Variational formulation of Eisenhart's unified theory

Eisenhart's classical unified field theory is based on a non-Riemannian affine connection related to the covariant derivative of the electromagnetic field tensor. The sourceless field equations of this theory arise from vanishing of the torsion trace and the symmetrized Ricci tensor. We formulate Eisenhart's theory from the metric-affine variational principle. In this formulation, a Lagrange multiplier constraining the torsion becomes the source for the Maxwell equations.Comment: 7 pages; published versio

An algorithm for generating quasiperiodic patterns and their approximants

An algorithm for projecting the interior of a hypercube in N-dimensions on to an m-dimensional subspace has been developed and incorporated into a computer program for generating quasiperiodic and periodic patterns in an n-dimensional subspace. Some aspects of the resulting orthorhombic approximants to Penrose tiling patterns are discussed and illustrated

Spectroscopy of drums and quantum billiards: perturbative and non-perturbative results

We develop powerful numerical and analytical techniques for the solution of the Helmholtz equation on general domains. We prove two theorems: the first theorem provides an exact formula for the ground state of an arbirtrary membrane, while the second theorem generalizes this result to any excited state of the membrane. We also develop a systematic perturbative scheme which can be used to study the small deformations of a membrane of circular or square shapes. We discuss several applications, obtaining numerical and analytical results.Comment: 29 pages, 12 figures, 7 tabl

The Effect of Random Surface Inhomogeneities on Microresonator Spectral Properties: Theory and Modeling at Millimeter Wave Range

The influence of random surface inhomogeneities on spectral properties of open microresonators is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields the method of eigen-mode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering which is the highly responsible for non-dissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object we use dielectric disc resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigen-frequencies and the Q-factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.Comment: 17+ pages, 5 figure

Stretching Instability of Helical Spring

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to step-like contraction and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur, and propose experimental tests of our predictions.Comment: 5 pages, 4 figure

Herschel observations of EXtra-Ordinary Sources (HEXOS): The present and future of spectral surveys with Herschel/HIFI

We present initial results from the Herschel GT key program: Herschel observations of EXtra-Ordinary Sources (HEXOS) and outline the promise and potential of spectral surveys with Herschel/HIFI. The HIFI instrument offers unprecedented sensitivity, as well as continuous spectral coverage across the gaps imposed by the atmosphere, opening up a largely unexplored wavelength regime to high-resolution spectroscopy. We show the spectrum of Orion KL between 480 and 560 GHz and from 1.06 to 1.115 THz. From these data, we confirm that HIFI separately measures the dust continuum and spectrally resolves emission lines in Orion KL. Based on this capability we demonstrate that the line contribution to the broad-band continuum in this molecule-rich source is ~20−40% below 1 THz and declines to a few percent at higher frequencies. We also tentatively identify multiple transitions of HD^(18)O in the spectra. The first detection of this rare isotopologue in the interstellar medium suggests that HDO emission is optically thick in the Orion hot core with HDO/H_2O ~ 0.02. We discuss the implications of this detection for the water D/H ratio in hot cores

An RNA interference screen for identifying downstream effectors of the p53 and pRB tumour suppressor pathways involved in senescence

Background: Cellular senescence is an irreversible cell cycle arrest that normal cells undergo in response to progressive shortening of telomeres, changes in telomeric structure, oncogene activation or oxidative stress and acts as an important tumour suppressor mechanism.Results: To identify the downstream effectors of the p53-p21 and p16-pRB tumour suppressor pathways crucial for mediating entry into senescence, we have carried out a loss-of-function RNA interference screen in conditionally immortalised human fibroblasts that can be induced to rapidly undergo senescence, whereas in primary cultures senescence is stochastic and occurs asynchronously. These cells are immortal but undergo a rapid irreversible arrest upon activation of the p53-p21 and p16-pRB pathways that can be readily bypassed upon their inactivation. The primary screen identified 112 known genes including p53 and another 29 shRNAmirs targetting as yet unidentified loci. Comparison of these known targets with genes known to be up-regulated upon senescence in these cells, by micro-array expression profiling, identified 4 common genes TMEM9B, ATXN10, LAYN and LTBP2/3. Direct silencing of these common genes, using lentiviral shRNAmirs, bypassed senescence in the conditionally immortalised cells.Conclusion: The senescence bypass screen identified TMEM9B, ATXN10, LAYN and LTBP2/3 as novel downstream effectors of the p53-p21 and p16-pRB tumour suppressor pathways. Although none of them has previously been linked to cellular senescence, TMEM9B has been suggested to be an upstream activator of NF-kappa B signalling which has been found to have a causal role in promoting senescence. Future studies will focus on determining on how many of the other primary hits also have a casual role in senescence and what is the mechanism of action

Transparent Anomalous Dispersion and Superluminal Light Pulse Propagation at a Negative Group Velocity

Anomalous dispersion cannot occur in a transparent passive medium where electromagnetic radiation is being absorbed at all frequencies, as pointed out by Landau and Lifshitz. Here we show, both theoretically and experimentally, that transparent linear anomalous dispersion can occur when a gain doublet is present. Therefore, a superluminal light pulse propagation can be observed even at a negative group velocity through a transparent medium with almost no pulse distortion. Consequently, a {\it negative transit time} is experimentally observed resulting in the peak of the incident light pulse to exit the medium even before entering it. This counterintuitive effect is a direct result of the {\it rephasing} process owing to the wave nature of light and is not at odds with either causality or Einstein's theory of special relativity.Comment: 12 journal pages, 9 figure

Nonsingular, big-bounce cosmology from spinor-torsion coupling

The Einstein-Cartan-Sciama-Kibble theory of gravity removes the constraint of general relativity that the affine connection be symmetric by regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between the torsion tensor and Dirac spinors generates a spin-spin interaction which is significant in fermionic matter at extremely high densities. We show that such an interaction averts the unphysical big-bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. This scenario also explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic.Comment: 7 pages; published versio