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

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

Particle motion around magnetized black holes: Preston-Poisson space-time

We analyze motion of massless and massive particles around black holes immersed in an asymptotically uniform magnetic field and surrounded by some mechanical structure, which provides the magnetic field. The space-time is described by Preston-Poisson metric, which is the generalization of the well-known Ernst metric with a new parameter, tidal force, characterizing the surrounding structure. The Hamilton-Jacobi equations allow separation of variables in the equatorial plane. The presence of tidal force from surroundings considerably changes parameters of the test particle motion: it increases the radius of circular orbits of particles, increases the binding energy of massive particles going from a given circular orbits to the innermost stable orbit near black hole. In addition, it increases the distance of minimal approach, time delay and bending angle for a ray of light propagating near black hole.Comment: 6 pages, RevTex, the version accepted for publication in Phys. Rev.

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

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

Nflation: multi-field inflationary dynamics and perturbations

We carry out numerical investigations of the dynamics and perturbations in the Nflation model of Dimopoulos et al. (2005). This model features large numbers of scalar fields with different masses, which can cooperate to drive inflation according to the assisted inflation mechanism. We extend previous work to include random initial conditions for the scalar fields, and explore the predictions for density perturbations and the tensor-to-scalar ratio. The tensor-to-scalar ratio depends only on the number of e-foldings and is independent of the number of fields, their masses, and their initial conditions. It therefore always has the same value as for a single massive field. By contrast, the scalar spectral index has significant dependence on model parameters. While normally multi-field inflation models make predictions for observable quantities which depend also on the unknown field initial conditions, we find evidence of a `thermodynamic' regime whereby the predicted spectral index becomes independent of initial conditions if there are enough fields. Only in parts of parameter space where the mass spectrum of the fields is extremely densely packed is the model capable of satisfying the tight observational constraints from WMAP3 observations.Comment: 6 pages RevTeX4, 4 figures included. Updated to match PRD accepted version. Analysis and conclusions unchanged. New references, especially astro-ph/0510441 which was first to give the general r=8/N resul

Some model-independent phenomenological consequences of flexible brane worlds

In this work we will review the main properties of brane-world models with low tension. Starting from very general principles, it is possible to obtain an effective action for the relevant degrees of freedom at low energies (branons). Using the cross sections for high-energy processes involving branons, we set bounds on the different parameters appearing in these models. We also show that branons provide a WIMP candidate for dark matter in a natural way. We consider cosmological constraints on its thermal and non-thermal relic abundances. We derive direct detection limits and compare those limits with the preferred parameter region in the case in which the EGRET excess in the diffuse galactic gamma rays is due to dark matter annihilation. Finally we will discuss the constraints coming from the precision tests of the Standard Model and the muon anomalous magnetic moment.Comment: 10 pages, 6 figures. Contribution to the Proceedings of the Second International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, IRGAC 2006, Barcelona, 11-15 July, 200