Brownian Motion in wedges, last passage time and the second arc-sine law

We consider a planar Brownian motion starting from $O$ at time $t=0$ and stopped at $t=1$ and a set $F= \{OI_i ; i=1,2,..., n\}$ of $n$ semi-infinite straight lines emanating from $O$. Denoting by $g$ the last time when $F$ is reached by the Brownian motion, we compute the probability law of $g$. In particular, we show that, for a symmetric $F$ and even $n$ values, this law can be expressed as a sum of $\arcsin$ or $(\arcsin)^2$ functions. The original result of Levy is recovered as the special case $n=2$. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed

Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions

The survival probability, S_N(t), of a diffusing prey (``lamb'') in the proximity of N diffusing predators (a ``pride of lions'') in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S_N(t) is proportional to t^{-beta_N}, with the decay exponent beta_N proportional to ln N. The crossover behavior as a function of the relative diffusivities of the lions and the lamb is also discussed. When N--->oo, the lamb survival probability exhibits a log-normal decay, exp(-ln^2 t).Comment: 12 pages, no figures, macro files prepended, to be submitted to J. Phys.

Does hardcore interaction change absorbing type critical phenomena?

It has been generally believed that hardcore interaction is irrelevant to absorbing type critical phenomena because the particle density is so low near an absorbing phase transition. We study the effect of hardcore interaction on the N species branching annihilating random walks with two offspring and report that hardcore interaction drastically changes the absorbing type critical phenomena in a nontrivial way. Through Langevin equation type approach, we predict analytically the values of the scaling exponents, $\nu_{\perp} = 2, z = 2, \alpha = 1/2, \beta = 2$ in one dimension for all N > 1. Direct numerical simulations confirm our prediction. When the diffusion coefficients for different species are not identical, $\nu_{\perp}$ and $\beta$ vary continuously with the ratios between the coefficients.Comment: 4 pages, 1 figur

Photovoltaic powered irrigation system applied to familiary agriculture

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel SuperiorA presente dissertaÃÃo tem como objetivo principal analisar a viabilidade tÃcnica e financeira de um sistema fotovoltaico autÃnomo para bombeamento de Ãgua aplicado na irrigaÃÃo de uma unidade de produÃÃo agrÃcola familiar. A unidade agrÃcola pesquisada està instalada no NÃcleo de Ensino e Pesquisa em Agricultura Urbana (NEPAU), que atua em parceria com o LaboratÃrio de Energias Alternativas (LEA), situados no Campus do PICI da Universidade Federal do CearÃ. A unidade ocupa uma Ãrea Ãtil de 43 m2, com um reservatÃrio de Ãgua que simula um aÃude, lago ou poÃo com capacidade de 3.534 litros, um motor bomba de 12 VDC e um mÃdulo fotovoltaico de 135 Wp. O sistema de irrigaÃÃo à constituÃdo por 12 micro-aspersores com pressÃo de trabalho de 7 psi, com raio de alcance de 1,2 m e vazÃo de 0,6 l/min. A unidade de produÃÃo consumiu 31.592 litros de Ãgua e demandou 5,2 kWh de energia elÃtrica ao longo de 44 dias de produÃÃo do coentro. Um sensor de umidade do solo foi utilizado para controlar a umidade do solo o que permitiu economizar 3.608 litros de Ãgua e 0,6 kWh de energia elÃtrica na produÃÃo de 23 kg de coentro. O custo de implantaÃÃo do sistema fotovoltaico de bombeamento desenvolvido foi de R$1.694,00. As eficiÃncias do mÃdulo fotovoltaico, conjunto motobomba e global foram de 8,4$ 1,694.00. The efficiencies of photovoltaic module, pump and global set were 8.4%, 42% and 3.5%, respectively. The return on capital invested time is 10 years without regard to any allowance and 8.4 years for a 20% allowance on capital invested in the acquisition of equipment