A Model for Classical Space-time Co-ordinates

Field equations with general covariance are interpreted as equations for a target space describing physical space time co-ordinates, in terms of an underlying base space with conformal invariance. These equations admit an infinite number of inequivalent Lagrangian descriptions. A model for reparametrisation invariant membranes is obtained by reversing the roles of base and target space variables in these considerations.Comment: 9 pages, Latex. This was the basis of a talk given at the Argonne National Laboratory 1996 Summer Institute : Topics on Non-Abelian Duality June 27-July 1

A systems analysis of solar power potential in coming decades

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaves 31-32).Energy is a very important aspect of human life. In the past few centuries, energy consumption has increased dramatically to a point where humans are very much dependant of energy. Under the current nonrenewable energy extraction technique of burning fossil fuels there are many externalities that are negatively impacting the earth. Society is approaching a limit where these formerly cheap forms of energy will become increasingly more expensive due to the difficulty of their extraction. As such, it is apparent that new renewable forms of energy will develop out of necessity to fulfill the energy demand. The purpose of this paper is to examine the different aspects of the promising area of solar energy. The conclusions of the analysis show that a portfolio of alternative energies will be necessary in the future with solar energy, in particular photovoltaic cells, filling the bulk of the energy generation.by Chris Bateman.S.B

Feasibility study of an Integrated Program for Aerospace vehicle Design (IPAD). Volume 3: Support of the design process

The user requirements for computer support of the IPAD design process are identified. The user-system interface, language, equipment, and computational requirements are considered

A probabilistic approach to some results by Nieto and Truax

In this paper, we reconsider some results by Nieto and Truax about generating functions for arbitrary order coherent and squeezed states. These results were obtained using the exponential of the Laplacian operator; more elaborated operational identities were used by Dattoli et al. \cite{Dattoli} to extend these results. In this note, we show that the operational approach can be replaced by a purely probabilistic approach, in the sense that the exponential of derivatives operators can be identified with equivalent expectation operators. This approach brings new insight about the kinks between operational and probabilistic calculus.Comment: 2nd versio

Capacitors can radiate - some consequences of the two-capacitor problem with radiation

We fill a gap in the arguments of Boykin et al [American Journal of Physics, Vol 70 No. 4, pp 415-420 (2002)] by not invoking an electric current loop (i.e. magnetic dipole model) to account for the radiation energy loss, since an obvious corollary of their results is that the capacitors should radiate directly even if the connecting wires are shrunk to zero length. That this is so is shown here by a direct derivation of capacitor radiation using an oscillating electric dipole radiator model for the capacitors as well as the alternative less widely known magnetic 'charge' current loop representation for an electric dipole [see for example "Electromagnetic Waves" by S.A.Schlekunoff, van Nostrand (1948)]. Implications for Electromagnetic Compliance (EMC) issues as well as novel antenna designs further motivate the purpose of this paper.Comment: 5 Pages with No figure

Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity

We examine the completeness of bi-orthogonal sets of eigenfunctions for non-Hermitian Hamiltonians possessing a spectral singularity. The correct resolutions of identity are constructed for delta like and smooth potentials. Their form and the contribution of a spectral singularity depend on the class of functions employed for physical states. With this specification there is no obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

Light-activated modulation and coupling in integrated polymer-liquid crystal systems

We explore the transfer of an incident light pattern onto the liquid crystal (LC) bulk in a photorefractive cell through an integrated photoconducting layer that modulates the electric field applied to the device. The electrical properties and the strength of modulation are investigated as a function of the incident light intensity as well as the frequency and amplitude of the applied voltage, for two LCs with very different electrical conductivity. A simplified electrical model of the cell is proposed, demonstrating that the LC conductivity is a key factor determining the beam-coupling strength

Perturbation theory in radial quantization approach and the expectation values of exponential fields in sine-Gordon model

A perturbation theory for Massive Thirring Model (MTM) in radial quantization approach is developed. Investigation of the twisted sector in this theory allows us to calculate the vacuum expectation values of exponential fields $exp iaphi (0)$ of the sine-Gordon theory in first order over Massive Thirring Models coupling constant. It appears that the apparent difficulty in radial quantization of massive theories, namely the explicite ''time'' dependence of the Hamiltonian, may be successfully overcome. The result we have obtained agrees with the exact formula conjectured by Lukyanov and Zamolodchikov and coincides with the analogous calculations recently carried out in dual angular quantization approach by one of the authors.Comment: 16 pages, no figures, LaTe