Matrix analysis of an anisotropic optical thin film

Based on Maxwell's equations, standard boundary conditions are imposed on resultant electric- and magnetic-field vectors at interfaces, and the propagating characteristics of extraordinary waves, such as the forward- and backward-propagating directions of wave vectors, rays and their corresponding refractive indices are determined in a uniaxially birefringent thin film. Furthermore, 2 x 2 characteristic matrices of a birefringent thin film are derived including multiple reflections for the extraordinary wave.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Validation of back-calculation equations for juvenile bluefish (Pomatomus saltatrix) with the use of tetracycline-marked otoliths

In recent years, a decrease in the abundance of bluefish (Pomatomus saltatrix) has been observed (Fahay et al., 1999; Munch and Conover, 2000) that has led to increased interest in a better understanding the life history of the species. Estimates of several young-of-the-year (YOY) life history characteristics, including the importance and use of estuaries as nursery habitat (Kendall and Walford, 1979) and size-dependant mortality (Hare and Cowen, 1997), are reliant upon the accuracy of growth determination. By using otoliths, it is possible to use back-calculation formulae (BCFs) to estimate the length at certain ages and stages of development for many species of fishes. Use of otoliths to estimate growth in this way can provide the same information as long-term laboratory experiments and tagging studies without the time and expense of rearing or recapturing fish. The difficulty in using otoliths in this way lies in validating that 1) there is constancy in the periodicity of the increment formation, and 2) there is no uncoupling of the relationship between somatic and otolith growth. To date there are no validation studies demonstrating the relationship between otolith growth and somatic growth for bluefish. Daily increment formation in otoliths has been documented for larval (Hare and Cowen, 1994) and juvenile bluefish (Nyman and Conover, 1988). Hare and Cowen (1995) found ageindependent variability in the ratio of otolith size to body length in early age bluefish, although these differences varied between ontogenetic stages. Furthermore, there have been no studies where an evaluation of back-calculation methods has been combined with a validation of otolithderived lengths for juvenile bluefish.

Bessel functions and equations of mathematical physics

The aim of this dissertation is to introduce Bessel functions to the reader, as well as studying some of their properties. Moreover, the final goal of this document is to present the most well- known applications of Bessel functions in physics.

A reassessment of equations for predicting natural mortality in Mediterranean teleosts

This brief article presents new empirical models for prediction of natural mortality (M) from growth parameters (L and K, W and K) in Mediterranean teleosts, based on 56 data sets presented in an earlier paper in the January 1993 issue of Naga, the ICLARM Quarterly in which models were presented that included temperature as a predictor variable, although its effect was nonsignificant and its partial slope had the "wrong" sign.

Empirical equations for the estimation of natural mortality in Mediterranean teleosts

Empirical relationships were established linking estimates of the instantaneous rate of natural mortality (M), the von Bertalanffy growth parameters, L sub( infinity ) (or W sub( infinity )) and K, and annual mean water temperature in 56 stocks of Mediterranean teleosts fish. It is suggested that these relationships generate for these fish more reliable estimates of M than the widely-used model of Pauly (1980, J. Cons. CIEM 33(3):175-192), which was based on 175 fish stocks, but included only five stocks from the Mediterranean.

Crank-Nicholson method for rate equations in powder random lasers

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)

Beverton and Holt equations: spreadsheet functions and uncertainty

This contribution illustrates how modern spreadsheets aid the calculation and visualization of yield models and how the effects of uncertainties may be incorporated using Monte Carlo simulation. It is argued that analogous approaches can be implemented for other assessment models of simple to medium complexity justifying wider use of spreadsheets in fisheries analysis and training.

James Clerk Maxwell e a unidade do mundo: modelos e metáforas na construção de teorias científicas

Esta é uma pesquisa sobre o uso de metáforas na construção de modelos por parte do físico escocês James Clerk Maxwell. O objetivo da pesquisa foi buscar compreender de que maneira o uso de metáforas e modelos é legítimo na ciência e em que medida contribui para seu sucesso. Além disso, busca compreender em que medida o uso de artifícios como modelos e analogias entre ramos distintos da ciência são impulsionadores de sucesso explicativo e preditivo da teoria do físico estudado. Explora as crenças teológicas e filosóficas do autor, que vê o mundo como unidade, permitindo a analogia entre ramos distintos da física. Seus desenvolvimentos em torno de teorias como calor, cores, óptica, magnetismo e eletricidade permitem evidenciar essa visão em todo o seu trabalho. Maxwell é considerado inaugurador de nova metodologia com o uso de modelos e metáforas. Explora o desenvolvimento da teoria das cores, da descrição matemática da estabilidade dos anéis de Saturno e o desenvolvimento da teoria dos gases como preâmbulo à discussão da teoria do eletromagnetismo. Descreve o desenvolvimento teórico do eletromagnetismo em seus diversos momentos. A construção da teoria do eletromagnetismo evidencia paulatino abandono do mecanicismo, uso intenso de modelos e metáforas temporários e ênfase na quantificação e no uso de experimentos. Discute o relacionamento de Maxwell com as discussões filosóficas, sociais e teológicas de sua época, seu engajamento em atividades práticas nesse sentido e suas influências científicas e filosóficas. Descreve e discute os textos filosóficos do cientista, em que se evidenciam sua ontologia, suas crenças teológicas e sua concepção de analogias. Discute a questão do uso de analogias em ciência e compara diversos autores que abordam o tema. A metodologia utilizada foi a de levantamento bibliográfico com análise crítica da literatura do autor e de seus comentadores, além de comentário crítico sobre os textos primários e secundários. Conclui que o sucesso científico de Maxwell deve-se à sua aposta numa unidade do mundo garantida por Deus, bem como na unidade entre o mundo e a mente humana, posturas que mostraram ser bem-sucedidas quando aplicadas à metodologia científica. Conclui também pela legitimidade e necessidade do uso de metáforas e modelos no empreendimento científico.