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

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

Accurate simulation estimates of phase behaviour in ternary mixtures with prescribed composition

This paper describes an isobaric semi-grand canonical ensemble Monte Carlo scheme for the accurate study of phase behaviour in ternary fluid mixtures under the experimentally relevant conditions of prescribed pressure, temperature and overall composition. It is shown how to tune the relative chemical potentials of the individual components to target some requisite overall composition and how, in regions of phase coexistence, to extract accurate estimates for the compositions and phase fractions of individual coexisting phases. The method is illustrated by tracking a path through the composition space of a model ternary Lennard-Jones mixture.Comment: 6 pages, 3 figure