The Hausdorff moments in statistical mechanics

A new method for solving the Hausdorff moment problem is presented which makes use of Pollaczek polynomials. This problem is severely ill posed; a regularized solution is obtained without any use of prior knowledge. When the problem is treated in the L 2 space and the moments are finite in number and affected by noise or round‐off errors, the approximation converges asymptotically in the L 2 norm. The method is applied to various questions of statistical mechanics and in particular to the determination of the density of states. Concerning this latter problem the method is extended to include distribution valued densities. Computing the Laplace transform of the expansion a new series representation of the partition function Z(β) (β=1/k BT ) is obtained which coincides with a Watson resummation of the high‐temperature series for Z(β)

Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge

The present work proposes a discussion on the self-energy of charged particles in the framework of nonlinear electrodynamics. We seek magnet- ically stable solutions generated by purely electric charges whose electric and magnetic fields are computed as solutions to the Born-Infeld equa- tions. The approach yields rich internal structures that can be described in terms of the physical fields with explicit analytic solutions. This suggests that the anomalous field probably originates from a magnetic excitation in the vacuum due to the presence of the very intense electric field. In addition, the magnetic contribution has been found to exert a negative pressure on the charge. This, in turn, balances the electric repulsion, in such a way that the self-interaction of the field appears as a simple and natural classical mechanism that is able to account for the stability of the electron charge.Comment: 8 pages, 1 figur

Development and demonstration of a renewable energy based demand/supply decision support tool for the building design profession

Future cities are likely to be characterised by a greater level of renewable energy systems deployment. Maximum impact will be achieved when such systems are used to offset local energy demands in contrast to current philosophy dictating the grid connection of large schemes. This paper reports on the development of a software tool, MERIT, for demand/ supply matching. The purpose of MERIT is to assist with the deployment of renewable energy systems at all scales. This paper describes the procedures used to match heterogeneous supply technologies to a set of demand profiles corresponding to the different possible fuel types

Development of a simulation-based decision support tool for renewable energy integration and demand-supply matching

This paper describes a simulation-based decision support tool, MERIT, which has been developed to assist in the assessment of renewable energy systems by focusing on the degree of match achievable between energy demand and supply. Models are described for the prediction of the performance of PV, wind and battery technologies. These models are based on manufacturers' specifications, location-related parameters and hourly weather data. The means of appraising the quality of match is outlined and examples are given of the application of the tool at the individual building and community levels

Generating Functional for Gauge Invariant Actions: Examples of Nonrelativistic Gauge Theories

We propose a generating functional for nonrelativistic gauge invariant actions. In particular, we consider actions without the usual magnetic term. Like in the Born-Infeld theory, there is an upper bound to the electric field strength in these gauge theories.Comment: 14 pages, 2 figures; v2: misprints correcte

Dynamics of the Born-Infeld dyons

The approach to the dynamics of a charged particle in the Born-Infeld nonlinear electrodynamics developed in [Phys. Lett. A 240 (1998) 8] is generalized to include a Born-Infeld dyon. Both Hamiltonian and Lagrangian structures of many dyons interacting with nonlinear electromagnetism are constructed. All results are manifestly duality invariant.Comment: 11 pages, LATE

Merit - An evaluation tool for 100% renewable energy provision

Islands represent an interesting challenge in terms of energy supply. A great deal of work has been carried out to look at specific aspects of this issue on different islands. Unfortunately, results from one study cannot be easily applied to other islands due to island-specific resources and energy-use profiles. A quantitative evaluation tool (MERIT) is presented here, which is able to match half-hourly energy demands (heat, electricity, hot water and transport) with local supplies. The program examines the energy balance on any scale, from an individual building through to an entire country, thereby providing a powerful and generic aid to decision making. This paper demonstrates the generality and usefulness of MERIT by using it to analyse the options for creating an energy-autonomous community on a typical, small island off the west coast of Scotland. Results are presented showing the feasibility of accomplishing 100% renewable provision on this island using available local resources

Non-diffracting Optical Beams in a Three-level Raman System

Diffractionless propagation of optical beams through atomic vapors is investigated. The atoms in the vapor are operated in a three-level Raman configuration. A suitably chosen control beam couples to one of the transitions, and thereby creates a spatially varying index of refraction modulation in the warm atomic vapor for a probe beam which couples to the other transition in the atoms. We show that a Laguerre-Gaussian control beam allows to propagate single Gaussian probe field modes as well as multi-Gaussian modes and non-Gaussian modes over macroscopic distances without diffraction. This opens perspectives for the propagation of arbitrary images through warm atomic vapors.Comment: 8 pages, 7 figure

Large tunable photonic band gaps in nanostructured doped semiconductors

A plasmonic nanostructure conceived with periodic layers of a doped semiconductor and passive semiconductor is shown to generate spontaneously surface plasmon polaritons thanks to its periodic nature. The nanostructure is demonstrated to behave as an effective material modeled by a simple dielectric function of ionic-crystal type, and possesses a fully tunable photonic band gap, with widths exceeding 50%, in the region extending from mid-infra-red to Tera-Hertz.Comment: 6 pages, 4 figures, publishe

In search of a working notion of lex sportiva

The emergence of a lex specialis regime and its interaction with the established, governing lex generalis in their overlapping spheres of application is always an intriguing legal relationship to explore. In this article, the focus will be on the development of legal principles and rules that have been/can be collectively described as lex sportiva. However, it is notable that those involved in the consideration, usage and application of this notion have not agreed as to the scope and delimitation of the concept. It is debated whether lex sportiva exists in the first place, its legal sources and its purpose. The risk is for the concept becoming redundant when not vilified as a hidden strategy to exclude non-sports-related law from the ambit of sport. Through an examination of the different propositions to the framework of the term, this article will shed light on the existence, utility and limits of the development of this conceptualisation