Exact results for hydrogen recombination on dust grain surfaces

The recombination of hydrogen in the interstellar medium, taking place on surfaces of microscopic dust grains, is an essential process in the evolution of chemical complexity in interstellar clouds. The H_2 formation process has been studied theoretically, and in recent years also by laboratory experiments. The experimental results were analyzed using a rate equation model. The parameters of the surface, that are relevant to H_2 formation, were obtained and used in order to calculate the recombination rate under interstellar conditions. However, it turned out that due to the microscopic size of the dust grains and the low density of H atoms, the rate equations may not always apply. A master equation approach that provides a good description of the H_2 formation process was proposed. It takes into account both the discrete nature of the H atoms and the fluctuations in the number of atoms on a grain. In this paper we present a comprehensive analysis of the H_2 formation process, under steady state conditions, using an exact solution of the master equation. This solution provides an exact result for the hydrogen recombination rate and its dependence on the flux, the surface temperature and the grain size. The results are compared with those obtained from the rate equations. The relevant length scales in the problem are identified and the parameter space is divided into two domains. One domain, characterized by first order kinetics, exhibits high efficiency of H_2 formation. In the other domain, characterized by second order kinetics, the efficiency of H_2 formation is low. In each of these domains we identify the range of parameters in which, the rate equations do not account correctly for the recombination rate. and the master equation is needed.Comment: 23 pages + 8 figure

Dose inseminante para fertilização artificial de ovócitos de dourado Insemination dose for artificial fertilization of dourado oocytes

Objetivou-se determinar a dose inseminante adequada para uso na fertilização artificial de ovócitos de dourado (Salminus brasiliensis). Os ovócitos foram distribuídos em delineamento inteiramente casualizado, e fertilizados com uma das relações espermatozoides/ovócito 6,0×10³; 6,0×10(4); 6,0×10(5); 6,0×10(6) ou 3,0×10(7), cada uma com quatro repetições. Considerou-se unidade experimental uma incubadora de volume útil de 2,5 L, contendo 2,0 mL de ovócitos não-hidratados. As taxas de fertilização foram mensuradas 8 horas após o início da fertilização. Com intuito de verificar possíveis efeitos da diluição seminal na movimentação dos espermatozoides, realizou-se a mensuração do tempo de duração da motilidade espermática dos espermatozoides de dourado, ativados por meio de diferentes relações de diluição: 6,8×10-5; 6,8×10-4; 6,8×10-3; 6,8×10-2; 3,4×10-1 e 1,0 mL de sêmen por mL de água. O tempo de duração da motilidade foi avaliado em delineamento inteiramente casualizado composto de seis tratamentos e três repetições. As taxas de fertilização apresentaram relação quadrática com o número de espermatozoides por ovócito. As relações de diluição do sêmen tiveram efeito inversamente proporcional sobre a duração da motilidade espermática. A relação que proporcionou melhores taxas de fertilização artificial de ovócitos de dourado (Salminus brasiliensis) foi de 30.722 espermatozoides por ovócio.<br>The objective of the present study was to determine the proper insemination dose of dourado (Salminus brasiliensis) oocytes. The oocytes were placed in a randomized complete design and fertilized with one of the spermatozoa.oocytes-1 ratio, 6.0×10³, 6.0×10(4), 6.0×10(5), 6.0×10(6), 3.0×10(7) SPZ:OOC, each one with four replications. An experimental unit was considered to be an incubator with a 2.5L useful volume containing 2.0 mL non-hydrated oocytes. The fertilization rates were measured eight hours after the start of fertilization. In order to ascertain the possible effects of seminal dilution on the spermatozoa motility, the duration time of the spermatic motility of the dourado spermatozoa was measured when activated by different dilution ratios 6.8×10-5; 6.8×10-4; 6.8×10-3; 6.8×10-2; 3.4×10-1 and 1.0 mL semen.mL water-1. The motility duration time was assessed in a randomized complete design, with six treatments and three repetitions. The fertilization rates showed a quadratic relationship with the number of spermatozoids per oocyte. The semen dilution ratios had an inversely proportional affect on the spermatic motility time. The spermatozoa:oocytes ratio that provided the best artificial fertilization rates of dourado (Salminus brasiliensis) oocytes was 30,722 spermatoids per oocyte