An approach to nonstandard quantum mechanics

We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus be treated on an equal footing. We show that the formalism extends the standard formulation of quantum mechanics. To this end we develop the Loeb-function calculus in nonstandard hulls. The idea is to perform calculations in a hyperfinite-dimensional space, but to interpret expectation values in the corresponding nonstandard hull. We further apply the framework to non-relativistic quantum scattering theory. For time-dependent scattering theory, we identify the starting time and the finishing time of a scattering experiment, and we obtain a natural separation of time scales on which the preparation process, the interaction process, and the detection process take place. For time-independent scattering theory, we derive rigorously explicit formulas for the M{\o}ller wave operators and the S-Matrix

General purpose computer programs for numerically analyzing linear ac electrical and electronic circuits for steady-state conditions

Digital computer programs determine steady-state performance characteristics of active and passive linear circuits. The ac analysis program solves the basic circuit parameters. The compiler program solves these circuit parameters and in addition provides a more versatile program by allowing the user to perform mathematical and logical operations

R^2 Dark Matter

There is a non-trivial four-derivative extension of the gravitational spectrum that is free of ghosts and phenomenologically viable. It is the so called $R^2$-gravity since it is defined by the only addition of a term proportional to the square of the scalar curvature. Just the presence of this term does not improve the ultraviolet behaviour of Einstein gravity but introduces one additional scalar degree of freedom that can account for the dark matter of our Universe.Comment: 6 pages, 1 figure, to appear in the Proceedings of the sixth International Workshop on the Dark Side of the Universe (DSU2010) Leon, Guanajuato, Mexico 1-6 June 201

The Potential of Freeform Construction Processes

The level of automation technology and processes control found in modern day construction lags significantly behind other industries such as automotive and aerospace. The construction industry has health and safety issues and still uses traditional methods of procurement. These problems are compounded by diminishing skills in the labour force. Methods of production must change if these issues are to be resolved and Freeform Construction is a collection of processes that could have potential impact. This paper outlines some of the major issues facing construction and sets a context with examples of digital fabrication in construction. Freeform Construction is defined and potential applications are presented and related to application scale. The viability of two potential applications are investigated in terms of cost.Mechanical Engineerin

Theoretical study of intramolecular vibrational relaxation of acetylenic CH vibration for v=1 and 2 in large polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si

Quantum calculations are reported for the intramolecular vibrational energy redistribution and absorption spectra of the first two excited states of the acetylenic CH stretch vibration in the polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si. Using approximate potential energy surfaces, comparison is made with the corresponding recent experimental spectra. It is found that a model of intramolecular vibrational relaxation based on the assumption of sequential off-resonance transitions via third and fourth order vibrational couplings (as opposed to direct high order couplings) is in agreement with experimental results on spectral linewidths. In a semiclassical limit this type of relaxation corresponds to a dynamic tunneling in phase space. It is shown that the local density of resonances of third and fourth order, rather than the total density of states, plays a central role for the relaxation. It is found that in the Si molecule an accidental absence of appropriate resonances results in a bottleneck in the initial stages of relaxation. As a result, an almost complete localization of the initially prepared excitation occurs. It is shown that an increase of the mass alone of the central atom from C to Si cannot explain the observed difference in the C and Si molecules. The spectral linewidths were calculated with the Golden Rule formula after prediagonalization of the relevant vibrational states which are coupled in the molecule to the CH vibration, directly or indirectly. For the spectral calculations, in addition to the direct diagonalization, a modified recursive residue generation method was used, allowing one to avoid diagonalization of the transformed Lanczos Hamiltonian. With this method up to 30 000 coupled states could be analyzed on a computer with relatively small memory. The efficiency of C programming language for the problem is discussed

Collisionless reconnection: Mechanism of self-ignition in thin current sheets

The spontaneous onset of magnetic reconnection in thin collisionless current sheets is shown to result from a thermal-anisotropy driven magnetic Weibel-mode, generating seed-magnetic field {\sf X}-points in the centre of the current layer.Comment: 8 pages, 6 figures, prepared for Annales Geophysica