In the laboratory stratified turbulence this tangling clustering is much more effective than a pure inertial clustering that has been observed in isothermal turbulence. In particular, in our experiments in oscillating grid isothermal turbulence in air without imposed mean temperature gradient, the inertial clustering is very weak for solid particles with the diameter 10 microns and Reynolds numbers Re =250. Our theoretical predictions are in a good agreement with the obtained experimental results.Comment: 16 pages, 4 figures, REVTEX4, revised versio

Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on request), submitted to J. Phys. (A): Math. Ge

The topological structure of scaling limits of large planar maps

We discuss scaling limits of large bipartite planar maps. If p is a fixed integer strictly greater than 1, we consider a random planar map M(n) which is uniformly distributed over the set of all 2p-angulations with n faces. Then, at least along a suitable subsequence, the metric space M(n) equipped with the graph distance rescaled by the factor n to the power -1/4 converges in distribution as n tends to infinity towards a limiting random compact metric space, in the sense of the Gromov-Hausdorff distance. We prove that the topology of the limiting space is uniquely determined independently of p, and that this space can be obtained as the quotient of the Continuum Random Tree for an equivalence relation which is defined from Brownian labels attached to the vertices. We also verify that the Hausdorff dimension of the limit is almost surely equal to 4.Comment: 45 pages Second version with minor modification

Improvement of the Jet-Vectoring through the Suppression of a Global Instability

Abstract. : The behaviour of the near-field region of a vertical rectangular jet of aspect ratio 4:1 controlled by a rotating cylinder placed on the jet major-axis is investigated experimentally using a new design facility. The objective is to investigate flow control strategies of a rectangular jet based on instability manipulation. It is found experimentally that the controlled jet exhibits similar behaviour to the one described theoretically and numerically by Hammond & Redekopp (1997a, b) on bluff-body wakes with higher control efficiency when the global instability mode is suppressed

The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations

We describe a basic framework for studying dynamic scaling that has roots in dynamical systems and probability theory. Within this framework, we study Smoluchowski's coagulation equation for the three simplest rate kernels $K(x,y)=2$, $x+y$ and $xy$. In another work, we classified all self-similar solutions and all universality classes (domains of attraction) for scaling limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here we add to this a complete description of the set of all limit points of solutions modulo scaling (the scaling attractor) and the dynamics on this limit set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine representation formula for eternal solutions of Smoluchowski's equation (Adv. Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on the scaling attractor, revealing these dynamics to be conjugate to a continuous dilation, and chaotic in a classical sense. Furthermore, our study of scaling limits explains how Smoluchowski dynamics ``compactifies'' in a natural way that accounts for clusters of zero and infinite size (dust and gel)

Combinatorics of bicubic maps with hard particles

We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting of the maps. Although these trees have no simple local characterization, we prove that their enumeration may be performed upon introducing a larger class of "admissible" trees with possibly doubly-occupied edges and summing them with appropriate signed weights. The proof relies on an extension of the cutting procedure allowing for the presence on the maps of special non-sectile edges. The admissible trees are characterized by simple local rules, allowing eventually for an exact enumeration of planar bicubic maps with hard particles. We also discuss generalizations for maps with particles subject to more general exclusion rules and show how to re-derive the enumeration of quartic maps with Ising spins in the present framework of admissible trees. We finally comment on a possible interpretation in terms of branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction and discussion/conclusion extended, minor corrections, references adde