Le equazioni di Maxwell

I fenomeni elettrici e magnetici erano stati considerati per centinaia di anni come fenomeni naturali indipendenti tra loro. Nella seconda metà del XIX secolo James Clerk Maxwell elaborò una teoria completa dell'elettromagnetismo alla quale contribuirono un gran numero di scienziati quali, tra gli altri, Charles Augustin de Coulomb, André-Marie Ampère, Hans Christian Ørsted, Carl Friedrich Gauss e Michel Faraday. Maxwell, in particolare, raccolse i diversi risultati conseguiti da questi ricercatori e li riformulò sotto forma di un insieme di equazioni, ora note col nome di equazioni di Maxwell. La formulazione di Maxwell della teoria unificata dell'elettromagnetismo è considerata tra le maggiori conquiste nella storia della Fisica e la sua influenza sui successivi sviluppi sia della Fisica che della Tecnologia può difficilmente essere sottovalutata. La società moderna è completamente dipendente dalle applicazioni dell'elettromagnetismo per le comunicazioni, i trasporti, il trasferimento dell'energia e può essere difficile per le persone di oggi comprendere fino a che punto un risultato scientifico di circa 160 anni fa influenzi la nostra esistenza. Questa nota ha l'obiettivo di tracciare il percorso storico che ha condotto alla formalizzazione matematica dell'elettromagnetismo classico

Literatures of Stress: Thermodynamic Physics and the Poetry and Prose of Gerard Manley Hopkins

This dissertation examines two of the various literatures of energy in Victorian Britain: the scientific literature of the North British school of energy physics, and the poetic and prose literature of Gerard Manley Hopkins. As an interdisciplinary effort, it is intended for several audiences. For readers interested in science history, it offers a history of two terms – stress and strain – central to modern physics. As well, in discussing the ideas of various scientific authors (primarily William John Macquorn Rankine, William Thomson, P.G. Tait, and James Clerk Maxwell), it indicates several contributions these figures made to larger culture. For readers of Hopkins’ poems and prose, this dissertation corresponds with a recent trend in criticism in its estimation of Hopkins as a scientifically informed writer, at least in his years post-Stonyhurst. Accordingly, this dissertation presents readings of Hopkins’ poetry and prose in light of developments in Victorian energy physics. Three claims span the chapters pertaining to Hopkins’ oeuvre: First, that Hopkins’ distinctive terminology of stress and instress expresses the energetic relations between objects. Second, that Hopkins’ metaphors and analogies are unusual in that they often signify literal relationships between things compared, particularly when metaphysical forms of stress or instress are likened to physical forms of energy. And third, that in Hopkins’ writings the natural world and the supernatural order of creation are contiguous, and that energy suffuses both

An Invitation to Generalized Minkowski Geometry

The present thesis contributes to the theory of generalized Minkowski spaces as a continuation of Minkowski geometry, i.e., the geometry of finite-dimensional normed spaces over the field of real numbers. In a generalized Minkowski space, distance and length measurement is provided by a gauge, whose definition mimics the definition of a norm but lacks the symmetry requirement. This seemingly minor change in the definition is deliberately chosen. On the one hand, many techniques from Minkowski spaces can be adapted to generalized Minkowski spaces because several phenomena in Minkowski geometry simply do not depend on the symmetry of distance measurement. On the other hand, the possible asymmetry of the distance measurement set up by gauges is nonetheless meaningful and interesting for applications, e.g., in location science. In this spirit, the presentation of this thesis is led mainly by minimization problems from convex optimization and location science which are appealing to convex geometers, too. In addition, we study metrically defined objects, which may receive a new interpretation when we measure distances asymmetrically. To this end, we use a combination of methods from convex analysis and convex geometry to relate the properties of these objects to the shape of the unit ball of the generalized Minkowski space under consideration