Zur Erinnerung an Gustav Robert Kirchhoff / Aufsätze von Robert v Helmholtz, August W. v. Hofmann, Friedrich Pockels und Emil Warburg zusammengestellt von Gabriele Dörflinger

Gustav Robert Kirchhoff (1824-1887) lehrte von 1854 bis 1875 als Physikprofessor an der Heidelberger Universität. Hier entdeckte er 1859/60 gemeinsam mit Robert Wilhelm Bunsen die Spektralanalyse. Die Aufsatzsammlung enthält: 1.) Robert von Helmholtz: Gustav Robert Kirchhoff 2.) August W. Hofmann: Gedächtnisrede auf Gustav Robert Kirchhoff 3.) Friedrich Pockels: Gustav Robert Kirchhoff 4.) Emil Warburg: Zur Erinnerung an Gustav Robert Kirchhof

Das befreite Braunschweig in drei Gesängen / von [Karl Friedrich] Pockels

This find is registered at Portable Antiquities of the Netherlands with number PAN-0001477

Robin conditions on the Euclidean ball

Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions. The method involves a large mass asymptotic limit which is carried out in detail for d=2 and d=4 incidentally producing some specific summations and identities. Extensive use is made of the Watson-Kober summation formula.Comment: 36p,JyTex, misprints corrected and a section on the massive case adde

Polyhedral Cosmic Strings

Quantum field theory is discussed in M\"obius corner kaleidoscopes using the method of images. The vacuum average of the stress-energy tensor of a free field is derived and is shown to be a simple sum of straight cosmic string expressions, the strings running along the edges of the corners. It does not seem possible to set up a spin-half theory easily.Comment: 15 pages, 4 text figures not include

Green's Function in Some Contributions of 19th Century Mathematicians

AbstractMany questions in mathematical physics lead to a solution in terms of a harmonic function in a closed region with given continuous boundary values. This problem is known as Dirichlet's problem, whose solution is based on an existence principle—the so-called Dirichlet's principle. However, in the second half of the 19th century many mathematicians doubted the validity of Dirichlet's principle. They used direct methods in order to overcome the difficulties arising from this principle and also to find an explicit solution of the Dirichlet problem at issue. Many years before, one of these methods had been developed by Green in 1828, which consists in finding a function—called a Green's function—satisfying certain conditions and appearing in the analytical expression of the solution of the given Dirichlet problem. Helmholtz, Riemann, Lipschitz, Carl and Franz Neumann, and Betti deduced functions similar to Green's function in order to solve problems in acoustics, electrodynamics, magnetism, theory of heat, and elasticity. Copyright 2001 Academic Press.Molte questioni fisico matematiche conducono a una soluzione in termini di una funzione armonica in una regione chiusa con dati valori continui al contorno. Questo problema è noto come problema di Dirichlet, la cui soluzione si basa su un principio di esistenza, il cosiddetto principio di Dirichlet. Tuttavia, nella seconda metà del diciannovesimo secolo, molti matematici cominciarono a mettere in dubbio la validità del principio di Dirichlet. Sia per superare le difficoltà sorte da tale principio, sia per trovare una soluzione esplicita del problema di Dirichlet dato, essi presero ad adoperare metodi diretti. Molti anni prima, uno di questi metodi era stato sviluppato da Green nel 1828 e consiste nel trovare una funzione, detta funzione di Green, che soddisfa certe condizioni e mediante la quale si rappresenta analiticamente la soluzione del problema di Dirichlet in questione. Helmholtz, Riemann, Lipschitz, Carl e Franz Neumann, e Betti dedussero delle funzioni simili alla funzione di Green allo scopo di risolvere problemi di acustica, elettrodinamica, magnetismo, teoria del calore ed elasticità. Copyright 2001 Academic Press.Nombreuses questions de physique mathématique mènent à une solution en termes d'une fonction harmonique dans une région fermée avec des valeurs continus donnés sur la frontière. Ce problème est connu comme problème de Dirichlet, la solution duquel est fondée sur un principe d'existence, le principe de Dirichlet. Cependant dans la seconde moitié du dix-neuvième siècle plusieurs mathématiciens mirent en doute la validité du principe de Dirichlet. Alors ils employèrent des méthodes directes soit pour surmonter le difficultés nées de ce principe, soit pour déduire une solution explicite du problème de Dirichlet en question. Avant plusieurs annèes une de ces méthodes a été développée par Green en 1828 et consiste à trouver une fonction, dite fonction de Green, qui satisfait certaines conditions et moyennant laquelle on représente analytiquement la solution du problème de Dirichlet donné. Helmholtz, Riemann, Lipschitz, Carl et Franz Neumann, et Betti déduisirent des fonctions semblables à la fonction de Green pour résoudre de problèmes d'acoustique, électrodynamique, magnétisme, théorie de la chaleur et élasticité. Copyright 2001 Academic Press.MSC 1991 subject classifications: 01A55, 31-03

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio

Membranes by the Numbers

Many of the most important processes in cells take place on and across membranes. With the rise of an impressive array of powerful quantitative methods for characterizing these membranes, it is an opportune time to reflect on the structure and function of membranes from the point of view of biological numeracy. To that end, in this article, I review the quantitative parameters that characterize the mechanical, electrical and transport properties of membranes and carry out a number of corresponding order of magnitude estimates that help us understand the values of those parameters.Comment: 27 pages, 12 figure