848 research outputs found
Asymptotic stability for nonlinear Kirchhoff systems
No full textWe study the asymptotic stability for solutions of the nonlinear damped Kirchhoff system, with homogeneous Dirichlet boundary conditions, under fairly natural assumptions on the external force f and the distributed damping Q. Then the results are extended to a more delicate problem involving also an internal dissipation of higher order, the so called strongly damped Kirchhoff system. Finally, the study is further extended to strongly damped Kirchhoff–polyharmonic systems, which model several interesting problems of the Woinowsky–Krieger type
The Category of Kirchhoff Relations
No full textWe define the category of Kirchhoff relations to consist of those Lagrangian relations that conserve total momentum – a condition that can also be interpreted as Kirchhoff’s current law. We study and characterize different subcategories of Kirchhoff relations and present universal sets of generators of the different subcategories of Kirchhoff relations. These generators can be interpreted as junctions of ideal wires, resistances, voltage sources and current source
Exponential decay of solutions of a semilinear Lipschitz Perturbation of Kirchhoff-Carrier Wave Equation
No full textIn this work study the existence of global solutions and exponential decay of energy of the mixed problem for perturbed Kirchhoff-Carrier wave equationu" - M(a(u)) Δu + F(u) + γ u’ = fwhere F is a Lipschitz function.Neste trabalho estuda-se a existência de solução global e o decaimento exponencial da solução do problema misto para a equação perturbada de Kirchhoff – Carrieru" - M(a(u)) Δu + F(u) + γ u’ = fonde F é uma função Lipschitzian
Asymptotic stability for anisotropic Kirchhoff systems
No full textAbstractWe study the question of asymptotic stability, as time tends to infinity, of solutions of dissipative anisotropic Kirchhoff systems, involving the p(x)-Laplacian operator, governed by time-dependent nonlinear damping forces and strongly nonlinear power-like variable potential energies. This problem had been considered earlier for potential energies which arise from restoring forces, whereas here we allow also the effect of amplifying forces. Global asymptotic stability can then no longer be expected, and should be replaced by local stability. The results are further extended to the more delicate problem involving higher order damping terms
Global Nonexistence for Nonlinear Kirchhoff Systems
No full textIn this paper we consider the problem of non-continuation of solutions of dissipative nonlinear Kirchhoff systems, involving the p(x)-Laplacian operator and governed by nonlinear driving forces f = f (t, x, u), as well as nonlinear external damping terms Q = Q(t, x, u, u_t ), both of which could significantly dependent on the time t . The theorems are obtained through the study of the natural energy Eu associated to the solutions u of the systems. Thanks to a new approach of the classical potential well and concavity methods, we show the nonexistence of global solutions, when the initial energy is controlled above by a critical value; that is, when the initial data belong to a specific region in the phase plane. Several consequences, interesting in applications, are given in particular subcases. The results are original also for the scalar standard wave equation when p(x)=2 and even for problems linearly damped
Modelamentos de Kirchhoff/Born para propagação de ondas
No full textOrientadores: Martin Tygel, Lucio Tunes dos SantosTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: Para descrever o campo de onda refletido de um único refletor (alvo) em um meio elástico anisotrópico não homogêneo existem duas aproximações integrais muito conhecidas. Estas são a integral de Born que integra sobre as perturbações supostamente pequenas em um volume contendo o refletor e a integral de Kirchhoff que integra o campo especularmente refletido ao longo do refletor. Nesta tese, mostramos que outras aproximações integrais podem ser obtidas a partir destas duas. A integral de Born pode ser transformada numa integral de superfície ao longo do refletor que é chamada de integral de Born-Kirchhoff por exibir características das duas integrais clássicas. Um outra aproximação integral se obtem por substituição do coeficiente de reflexão utilizado na aproximação de Kirchhoff por uma versão que deixa a expressão resultante recíproca. Esta aproximação é chamada de integral de Kirchhoff Recíproca. Todas estas aproximações em integrais de superfície tem a mesma contribuição no ponto de reflexão especular. Assim, a avaliação assintótica de todas elas usando o método de fase estacionária fornece a expressão da teoria de raios. Investigamos estas aproximações numericamente para o caso acústico. Em nossos experimentos numéricos, todas as integrais mencionadas aproximam razoavelmente bem o campo de onda refletido (calculado pelo método de Diferenças Finitas). Porém, a qualidade da aproximação depende do modelo investigado. Também não se pode determinar um método que forneça sempre o melhor resultado. Apesar disso, a aproximação pela integral de Born-Kirchhoff mostrou-se a mais estável, fornecendo em todos os exemplos estudados um resultado de boa qualidade, sendo ou o melhor ou perto do melhor. Além disso, o tempo computacional para este método é (junto com o da aproximação Kirchhoff Recíproca) o mais baixo de todos os métodos sob investigação.Abstract: To describe the reflected wavefield of a single (target) reflector in an elastic anisotropic medium, there exist two well-known integral approximations. These are the Born integral that integrates over supposedly small perturbations within a volume that contains the reflector, and the Kirchhoff integral that integrates over the specularly reflected field along the reflector. In this theses, we show that other integral approximations can be obtained starting from these two. The Born integral can be transformed into a surface integral along the reflector, which is called the Born-Kirchhoff integral since it exhibits characteristics of both the classical integral. Another integral approximation is obtained by substituting the reflection coefficient that is used in the Kirchhoff approximation by another version that turns the resulting integral expression reciprocal. This approximation is called the Reciprocal Kirchhoff integral. All these approximations in the form of surface integrals contain the same contribution at the specular reflection point. Therefore, their asymptotic evaluations using the stationary-phase method yields the ray-theory expression. We numerically investigate these approximations in the acoustic case. In all our numerical experiments, all above integrals approximate the reflected wavefield (as calculated by the Finite Differences method) quite well. However, the quality of the approximation depends on the investigated model. Also, a method that would always provide the best approximation cannot be determined. In spite of that, the Born-Kirchhoff integral proved to be the most stable approximation that yielded in all studied examples a result of good quality, either the best one or close to the best one. Moreover, the computation time for this method is (together with that for the Reciprocal Kirchhoff approximation) the smallest one of all methods under investigation.DoutoradoDoutor em Matemática Aplicad
Dialectical Logic K-model: On Multidimensional Discrete Dynamical Sampling System and Further Properties of Kirchhoff Matrices
No full textIn order to solve the problem of multidimensional logic variable true value function remarked in the paper(Yaozhi Jiang., 2017), now author has used discrete multiple Fourier transform to deal with the problem remarked above, and obtained an theoretical formulations of discrete multidimensional Fourier transform for that multidimensional logic variable true value function is unknown or we need the frequency properties of multidimensional logic variable true value function. Another problem is about further and deeper properties of Kirchhoff matrices defined in author’s paper(Yaozhi Jiang., 2017), author has established a series of matrix expression for Kirchhoff laws and some new properties of Kirchhoff matrices. These results are all compute-able and complicated. </jats:p
The Kirchhoff Formulas for Moving Surfaces in Aerocoustics - The Subsonic and Supersonic Case
No full textOne of the active areas of computational aeroacoustics is the application of the Kirchhoff formulas to the problems of the rotating machinery noise prediction. The original Kirchhoff formula was derived for a stationary surface. In 1988, Farassat and Myers derived a Kirchhoff Formula obtained originally by Morgans using modern mathematics. These authors gave a formula particularly useful for applications in aeroacoustics. This formula is for a surface moving at subsonic speed. Later in 1995 these authors derived the Kirchhoff formula for a supersonically moving surface. This technical memorandum presents the viewgraphs of a day long workshop by the author on the derivation of the Kirchhoff formulas. All necessary background mathematics such as differential geometry and multidimensional generalized function theory are discussed in these viewgraphs. Abstraction is kept at minimum level here. These viewgraphs are also suitable for understanding the derivation and obtaining the solutions o..
Investigating Understanding
No full textWith a fresh and innovative perspective, Leonie Kirchhoff introduces an interdisciplinary xamination of literary understanding, drawing upon cognitive, educational, and literary studies. At the heart of the study is a fascinating exploration of explanatory annotations written by university students, providing valuable insights into the complexities of understanding poetry in general and the timeless verses of Shakespeare’s “Sonnet 43” in particular. The students’ annotations serve as a distinctive methodological tool, en abling the author to critically evaluate the existing research on understanding as presented by the three fields of study. Through this rigorous exploration, the author maps and reflects on long-term hermeneutic processes. This scholarly work provides a unique contribution to the field and offers an essential resource for academics, researchers, and scholars seeking a deeper understanding of the intricate processes involved in literary understanding
The Kirchhoff Formulas for Moving Surfaces in Aeroacoustics - The Subsonic and Supersonic Cases
No full textOne of the active areas of computational aeroacoustics is the application of the Kirchhoff formulas to the problems of the rotating machinery noise predictions. The original Kirchhoff formula was derived for a stationary surface. In 1988, Farassat and Myers derived a Kirchhoff Formula obtained originally by Morgans using modem mathematics. These authors gave a formula particularly useful for applications in aeroacoustics. This formula is for a surface moving at subsonic speed. Later in 1995 these authors derived the Kirchhoff formula for a super-sonically moving surface. This technical memorandum presents the viewgraphs of a day long workshop by the author on the derivation of the Kirchhoff formulas. All necessary background mathematics such as differential geometry and multidimensional generalized function theory are discussed in these viewgraphs. Abstraction is kept at minimum level here. These viewgraphs are also suitable for understanding the derivation and obtaining the solutions of the Ffowcs Williams-Hawkings equation. In the first part of this memorandum, some introductory remarks are made on generalized functions, the derivation of the Kirchhoff formulas and the development and validation of Kirchhoff codes. Separate lists of references by Lyrintzis, Long, Strawn and their co-workers are given in this memorandum. This publication is aimed at graduate students, physicists and engineers who are in need of the understanding and applications of the Kirchhoff formulas in acoustics and electromagnetics
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