Normal-mode sound propagation in an ocean with sinusoidal surface waves

The normal-mode solution to the problem of acoustic wave propagation in an isovelocity ocean with a wavy surface is considered. The surface wave amplitude is assumed to be small compared to the acoustic wavelength, and the method of multiple scales is employed to study the interaction between normal-mode acoustic waves and the surface waves. A nonresonant interaction causes small fluctuations of the amplitude and phase of the acoustic wave at a rate dependent on the frequency of the surface wave. Backscatter occurs if the wavenumber of the surface wave is larger than that of the acoustic wave. The interaction becomes resonant if appropriate phase-matching conditions are satisfied. In this case, two acoustic normal modes get coupled, resulting in a large-scale periodic exchange of energy from one mode to another.

Two forms of Pf1 Inovirus: X-ray diffraction studies on a structural phase transition and a calculated libration normal mode of the asymmetric unit

Inovirus is a helical array of alpha-helical protein asymmetric units surrounding a DNA core. X-ray fibre diffraction studies show that the Pf1 species of Inovirus can undergo a reversible temperature-induced transition between two similar structural forms having slightly different virion helix parameters. Molecular models of the two forms show no evidence for altered interactions between the protein and either the solvent or the viral DNA; but there are significant differences in the shape and orientation of the protein asymmetric unit, related to the changes in the virion parameters. Normal modes involving libration of whole asymmetric units are in a frequency range with appreciable entropy of libration, and the structural transition may be related to changes in libration.

Two forms of PF1 INOVIRUS: X-ray diffraction studies on a structural phase transition and a calculated libration normal mode of the assymetric unit

Inovirus is a helical array of agr-helical protein asymmetric units surrounding a DNA core. X-ray fibre diffraction studies show that the Pf1 species of Inovirus can undergo a reversible temperature-induced transition between two similar structural forms having slightly different virion helix parameters. Molecular models of the two forms show no evidence for altered interactions between the protein and either the solvent or the viral DNA; but there are significant differences in the shape and orientation of the protein asymmetric unit, related to the changes in the virion parameters. Normal modes involving libration of whole asymmetric units are in a frequency range with appreciable entropy of libration, and the structural transition may be related to changes in libration.

Normal mode sound propagation in an ocean with random narrow-band surface waves

Normal mode sound propagation in an isovelocity ocean with random narrow-band surface waves is considered, assuming the root-mean-square wave height to be small compared to the acoustic wavelength. Nonresonant interaction among the normal modes is studied straightforward perturbation technique. The more interesting case of resonant interaction is investigated using the method of multiple scales to obtain a pair of stochastic coupled amplitude equations which are solved using the Peano-Baker expansion technique. Equations for the spatial evolution of the first and second moments of the mode amplitudes are also derived and solved. It is shown that, irrespective of the initial conditions, the mean values of the mode amplitudes tend to zero asymptotically with increasing range, the mean-square amplitudes tend towards a state of equipartition of energy, and the total energy of the modes is conserved.

Intramolecular hydrogen bond: Can it be part of the basis set of valence internal coordinates in normal mode analysis?

It has been shown earlier1] that the relaxed force constants (RFCs) could be used as a measure of bond strength only when the bonds form a part of the complete valence internal coordinates (VIC) basis. However, if the bond is not a part of the complete VIC basis, its RFC is not necessarily a measure of bond strength. Sometimes, it is possible to have a complete VIC basis that does not contain the intramolecular hydrogen bond (IMHB) as part of the basis. This means the RFC of IMHB is not necessarily a measure of bond strength. However, we know that IMHB is a weak bond and hence its RFC has to be a measure of bond strength. We resolve this problem of IMHB not being part of the complete basis by postulating `equivalent' basis sets where IMHB is part of the basis at least in one of the equivalent sets of VIC. As long as a given IMHB appears in one of the equivalent complete VIC basis sets, its RFC could be used as a measure of bond strength parameter.

Scan cell reordering to minimize peak power during test cycle: A graph theoretic approach

Scan circuit is widely practiced DFT technology. The scan testing procedure consist of state initialization, test application, response capture and observation process. During the state initialization process the scan vectors are shifted into the scan cells and simultaneously the responses captured in last cycle are shifted out. During this shift operation the transitions that arise in the scan cells are propagated to the combinational circuit, which inturn create many more toggling activities in the combinational block and hence increases the dynamic power consumption. The dynamic power consumed during scan shift operation is much more higher than that of normal mode operation.

Hydrodynamics from the D1-brane

We study the hydrodynamic properties of strongly coupled SU(N) Yang-Mills theory of the D1-brane at finite temperature in the framework of gauge/gravity duality. The only non-trivial viscous transport coefficient in 1+1 dimensions is the bulk viscosity. We evaluate the bulk viscosity by isolating the quasi-normal mode corresponding to the sound channel for the gravitational background of the D1-brane. We find that the ratio of the bulk viscosity to the entropy density to be 1/4 pi. This ratio continues to be 1/4 pi also in the regime when the D1-brane Yang-Mills theory is dual to the gravitational background of the fundamental string. Our analysis shows that this ratio is equal to 1/4 pi for a class of gravitational backgrounds dual to field theories in 1+1 dimensions obtained by considering D1-branes at cones over Sasaki-Einstein 7-manifolds.

Global lopsided instability in a purely stellar galactic disc

It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A(1), increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction (approximately a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the groundstate lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N-body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global m = 1 instabilities, with almost zero pattern speed.

Stability of a cylindrical plasma in the presence of a monotonic field-II

The stability of an incompressible inviscid, perfectly conducting cylindrical plasma against azimuthal disturbances in the presence of a monotonic decreasing magnetic field having a constant pitch is discussed by using energy principle. The results obtained by this principle are compared for m = 1 mode (which is a dangerous mode in which there is a lateral shift of the entire column) with that obtained by normal mode analysis. It is found that m = 1 mode is always unstable. Further, an axial line current, external axial field and the surface tension tend to stabilise m ≠ modes.

Raman spectrum of strontium titanate

The Raman spectrum of strontium titanate has been recorded using λ 4358 of mercury as exciter. The observed spectrum consists of 7 Raman lines, one of which is of low frequency, as expected from the recent theory of Cochran. 6 of these Raman lines have been interpreted as the first order spectrum arising from a small deviation of the cubic strontium titanate from its idealized symmetry. It has been shown that one normal mode of SrTiO3 neglected by J.T. Last, will be really active in infrared absorption in the region of 440 cm-1 and that it has to be taken into account in the interpretation of the infrared spectra of titanates. The four vibrational modes of the unit cell of SrTiO3 correspond to frequencies of 90, 335, 441 and 620 cm-1 observed in Raman effect. The large width of the Raman lines and the additional lines at 256 cm-1 and 726 cm-1 have been attributed to a splitting of the longitudinal and transverse optical modes. With the observed frequencies it has been found possible to account for in a satisfactory manner the specific heat of SrTiO3 in the range 54·84° K to 1800° K.

A sufficient criterion for Rayleigh-Taylor instability of incompressible viscous three-layer flow

Using normal mode analysis Rayleigh-Taylor instability is investigated for three-layer viscous stratified incompressible steady flow, when the top 3rd and bottom 1st layers extend up to infinity, the middle layer has a small thickness δ. The wave Reynolds number in the middle layer is assumed to be sufficiently small. A dispersion relation (a seventh degree polynomial in wave frequency ω) valid up to the order of the maximal value of all possible Kj (j less-than-or-equals, slant 0, K is the wave number) in each coefficient of the polynomial is obtained. A sufficient condition for instability is found out for the first time, pursuing a medium wavelength analysis. It depends on ratios (α and β) of the coefficients of viscosity, the thickness of the middle layer δ, surface tension ratio T and wave number K. This is a new analytical criterion for Rayleigh-Taylor instability of three-layer fluids. It recovers the results of the corresponding problem for two-layer fluids. Among the results obtained, it is observed that taking the coefficients of viscosity of 2nd and 3rd layers same can inhibit the effect of surface tension completely. For large wave number K, the thickness of the middle layer should be correspondingly small to keep the domain of dependence of the threshold wave number Kc constant for fixed α, β and T.

Path integral description of polymers using fractional Brownian walks

The statistical properties of fractional Brownian walks are used to construct a path integral representation of the conformations of polymers with different degrees of bond correlation. We specifically derive an expression for the distribution function of the chains’ end‐to‐end distance, and evaluate it by several independent methods, including direct evaluation of the discrete limit of the path integral, decomposition into normal modes, and solution of a partial differential equation. The distribution function is found to be Gaussian in the spatial coordinates of the monomer positions, as in the random walk description of the chain, but the contour variables, which specify the location of the monomer along the chain backbone, now depend on an index h, the degree of correlation of the fractional Brownian walk. The special case of h=1/2 corresponds to the random walk. In constructing the normal mode picture of the chain, we conjecture the existence of a theorem regarding the zeros of the Bessel function.

Monte Carlo and molecular dynamics simulation of argon clusters andn-alkanes in the confined regions of zeolites

Geometry and energy of argon clusters confined in zeolite NaCaA are compared with those of free clusters. Results indicate the possible existence of magic numbers among the confined clusters. Spectra obtained from instantaneous normal mode analysis of free and confined clusters give a larger percentage of imaginary frequencies for the latter indicating that the confined cluster atoms populate the saddle points of the potential energy surface significantly. The variation of the percentage of imaginary frequencies with temperature during melting is akin to the variation of other properties. It is shown that confined clusters might exhibit inverse surface melting, unlike medium-to-large-sized free clusters that exhibit surface melting. Configurational-bias Monte Carte (CBMC) simulations of n-alkanes in zeolites Y and A are reported. CBMC method gives reliable estimates of the properties relating to the conformation of molecules. Changes in the conformational properties of n-butane and other longer n-alkanes such as n-hexane and n-heptane when they are confined in different zeolites are presented. The changes in the conformational properties of n-butane and n-hexane with temperature and concentration is discussed. In general, in zeolite Y as well as A, there is significant enhancement of the gauche population as compared to the pure unconfined fluid.

Excited state structure and dynamics of p-benzoquinone and bromanil from time-resolved resonance Raman spectra and simulation

p-Benzoquinone and its halogen substituted derivatives are known to have differing reactivities in the triplet excited state. While bromanil catalyzes the reduction of octaethylporphyrin most efficiently among the halogenated p-benzoquinones, the reaction does not take place in presence of the unsubstituted p-benzoquinone (T. Nakano and Y. Mori, Bull. Chem. Soc. Jpn., 67, 2627 (1994)). Understanding of such differences requires a detailed knowledge of the triplet state structures, normal mode compositions and excited state dynamics. In this paper, we apply a recently presented scheme (M. Puranik, S. Umapathy, J. G. Snijders, and J. Chandrasekhar, J. Chem, Phys., 115, 6106 (2001)) that combines parameters from experiment and computation in a wave packet dynamics simulation to the triplet states of p-benzoquinone and bromanil. The absorption and resonance Raman spectra of both the molecules have been simulated. The normal mode compositions and mode specific excited state displacements have been presented and compared. Time-dependent evolution of the absorption and Raman overlaps for all the observed modes has been discussed in detail. In p-benzoquinone, the initial dynamics is along the C=C stretching and C-H bending modes whereas in bromanil nearly equal displacements are observed along all the stretching coordinates.

Investigation of short-time isomerization dynamics in p-nitroazobenzene from resonance Raman intensity analysis

Resonance Raman (RR) spectra are presented for p-nitroazobenzene dissolved in chloroform using 18 excitation Wavelengths, covering the region of (1)(n --> pi*) electronic transition. Raman intensities are observed for various totally symmetric fundamentals, namely, C-C, C-N, N=N, and N-O stretching vibrations, indicating that upon photoexcitation the excited-state evolution occurs along all of these vibrational coordinates. For a few fundamentals, interestingly, in p-nitroazobenzene, it is observed that the RR intensities decrease near the maxima of the resonant electronic (1)(n --> pi*) transition. This is attributed to the interference from preresonant scattering due to the strongly allowed (1)(pi --> pi*) electronic transition. The electronic absorption spectrum and the absolute Raman cross section for the nine Franck-Condon active fundamentals of p-nitroazobenzene have been successfully modeled using Heller's time-dependent formalism for Raman scattering. This employs harmonic description of the lowest energy (1)(n --> pi*) potential energy surface. The short-time isomerization dynamics is then examined from a priori knowledge of the ground-state normal mode descriptions of p-nitroazobenzene to convert the wave packet motion in dimensionless normal coordinates to internal coordinates. It is observed that within 20 fs after photoexcitation in p-nitroazobenzene, the N=N and C-N stretching vibrations undergo significant changes and the unsubstituted phenyl ring and the nitro stretching vibrations are also distorted considerably.