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.

Length-weight relationship of marine fishes from southern Brazil

The relationship between length (L) and weight (W) was estimated for 80 species belonging to 50 families of marine fishes from the shelf and upper slope of southern Brazil (lat. 28°S - 34°S). Sample sizes (n) for different species ranged from 11 to 14 741 specimens collected from commercial landings and research surveys. The fit of the equations (W=aLb) with a and b parameters estimated from regular and functional regression (of log-transformed weight and length data) as well as from a non-linear iterative process using the quasi-Newton algorithm were compared. The non-linear method gave the most accurate estimates in terms of residual sum of squares. Differences were less than 2.3% for n>500 compared with predictive regressions and 1.5% compared with functional regressions. No difference was observed between both predictive and functional regressions. Determination coefficients (r2) increased with sample size, and the highest r2 were obtained for 50

A simulation model of the dynamics of Peruvian anchoveta (Engraulis ringens)

The article describes the key elements of a model simulating the dynamics of the anchoveta (Engraulis ringens) in the Peruvian upwelling system (4 degrees to 14 degrees South). This model, based on coupled differential equations, is parametrized mainly using empirical data and functional relationships presented in two volumes issued by ICLARM in 1987 and 1989, and may thus be viewed as test of the hypotheses presented therein. Results to date suggest that present knowledge of mechanisms controlling the anchoveta stock is essentially consistent, and sufficient to build a model reflecting essential features of the stock biomass and recruitment dynamics.

Energetics and Structural Characterization of the large-scale Functional Motion of Adenylate Kinase

Adenylate Kinase (AK) is a signal transducing protein that regulates cellular energy homeostasis balancing between different conformations. An alteration of its activity can lead to severe pathologies such as heart failure, cancer and neurodegenerative diseases. A comprehensive elucidation of the large-scale conformational motions that rule the functional mechanism of this enzyme is of great value to guide rationally the development of new medications. Here using a metadynamics-based computational protocol we elucidate the thermodynamics and structural properties underlying the AK functional transitions. The free energy estimation of the conformational motions of the enzyme allows characterizing the sequence of events that regulate its action. We reveal the atomistic details of the most relevant enzyme states, identifying residues such as Arg119 and Lys13, which play a key role during the conformational transitions and represent druggable spots to design enzyme inhibitors. Our study offers tools that open new areas of investigation on large-scale motion in proteins.

Copolímeros à base de estireno e anidrido maleico: caracterização e estudo viscosimétrico

Copolímeros à base de estireno e anidrido maleico (SMA) são materiais sintéticos comercialmente disponíveis, obtidos pela reação dos dois monômeros citados em diferentes proporções, resultando em materiais versáteis, e disponíveis em diferentes graus de massas e porcentagens molares de anidrido maleico. São considerados polímeros funcionais devido à reatividade do grupamento anidrido maleico presente na cadeia polimérica. Por este motivo, esses materiais possuem vasta gama de aplicações, e elevada importância em diversas áreas, principalmente por terem baixa toxicidade, boa resistência térmica e boa estabilidade dimensional. Dessa forma, para melhor aplicação desses copolímeros, é muito importante o conhecimento dos parâmetros relativos ao seu comportamento em solução. A viscosimetria, em especial, é um método simples, útil e apropriado para fornecer essas informações. Os parâmetros viscosimétricos podem ser matematicamente calculados por extrapolação gráfica, entretanto a geração dos dados experimentais é mais demorada. Em contrapartida, é possível que a determinação experimental seja feita de forma mais rápida, por um único ponto, procedimento esse que desperta tanto o interesse acadêmico quanto o industrial. Neste trabalho, foram empregados os dois métodos de cálculo, utilizando solventes puros, misturas de solventes e três amostras de copolímeros à base de SMA. As determinações foram conduzidas a 40C. Os copolímeros utilizados possuiam teores de anidrido maleico de 50%, 45% e 40%, sendo os dois últimos esterificados com butil-metil-éster e sec-butil-metil-éster, respectivamente. Os solventes utilizados foram: N-metil-pirrolidona (NMP), tetrahidrofurano (THF) e suas respectivas misturas 1:1 com metil-etil-cetona (MEK), ou seja, (NMP:MEK) e THF:MEK, sendo a MEK um não solvente para o copolímero não esterificado. As equações utilizadas para extrapolação gráfica foram as de Huggins, Kraemer e Schulz-Blaschke. As equações empregadas em um único ponto foram as de Solomon-Ciuta, Deb-Chanterjee e novamente Schulz-Blaschke. Os resultados obtidos foram comparados e avaliou-se a possibilidade da utilização do método mais rápido, por um único ponto, para os sistemas estudados através dos desvios percentuais tendo como padrão os resultados da equação de Huggins. A equação de Deb-Chanterjee foi a mais adequada aos sistemas em NMP, que foi também o melhor solvente para as amostras. Os resultados obtidos na mistura NMP:MEK sugeriram que a viscosimetria pode ter sido um método sensível às pequenas diferenças estruturais entre os grupos pendentes nas amostras esterificadas. Paralelamente, realizou-se análises de espectroscopia na região do infravermelho (FTIR), análise termogravimétrica (TGA) e ensaios dinâmico-mecânicos (DMA) para a caracterização estrutural e térmica das amostras. Somente os resultados obtidos a partir de DMA indicaram diferenças entre as amostras esterificadas

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.