Probabilistic ballistic annihilation with continuous velocity distributions

We investigate the problem of ballistically controlled reactions where particles either annihilate upon collision with probability $p$, or undergo an elastic shock with probability $1-p$. Restricting to homogeneous systems, we provide in the scaling regime that emerges in the long time limit, analytical expressions for the exponents describing the time decay of the density and the root-mean-square velocity, as continuous functions of the probability $p$ and of a parameter related to the dissipation of energy. We work at the level of molecular chaos (non-linear Boltzmann equation), and using a systematic Sonine polynomials expansion of the velocity distribution, we obtain in arbitrary dimension the first non-Gaussian correction and the corresponding expressions for the decay exponents. We implement Monte-Carlo simulations in two dimensions, that are in excellent agreement with our analytical predictions. For $p<1$, numerical simulations lead to conjecture that unlike for pure annihilation ($p=1$), the velocity distribution becomes universal, i.e. does not depend on the initial conditions.Comment: 10 pages, 9 eps figures include

Enfermidades digitais em vacas de aptidão leiteira: associação com mastite clínica, metrites e aspectos epidemiológicos Foot diseases in dairy cows: association with clinical mastitis, metrites and predisposed factors

Utilizaram-se nesse estudo 5300 vacas de aptidão leiteira, provenientes de 80 propriedades rurais, que adotavam manejo intensivo ou semi-extensivo, com o objetivo de averiguar a existência de possível associação entre enfermidades digitais, mastite clínica e/ou metrite e identificar possíveis fatores de risco das enfermidades digitais. Em 325 (6,13%) vacas foram diagnosticados apenas enfermidades digitais, em 35 (0,66%) enfermidades digitais e mastite clínica, em 52 (0,98%) enfermidades digitais e metrite, em 28 (0,53%) enfermidades digitais, mastite clínica e metrite, em 128 (2,42%) apenas metrite, em 165 (3,11%) somente mastite clínica, e em 89 (1,68%) vacas metrite e mastite clínica. As mudanças bruscas na alimentação, o excesso de sujidades nas instalações, os pisos irregulares e abrasivos, a não utilização ou uso incorreto de pedilúvio, a falta de casqueamento preventivo, a ausência de quarentena, e a aquisição de animais sem a preocupação com o aspecto sanitário foram considerados os fatores de risco de maior ocorrência. Foi constatada diferença significativa entre a ocorrência de enfermidades digitais, mastite clínica e metrite, além de associação fraca entre tais enfermidades, concluindo-se que não houve relação expressiva entre enfermidades podais, mastite clínica e metrite em vacas lactantes.<br>With the objective to investigate a possible association between foot diseases, clinical mastitis and/or metritis and predisposing factors for foot diseases, 5300 dairy cows from 80 intensive and semi-intensive farms were used. In 325 (6.13%) cows only foot disease was diagnosed, in 35 (0.66%) foot disease and clinical mastitis, in 52 (0.98%) foot disease and metritis, in 28 (0.53%) foot disease, clinical mastitis and metritis, in 128 (2.42%) only metritis, in 165 (3.11%) only clinical mastitis, and in 89 (1.68%) cows metritis and clinical mastitis. Rapid changes in the diet, high exposure time of hoof horn to slurry and wet conditions, concrete floors, use of footbaths, low frequency of claw trimming, irregular quarantine, and no attention to health aspects during acquisition of the animals were considered as major risk factors for the occurrence of those diseases. The McNemar test for dependent samples showed significant statistical differences between the occurrence of foot disease, clinical mastitis and metritis, in spite of the poor association between those diseases. It was concluded that there was no expressive relationship between foot diseases, clinical mastitis and metritis in lactent cows