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)

Influence of phosphated cross-linked high amylose on in vitro release of different drugs

The influence of structural characteristics of high amylose cross-linked at different degrees on the release of drugs with important molecular differences, namely sodium diclophenac (SD) and nicotinamide (NI), was assessed in vitro from non-compacted systems. The release profiles were related with classical kinetic mathematical models for better understanding of the release mechanism. An increase in polymer cross-linking degree resulted in longer release time for both drugs, although SD generally was released slower than NI. SD release from samples cross-linked at 2% of basis was driven mainly by Fickian diffusion, while from samples cross-linked at 4% of basis follows anomalous mechanism. Inversely, anomalous mechanism was responsible for NI release from 2% samples and Fickian diffusion from 4% samples. Results suggest that the performance of cross-linked high amylose as excipient for controlled drug release not only depends on cross-linking degree but also is highly influenced by structural characteristics of the drug. (C) 2009 Elsevier Ltd. All rights reserved.

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

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

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.

Non-linear growth models for bullfrog tadpoles

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

TWO DECOMPOSITION APPROACHES APPLIED TO THE MULTI-AREA OPTIMAL REACTIVE POWER FLOW PROBLEM

This paper applies two methods of mathematical decomposition to carry out an optimal reactive power flow (ORPF) in a coordinated decentralized way in the context of an interconnected multi-area power system. The first method is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). The second method uses a decomposition technique based on the Karush-Kuhn-Tucker (KKT) first-order optimality conditions. The viability of each method to be used in the decomposition of multi-area ORPF is studied and the corresponding mathematical models are presented. The IEEE RTS-96, the IEEE 118-bus test systems and a 9-bus didactic system are used in order to show the operation and effectiveness of the decomposition methods.

Evaluation and identification of lightning models by artificial neural networks

This paper describes a novel approach for mapping lightning models using artificial neural networks. The networks acts as identifier of structural features of the lightning models so that output parameters can be estimated and generalized from an input parameter set. Simulation examples are presented to validate the proposed approach. More specifically, the neural networks are used to compute electrical field intensity and critical disruptive voltage taking into account several atmospheric and structural factors, such as pressure, temperature, humidity, distance between phases, height of bus bars, and wave forms. A comparative analysis with other approaches is also provided to illustrate this new methodology.

A comparative evaluation of open loop and closed loop drug administration strategies in the treatment of AIDS.

In recent years, many researchers in the field of biomedical sciences have made successful use of mathematical models to study, in a quantitative way, a multitude of phenomena such as those found in disease dynamics, control of physiological systems, optimization of drug therapy, economics of the preventive medicine and many other applications. The availability of good dynamic models have been providing means for simulation and design of novel control strategies in the context of biological events. This work concerns a particular model related to HIV infection dynamics which is used to allow a comparative evaluation of schemes for treatment of AIDS patients. The mathematical model adopted in this work was proposed by Nowak & Bangham, 1996 and describes the dynamics of viral concentration in terms of interaction with CD4 cells and the cytotoxic T lymphocytes, which are responsible for the defense of the organism. Two conceptually distinct techniques for drug therapy are analyzed: Open Loop Treatment, where a priori fixed dosage is prescribed and Closed Loop Treatment, where the doses are adjusted according to results obtained by laboratory analysis. Simulation results show that the Closed Loop Scheme can achieve improved quality of the treatment in terms of reduction in the viral load and quantity of administered drugs, but with the inconvenience related to the necessity of frequent and periodic laboratory analysis.

One-dimensional analytical model for oxide thin film growth on Ti metal layers during laser heating in air

This paper presents the theoretical and experimental results for oxide thin film growth on titanium films previously deposited over glass substrate. Ti films of thickness 0.1 μm were heated by Nd:YAG laser pulses in air. The oxide tracks were created by moving the samples with a constant speed of 2 mm/s, under the laser action. The micro-topographic analysis of the tracks was performed by a microprofiler. The results taken along a straight line perpendicular to the track axis revealed a Gaussian profile that closely matches the laser's spatial mode profile, indicating the effectiveness of the surface temperature gradient on the film's growth process. The sample's micro-Raman spectra showed two strong bands at 447 and 612 cm -1 associated with the TiO 2 structure. This is a strong indication that thermo-oxidation reactions took place at the Ti film surface that reached an estimated temperature of 1160 K just due to the action of the first pulse. The results obtained from the numerical integration of the analytical equation which describes the oxidation rate (Wagner equation) are in agreement with the experimental data for film thickness in the high laser intensity region. This shows the partial accuracy of the one-dimensional model adopted for describing the film growth rate. © 2001 Elsevier Science B.V.

Modified barrier method for optimal power flow problem

In this paper is presented a new approach for optimal power flow problem. This approach is based on the modified barrier function and the primal-dual logarithmic barrier method. A Lagrangian function is associated with the modified problem. The first-order necessary conditions for optimality are fulfilled by Newton's method, and by updating the barrier terms. The effectiveness of the proposed approach has been examined by solving the Brazilian 53-bus, IEEE118-bus and IEEE162-bus systems.

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.

Remarks on orthotropic elastic models applied to wood

Wood is generally considered an anisotropic material. In terms of engineering elastic models, wood is usually treated as an orthotropic material. This paper presents an analysis of two principal anisotropic elastic models that are usually applied to wood. The first one, the linear orthotropic model, where the material axes L (Longitudinal), R(radial) and T(tangential) are coincident with the Cartesian axes (x, y, z), is more accepted as wood elastic model. The other one, the cylindrical orthotropic model is more adequate of the growth caracteristics of wood but more mathematically complex to be adopted in practical terms. Specifically due to its importance in wood elastic parameters, this paper deals with the fiber orientation influence in these models through adequate transformation of coordinates. As a final result, some examples of the linear model, which show the variation of elastic moduli, i.e., Young's modulus and shear modulus, with fiber orientation are presented.