NMR relaxation study of disorder in the mixed system BP x GPI(1-x) and the low temperature transition from classical to quantum rotation

1H NMR spin-lattice relaxation time (T1) studies have been carried out in the temperature range 100 K to 4 K, at two Larmor frequencies 11.4 and 23.3 MHz, in the mixed system of betaine phosphate and glycine phosphite (BPxGPI(1-x)), to study the effects of disorder on the proton group dynamics. Analysis of T1 data indicates the presence of a number of inequivalent methyl groups and a gradual transition from classical reorientations to quantum tunneling rotations. At lower temperatures, microstructural disorder in the local environments of the methyl groups, result in a distribution in the activation energy (Ea) and the torsional energy gap (E01). For certain values of x, the magnetisation recovery shows biexponential behaviour at lower temperatures.

Non-diffusive classical transport in a medium with static randomness

The probability distribution for the displacement x of a particle moving in a one-dimensional continuum is derived exactly for the general case of combined static and dynamic gaussian randomness of the applied force. The dynamics of the particle is governed by the high-friction limit of Brownian motion discussed originally by Einstein and Smoluchowski. In particular, the mean square displacement of the particle varies as t2 for t to infinity . This ballistic motion induced by the disorder does not give rise to a 1/f power spectrum, contrary to recent suggestions based on the above dynamical model.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.

Hanle-Zeeman redistribution matrix. I. Classical theory expressions in the laboratory frame

Polarized scattering in spectral lines is governed by a 4; 4 matrix that describes how the Stokes vector is scattered and redistributed in frequency and direction. Here we develop the theory for this redistribution matrix in the presence of magnetic fields of arbitrary strength and direction. This general magnetic field case is called the Hanle- Zeeman regime, since it covers both of the partially overlapping weak- and strong- field regimes in which the Hanle and Zeeman effects dominate the scattering polarization. In this general regime, the angle-frequency correlations that describe the so-called partial frequency redistribution (PRD) are intimately coupled to the polarization properties. We develop the theory for the PRD redistribution matrix in this general case and explore its detailed mathematical properties and symmetries for the case of a J = 0 -> 1 -> 0 scattering transition, which can be treated in terms of time-dependent classical oscillator theory. It is shown how the redistribution matrix can be expressed as a linear superposition of coherent and noncoherent parts, each of which contain the magnetic redistribution functions that resemble the well- known Hummer- type functions. We also show how the classical theory can be extended to treat atomic and molecular scattering transitions for any combinations of quantum numbers.

Systematic bias in MODIS dust aerosol retrieval at Kanpur (AERONET), Indo-Gangetic Basin - art.no.640816

We have compared the spectral aerosol optical depth (AOD) and aerosol fine mode fraction (AFMF) derived from Moderate Resolution Imaging Spectroradiometer (MODIS) with those of Aerosol Robotic Network (AERONET) at Kanpur (26.45N, 80.35E), northern India for the pre-monsoon season (March to June, 2001-2005). We found that MODIS systematically overestimates AOD during pre-monsoon season (known to be influenced by dust transport from north-west of India). The errors in AOD were correlated with the MODIS top-of-atmosphere apparent surface reflectance in 2.1 mu m channel (rho*(2.1)). MODIS aerosol algorithm uses p*(2.1) to derive the surface reflectance in visible channels (rho(0.47), rho(0.66)) using an empirical mid IR-visible correlation (rho(0.47) = rho(2.1)/4, rho(0.66) = rho(2.1)/2). The large uncertainty in estimating surface reflectance in visible channels (Delta rho(0.66)+/- 0.04, Delta rho(0.47)+/- 0.02) at higher values of p*(2.1) (p*(2.1) > 0.18) leads to higher aerosol contribution in the total reflected radiance at top-of atmosphere to compensate for the reduced surface reflectance in visible channels and thus leads to overestimation of AOD. This was also reflected in the very low values of AFMF during pre-monsoon whose accuracy depends on the aerosol path radiance in 0.47 and 0.66 mu m channels and aerosol models. The errors in AOD were also high in the scattering angle range 110 degrees-140 degrees, where the effect of dust non-spherity on its optical properties is significant. The direct measurements of spectral surface reflectance are required over the Indo-Gangetic basin in order to validate the mid IR-visible relationship. MODIS aerosol models should also be modified to incorporate the effect of non-spherity of dust aerosols.

Real-time image denoising algorithm in teleradiology systems - art.no.606304

Denoising of medical images in wavelet domain has potential application in transmission technologies such as teleradiology. This technique becomes all the more attractive when we consider the progressive transmission in a teleradiology system. The transmitted images are corrupted mainly due to noisy channels. In this paper, we present a new real time image denoising scheme based on limited restoration of bit-planes of wavelet coefficients. The proposed scheme exploits the fundamental property of wavelet transform - its ability to analyze the image at different resolution levels and the edge information associated with each sub-band. The desired bit-rate control is achieved by applying the restoration on a limited number of bit-planes subject to the optimal smoothing. The proposed method adapts itself to the preference of the medical expert; a single parameter can be used to balance the preservation of (expert-dependent) relevant details against the degree of noise reduction. The proposed scheme relies on the fact that noise commonly manifests itself as a fine-grained structure in image and wavelet transform allows the restoration strategy to adapt itself according to directional features of edges. The proposed approach shows promising results when compared with unrestored case, in context of error reduction. It also has capability to adapt to situations where noise level in the image varies and with the changing requirements of medical-experts. The applicability of the proposed approach has implications in restoration of medical images in teleradiology systems. The proposed scheme is computationally efficient.

Elimination of cross-talk in diffuse optical tomographic reconstructions through a weighted update procedure: results of simulation study - art. no. 61640S

Reconstructions in optical tomography involve obtaining the images of absorption and reduced scattering coefficients. The integrated intensity data has greater sensitivity to absorption coefficient variations than scattering coefficient. However, the sensitivity of intensity data to scattering coefficient is not zero. We considered an object with two inhomogeneities (one in absorption and the other in scattering coefficient). The standard iterative reconstruction techniques produced results, which were plagued by cross talk, i.e., the absorption coefficient reconstruction has a false positive corresponding to the location of scattering inhomogeneity, and vice-versa. We present a method to remove cross talk in the reconstruction, by generating a weight matrix and weighting the update vector during the iteration. The weight matrix is created by the following method: we first perform a simple backprojection of the difference between the experimental and corresponding homogeneous intensity data. The built up image has greater weightage towards absorption inhomogeneity than the scattering inhomogeneity and its appropriate inverse is weighted towards the scattering inhomogeneity. These two weight matrices are used as multiplication factors in the update vectors, normalized backprojected image of difference intensity for absorption inhomogeneity and the inverse of the above for the scattering inhomogeneity, during the image reconstruction procedure. We demonstrate through numerical simulations, that cross-talk is fully eliminated through this modified reconstruction procedure.

Molecular theory of solvation and solvation dynamics of a classical ion in a dipolar liquid

A microscopic theory of equilibrium solvation and solvation dynamics of a classical, polar, solute molecule in dipolar solvent is presented. Density functional theory is used to explicitly calculate the polarization structure around a solvated ion. The calculated solvent polarization structure is different from the continuum model prediction in several respects. The value of the polarization at the surface of the ion is less than the continuum value. The solvent polarization also exhibits small oscillations in space near the ion. We show that, under certain approximations, our linear equilibrium theory reduces to the nonlocal electrostatic theory, with the dielectric function (c(k)) of the liquid now wave vector (k) dependent. It is further shown that the nonlocal electrostatic estimate of solvation energy, with a microscopic c(k), is close to the estimate of linearized equilibrium theories of polar liquids. The study of solvation dynamics is based on a generalized Smoluchowski equation with a mean-field force term to take into account the effects of intermolecular interactions. This study incorporates the local distortion of the solvent structure near the ion and also the effects of the translational modes of the solvent molecules.The latter contribution, if significant, can considerably accelerate the relaxation of solvent polarization and can even give rise to a long time decay that agrees with the continuum model prediction. The significance of these results is discussed.