Asymptotics of self-similar solutions to coagulation equations with product kernel

We consider mass-conserving self-similar solutions for Smoluchowski's coagulation equation with kernel $K(\xi,\eta)= (\xi \eta)^{\lambda}$ with $\lambda \in (0,1/2)$. It is known that such self-similar solutions $g(x)$ satisfy that $x^{-1+2\lambda} g(x)$ is bounded above and below as $x \to 0$. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function $h(x)=h_{\lambda} x^{-1+2\lambda} g(x)$ in the limit $\lambda \to 0$. It turns out that $h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)$ as $x \to 0$. As $x$ becomes larger $h$ develops peaks of height $1/\lambda$ that are separated by large regions where $h$ is small. Finally, $h$ converges to zero exponentially fast as $x \to \infty$. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE

Parallel Excluded Volume Tempering for Polymer Melts

We have developed a technique to accelerate the acquisition of effectively uncorrelated configurations for off-lattice models of dense polymer melts which makes use of both parallel tempering and large scale Monte Carlo moves. The method is based upon simulating a set of systems in parallel, each of which has a slightly different repulsive core potential, such that a thermodynamic path from full excluded volume to an ideal gas of random walks is generated. While each system is run with standard stochastic dynamics, resulting in an NVT ensemble, we implement the parallel tempering through stochastic swaps between the configurations of adjacent potentials, and the large scale Monte Carlo moves through attempted pivot and translation moves which reach a realistic acceptance probability as the limit of the ideal gas of random walks is approached. Compared to pure stochastic dynamics, this results in an increased efficiency even for a system of chains as short as $N = 60$ monomers, however at this chain length the large scale Monte Carlo moves were ineffective. For even longer chains the speedup becomes substantial, as observed from preliminary data for $N = 200$

Axisymmetric pulse recycling and motion in bulk semiconductors

The Kroemer model for the Gunn effect in a circular geometry (Corbino disks) has been numerically solved. The results have been interpreted by means of asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric pulses of the electric field are periodically shed by an inner circular cathode. These pulses decay as they move towards the outer anode, which they may not reach. As a pulse advances, the external current increases continuously until a new pulse is generated. Then the current abruptly decreases, in agreement with existing experimental results. Depending on the bias, more complex patterns with multiple pulse shedding are possible.Comment: 8 pages, 15 figure

Partial domain wall partition functions

We consider six-vertex model configurations on an n-by-N lattice, n =< N, that satisfy a variation on domain wall boundary conditions that we define and call "partial domain wall boundary conditions". We obtain two expressions for the corresponding "partial domain wall partition function", as an (N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions of the same object, that each is a discrete KP tau-function, and, recalling that these determinants represent tree-level structure constants in N=4 SYM, we show that introducing 1-loop corrections, as proposed by N Gromov and P Vieira, preserves the determinant structure.Comment: 30 pages, LaTeX. This version, which appeared in JHEP, has an abbreviated abstract and some minor stylistic change

A gene-tree test of the traditional taxonomy of American deer: the importance of voucher specimens, geographic data, and dense sampling

The taxonomy of American deer has been established almost entirely on the basis of morphological data and without the use of explicit phylogenetic methods; hence, phylogenetic analyses including data for all of the currently recognized species, even if based on a single gene, might improve current understanding of their taxonomy. We tested the monophyly of the morphology-defined genera and species of New World deer (Odocoileini) with phylogenetic analyses of mitochondrial DNA sequences. This is the first such test conducted using extensive geographic and taxonomic sampling. Our results do not support the monophyly of Mazama, Odocoileus, Pudu, M. americana, M. nemorivaga, Od. hemionus, and Od. virginianus. Mazama contains species that belong to other genera. We found a novel sister-taxon relationship between “Mazama” pandora and a clade formed by Od. hemionus columbianus and Od. h. sitkensis, and transfer pandora to Odocoileus. The clade formed by Od. h. columbianus and Od. h. sitkensis may represent a valid species, whereas the remaining subspecies of Od. hemionus appear closer to Od. virginianus. Pudu (Pudu) puda was not found sister to Pudu (Pudella) mephistophiles. If confirmed, this result will prompt the recognition of the monotypic Pudella as a distinct genus. We provide evidence for the existence of an undescribed species now confused with Mazama americana, and identify other instances of cryptic, taxonomically unrecognized species-level diversity among populations here regarded as Mazama temama, “Mazama” nemorivaga, and Hippocamelus antisensis. Noteworthy records that substantially extend the known distributions of M. temama and “M.” gouazoubira are provided, and we unveil a surprising ambiguity regarding the distribution of “M.” nemorivaga, as it is described in the literature. The study of deer of the tribe Odocoileini has been hampered by the paucity of information regarding voucher specimens and the provenance of sequences deposited in GenBank. We pinpoint priorities for future systematic research on the tribe Odocoileini.Eliécer E. Gutiérrez, Kristofer M. Helgen, Molly M. McDonough, Franziska Bauer, Melissa T.R. Hawkins, Luis A. Escobedo-Morales, Bruce D. Patterson, Jesus E. Maldonad

Temperature and density extrapolations in canonical ensemble Monte Carlo simulations

We show how to use the multiple histogram method to combine canonical ensemble Monte Carlo simulations made at different temperatures and densities. The method can be applied to study systems of particles with arbitrary interaction potential and to compute the thermodynamic properties over a range of temperatures and densities. The calculation of the Helmholtz free energy relative to some thermodynamic reference state enables us to study phase coexistence properties. We test the method on the Lennard-Jones fluids for which many results are available.Comment: 5 pages, 3 figure

Free boundary problems describing two-dimensional pulse recycling and motion in semiconductors

An asymptotic analysis of the Gunn effect in two-dimensional samples of bulk n-GaAs with circular contacts is presented. A moving pulse far from contacts is approximated by a moving free boundary separating regions where the electric potential solves a Laplace equation with subsidiary boundary conditions. The dynamical condition for the motion of the free boundary is a Hamilton-Jacobi equation. We obtain the exact solution of the free boundary problem (FBP) in simple one-dimensional and axisymmetric geometries. The solution of the FBP is obtained numerically in the general case and compared with the numerical solution of the full system of equations. The agreement is excellent so that the FBP can be adopted as the basis for an asymptotic study of the multi-dimensional Gunn effect.Comment: 19 pages, 9 figures, Revtex. To appear in Phys. Rev.

Dependência da cobertura de céu nas frações solares Global, Difusa e Direta do espectro infravermelho em Botucatu/SP/Brasil

É descrito no trabalho a obtenção das frações solares KGIV = (HdGIV/HGd), KdIV = (HddIV/Hdd) e KDIV = (HdDIV/HDd) nas condições de cobertura de céu total e para quatro tipos discretos de coberturas de céu. A base de dados das radiações dos dois espectros foi medida no período de 2003 a 2006 em Botucatu/SP/Brasil. Os valores obtidos para cobertura de céu total foram: KdGIV = 46,1%, KddIV = 38,2% e KdDIV = 51,1%. Nas coberturas discretas o valor da fração KGIV = 43,3%foi menor na cobertura nebulosa, e KGIV = 46,9% foi maior na cobertura céu aberto. Ao contrario,a fração KdIV = 41,0% foi maior na cobertura nebulosa, e KdIV = 25,0%foi menor na céu aberto. O valor da fração KDIV não variou em função da cobertura de céu: KDIV = 51,0%foi igual nas coberturas nebulosa e aberta.The study describes linear equations for four sky covers, which express the dependence of cloud, water vapour and aerosol variations in the atmosphere on the values of the ratios HGNIR/HG, HdNIR/HdeandHDNIR/HD. The value of the fraction HGNIR/HG = 43,3% is lower in the cloudy cover, while HGNIR/HdG = 46,9% is higher in the clear sky condition. On the contrary, the fraction HdNIR/Hd = 41,0% is higher in the cloudy cover, while HdNIR/Hd = 25,0% is lower in the clear sky condition. No variation was found in the value of the fraction HDNIR/HD as a function of the sky cover. The ratio HDNIR/HD = 51,0% is the same in the cloudy cover and clear sky condition.Tema 11: Radiación solar y clima.Facultad de Arquitectura y Urbanism

Dependência da cobertura de céu nas frações solares Global, Difusa e Direta do espectro infravermelho em Botucatu/SP/Brasil

É descrito no trabalho a obtenção das frações solares KGIV = (HdGIV/HGd), KdIV = (HddIV/Hdd) e KDIV = (HdDIV/HDd) nas condições de cobertura de céu total e para quatro tipos discretos de coberturas de céu. A base de dados das radiações dos dois espectros foi medida no período de 2003 a 2006 em Botucatu/SP/Brasil. Os valores obtidos para cobertura de céu total foram: KdGIV = 46,1%, KddIV = 38,2% e KdDIV = 51,1%. Nas coberturas discretas o valor da fração KGIV = 43,3%foi menor na cobertura nebulosa, e KGIV = 46,9% foi maior na cobertura céu aberto. Ao contrario,a fração KdIV = 41,0% foi maior na cobertura nebulosa, e KdIV = 25,0%foi menor na céu aberto. O valor da fração KDIV não variou em função da cobertura de céu: KDIV = 51,0%foi igual nas coberturas nebulosa e aberta.The study describes linear equations for four sky covers, which express the dependence of cloud, water vapour and aerosol variations in the atmosphere on the values of the ratios HGNIR/HG, HdNIR/HdeandHDNIR/HD. The value of the fraction HGNIR/HG = 43,3% is lower in the cloudy cover, while HGNIR/HdG = 46,9% is higher in the clear sky condition. On the contrary, the fraction HdNIR/Hd = 41,0% is higher in the cloudy cover, while HdNIR/Hd = 25,0% is lower in the clear sky condition. No variation was found in the value of the fraction HDNIR/HD as a function of the sky cover. The ratio HDNIR/HD = 51,0% is the same in the cloudy cover and clear sky condition.Tema 11: Radiación solar y clima.Facultad de Arquitectura y Urbanism

Dependência da cobertura de céu nas frações solares Global, Difusa e Direta do espectro infravermelho em Botucatu/SP/Brasil

É descrito no trabalho a obtenção das frações solares KGIV = (HdGIV/HGd), KdIV = (HddIV/Hdd) e KDIV = (HdDIV/HDd) nas condições de cobertura de céu total e para quatro tipos discretos de coberturas de céu. A base de dados das radiações dos dois espectros foi medida no período de 2003 a 2006 em Botucatu/SP/Brasil. Os valores obtidos para cobertura de céu total foram: KdGIV = 46,1%, KddIV = 38,2% e KdDIV = 51,1%. Nas coberturas discretas o valor da fração KGIV = 43,3%foi menor na cobertura nebulosa, e KGIV = 46,9% foi maior na cobertura céu aberto. Ao contrario,a fração KdIV = 41,0% foi maior na cobertura nebulosa, e KdIV = 25,0%foi menor na céu aberto. O valor da fração KDIV não variou em função da cobertura de céu: KDIV = 51,0%foi igual nas coberturas nebulosa e aberta.The study describes linear equations for four sky covers, which express the dependence of cloud, water vapour and aerosol variations in the atmosphere on the values of the ratios HGNIR/HG, HdNIR/HdeandHDNIR/HD. The value of the fraction HGNIR/HG = 43,3% is lower in the cloudy cover, while HGNIR/HdG = 46,9% is higher in the clear sky condition. On the contrary, the fraction HdNIR/Hd = 41,0% is higher in the cloudy cover, while HdNIR/Hd = 25,0% is lower in the clear sky condition. No variation was found in the value of the fraction HDNIR/HD as a function of the sky cover. The ratio HDNIR/HD = 51,0% is the same in the cloudy cover and clear sky condition.Tema 11: Radiación solar y clima.Facultad de Arquitectura y Urbanism