Mathematical models of generalized diffusion

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u(t) = 2 lambda (2)(uu(x))(x) + lambda (2)u(xxxx)), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Mathematical models for Isoptera (Insecta) mound growth

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Test systems and mathematical models for transmission network expansion planning

The data of four networks that can be used in carrying out comparative studies with methods for transmission network expansion planning are given. These networks are of various types and different levels of complexity. The main mathematical formulations used in transmission expansion studies-transportation models, hybrid models, DC power flow models, and disjunctive models are also summarised and compared. The main algorithm families are reviewed-both analytical, combinatorial and heuristic approaches. Optimal solutions are not yet known for some of the four networks when more accurate models (e.g. The DC model) are used to represent the power flow equations-the state of the art with regard to this is also summarised. This should serve as a challenge to authors searching for new, more efficient methods.

Use of mathematical models in the study of bodily growth in GIFT strain Nile tilapia

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Signal-flow graphs: Direct method of reduction and MATLAB implementation

Block diagrams and signal-flow graphs are used to represent and to obtain the transfer function of interconnected systems. The reduction of signal-flow graphs is considered simpler than the reduction of block diagrams for systems with complex interrelationships. Signal-flow graphs reduction can be made without graphic manipulations of diagrams, and it is attractive for a computational implementation. In this paper the authors propose a computational method for direct reduction of signal-flow graphs. This method uses results presented in this paper about the calculation of literal determinants without symbolic mathematics tools. The Cramer's rule is applied for the solution of a set of linear equations, A program in MATLAB language for reduction of signal-flow graphs with the proposed method is presented.

Short and long period optimization of drug doses in the treatment of AIDS

Técnicas de otimização numérica são úteis na solução de problemas de determinação da melhor entrada para sistemas descritos por modelos matemáticos e cujos objetivos podem ser expressos de uma maneira quantitativa. Este trabalho aborda o problema de otimizar as dosagens dos medicamentos no tratamento da AIDS em termos de um balanço entre a resposta terapêutica e os efeitos colaterais. Um modelo matemático para descrever a dinâmica do vírus HIV e células CD4 é utilizado para calcular a dosagem ótima do medicamento no tratamento a curto prazo de pacientes com AIDS por um método de otimização direta utilizando uma função custo do tipo Bolza. Os parâmetros do modelo foram ajustados com dados reais obtidos da literatura. Com o objetivo de simplificar os procedimentos numéricos, a lei de controle foi expressa em termos de uma expansão em séries que, após truncamento, permite obter controles sub-ótimos. Quando os pacientes atingem um estado clínico satisfatório, a técnica do Regulador Linear Quadrático (RLQ) é utilizada para determinar a dosagem permanente de longo período para os medicamentos. As dosagens calculadas utilizando a técnica RLQ , tendem a ser menores do que a equivalente terapia de dose constante em termos do expressivo aumento na contagem das células T+ CD4 e da redução da densidade de vírus livre durante um intervalo fixo de tempo.

H2 and/or H∞-norm model reduction of uncertain discrete-time systems

This paper addresses the problem of model reduction for uncertain discrete-time systems with convex bounded (polytope type) uncertainty. A reduced order precisely known model is obtained in such a way that the H2 and/or the H∞ guaranteed norm of the error between the original (uncertain) system and the reduced one is minimized. The optimization problems are formulated in terms of coupled (non-convex) LMIs - Linear Matrix Inequalities, being solved through iterative algorithms. Examples illustrate the results.

Global optimization approach for the H2-norm model reduction problem

A branch and bound algorithm is proposed to solve the H2-norm model reduction problem for continuous-time linear systems, with conditions assuring convergence to the global optimum in finite time. The lower and upper bounds used in the optimization procedure are obtained through Linear Matrix Inequalities formulations. Examples illustrate the results.

Distribution line models analysis for loss calculation within three-phase three-wire power flow algorithms

Three-phase three-wire power flow algorithms, as any tool for power systems analysis, require reliable impedances and models in order to obtain accurate results. Kron's reduction procedure, which embeds neutral wire influence into phase wires, has shown good results when three-phase three-wire power flow algorithms based on current summation method were used. However, Kron's reduction can harm reliabilities of some algorithms whose iterative processes need loss calculation (power summation method). In this work, three three-phase three-wire power flow algorithms based on power summation method, will be compared with a three-phase four-wire approach based on backward-forward technique and current summation. Two four-wire unbalanced medium-voltage distribution networks will be analyzed and results will be presented and discussed. © 2004 IEEE.

Diagnosis of a compacted area for mining through the mechanical resistance to the penetration using geostatistical methods in the Amazon Forest

The mining process promotes land modification and complete landscape alteration. Those alterations in the surface are shown more obviously in the aesthetical aspect as the visual elements of form, texture, climbs, complexity and color which composes the landscape. As a consequence, mining has impacts on the topography, in the soil, in the vegetation and in the area's drainage, with a direct influence on the enterprise. A quite common problem in the recovery of degraded areas in mineral exploration is the compaction of the soil due to the intense traffic of machines and earth movement. The most common problem of the compaction of a degraded surface is an increase of the mechanical resistance to the penetration of plant roots, a reduction of the aeration, an alteration of the flow of water and heat, also in the availability of water and nutrients. Thus, the present work had the basic objective of diagnosing the compaction of an area degraded by mining in a spacial way, through the mechanical resistance and the penetration, to guide the future subsoiling in the area requiring recovery. Through the studies, it was concluded that the krigagem method in agreement with the space variation allows the division of the area under study into sub areas facilitating a future work to reduce costs and unnecessary interference to the atmosphere. The method was shown to be quite appropriate and it can be used in the diagnosis of compaction in a degraded area by mining, foreseeing the subsoiling requirement.

Stability analysis of power system including facts (TCSC) effects by direct method approach

The problem of power system stability including the effects of a flexible alternating current transmission system (FACTS) is approached. First, the controlled series compensation is considered in the machine against infinite bar system and its effects are taken into account by means of construction of a Lyapunov function (LF). This simple system is helpful in order to understand the form the device affects dynamic and transient performance of the power system. After, the multimachine case is considered and it is shown that the single-machine results apply to multimachine systems. An energy-form Lyapunov function is derived for the power system including the FACTS device and it is used to analyse damping and synchronizing effects due to the FACTS device in single-machine as well as in multimachine power systems. © 2005 Elsevier Ltd. All rights reserved.

Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

Study of direct CP violation in B±→J/ ψK±(π±) decays

We present a search for direct CP violation in B±→J/ ψK±(π±) decays. The event sample is selected from 2.8fb-1 of pp̄ collisions recorded by D0 experiment in run II of the Fermilab Tevatron Collider. The charge asymmetry ACP(B+→J/ψK+)=+0.0075±0. 0061(stat)±0.0030(syst) is obtained using a sample of approximately 40000 B±→J/ψK± decays. The achieved precision is of the same level as the expected deviation predicted by some extensions of the standard model. We also measured the charge asymmetry ACP(B+→J/ψπ+)=-0. 09±0.08(stat)±0.03(syst). © 2008 The American Physical Society.

Efeitos ambientais e genéticos sobre escores visuais e ganho de peso à desmama de animais formadores da raça Brangus

Estudaram-se os efeitos da idade da vaca ao parto e da idade do animal à desmama, bem como os efeitos genéticos aditivo direto e materno e da heterozigose individual, sobre os escores visuais de conformação, precocidade e musculatura e ganho de peso do nascimento à desmama, de animais formadores da raça Brangus. Foram analisados 53.683, 45.136, 52.937 e 56.471 dados de conformação, precocidade e musculatura à desmama e ganho de peso do nascimento à desmama, respectivamente, de animais nascidos entre 1986 e 2002, provenientes do arquivo zootécnico da empresa Gensys Consultores Associados S/C Ltda. Os efeitos de ambiente e genéticos sobre as características em estudo foram analisados pelo método de quadrados mínimos usando modelos matemáticos que incluíram grupo de contemporâneos como variável classificatória e a idade da vaca ao parto, a idade do animal à desmama e os efeitos aditivo direto e materno e da heterozigose individual como co-variáveis. Todos os efeitos incluídos nos modelos afetaram significativamente as características avaliadas, com exceção do efeito da idade da vaca ao parto sobre o ganho de peso do nascimento à desmama e do efeito aditivo materno sobre todas as características estudadas. Os efeitos ambientais e genéticos revelaram-se importantes fontes de variação para as características estudadas e devem, pois, ser considerados na distinção e comparação dos animais para seleção.

Applied models to biodegradation kinetics of lubricant and vegetable oils in wastewater

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)