Mode-coupling glass transition in a fluid confined by a periodic potential

We show that a fluid under strong spatially periodic confinement displays a glass transition within mode-coupling theory at a much lower density than the corresponding bulk system. We use fluctuating hydrodynamics, with confinement imposed through a periodic potential whose wavelength plays an important role in our treatment. To make the calculation tractable we implement a detailed calculation in one dimension. Although we do not expect simple 1d fluids to show a glass transition, our results are indicative of the behavior expected in higher dimensions. In a certain region of parameter space we observe a three-step relaxation reported recently in computer simulations [S. H. Krishnan, Ph.D. thesis, Indian Institute of Science (2005); Kim et al., Eur. Phys. J. Special Topics 189, 135 (2010)] and a glass-glass transition. We compare our results to those of Krakoviack [Phys. Rev. E 75, 031503 (2007)] and Lang et al. [Phys. Rev. Lett. 105, 125701 (2010)].

Particle dynamics in the channel flow of a turbulent particle-gas suspension at high Stokes number. Part 2. Comparison of fluctuating force simulations and experiments

The particle and fluid velocity fluctuations in a turbulent gas-particle suspension are studied experimentally using two-dimensional particle image velocimetry with the objective of comparing the experiments with the predictions of fluctuating force simulations. Since the fluctuating force simulations employ force distributions which do not incorporate the modification of fluid turbulence due to the particles, it is of importance to quantify the turbulence modification in the experiments. For experiments carried out at a low volume fraction of 9.15 x 10(-5) (mass loading is 0.19), where the viscous relaxation time is small compared with the time between collisions, it is found that the gas-phase turbulence is not significantly modified by the presence of particles. Owing to this, quantitative agreement is obtained between the results of experiments and fluctuating force simulations for the mean velocity and the root mean square of the fluctuating velocity, provided that the polydispersity in the particle size is incorporated in the simulations. This is because the polydispersity results in a variation in the terminal velocity of the particles which could induce collisions and generate fluctuations; this mechanism is absent if all of the particles are of equal size. It is found that there is some variation in the particle mean velocity very close to the wall depending on the wall-collision model used in the simulations, and agreement with experiments is obtained only when the tangential wall-particle coefficient of restitution is 0.7. The mean particle velocity is in quantitative agreement for locations more than 10 wall units from the wall of the channel. However, there are systematic differences between the simulations and theory for the particle concentrations, possibly due to inadequate control over the particle feeding at the entrance. The particle velocity distributions are compared both at the centre of the channel and near the wall, and the shape of the distribution function near the wall obtained in experiments is accurately predicted by the simulations. At the centre, there is some discrepancy between simulations and experiment for the distribution of the fluctuating velocity in the flow direction, where the simulations predict a bi-modal distribution whereas only a single maximum is observed in the experiments, although both distributions are skewed towards negative fluctuating velocities. At a much higher particle mass loading of 1.7, where the time between collisions is smaller than the viscous relaxation time, there is a significant increase in the turbulent velocity fluctuations by similar to 1-2 orders of magnitude. Therefore, it becomes necessary to incorporate the modified fluid-phase intensity in the fluctuating force simulation; with this modification, the mean and mean-square fluctuating velocities are within 20-30% of the experimental values.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice.We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation η and η + dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary

Structure of DNA-functionalized dendrimer nanoparticles

Atomistic molecular dynamics simulations have been carried out to reveal the characteristic features of ethylenediamine (EDA) cored protonated (corresponding to neutral pH) poly amido amine (PAMAM) dendrimers of generation 3 (G3) and 4 (G4) that are functionalized with single strand DNAs (ssDNAs). The four ssDNA strands that are attached via an alkythiolate [-S(CH(2))(6)-] linker molecule to the free amine groups on the surface of the PAMAM dendrimers are observed to undergo a rapid conformational change during the 25 ns long simulation period. From the RMSD values of ssDNAs, we find relative stability in the case of purine rich (having more adenine and guanine) ssDNA strands than pyrimidine rich (thymine and cytosine) ssDNA strands. The degree of wrapping of ssDNA strands on the dendrimer molecule was found to be influenced by the charge ratio of DNA and the dendrimer. As the G4 dendrimer contains relatively more positive charge than G3 dendrimer, we observe extensive wrapping of ssDNAs on the G4 dendrimer than G3 dendrimer. This might indicate that DNA functionalized G3 dendrimer is more suitable to construct higher order nanostructures. The linker molecule was also found to undergo drastic conformational change during the simulation. During nanosecond long simulation some portion of the linker molecule was found to be lying nearly flat on the surface of the dendrimer molecule. The ssDNA strands along with the linkers are seen to penetrate the surface of the dendrimer molecule and approach closer to the center of the dendrimer indicating the soft sphere nature of the dendrimer molecule. The effective radius of DNA-functionalized dendrimer nanoparticles was found to be independent of base composition of ssDNAs and was observed to be around 19.5 angstrom and 22.4 angstrom when we used G3 and G4 PAMAM dendrimers as the core of the nanoparticle respectively. The observed effective radius of DNA-functionalized dendrimer molecules apparently indicates the significant shrinkage in the structure that has taken place in dendrimer, linker and DNA strands. As a whole our results describe the characteristic features of DNA-functionalized dendrimer nanoparticles and can be used as strong inputs to design effectively the DNA-dendrimer nanoparticle self-assembly for their active biological applications.

Characterization of the dynamics of glass-forming liquids from the properties of the potential energy landscape

We develop a framework for understanding the difference between strong and fragile behavior in the dynamics of glass-forming liquids from the properties of the potential energy landscape. Our approach is based on a master equation description of the activated jump dynamics among the local minima of the potential energy (the so-called inherent structures) that characterize the potential energy landscape of the system. We study the dynamics of a small atomic cluster using this description as well as molecular dynamics simulations and demonstrate the usefulness of our approach for this system. Many of the remarkable features of the complex dynamics of glassy systems emerge from the activated dynamics in the potential energy landscape of the atomic cluster. The dynamics of the system exhibits typical characteristics of a strong supercooled liquid when the system is allowed to explore the full configuration space. This behavior arises because the dynamics is dominated by a few lowest-lying minima of the potential energy and the potential energy barriers between these minima. When the system is constrained to explore only a limited region of the potential energy landscape that excludes the basins of attraction of a few lowest-lying minima, the dynamics is found to exhibit the characteristics of a fragile liquid.

Effect of base dissipation on the granular flow down an inclined plane

The effect of base dissipation on the granular flow down an inclined plane is examined by altering the coefficient of restitution between the moving and base particles in discrete element (DE) simulations. The interaction laws between two moving particles are kept fixed, and the coefficient of restitution (damping constant in the DE simulations) between the base and moving particles are altered to reduce dissipation, and inject energy from the base. The energy injection does result in an increase in the strain rate by up to an order of magnitude, and the temperature by up to two orders of magnitude at the base. However, the volume fraction, strain rate and temperature profiles in the bulk (above about 15 particle diameters from the base) are altered very little by the energy injection at the base. We also examine the variation of h(stop), the minimum height at the cessation of flow, with energy injection from the base. It is found that at a fixed angle of inclination, h(stop) decreases as the energy dissipation at the base decreases.

Critical behavior at depinning of driven disordered vortex matter in 2H-NbS2

We report unusual jamming in driven ordered vortex flow in 2H-NbS2. Reinitiating movement in these jammed vortices with a higher driving force and halting it thereafter once again with a reduction in drive leads to a critical behavior centered around the depinning threshold via divergences in the lifetimes of transient states, validating the predictions of a recent simulation study Reichhardt and Olson Reichhardt, Phys. Rev. Lett. 103, 168301 (2009)] which also pointed out a correspondence between plastic depinning in vortex matter and the notion of random organization proposed Corte et al., Nat. Phys. 4, 420 (2008)] in the context of sheared colloids undergoing diffusive motion.

Analysis of Parameter Values in the van der Waals and Platteeuw Theory for Methane Hydrates Using Monte Carlo Molecular Simulations

The van der Waals and Platteuw (vdVVP) theory has been successfully used to model the thermodynamics of gas hydrates. However, earlier studies have shown that this could be due to the presence of a large number of adjustable parameters whose values are obtained through regression with experimental data. To test this assertion, we carry out a systematic and rigorous study of the performance of various models of vdWP theory that have been proposed over the years. The hydrate phase equilibrium data used for this study is obtained from Monte Carlo molecular simulations of methane hydrates. The parameters of the vdWP theory are regressed from this equilibrium data and compared with their true values obtained directly from simulations. This comparison reveals that (i) methane-water interactions beyond the first cage and methane-methane interactions make a significant contribution to the partition function and thus cannot be neglected, (ii) the rigorous Monte Carlo integration should be used to evaluate the Langmuir constant instead of the spherical smoothed cell approximation, (iii) the parameter values describing the methane-water interactions cannot be correctly regressed from the equilibrium data using the vdVVP theory in its present form, (iv) the regressed empty hydrate property values closely match their true values irrespective of the level of rigor in the theory, and (v) the flexibility of the water lattice forming the hydrate phase needs to be incorporated in the vdWP theory. Since methane is among the simplest of hydrate forming molecules, the conclusions from this study should also hold true for more complicated hydrate guest molecules.

Stabilized SPH-based simulations of impact dynamics using acceleration-corrected artificial viscosity

Artificial viscosity in SPH-based computations of impact dynamics is a numerical artifice that helps stabilize spurious oscillations near the shock fronts and requires certain user-defined parameters. Improper choice of these parameters may lead to spurious entropy generation within the discretized system and make it over-dissipative. This is of particular concern in impact mechanics problems wherein the transient structural response may depend sensitively on the transfer of momentum and kinetic energy due to impact. In order to address this difficulty, an acceleration correction algorithm was proposed in Shaw and Reid (''Heuristic acceleration correction algorithm for use in SPH computations in impact mechanics'', Comput. Methods Appl. Mech. Engrg., 198, 3962-3974) and further rationalized in Shaw et al. (An Optimally Corrected Form of Acceleration Correction Algorithm within SPH-based Simulations of Solid Mechanics, submitted to Comput. Methods Appl. Mech. Engrg). It was shown that the acceleration correction algorithm removes spurious high frequency oscillations in the computed response whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. In this paper, we aim at gathering further insights into the acceleration correction algorithm by further exploring its application to problems related to impact dynamics. The numerical evidence in this work thus establishes that, together with the acceleration correction algorithm, SPH can be used as an accurate and efficient tool in dynamic, inelastic structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the plasma in the disk is essentially collisionless. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell plasma simulations. We focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field, B, until the Alfven velocity, v(A), is comparable to the speed of light, c (independent of the initial value of v(A)/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the pressure perpendicular to B being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume-averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission-from the radio to the gamma-rays-of systems such as Sgr A*.

How good are the simulations of tropical SST-rainfall relationship by IPCC AR4 atmospheric and coupled models?

The failure of atmospheric general circulation models (AGCMs) forced by prescribed SST to simulate and predict the interannual variability of Indian/Asian monsoon has been widely attributed to their inability to reproduce the actual sea surface temperature (SST)-rainfall relationship in the warm Indo-Pacific oceans. This assessment is based on a comparison of the observed and simulated correlation between the rainfall and local SST. However, the observed SSTconvection/rainfall relationship is nonlinear and for this a linear measure such as the correlation is not an appropriate measure. We show that the SST-rainfall relationship simulated by atmospheric and coupled general circulation models in IPCC AR4 is nonlinear, as observed, and realistic over the tropical West Pacific (WPO) and the Indian Ocean (IO). The SST-rainfall pattern simulated by the coupled versions of these models is rather similar to that from the corresponding atmospheric one, except for a shift of the entire pattern to colder/warmer SSTs when there is a cold/warm bias in the coupled version.

A drop of active matter

We study theoretically the hydrodynamics of a fluid drop containing oriented filaments endowed with active contractile or extensile stresses and placed on a solid surface. The active stresses alter qualitatively the wetting properties of the drop, leading to new spreading laws and novel static drop shapes. Candidate systems for testing our predictions include cytoskeletal extracts with motors and ATP, suspensions of bacteria or pulsatile cells, or fluids laden with artificial self-propelled colloids.

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, mu(c), however, is not known. Application of the quasispecies theory to determine mu(c) poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and mu(c). We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated mu(c) to be 7 x 10(-5) -1 x 10(-4) substitutions/site/replication, similar to 2-6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, mu(c) increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of mu(c) may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.

Supersymmetric Chern-Simons theories with vector matter

In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N = 2 supersymmetric model (with one chiral field) for all values of the `t Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.