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.

Dynamical Transition of Water in the Grooves of DNA Duplex at Low Temperature

At low temperature (below its freezing/melting temperature), liquid water under confinement is known to exhibit anomalous dynamical features. Here we study structure and dynamics of water in the grooves of a long DNA duplex using molecular dynamics simulations with TIP5P potential at low temperature. We find signatures of a dynamical transition in both translational and orientational dynamics of water molecules in both the major and the minor grooves of a DNA duplex. The transition occurs at a slightly higher temperature (TGL ≈ 255 K) than the temperature at which the bulk water is found to undergo a dynamical transition, which for the TIP5P potential is at 247 K. Groove water, however, exhibits markedly different temperature dependence of its properties from the bulk. Entropy calculations reveal that the minor groove water is ordered even at room temperature, and the transition at T ≈ 255 K can be characterized as a strong-to-strong dynamical transition. Confinement of water in the grooves of DNA favors the formation of a low density four-coordinated state (as a consequence of enthalpy−entropy balance) that makes the liquid−liquid transition stronger. The low temperature water is characterized by pronounced tetrahedral order, as manifested in the sharp rise near 109° in the O−O−O angle distribution. We find that the Adams−Gibbs relation between configurational entropy and translational diffusion holds quite well when the two quantities are plotted together in a master plot for different region of aqueous DNA duplex (bulk, major, and minor grooves) at different temperatures. The activation energy for the transfer of water molecules between different regions of DNA is found to be weakly dependent on temperature.

Practical Algorithms For Mean Velocity Estimation In Pulse Doppler Weather Radars Using A Small Number Of Samples

Doppler weather radars with fast scanning rates must estimate spectral moments based on a small number of echo samples. This paper concerns the estimation of mean Doppler velocity in a coherent radar using a short complex time series. Specific results are presented based on 16 samples. A wide range of signal-to-noise ratios are considered, and attention is given to ease of implementation. It is shown that FFT estimators fare poorly in low SNR and/or high spectrum-width situations. Several variants of a vector pulse-pair processor are postulated and an algorithm is developed for the resolution of phase angle ambiguity. This processor is found to be better than conventional processors at very low SNR values. A feasible approximation to the maximum entropy estimator is derived as well as a technique utilizing the maximization of the periodogram. It is found that a vector pulse-pair processor operating with four lags for clear air observation and a single lag (pulse-pair mode) for storm observation may be a good way to estimate Doppler velocities over the entire gamut of weather phenomena.

Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Adsorption isotherms for neutral organic compounds-A hierarchy in modelling: Part II

A two-state model allowing for size disparity between the solvent and the adsorbate is analysed to derive the adsorption isotherm for electrosorption of organic compounds. Explicity, the organic adsorbate is assumed to occupy "n" lattice sites at the interface as compared to "one" by the solvent. The model parameters are the respective permanent and induced dipole moments apart from the nearest neighbour distance. The coulombic interactions due to permanent and induced dipole moments, discreteness of charge effects, and short-range and specific substrate interactions have all been incorporated. The adsorption isotherm is then derived using mean field approximation (MFA) and is found to be more general than the earlier multi-site versions of Bockris and Swinkels, Mohilner et al., and Bennes, as far as the entropy contributions are concerned. The role of electrostatic forces is explicity reflected in the adsorption isotherm via the Gibbs energy of adsorption term which itself is a quadratic function of the electrode charge-density. The approximation implicit in the adsorption isotherm of Mohilner et al. or Bennes is indicated briefly.

A Fuzzy Approximation Scheme for Sequential Learning in Pattern Recognition

An adaptive learning scheme, based on a fuzzy approximation to the gradient descent method for training a pattern classifier using unlabeled samples, is described. The objective function defined for the fuzzy ISODATA clustering procedure is used as the loss function for computing the gradient. Learning is based on simultaneous fuzzy decisionmaking and estimation. It uses conditional fuzzy measures on unlabeled samples. An exponential membership function is assumed for each class, and the parameters constituting these membership functions are estimated, using the gradient, in a recursive fashion. The induced possibility of occurrence of each class is useful for estimation and is computed using 1) the membership of the new sample in that class and 2) the previously computed average possibility of occurrence of the same class. An inductive entropy measure is defined in terms of induced possibility distribution to measure the extent of learning. The method is illustrated with relevant examples.

Do H-functions always increase during Violent Relaxation

Recent work on the violent relaxation of collisionless stellar systems has been based on the notion of a wide class of entropy functions. A theorem concerning entropy increase has been proved. We draw attention to some underlying assumptions that have been ignored in the applications of this theorem to stellar dynamical problems. Once these are taken into account, the use of this theorem is at best heuristic. We present a simple counter-example.

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.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Thermodynamic and kinetic studies on saccharide binding to soya-bean agglutinin.

The fluorescence of N-dansylgalactosamine [N-(5-dimethylaminonaphthalene-1-sulphonyl)galactosamine] was enhanced 11-fold with a 25 nm blue-shift in the emission maximum upon binding to soya-bean agglutinin (SBA). This change was used to determine the association constants and thermodynamic parameters for this interaction. The association constant of 1.51 X 10(6) M-1 at 20 degrees C indicated a very strong binding, which is mainly due to a relatively small entropy value, as revealed by the thermodynamic parameters: delta G = -34.7 kJ X mol-1, delta H = -37.9 kJ X mol-1 and delta S = -10.9 J X mol-1 X K-1. The specific binding of this sugar to SBA shows that the lectin can accommodate a large hydrophobic substituent on the C-2 of galactose. Binding of non-fluorescent ligands, studied by monitoring the fluorescence changes when they are added to a mixture of SBA and N-dansylgalactosamine, indicates that a hydrophobic substituent at the anomeric position increases the affinity of the interaction. The C-6 hydroxy group also stabilizes the binding considerably. Kinetics of binding of N-dansylgalactosamine to SBA studied by stopped-flow spectrofluorimetry are consistent with a single-step mechanism and yielded k+1 = 2.4 X 10(5) M-1 X s-1 and k-1 = 0.2 s-1 at 20 degrees C. The activation parameters indicate an enthalpicly controlled association process.

Thermal studies on melting and crystallization of polyamide fibres

Effect of heating rate on melting and crystallization of polyamide fibres has been examined using differential scanning calorimetric (DSC) technique. Peak temperature for melting (T m) and crystallization (T k) get suppressed with the increase in the heating rate which has been explained on the basis of chain orientation. Heat of melting (DeltaH m) and crystallization (DeltaH k) have been measured.DeltaH m vs. T m shows a nonlinear dependence which has been explained on the basis of entropy change. Quantitative difference inDeltaH m andDeltaH k values has been explained on the basis of orientation and degradation of the polymer.

Microstructure and mechanical properties of unidirectionally solidified Al-Si-Ni ternary eutectic

Al-10.98 pct Si-4.9 pct Ni ternary eutectic alloy was unidirectionally solidified at growth rates from 1.39μm/sec to 6.95μm/sec. Binary Al-Ni and Al-Si eutectics prepared from the same purity metals were also solidified under similar conditions to characterize the growth conditions under the conditions of present study. NiAl3 phase appeared as fibers in the binary Al-Ni eutectic and silicon appeared as irregular plates in the binary Al-Si eutectic. However, in the ternary Al-Si-Ni eutectic alloy both NiAl3 and silicon phases appeared as irregular plates dispersed in α-Al phase, without any regular repctitive arrangement. The size and spacing of NiAl3 and Si platelets in cone shaped colonies decreased with an increase in the growth rate of the ternary eutectic. Examination of specimen quenched during unidirectional solidification indicated that the ternary eutectic grows with a non-planar interface with both Si and NiAl3 phases protruding into the liquid. It is concluded that it will be difficult to grow regular ternary eutectic structures even if only one phase has a high entropy of melting. The tensile strength and modulus of unidirectionally solidified Al-Si-Ni eutectic was lower than the chill cast alloys of the same composition, and decreased with a decrease in growth rate. Tensile modulus and strength of ternary Al-Si-Ni eutectic alloys was greater than binary Al-Si eutectic alloy under similar growth conditions, both in the chill cast and in unidirectionally solidified conditions.

On walls of marginal stability in N=2 string theories

We study the properties of walls of marginal stability for BPS decays in a class of N = 2 theories. These theories arise in N = 2 string compactifications obtained as freely acting orbifolds of N = 4 theories, such theories include the STU model and the FHSV model. The cross sections of these walls for a generic decay in the axion-dilaton plane reduce to lines or circles. From the continuity properties of walls of marginal stability we show that central charges of BPS states do not vanish in the interior of the moduli space. Given a charge vector of a BPS state corresponding to a large black hole in these theories, we show that all walls of marginal stability intersect at the same point in the lower half of the axion-dilaton plane. We isolate a class of decays whose walls of marginal stability always lie in a region bounded by walls formed by decays to small black holes. This enables us to isolate a region in moduli space for which no decays occur within this class. We then study entropy enigma decays for such models and show that for generic values of the moduli, that is when moduli are of order one compared to the charges, entropy enigma decays do not occur in these models.

Urban Growth Analysis Using Spatial and Temporal Data

Urban growth identification, quantification, knowledge of rate and the trends of growth would help in regional planning for better infrastructure provision in environmentally sound way. This requires analysis of spatial and temporal data, which help in quantifying the trends of growth on spatial scale. Emerging technologies such as Remote Sensing, Geographic Information System (GIS) along with Global Positioning System (GPS) help in this regard. Remote sensing aids in the collection of temporal data and GIS helps in spatial analysis. This paper focuses on the analysis of urban growth pattern in the form of either radial or linear sprawl along the Bangalore - Mysore highway. Various GIS base layers such as builtup areas along the highway, road network, village boundary etc. were generated using collateral data such as the Survey of India toposheet, etc. Further, this analysis was complemented with the computation of Shannon's entropy, which helped in identifying prevalent sprawl zone, rate of growth and in delineating potential sprawl locations. The computation Shannon's entropy helped in delineating regions with dispersed and compact growth. This study reveals that the Bangalore North and South taluks contributed mainly to the sprawl with 559% increase in built-up area over a period of 28 years and high degree of dispersion. The Mysore and Srirangapatna region showed 128% change in built-up area and a high potential for sprawl with slightly high dispersion. The degree of sprawl was found to be directly proportional to the distances from the cities.

Thermodynamics of Monosaccharide and Disaccharide Binding to Erythrina corallodendron Lectin

Isothermal titration calorimetry measurements of the binding of 2′-fucosyllactose, lactose, N-acetyllactosamine, galactopyranose, 2-acetamido-2-deoxygalactopyranoside, methyl α-N-dansylgalactosaminide (Me-α-DNS-GalN), methyl α-D-galactopyranoside, methyl β-D-galactopyranoside, and fucose to Erythrina corallodendron lectin (ECorL), a dimer with one binding site per subunit, were performed at 283-286 and 297-299 K. The site binding enthalpies, ΔHb, with the exception of Me-α-DNS-GalN, are the same at both temperatures and range from −47.1 ± 1.0 kJ mol−1 for N-acetyllactosamine to −4.4 ± 0.3 kJ mol−1 for fucose, and the site binding constants range from 3.82 ± 0.9 × 105 M−1 for Me-α-DNS-GalN at 283.2 K to 0.46 ± 0.05 × 103 M−1 for fucose at 297.2 K. The binding reactions are mainly enthalpically driven except for fucose and exhibit enthalpy-entropy compensation. The binding enthalpies of the disaccharides are about twice the binding enthalpies of the monosaccharides in contrast to concanavalin A where the binding enthalpies do not double for the disaccharides. Differential scanning calorimetry measurements show that denaturation of the ECorL dimer results in dissociation into its monomer subunits. The binding constants from the increase in denaturation temperature of ECorL in the presence of saccharides are in agreement with values from isothermal titration calorimetry results. The thermal denaturation of ECorL occurs around 333 K, well below the 344-360 K denaturation temperature of other legume lectins of similar size and tertiary structure, undoubtedly due to the difference in its quaternary structure relative to other legume lectins. This is also apparent from the independent unfolding of its two domains.