Projecting low and extensive dimensional chaos from spatio-temporal dynamics

We review the spatio-temporal dynamical features of the Ananthakrishna model for the Portevin-Le Chatelier effect, a kind of plastic instability observed under constant strain rate deformation conditions. We then establish a qualitative correspondence between the spatio-temporal structures that evolve continuously in the instability domain and the nature of the irregularity of the scalar stress signal. Rest of the study is on quantifying the dynamical information contained in the stress signals about the spatio-temporal dynamics of the model. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatio-temporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands. The stress signals in the partially propagating to fully propagating bands turn to have features of extensive chaos.

Robustness of early warning signals of regime shifts in time-delayed ecological models

Various ecological and other complex dynamical systems may exhibit abrupt regime shifts or critical transitions, wherein they reorganize from one stable state to another over relatively short time scales. Because of potential losses to ecosystem services, forecasting such unexpected shifts would be valuable. Using mathematical models of regime shifts, ecologists have proposed various early warning signals of imminent shifts. However, their generality and applicability to real ecosystems remain unclear because these mathematical models are considered too simplistic. Here, we investigate the robustness of recently proposed early warning signals of regime shifts in two well-studied ecological models, but with the inclusion of time-delayed processes. We find that the average variance may either increase or decrease prior to a regime shift and, thus, may not be a robust leading indicator in time-delayed ecological systems. In contrast, changing average skewness, increasing autocorrelation at short time lags, and reddening power spectra of time series of the ecological state variable all show trends consistent with those of models with no time delays. Our results provide insights into the robustness of early warning signals of regime shifts in a broader class of ecological systems.

Solvation dynamics of tryptophan in water-dimethyl sulfoxide binary mixture: In search of molecular origin of composition dependent multiple anomalies

Experimental and simulation studies have uncovered at least two anomalous concentration regimes in water-dimethyl sulfoxide (DMSO) binary mixture whose precise origin has remained a subject of debate. In order to facilitate time domain experimental investigation of the dynamics of such binary mixtures, we explore strength or extent of influence of these anomalies in dipolar solvation dynamics by carrying out long molecular dynamics simulations over a wide range of DMSO concentration. The solvation time correlation function so calculated indeed displays strong composition dependent anomalies, reflected in pronounced non-exponential kinetics and non-monotonous composition dependence of the average solvation time constant. In particular, we find remarkable slow-down in the solvation dynamics around 10%-20% and 35%-50% mole percentage. We investigate microscopic origin of these two anomalies. The population distribution analyses of different structural morphology elucidate that these two slowing down are reflections of intriguing structural transformations in water-DMSO mixture. The structural transformations themselves can be explained in terms of a change in the relative coordination number of DMSO and water molecules, from 1DMSO:2H(2)O to 1H(2)O:1DMSO and 1H(2)O:2DMSO complex formation. Thus, while the emergence of first slow down (at 15% DMSO mole percentage) is due to the percolation among DMSO molecules supported by the water molecules (whose percolating network remains largely unaffected), the 2nd anomaly (centered on 40%-50%) is due to the formation of the network structure where the unit of 1DMSO:1H(2)O and 2DMSO:1H(2)O dominates to give rise to rich dynamical features. Through an analysis of partial solvation dynamics an interesting negative cross-correlation between water and DMSO is observed that makes an important contribution to relaxation at intermediate to longer times.

Relation Between the Diffusivity, Viscosity, and Ionic Radius of LiCl in Water, Methanol, and Ethylene Glycol: A Molecular Dynamics Simulation

A molecular dynamics (MD) investigation of LiCl in water, methanol, and ethylene glycol (EG) at 298 K is reported. Several; structural and dynamical properties of the ions as well as the solvent such as self-diffusivity, radial distribution functions, void and neck distributions, velocity autocorrelation functions, and mean residence times of solvent in the first solvation shell have been computed. The results show that the reciprocal relationship between the self-diffusivity of the ions and the viscosity is valid in almost all solvents with the exception of water. From an analysis of radial distribution functions and coordination numbers the nature of hydrogen bonding within the solvent and its influence on the void and neck distribution becomes evident. It is seen that the solvent solvent interaction is important in EG while solute solvent interactions dominate in water and methanol. From Voronoi tessellation, it is seen that the voids and necks within methanol are larger as compared to those within water or EG. On the basis of the void and neck distributions obtained from MD simulations and literature experimental data of limiting ion conductivity for various ions of different sizes we show that there is a relation between the void and neck radius on e one hand and dependence of conductivity on the ionic radius on the other. It is shown that the presence of large diameter voids and necks in methanol is responsible for maximum in limiting ion conductivity (lambda(0)) of TMA(+), while in water in EG, the maximum is seen for Rb+. In the case of monovalent anions, maximum in lambda(0) as a function ionic radius is seen for Br- in water EG but for the larger ClO4- ion in methanol. The relation between the void and neck distribution and the variation in lambda(0) with ionic radius arises via the Levitation effect which is discussed. These studies show the importance of the solvent structure and the associated void structure.

Wireless Network-Coded Bidirectional Relaying Using Latin Squares for M-PSK Modulation

The design of modulation schemes for the physical layer network-coded two-way relaying scenario is considered with a protocol which employs two phases: multiple access (MA) phase and broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of MA interference which occurs at the relay during the MA phase and all these network coding maps should satisfy a requirement called the exclusive law. We show that every network coding map that satisfies the exclusive law is representable by a Latin Square and conversely, that this relationship can be used to get the network coding maps satisfying the exclusive law. The channel fade states for which the minimum distance of the effective constellation at the relay become zero are referred to as the singular fade states. For M - PSK modulation (M any power of 2), it is shown that there are (M-2/4 - M/2 + 1) M singular fade states. Also, it is shown that the constraints which the network coding maps should satisfy so that the harmful effects of the singular fade states are removed, can be viewed equivalently as partially filled Latin Squares (PFLS). The problem of finding all the required maps is reduced to finding a small set of maps for M - PSK constellations (any power of 2), obtained by the completion of PFLS. Even though the completability of M x M PFLS using M symbols is an open problem, specific cases where such a completion is always possible are identified and explicit construction procedures are provided. Having obtained the network coding maps, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map chosen in a particular region. It is shown that the complex plane can be partitioned into two regions: a region in which any network coding map which satisfies the exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for M = 4-PSK signal set by Koike-Akino et al., when specialized for Simulation results show that the proposed scheme performs better than the conventional exclusive-OR (XOR) network coding and in some cases outperforms the scheme proposed by Koike-Akino et al.

An automated approach to network features of protein structure ensembles

Network theory applied to protein structures provides insights into numerous problems of biological relevance. The explosion in structural data available from PDB and simulations establishes a need to introduce a standalone-efficient program that assembles network concepts/parameters under one hood in an automated manner. Herein, we discuss the development/application of an exhaustive, user-friendly, standalone program package named PSN-Ensemble, which can handle structural ensembles generated through molecular dynamics (MD) simulation/NMR studies or from multiple X-ray structures. The novelty in network construction lies in the explicit consideration of side-chain interactions among amino acids. The program evaluates network parameters dealing with topological organization and long-range allosteric communication. The introduction of a flexible weighing scheme in terms of residue pairwise cross-correlation/interaction energy in PSN-Ensemble brings in dynamical/chemical knowledge into the network representation. Also, the results are mapped on a graphical display of the structure, allowing an easy access of network analysis to a general biological community. The potential of PSN-Ensemble toward examining structural ensemble is exemplified using MD trajectories of an ubiquitin-conjugating enzyme (UbcH5b). Furthermore, insights derived from network parameters evaluated using PSN-Ensemble for single-static structures of active/inactive states of 2-adrenergic receptor and the ternary tRNA complexes of tyrosyl tRNA synthetases (from organisms across kingdoms) are discussed. PSN-Ensemble is freely available from http://vishgraph.mbu.iisc.ernet.in/PSN-Ensemble/psn_index.html.

Wireless network-coded accumulate-compute and forward two-way relaying

The design of modulation schemes for the physical layer network-coded two way wireless relaying scenario is considered. It was observed by Koike-Akino et al. for the two way relaying scenario, that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA Phase and all these network coding maps should satisfy a requirement called exclusive law. We extend this approach to an Accumulate-Compute and Forward protocol which employs two phases: Multiple Access (MA) phase consisting of two channel uses with independent messages in each channel use, and Broadcast (BC) phase having one channel use. Assuming that the two users transmit points from the same 4-PSK constellation, every such network coding map that satisfies the exclusive law can be represented by a Latin Square with side 16, and conversely, this relationship can be used to get the network coding maps satisfying the exclusive law. Two methods of obtaining this network coding map to be used at the relay are discussed. Using the structural properties of the Latin Squares for a given set of parameters, the problem of finding all the required maps is reduced to finding a small set of maps. Having obtained all the Latin Squares, the set of all possible channel realizations is quantized, depending on which one of the Latin Squares obtained optimizes the performance. The quantization thus obtained, is shown to be the same as the one obtained in [7] for the 2-stage bidirectional relaying.

Channel quantization for physical layer network-coded two-way relaying

The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. In other words, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map giving the best performance in a particular region. We obtain such a quantization analytically for the case when M-PSK (for M any power of 2) is the signal set used during the MA phase. We show that the complex plane can be classified into two regions: a region in which any network coding map which satisfies the so called exclusive law gives the same best performance and a region in which the choice of the network coding map affects the performance, which is further quantized based on the choice of the network coding map which optimizes the performance. The quantization thus obtained analytically, leads to the same as the one obtained using computer search for 4-PSK signal set by Koike-Akino et al., for the specific value of M = 4.

Anomalous phase transitions in soft colloid-polymer binary mixtures

We have shown earlier [1] that these PGNPs resemble star polymers or spherical brushes in terms of their morphology in the melt. However, these particles show dynamics in melt which is quite different from other soft colloidal particles. Since most of the work on soft colloidal particles have been performed in solutions we have now explored the phase behavior of the PGNPs in good solvent using microscopic structural and dynamical measurements on binary mixtures of homopolymers and soft colloids consisting of polymer grafted nanoparticles. We observe anomalous structural and dynamical phase transitions of these binary mixtures, including appearance of spontaneous orientational alignment and logarithmic structural relaxations, as a function of added homopolymers of different molecular weights. Our experiments points to the possibility of exploiting the phase space in density and homopolymer size, of such hybrid systems, to create new materials with unique properties.

On generalized gravitational entropy, squashed cones and holography

We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.

Image deconvolution research: its scope and importance in live cell microscopy

Fluorescence microscopy has become an indispensable tool in cell biology research due its exceptional specificity and ability to visualize subcellular structures with high contrast. It has highest impact when applied in 4D mode, i.e. when applied to record 3D image information as a function of time, since it allows the study of dynamic cellular processes in their native environment. The main issue in 4D fluorescence microscopy is that the phototoxic effect of fluorescence excitation gets accumulated during 4D image acquisition to the extent that normal cell functions are altered. Hence to avoid the alteration of normal cell functioning, it is required to minimize the excitation dose used for individual 2D images constituting a 4D image. Consequently, the noise level becomes very high degrading the resolution. According to the current status of technology, there is a minimum required excitation dose to ensure a resolution that is adequate for biological investigations. This minimum is sufficient to damage light-sensitive cells such as yeast if 4D imaging is performed for an extended period of time, for example, imaging for a complete cell cycle. Nevertheless, our recently developed deconvolution method resolves this conflict forming an enabling technology for visualization of dynamical processes of light-sensitive cells for durations longer than ever without perturbing normal cell functioning. The main goal of this article is to emphasize that there are still possibilities for enabling newer kinds of experiment in cell biology research involving even longer 4D imaging, by only improving deconvolution methods without any new optical technologies.

Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Doping a Correlated Band Insulator: A New Route to Half-Metallic Behavior

We demonstrate in a simple model the surprising result that turning on an on-site Coulomb interaction U in a doped band insulator leads to the formation of a half-metallic state. In the undoped system, we show that increasing U leads to a first order transition at a finite value U-AF between a paramagnetic band insulator and an antiferomagnetic Mott insulator. Upon doping, the system exhibits half-metallic ferrimagnetism over a wide range of doping and interaction strengths on either side of U-AF. Our results, based on dynamical mean field theory, suggest a new route to half metallicity, and will hopefully motivate searches for new materials for spintronics.

Reentrant Superspin Glass Phase in a La0.82Ca0.18MnO3 Ferromagnetic Insulator

We report results of the magnetization and ac susceptibility measurements down to very low fields on a single crystal of the perovskite manganite, La-0.82 Ca-0.18 MnO3. This composition falls in the intriguing ferromagnetic insulator region of the manganite phase diagram. In contrast to earlier beliefs, our investigations reveal that magnetically (and in every other sense), this is a single- phase system with a ferromagnetic ordering temperature of around 170 K. However, this ferromagnetic state is magnetically frustrated, and the system exhibits pronounced glassy dynamics below 90 K. Based on measured dynamical properties, we propose that this quasi-long-ranged ferromagnetic phase, and the associated superspin glass behavior, is the true magnetic state of the system, rather than being a macroscopic mixture of ferromagnetic and antiferromagnetic phases, as often suggested. Our results provide an understanding of the quantum phase transition from an antiferromagnetic insulator to a ferromagnetic metal via this ferromagnetic state as a function of x in La1-xCaxMnO3, in terms of the possible formation of magnetic polarons.

Suppression of gravitational instabilities by dominant dark matter halo in low-surface-brightness galaxies

The low-surface-brightness galaxies are gas rich and yet have a low star formation rate; this is a well-known puzzle. The spiral features in these galaxies are weak and difficult to trace, although this aspect has not been studied much. These galaxies are known to be dominated by the dark matter halo from the innermost regions. Here, we do a stability analysis for the galactic disc of UGC 7321, a low-surface-brightness, superthin galaxy, for which the various observational input parameters are available. We show that the disc is stable against local, linear axisymmetric and non-axisymmetric perturbations. The Toomre Q parameter values are found to be large (>> 1) mainly due to the low disc surface density, and the high rotation velocity resulting due to the dominant dark matter halo, which could explain the observed low star formation rate. For the stars-alone case, the disc shows finite swing amplification but the addition of dark matter halo suppresses that amplification almost completely. Even the inclusion of the low-dispersion gas which constitutes a high disc mass fraction does not help in causing swing amplification. This can explain why these galaxies do not show strong spiral features. Thus, the dynamical effect of a halo that is dominant from inner regions can naturally explain why star formation and spiral features are largely suppressed in low-surface-brightness galaxies, making these different from the high-surface-brightness galaxies.