Triangleland. I. Classical dynamics with exchange of relative angular momentum

In Euclidean relational particle mechanics, only relative times, relative angles and relative separations are meaningful. Barbour--Bertotti (1982) theory is of this form and can be viewed as a recovery of (a portion of) Newtonian mechanics from relational premises. This is of interest in the absolute versus relative motion debate and also shares a number of features with the geometrodynamical formulation of general relativity, making it suitable for some modelling of the problem of time in quantum gravity. I also study similarity relational particle mechanics (`dynamics of pure shape'), in which only relative times, relative angles and {\sl ratios of} relative separations are meaningful. This I consider firstly as it is simpler, particularly in 1 and 2 d, for which the configuration space geometry turns out to be well-known, e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail. Secondly, the similarity model occurs as a sub-model within the Euclidean model: that admits a shape--scale split. For harmonic oscillator like potentials, similarity triangleland model turns out to have the same mathematics as a family of rigid rotor problems, while the Euclidean case turns out to have parallels with the Kepler--Coulomb problem in spherical and parabolic coordinates. Previous work on relational mechanics covered cases where the constituent subsystems do not exchange relative angular momentum, which is a simplifying (but in some ways undesirable) feature paralleling centrality in ordinary mechanics. In this paper I lift this restriction. In each case I reduce the relational problem to a standard one, thus obtain various exact, asymptotic and numerical solutions, and then recast these into the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure

Triangleland. II. Quantum Mechanics of Pure Shape

Relational particle models are of value in the absolute versus relative motion debate. They are also analogous to the dynamical formulation of general relativity, and as such are useful for investigating conceptual strategies proposed for resolving the problem of time in quantum general relativity. Moreover, to date there are few explicit examples of these at the quantum level. In this paper I exploit recent geometrical and classical dynamics work to provide such a study based on reduced quantization in the case of pure shape (no scale) in 2-d for 3 particles (triangleland) with multiple harmonic oscillator type potentials. I explore solutions for these making use of exact, asymptotic, perturbative and numerical methods. An analogy to the mathematics of the linear rigid rotor in a background electric field is useful throughout. I argue that further relational models are accessible by the methods used in this paper, and for specific uses of the models covered by this paper in the investigation of the problem of time (and other conceptual and technical issues) in quantum general relativity.Comment: Journal Reference added, minor updates to References and Figure

Spin Relaxation Resonances Due to the Spin-Axis Interaction in Dense Rubidium and Cesium Vapor

Resonances in the magnetic decoupling curves for the spin relaxation of dense alkali-metal vapors prove that much of the relaxation is due to the spin-axis interaction in triplet dimers. Initial estimates of the spin-axis coupling coefficients for the dimers are 290 MHz for Rb; 2500 MHz for Cs.Comment: submitted to Physical Review Letters, text + 3 figure

Entrance Channel X-HF (X=Cl, Br, and I) Complexes studied by High-Resolution Infrared Laser Spectroscopy in Helium Nanodroplets

Rotationally resolved infrared spectra are reported for halogen atom - HF free radical complexes formed in helium nanodroplets. An effusive pyrolysis source is used to dope helium droplets with Cl, Br and I atoms, formed by thermal dissociation of Cl$_2$, Br$_2$ and I$_2$. A single hydrogen fluoride molecule is then added to the droplets, resulting in the formation of the X-HF complexes of interest. Analysis of the resulting spectra confirms that the observed species have $^2\Pi_{3/2}$ ground electronic states, consistent with the linear hydrogen bound structures predicted from theory. Stark spectra are also reported for these species, from which the permanent electric dipole moments are determined.Comment: 41 pages, 16 figures, 5 table

Modern optical astronomy: technology and impact of interferometry

The present `state of the art' and the path to future progress in high spatial resolution imaging interferometry is reviewed. The review begins with a treatment of the fundamentals of stellar optical interferometry, the origin, properties, optical effects of turbulence in the Earth's atmosphere, the passive methods that are applied on a single telescope to overcome atmospheric image degradation such as speckle interferometry, and various other techniques. These topics include differential speckle interferometry, speckle spectroscopy and polarimetry, phase diversity, wavefront shearing interferometry, phase-closure methods, dark speckle imaging, as well as the limitations imposed by the detectors on the performance of speckle imaging. A brief account is given of the technological innovation of adaptive-optics (AO) to compensate such atmospheric effects on the image in real time. A major advancement involves the transition from single-aperture to the dilute-aperture interferometry using multiple telescopes. Therefore, the review deals with recent developments involving ground-based, and space-based optical arrays. Emphasis is placed on the problems specific to delay-lines, beam recombination, polarization, dispersion, fringe-tracking, bootstrapping, coherencing and cophasing, and recovery of the visibility functions. The role of AO in enhancing visibilities is also discussed. The applications of interferometry, such as imaging, astrometry, and nulling are described. The mathematical intricacies of the various `post-detection' image-processing techniques are examined critically. The review concludes with a discussion of the astrophysical importance and the perspectives of interferometry.Comment: 65 pages LaTeX file including 23 figures. Reviews of Modern Physics, 2002, to appear in April issu

Diffusion of a soluble protein, photoactivatable GFP, through a sensory cilium

Transport of proteins to and from cilia is crucial for normal cell function and survival, and interruption of transport has been implicated in degenerative and neoplastic diseases. It has been hypothesized that the ciliary axoneme and structures adjacent to and including the basal bodies of cilia impose selective barriers to the movement of proteins into and out of the cilium. To examine this hypothesis, using confocal and multiphoton microscopy we determined the mobility of the highly soluble photoactivatable green fluorescent protein (PAGFP) in the connecting cilium (CC) of live Xenopus retinal rod photoreceptors, and in the contiguous subcellular compartments bridged by the CC, the inner segment (IS) and the outer segment (OS). The estimated axial diffusion coefficients are DCC = 2.8 ± 0.3, DIS = 5.2 ± 0.6, and DOS = 0.079 ± 0.009 µm2 s−1. The results establish that the CC does not pose a major barrier to protein diffusion within the rod cell. However, the results also reveal that axial diffusion in each of the rod’s compartments is substantially retarded relative to aqueous solution: the axial diffusion of PAGFP was retarded ∼18-, 32- and 1,000-fold in the IS, CC, and OS, respectively, with ∼20-fold of the reduction in the OS attributable to tortuosity imposed by the lamellar disc membranes. Previous investigation of PAGFP diffusion in passed, spherical Chinese hamster ovary cells yielded DCHO = 20 µm2 s−1, and estimating cytoplasmic viscosity as Daq/DCHO = 4.5, the residual 3- to 10-fold reduction in PAGFP diffusion is ascribed to sub-optical resolution structures in the IS, CC, and OS compartments

Pattern electroretinogram (PERG) and pattern visual evoked potential (PVEP) in the early stages of Alzheimer’s disease

Alzheimer’s disease (AD) is one of the most common causes of dementia in the world. Patients with AD frequently complain of vision disturbances that do not manifest as changes in routine ophthalmological examination findings. The main causes of these disturbances are neuropathological changes in the visual cortex, although abnormalities in the retina and optic nerve cannot be excluded. Pattern electroretinogram (PERG) and pattern visual evoked potential (PVEP) tests are commonly used in ophthalmology to estimate bioelectrical function of the retina and optic nerve. The aim of this study was to determine whether retinal and optic nerve function, measured by PERG and PVEP tests, is changed in individuals in the early stages of AD with normal routine ophthalmological examination results. Standard PERG and PVEP tests were performed in 30 eyes of 30 patients with the early stages of AD. The results were compared to 30 eyes of 30 normal healthy controls. PERG and PVEP tests were recorded in accordance with the International Society for Clinical Electrophysiology of Vision (ISCEV) standards. Additionally, neural conduction was measured using retinocortical time (RCT)—the difference between P100-wave latency in PVEP and P50-wave implicit time in PERG. In PERG test, PVEP test, and RCT, statistically significant changes were detected. In PERG examination, increased implicit time of P50-wave (P < 0.03) and amplitudes reductions in P50- and N95-waves (P < 0.0001) were observed. In PVEP examination, increased latency of P100-wave (P < 0.0001) was found. A significant increase in RCT (P < 0.0001) was observed. The most prevalent features were amplitude reduction in N95-wave and increased latency of P100-wave which were seen in 56.7% (17/30) of the AD eyes. In patients with the early stages of AD and normal routine ophthalmological examination results, dysfunction of the retinal ganglion cells as well as of the optic nerve is present, as detected by PERG and PVEP tests. These dysfunctions, at least partially, explain the cause of visual disturbances observed in patients with the early stages of AD

Coherent excitation, incoherent excitation, and adiabatic states

Coherent excitation of an atomic excited state occurs during the propagation of near-resonant light pulses and is responsible for the induced polarization. Simultaneously, incoherent excitation occurs due to the relaxation processes described by the absorption coefficient. Here, the theory for the coherent and incoherent excitation is initially presented in terms of the traditional vector model. While a complete understanding of the two-level system is provided by the vector model, it is shown to be incomplete when the problem of directly monitoring the coherent and incoherent excitation is considered. This is because this latter problem involves more than two levels. For this more complicated multilevel problem, adiabatic states are introduced to gain further understanding. The adiabatic states are the stationary states of the atom in the presence of the near-resonant laser field; they help to explain the intimate connection between the coherent excitation and the two-photon resonance. Experimental measurements of the coherent and incoherent excitation associated with near-resonant pulse propagation in Rb vapor are presented. The double-resonance technique used a relatively strong pulsed dye laser tuned near the 5S1/2 5P1/2 transition (7948 A) of Rb to produce the coherent and incoherent excitation, and a weak, tunable cw dye laser tuned in the region of the 5P1/2 6D3/2 transition (6206 A) to monitor this excitation, In agreement with theory, the experimental results demonstrate that coherent excitation is responsible for two-photon absorption, while the incoherent excitation corresponds to one-photon absorption to the 5P1/2 state.Peer reviewedElectrical and Computer Engineerin

Origins of cellular geometry

Cells are highly complex and orderly machines, with defined shapes and a startling variety of internal organizations. Complex geometry is a feature of both free-living unicellular organisms and cells inside multicellular animals. Where does the geometry of a cell come from? Many of the same questions that arise in developmental biology can also be asked of cells, but in most cases we do not know the answers. How much of cellular organization is dictated by global cell polarity cues as opposed to local interactions between cellular components? Does cellular structure persist across cell generations? What is the relationship between cell geometry and tissue organization? What ensures that intracellular structures are scaled to the overall size of the cell? Cell biology is only now beginning to come to grips with these questions