A New Description of Nuclear Rotational Motion in terms of Intrinsic Pair Mode

A new method describing nuclear rotational motion microscopically is proposed. We extract the rotational Hamiltonian by introducing the intrinsic pair modes which commute with the rotational mode. Thereby the rotational mode is not treated as zero energy mode in contrast with the conventional RPA formalism so that we circumvent the difficulty related with infrared divergence. The wave function is constructed by angular momentum projection on each intrinsic state. Without numerical integration for projection we calculate the matrix elements analytically under a certain approximation. The numerical calculations are carried out to illustrate the applicability of our method and they show that our method works well.Comment: 14pages,1figur

Tight-binding study of structure and vibrations of amorphous silicon

We present a tight-binding calculation that, for the first time, accurately describes the structural, vibrational and elastic properties of amorphous silicon. We compute the interatomic force constants and find an unphysical feature of the Stillinger-Weber empirical potential that correlates with a much noted error in the radial distribution function associated with that potential. We also find that the intrinsic first peak of the radial distribution function is asymmetric, contrary to usual assumptions made in the analysis of diffraction data. We use our results for the normal mode frequencies and polarization vectors to obtain the zero-point broadening effect on the radial distribution function, enabling us to directly compare theory and a high resolution x-ray diffraction experiment

Large-Scale Structure and Gravitational Waves III: Tidal Effects

The leading locally observable effect of a long-wavelength metric perturbation corresponds to a tidal field. We derive the tidal field induced by scalar, vector, and tensor perturbations, and use second order perturbation theory to calculate the effect on the locally measured small-scale density fluctuations. For sub-horizon scalar perturbations, we recover the standard perturbation theory result ($F_2$ kernel). For tensor modes of wavenumber $k_L$, we find that effects persist for $k_L\tau \gg 1$, i.e. even long after the gravitational wave has entered the horizon and redshifted away, i.e. it is a "fossil" effect. We then use these results, combined with the "ruler perturbations" of arXiv:1204.3625, to predict the observed distortion of the small-scale matter correlation function induced by a long-wavelength tensor mode. We also estimate the observed signal in the B mode of the cosmic shear from a gravitational wave background, including both tidal (intrinsic alignment) and projection (lensing) effects. The non-vanishing tidal effect in the $k_L\tau \gg 1$ limit significantly increases the intrinsic alignment contribution to shear B modes, especially at low redshifts $z \lesssim 2$.Comment: 24 pages, 4 figures; v2: added references and corrected typos; v3: corrected factor of 2 in Sec. VI and intrinsic alignment matching, conclusions unchange

Learning intrinsic excitability in medium spiny neurons

We present an unsupervised, local activation-dependent learning rule for intrinsic plasticity (IP) which affects the composition of ion channel conductances for single neurons in a use-dependent way. We use a single-compartment conductance-based model for medium spiny striatal neurons in order to show the effects of parametrization of individual ion channels on the neuronal activation function. We show that parameter changes within the physiological ranges are sufficient to create an ensemble of neurons with significantly different activation functions. We emphasize that the effects of intrinsic neuronal variability on spiking behavior require a distributed mode of synaptic input and can be eliminated by strongly correlated input. We show how variability and adaptivity in ion channel conductances can be utilized to store patterns without an additional contribution by synaptic plasticity (SP). The adaptation of the spike response may result in either "positive" or "negative" pattern learning. However, read-out of stored information depends on a distributed pattern of synaptic activity to let intrinsic variability determine spike response. We briefly discuss the implications of this conditional memory on learning and addiction.Comment: 20 pages, 8 figure

Waveguides With Non-Parallel Planar Boundaries

The major part of this work is concerned with spectrally synthesised fields, in two dimensional tapered waveguides with planar boundaries. The derivation of the spectral objects of interest are from work by Arnold and Felsen [1], in which the tracking of plane wave species throughout the wedge environment is manipulated into a modal form. The collective form of the ray species (mode) is facilitated by the application of the Euler-Maclaurin summation formula [2]. The application of this summation formula furnishes the concept of an Intrinsic Mode and a source induced field which is maintained to be a Green's function for the tapered geometry. Numerical calculation of Intrinsic Modes has been a feature of several authors' work [3,4,5,6], but in this exposition a highly efficient numerical algorithm is developed, by using Fast Fourier Transform routines [7], which exploit the oscillatory nature of the spectrum. This high efficiency enables confirmation of the power conserving property of the Intrinsic Mode on a transverse cross--section as it traverses the cut-off region of the Adiabatic Mode, provided that at least an asymptotic form of the Euler-Maclaurin remainder is included. The Intrinsic Mode and the source induced spectral field are shown to be exact solutions of the tapered geometry (excluding the apex) and the latter is demonstrated to possess all the properties of a Green's function. This work also examines derivations and properties of four different contemporary theories, and attaches plane wave significance to their approximations by consideration of their wave vector loci. The marching algorithm methods--- Beam Propagation Method [8] and the Parabolic Equation Method [9]--- are compared and assessed with the Intrinsic Mode and the Green's function for the wedge environment (calculated using Fast Fourier Transforms). The final section deals with applications of the Green's function using the Kirchhoff integral representation. Here propagation of fields represented on a boundary are investigated. A method of calculating reflection loss from simple connected structures is also examined