Transformadas integrais, modelagem fracionária e o sistema de Lotka-Volterra

Pós-graduação em Biometria - IBB

Potenciais singulares na equação de Schrodinger unidimensional via transformada de Laplace

The present work has as its goal to treat well known and interesting unidimensional cases from quantum mechanics through an unusual approach within this eld of physics. The operational method of Laplace transform, in spite of its use by Erwin Schrödinger in 1926 when treating the radial equation for the hydrogen atom, turned out to be forgotten for decades. However, the method has gained attention again for its use as a powerful tool from mathematical physics applied to the quantum mechanics, appearing in recent works. The method is specially suitable to the approach of cases where we have potential functions with even parity, because this implies in eigenfunctions with de ned parity, and since the domain of this transform ranges from 0 to ∞, it su ces that we nd the eigenfunction in the positive semi axis and, with the boundary conditions imposed over the eigenfunction at the origin plus the continuity (discontinuity) of the eigenfunction and its derivative, we make the odd, even or both parity extensions so we can get the eigenfunction along all the axis. Factoring the eigenfunction behavior at in nity and origin, we take the due care with the points that might bring us problems in the later steps of the solving process, thus we can manipulate the Schrödinger's Equation regardless of time, so that way we make it convenient to the application of Laplace transform. The Chapter 3 shows the methodology that must be followed in order to search for the solutions to each problem

Solução da equação de difusão unidimensional transiente para o estudo da dispersão de poluentes na camada limite planetária

Neste trabalho apresenta-se uma solução analítica para a dispersão vertical turbulenta em uma Camada Limite Convectiva e em uma Camada Limite Estável. A equação analisada considera a difusão com velocidades finitas, o que representa o transporte turbulento fisicamente correto. Considerando o caráter não-local, adicionam-se na equação que representa uma fonte área instantânea, termos como: o tempo de relaxação, a assimetria, a escala de tempo Lagrangeana e a velocidade turbulenta vertical. A solução é obtida utilizando-se a técnica da Transformada de Laplace. Os parâmetros que encerram a turbulência são derivados da teoria de difusão estatística de Taylor combinada com a teoria de similaridade. Foram utilizados coeficientes de difusão especáficos para cada uma das camadas. A transformada inversa é obtida através do esquema numérico de quadratura Gaussiana. São apresentadas várias simulações para diferentes alturas de fonte área e obtém-se o valor da concentração para alturas próximas ao solo e próximas ao topo da Camada Limite Planetária. A inserção do termo de contra-gradiente na equação resultou em uma pequena influência na concentração de poluentes, observada de forma mais expressiva na Camada Limite Convectiva.

Análisis vectorial, ecuaciones diferenciales y transformadas de Fourier y de Laplace.

La presente obra está pensada como libro de texto para la asignatura de cálculo de los diferentes estudios de la Escuela Técnica Superior de Ingenieros Industriales y de Telecomunicación de la Universidad de Cantabria. A medida que se presenta la teoría se incluye, con objeto de ilustrarla, un buen número de ejemplos sencillos. Cada capítulo finaliza con ejercicios resueltos detalladamente y una relación de ejercicios propuestos, algunos de ellos incluídos en exámen. Se desarrollan cuatro temas fundamentalmente: cálculo vectorial, ecuaciones diferenciales ordinarias, integral de Fourier y transformada de Laplace.

Application of Laplace transform technique to the solution of certain third-order non-linear systems

A number of papers have appeared on the application of operational methods and in particular the Laplace transform to problems concerning non-linear systems of one kind or other. This, however, has met with only partial success in solving a class of non-linear problems as each approach has some limitations and drawbacks. In this study the approach of Baycura has been extended to certain third-order non-linear systems subjected to non-periodic excitations, as this approximate method combines the advantages of engineering accuracy with ease of application to such problems. Under non-periodic excitations the method provides a procedure for estimating quickly the maximum response amplitude, which is important from the point of view of a designer. Limitations of such a procedure are brought out and the method is illustrated by an example taken from a physical situation.

关于Young-Laplace公式的吉布斯自由能证明

对于为论证球形液滴附加压强的Young-Laplace公式而设计的一个理想实验,有文献试图借助吉布斯自由能函数进行证明,本文给出符合这一条件的证明方法.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Recorrido y reflexiones en torno al pensamiento analítico de Georges Laplace: movimiento, interdependencia y arquetipos en la construcción de una arqueología científica

Homenaje a Georges Laplace, realizado en Vitoria-Gasteiz el 13,14 y 15 de noviembre de 2012. Edición a cargo de Aitor Calvo, Aitor Sánchez, Maite García-Rojas y Mónica Alonso-Eguíluz.

Arqueozoología analítica. Otro ejemplo práctico derivado de la obra de Georges Laplace

Homenaje a Georges Laplace, realizado en Vitoria-Gasteiz el 13,14 y 15 de noviembre de 2012. Edición a cargo de Aitor Calvo, Aitor Sánchez, Maite García-Rojas y Mónica Alonso-Eguíluz.

Ecuaciones diferenciales ordinarias para estudiantes de Física

Conceptos fundamentales. - Ecuaciones de primer orden. - Ecuaciones de orden superior. - Sistemas de ecuaciones. - Transformación de Laplace. - Solución para series de ecuaciones lineales. - Métodos aproximados. - Teoría de la estabilidad. - Problemas de contorno de Sturm-Liouville. - Apéndice: Teoremas fundamentales. Métodos simbólicos. Resumen de métodos analíticos exactos. Definición y propiedades de algunas funciones. Tablas de transformadas de Laplace. Tablas de transformadas de Fourier. Soluciones y sugerencias para algunos ejercicios.

Permanencias transformadas. Arquitectura industrial del movimiento moderno en Gipuzkoa (1928-1959)

598 p.