The statistical bootstrap model

A review is presented of the statistical bootstrap model of Hagedorn and Frautschi. This model is an attempt to apply the methods of statistical mechanics in high-energy physics, while treating all hadron states (stable or unstable) on an equal footing. A statistical calculation of the resonance spectrum on this basis leads to an exponentially rising level density ρ(m) ~ cm^-3 e^βom at high masses.

In the present work, explicit formulae are given for the asymptotic dependence of the level density on quantum numbers, in various cases. Hamer and Frautschi's model for a realistic hadron spectrum is described.

A statistical model for hadron reactions is then put forward, analogous to the Bohr compound nucleus model in nuclear physics, which makes use of this level density. Some general features of resonance decay are predicted. The model is applied to the process of NN annihilation at rest with overall success, and explains the high final state pion multiplicity, together with the low individual branching ratios into two-body final states, which are characteristic of the process. For more general reactions, the model needs modification to take account of correlation effects. Nevertheless it is capable of explaining the phenomenon of limited transverse momenta, and the exponential decrease in the production frequency of heavy particles with their mass, as shown by Hagedorn. Frautschi's results on "Ericson fluctuations" in hadron physics are outlined briefly. The value of β_o required in all these applications is consistently around [120 MeV]^-1 corresponding to a "resonance volume" whose radius is very close to ƛ_π. The construction of a "multiperipheral cluster model" for high-energy collisions is advocated.

On statistical treatment of the results of parallel trails with special reference to fishery research

Parallel trials form a most important part of the technique of scientific experimentation. Such trials may be divided into two; categories. In the first the results are comparable measurements of one kind or another. In the second the data consist of records of the number of times a certain 'event' has occurred in the two sets of trials compared. Only trials of the second category are dealt with here. In this paper all the reliable methods of testing for significance the results of parallel trials of a certain type with special reference to fishery research are described fully. Some sections relate to exact, others to approximate tests. The only advantage in the use of the latter lies in the fact that they are often the more expeditious. Apart from this it is always preferable to use exact methods.

A-SCALA: an age-structured statistical catch-at-length analysis for assessing tuna stocks in the eastern tropical Pacific Ocean

English: We describe an age-structured statistical catch-at-length analysis (A-SCALA) based on the MULTIFAN-CL model of Fournier et al. (1998). The analysis is applied independently to both the yellowfin and the bigeye tuna populations of the eastern Pacific Ocean (EPO). We model the populations from 1975 to 1999, based on quarterly time steps. Only a single stock for each species is assumed for each analysis, but multiple fisheries that are spatially separate are modeled to allow for spatial differences in catchability and selectivity. The analysis allows for error in the effort-fishing mortality relationship, temporal trends in catchability, temporal variation in recruitment, relationships between the environment and recruitment and between the environment and catchability, and differences in selectivity and catchability among fisheries. The model is fit to total catch data and proportional catch-at-length data conditioned on effort. The A-SCALA method is a statistical approach, and therefore recognizes that the data collected from the fishery do not perfectly represent the population. Also, there is uncertainty in our knowledge about the dynamics of the system and uncertainty about how the observed data relate to the real population. The use of likelihood functions allow us to model the uncertainty in the data collected from the population, and the inclusion of estimable process error allows us to model the uncertainties in the dynamics of the system. The statistical approach allows for the calculation of confidence intervals and the testing of hypotheses. We use a Bayesian version of the maximum likelihood framework that includes distributional constraints on temporal variation in recruitment, the effort-fishing mortality relationship, and catchability. Curvature penalties for selectivity parameters and penalties on extreme fishing mortality rates are also included in the objective function. The mode of the joint posterior distribution is used as an estimate of the model parameters. Confidence intervals are calculated using the normal approximation method. It should be noted that the estimation method includes constraints and priors and therefore the confidence intervals are different from traditionally calculated confidence intervals. Management reference points are calculated, and forward projections are carried out to provide advice for making management decisions for the yellowfin and bigeye populations. Spanish: Describimos un análisis estadístico de captura a talla estructurado por edad, A-SCALA (del inglés age-structured statistical catch-at-length analysis), basado en el modelo MULTIFAN- CL de Fournier et al. (1998). Se aplica el análisis independientemente a las poblaciones de atunes aleta amarilla y patudo del Océano Pacífico oriental (OPO). Modelamos las poblaciones de 1975 a 1999, en pasos trimestrales. Se supone solamente una sola población para cada especie para cada análisis, pero se modelan pesquerías múltiples espacialmente separadas para tomar en cuenta diferencias espaciales en la capturabilidad y selectividad. El análisis toma en cuenta error en la relación esfuerzo-mortalidad por pesca, tendencias temporales en la capturabilidad, variación temporal en el reclutamiento, relaciones entre el medio ambiente y el reclutamiento y entre el medio ambiente y la capturabilidad, y diferencias en selectividad y capturabilidad entre pesquerías. Se ajusta el modelo a datos de captura total y a datos de captura a talla proporcional condicionados sobre esfuerzo. El método A-SCALA es un enfoque estadístico, y reconoce por lo tanto que los datos obtenidos de la pesca no representan la población perfectamente. Además, hay incertidumbre en nuestros conocimientos de la dinámica del sistema e incertidumbre sobre la relación entre los datos observados y la población real. El uso de funciones de verosimilitud nos permite modelar la incertidumbre en los datos obtenidos de la población, y la inclusión de un error de proceso estimable nos permite modelar las incertidumbres en la dinámica del sistema. El enfoque estadístico permite calcular intervalos de confianza y comprobar hipótesis. Usamos una versión bayesiana del marco de verosimilitud máxima que incluye constreñimientos distribucionales sobre la variación temporal en el reclutamiento, la relación esfuerzo-mortalidad por pesca, y la capturabilidad. Se incluyen también en la función objetivo penalidades por curvatura para los parámetros de selectividad y penalidades por tasas extremas de mortalidad por pesca. Se usa la moda de la distribución posterior conjunta como estimación de los parámetros del modelo. Se calculan los intervalos de confianza usando el método de aproximación normal. Cabe destacar que el método de estimación incluye constreñimientos y distribuciones previas y por lo tanto los intervalos de confianza son diferentes de los intervalos de confianza calculados de forma tradicional. Se calculan puntos de referencia para el ordenamiento, y se realizan proyecciones a futuro para asesorar la toma de decisiones para el ordenamiento de las poblaciones de aleta amarilla y patudo.

Statistical approach to bulk inclusion initialized damage in films

In experiments, we have found an abnormal relationship between probability of laser induced damage and number density of surface inclusion. From results of X-ray diffraction (XRD) and laser induced damage, we have drawn a conclusion that bulk inclusion plays a key role in damage process. Combining thermo-mechanical damage process and statistics of inclusion density distribution, we have deduced an equation which reflects the relationship between probability of laser induced damage, number density of inclusion, power density of laser pulse, and thickness of films. This model reveals that relationship between critical sizes of the dangerous inclusions (dangerous inclusions refer to the inclusions which can initialize film damage), embedded depth of inclusions, thermal diffusion length and tensile strength of films. This model develops the former work which is the statistics about surface inclusion. (c) 2006 Elsevier B.V. All rights reserved.