Growing length and time scales in glass-forming liquids

The glass transition, whereby liquids transform into amorphous solids at low temperatures, is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liquid upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam-Gibbs theory, have sought to relate growing relaxation times to length scales associated with spatial correlations in liquid structure or motion of molecules, the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of molecules leading to structural relaxation, termed ``spatially heterogeneous dynamics,'' provide fresh impetus in this direction. A powerful approach to extract length scales in critical phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale associated with spatially heterogeneous dynamics, which grows as temperature decreases. However, relaxation times that also grow with decreasing temperature do not exhibit standard finite-size scaling with this length. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions.

Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

A H-1-NMR STUDY OF BILIRUBIN IX-ALPHA SOLUBILIZATION BY CHOLATE MICELLES - APPLICATION OF NUCLEAR OVERHAUSER EFFECTS

The solubilization of bilirubin IX-Alpha in aqueous solution by sodium cholate micelles has been examined by 270 MHz 1H-NMR spectroscopy. Incorporation of bilirubin into the micelles is accompanied by specific shifts of bilirubin vinyl and bridgehead protons and the C18 and C19 methyl groups of the steroid. The observed chemical shifts show a monotonic concentration dependence suggesting that changes in aggregation size are continuous. Nuclear Overhauser effects (NOE) have been shown to be a useful probe or micellization. A 4:1 cholate/bilirubin mixture has been investigated by difference NOE spectroscopy. The observation of intermolecular nuclear Overhauser effects between peripheral protons of bilirubin and cholate are diagnostic of spatially proximate groups. Inter-cholate nuclear Overhauser effects increase in magnitude upon bilirubin incorporation suggesting closer packing of steroid molecules on solubilization of the pigment. Intramolecular nuclear Overhauser effects observed for solubilized bilirubin are consistent with a compact intramolecularly hydrogen-bonded conformation resembling that determined for bilirubin in the solid state.

Laminar flow of a suspension in a curved pipe with varying curvature

The laminar flow of a fairly concentrated suspension (in which the volume fraction Z of the solid particles < 0.4) in a spatially varying periodically curved pipe has been examined numerically. Unlike the case of interacting suspension flows, the particles are found to flow in a well-mixed fashion, altering both the axial and circumferential velocities and consequently the fluid flux in the tube, depending on their diffusivity and inertia. The magnitude of shear stress at the wall is enhanced, suggesting that, if applied to vascular system, the vascular wall could be prone to ulceration during pathological situations like polycythemia. The delay in adaptation of the deviation in Poiseuille flow velocity to the curvature changes is also discussed in detail.

Identification of dynamical systems with fractional derivative damping models using inverse sensitivity analysis

The problem of identifying parameters of time invariant linear dynamical systems with fractional derivative damping models, based on a spatially incomplete set of measured frequency response functions and experimentally determined eigensolutions, is considered. Methods based on inverse sensitivity analysis of damped eigensolutions and frequency response functions are developed. It is shown that the eigensensitivity method requires the development of derivatives of solutions of an asymmetric generalized eigenvalue problem. Both the first and second order inverse sensitivity analyses are considered. The study demonstrates the successful performance of the identification algorithms developed based on synthetic data on one, two and a 33 degrees of freedom vibrating systems with fractional dampers. Limited studies have also been conducted by combining finite element modeling with experimental data on accelerances measured in laboratory conditions on a system consisting of two steel beams rigidly joined together by a rubber hose. The method based on sensitivity of frequency response functions is shown to be more efficient than the eigensensitivity based method in identifying system parameters, especially for large scale systems.

Spatial correlations around a Kondo impurity

We present a method for calculating zero-frequency, spatially varying response and correlation functions around a magnetic impurity in metals. We illustrate the procedure which involves a combination of perturbative scaling and nonperturbative renormalization-group methods for the spin-(1/2) Kondo impurity. We explain the factorization of the temperature and spatial dependence of the Knight shift observed in NMR experiments.

Optical and Physical Properties of Atmospheric Aerosols over the Bay of Bengal during ICARB

Simultaneous and collocated measurements of total and hemispherical backscattering coefficients (σ and β, respectively) at three wavelengths, mass size distributions, and columnar spectral aerosol optical depth (AOD) were made onboard an extensive cruise experiment covering, for the first time, the entire Bay of Bengal (BoB) and northern Indian Ocean. The results are synthesized to understand the optical properties of aerosols in the marine atmospheric boundary layer and their dependence on the size distribution. The observations revealed distinct spatial and spectral variations of all the aerosol parameters over the BoB and the presence of strong latitudinal gradients. The size distributions varied spatially, with the majority of accumulation modes decreasing from north to south. The scattering coefficient decreased from very high values (resembling those reported for continental/urban locations) in the northern BoB to very low values seen over near-pristine environments in the southeastern BoB. The average mass scattering efficiency of BoB aerosols was found to be 2.66 ± 0.1 m2 g−1 at 550 nm. The spectral dependence of columnar AOD deviated significantly from that of the scattering coefficients in the northern BoB, implying vertical heterogeneity in the aerosol type in that region. However, a more homogeneous scenario was observed in the southern BoB. Simultaneous lidar and in situ measurements onboard an aircraft over the ocean revealed the presence of elevated aerosol layers of enhanced extinction at altitudes of 1 to 3 km with an offshore extent of a few hundred kilometers. Back-trajectory analyses showed these layers to be associated with advection from west Asia and western India. The large spatial variations and vertical heterogeneity in aerosol properties, revealed by the present study, need to be included in the regional radiative forcing over the Bay of Bengal.

Reliability Optimization using SLUMT

This paper is concerned with the reliability optimization of a spatially redundant system, subject to various constraints, by using nonlinear programming. The constrained optimization problem is converted into a sequence of unconstrained optimization problems by using a penalty function. The new problem is then solved by the conjugate gradient method. The advantages of this method are highlighted.

Additional binding sites in lysozyme. X-ray analysis of lysozyme complexes with bromophenol red and bromophenol blue

The binding sites in hen egg-white lysozyme for neutral bromophenol red (BPR) and ionized bromophenol blue (BPB) have been characterized at 2 Å resolution. In either case, the dye-bound enzyme is active against the polysaccharide, but not against the cell wall. Both binding sites are outside, but close to, the hexasaccharide binding cleft in the enzyme. The binding site of BPR made up of Arg5, Lys33, Phe34, Asn37, Phe38, Ala122, Trp123 and possibly Arg125, is dose to subsite F while that of BPB made up of Tyr20, Arg21, Asn93, Lys96, Lys97 and Ser100, is close to subsites A and B. The binding sites of the neutral dye and the ionized dye are thus spatially far apart. The peptide component of the bacterial cell wall probably interacts with these cells during enzyme action. Such interactions are perhaps necessary for appropriately positioning the enzyme molecule on the bacterial cell wall.

Effect of soil variability on the bearing capacity of clay and in slope stability problems

Site-specific geotechnical data are always random and variable in space. In the present study, a procedure for quantifying the variability in geotechnical characterization and design parameters is discussed using the site-specific cone tip resistance data (qc) obtained from static cone penetration test (SCPT). The parameters for the spatial variability modeling of geotechnical parameters i.e. (i) existing trend function in the in situ qc data; (ii) second moment statistics i.e. analysis of mean, variance, and auto-correlation structure of the soil strength and stiffness parameters; and (iii) inputs from the spatial correlation analysis, are utilized in the numerical modeling procedures using the finite difference numerical code FLAC 5.0. The influence of consideration of spatially variable soil parameters on the reliability-based geotechnical deign is studied for the two cases i.e. (a) bearing capacity analysis of a shallow foundation resting on a clayey soil, and (b) analysis of stability and deformation pattern of a cohesive-frictional soil slope. The study highlights the procedure for conducting a site-specific study using field test data such as SCPT in geotechnical analysis and demonstrates that a few additional computations involving soil variability provide a better insight into the role of variability in designs.

Assimilation of remote sensing and hydrological data using adaptive filtering techniques for watershed modelling

The knowledge of hydrological variables (e. g. soil moisture, evapotranspiration) are of pronounced importance in various applications including flood control, agricultural production and effective water resources management. These applications require the accurate prediction of hydrological variables spatially and temporally in watershed/basin. Though hydrological models can simulate these variables at desired resolution (spatial and temporal), often they are validated against the variables, which are either sparse in resolution (e. g. soil moisture) or averaged over large regions (e. g. runoff). A combination of the distributed hydrological model (DHM) and remote sensing (RS) has the potential to improve resolution. Data assimilation schemes can optimally combine DHM and RS. Retrieval of hydrological variables (e. g. soil moisture) from remote sensing and assimilating it in hydrological model requires validation of algorithms using field studies. Here we present a review of methodologies developed to assimilate RS in DHM and demonstrate the application for soil moisture in a small experimental watershed in south India.

Extending temporal simulations

Direct numerical simulations (DNS) of spatially growing turbulent shear layers may be performed as temporal simulations by solving the governing equations with some additional terms while imposing streamwise periodicity. These terms are functions of the means whose spatial growth is calculated easily and accurately from statistics of the temporal DNS. Equations for such simulations are derived.

Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control chemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Diurnal-scale signatures of monsoon rainfall over the Indian region from TRMM satellite observations

One of the most important modes of summer season precipitation variability over the Indian region, the diurnal cycle, is studied using the Tropical Rainfall Measuring Mission 3-hourly, 0.25 degrees x 0.25 degrees 3B42 rainfall product for nine years (1999-2007). Most previous studies have provided an analysis of a single year or a few years of satellite-or station-based rainfall data. Our study aims to systematically analyze the statistical characteristics of the diurnal-scale signature of rainfall over the Indian and surrounding regions. Using harmonic analysis, we extract the signal corresponding to diurnal and subdiurnal variability. Subsequently, the 3-hourly time period or the octet of rainfall peak for this filtered signal, referred to as the ``peak octet,'' is estimated, with care taken to eliminate spurious peaks arising out of Gibbs oscillations. Our analysis suggests that over the Bay of Bengal, there are three distinct modes of the peak octet of diurnal rainfall corresponding to 1130, 1430, and 1730 Indian standard time (IST), from the north central to south bay. This finding could be seen to be consistent with southward propagation of the diurnal rainfall pattern reported by earlier studies. Over the Arabian Sea, there is a spatially coherent pattern in the mode of the peak octet (1430 IST), in a region where it rains for more than 30% of the time. In the equatorial Indian Ocean, while most of the western part shows a late night/early morning peak, the eastern part does not show a spatially coherent pattern in the mode of the peak octet owing to the occurrence of a ual maxima (early morng and early/late afternoon). The imalayan foothills were found to have a mode of peak octet corresponding to 0230 IST, whereas over the Burmese mountains and the Western Ghats (west coast of India) the rainfall peaks during late afternoon/early evening (1430-1730 IST). This implies that the phase of the diurnal cycle over inland orography (e. g., Himalayas) is significantly different from coastal orography (e. g., Western Ghats). We also find that over the Gangetic plains, the peak octet is around 1430 IST, a few hours earlier compared to the typical early evening maxima over land.

Mapping of fuelwood trees using geoinformatics

Rural population of India constitutes about 70% of the total population and traditional fuels account for 75% of the rural energy needs. Depletion of woodlands coupled with the persistent dependency on fuel wood has posed a serious problem for household energy provision in many parts. This study highlights that the traditional fuels still meet 85-95% of fuel needs in rural areas of Kolar district: people prefer fuel wood for cooking and agriculture residues for water heating and other purposes. However, rapid changes in land cover and land use in recent times have affected these traditional fuels availability necessitating inventorying, mapping and monitoring of bioresources for sustainable management of bioresources. Remote sensing data (Multispectal and Panchromatic), Geographic Information System (GIS), field surveys and non-destructive sampling were used to assess spatially the availability and demand of energy. Field surveys indicate that rural household depends on species such as Prosopis juliflora, Acacia nilotica, Acacia auriculiformis to meet fuel wood requirement for domestic activities. Hence, to take stock of fuel wood availability, mapping was done at species level (with 88% accuracy) considering villages as sampling units using fused multispectral and panchromatic data. (C) 2009 Elsevier Ltd. All rights reserved.