Redução de dimensionalidade em equilíbrio de fases fluidas

Atualmente, existem modelos matemáticos capazes de preverem acuradamente as relações entre propriedades de estado; e esta tarefa é extremamente importante no contexto da Engenharia Química, uma vez que estes modelos podem ser empregados para avaliar a performance de processos químicos. Ademais, eles são de fundamental importância para a simulação de reservatórios de petróleo e processos de separação. Estes modelos são conhecidos como equações de estado, e podem ser usados em problemas de equilíbrios de fases, principalmente em equilíbrios líquido-vapor. Recentemente, um teorema matemático foi formulado (Teorema de Redução), fornecendo as condições para a redução de dimensionalidade de problemas de equilíbrios de fases para misturas multicomponentes descritas por equações de estado cúbicas e regras de mistura e combinação clássicas. Este teorema mostra como para uma classe bem definidade de modelos termodinâmicos (equações de estado cúbicas e regras de mistura clássicas), pode-se reduzir a dimensão de vários problemas de equilíbrios de fases. Este método é muito vantajoso para misturas com muitos componentes, promovendo uma redução significativa no tempo de computação e produzindo resultados acurados. Neste trabalho, apresentamos alguns experimentos numéricos com misturas-testes usando a técnica de redução para obter pressões de ponto de orvalho sob especificação de temperaturas.

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Regional and seasonal patterns of epipelagic fish assemblages from the central California Current

The coastal Pacific Ocean off northern and central California encompasses the strongest seasonal upwelling zone in the California Current ecosystem. Headlands and bays here generate complex circulation features and confer unusual oceanographic complexity. We sampled the coastal epipelagic fish community of this region with a surface trawl in the summer and fall of 2000–05 to assess patterns of spatial and temporal community structure. Fifty-three species of fish were captured in 218 hauls at 34 fixed stations, with clupeiform species dominating. To examine spatial patterns, samples were grouped by location relative to a prominent headland at Point Reyes and the resulting two regions, north coast and Gulf of the Farallones, were plotted by using nonmetric multidimensional scaling. Seasonal and interannual patterns were also examined, and representative species were identified for each distinct community. Seven oceanographic variables measured concurrently with trawling were plotted by principal components analysis and tested for correlation with biotic patterns. We found significant differences in community structure by region, year, and season, but no interaction among main effects. Significant differences in oceanographic conditions mirrored the biotic patterns, and a match between biotic and hydrographic structure was detected. Dissimilarity between assemblages was mostly the result of differences in abundance and frequency of occurrence of about twelve common species. Community patterns were best described by a subset of hydrographic variables, including water depth, distance from shore, and any one of several correlated variables associated with upwelling intensity. Rather than discrete communities with clear borders and distinct member species, we found gradients in community structure and identified stations with similar fish communities by region and by proximity to features such as the San Francisco Bay.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Multiple stable reference points in oyster populations: implications for reference point-based management

In the second of two companion articles, a 54-year time series for the oyster population in the New Jersey waters of Delaware Bay is analyzed to examine how the presence of multiple stable states affects reference-point–based management. Multiple stable states are described by four types of reference points. Type I is the carrying capacity for the stable state: each has associated with it a type-II reference point wherein surplus production reaches a local maximum. Type-II reference points are separated by an intermediate surplus production low (type III). Two stable states establish a type-IV reference point, a point-of-no-return that impedes recovery to the higher stable state. The type-II to type-III differential in surplus production is a measure of the difficulty of rebuilding the population and the sensitivity of the population to collapse at high abundance. Surplus production projections show that the abundances defining the four types of reference points are relatively stable over a wide range of uncertainties in recruitment and mortality rates. The surplus production values associated with type-II and type-III reference points are much more uncertain. Thus, biomass goals are more easily established than fishing mortality rates for oyster population