Temperature-dependent stability of stacking faults in Al, Cu and Ni: first-principles analysis

We present comparative analysis of microscopic mechanisms relevant to plastic deformation of the face-centered cubic (FCC) metals Al, Cu, and Ni, through determination of the temperature-dependent free energies of intrinsic and unstable stacking faults along 1 (1) over bar 0] and 1 (2) over bar 1] on the (1 1 1) plane using first-principles density-functional-theory-based calculations. We show that vibrational contribution results in significant decrease in the free energy of barriers and intrinsic stacking faults (ISFs) of Al, Cu, and Ni with temperature, confirming an important role of thermal fluctuations in the stability of stacking faults (SFs) and deformation at elevated temperatures. In contrast to Al and Ni, the vibrational spectrum of the unstable stacking fault (USF1 (2) over bar 1]) in Cu reveals structural instabilities, indicating that the energy barrier (gamma(usf)) along the (1 1 1)1 (2) over bar 1] slip system in Cu, determined by typical first-principles calculations, is an overestimate, and its commonly used interpretation as the energy release rate needed for dislocation nucleation, as proposed by Rice (1992 J. Mech. Phys. Solids 40 239), should be taken with caution.

Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models

Using numerical diagonalization we study the crossover among different random matrix ensembles (Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE) and Gaussian symplectic ensemble (GSE)) realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one-dimensional lattice model of interacting hard-core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin-orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system.

A new microscopic insight into membrane penetration and reorganization by PETIM dendrimers

Dendrimers are highly branched polymeric nanoparticles whose structure and topology, largely, have determined their efficacy in a wide range of studies performed so far. An area of immense interest is their potential as drug and gene delivery vectors. Realizing this potential, depending on the nature of cell surface-dendrimer interactions, here we report controlled model membrane penetration and reorganization, using a model supported lipid bilayer and poly(ether imine) (PETIM) dendrimers of two generations. By systematically varying the areal density of the lipid bilayers, we provide a microscopic insight, through a combination of high resolution scattering, atomic force microscopy and atomistic molecular dynamics simulations, into the mechanism of PETIM dendrimer membrane penetration, pore formation and membrane re-organization induced by such interactions. Our work represents the first systematic observation of a regular barrel-like membrane spanning pore formation by dendrimers, tunable through lipid bilayer packing, without membrane disruption.

Multidimensional free energy surface of unfolding of HP-36: Microscopic origin of ruggedness

The protein folding funnel paradigm suggests that folding and unfolding proceed as directed diffusion in a multidimensional free energy surface where a multitude of pathways can be traversed during the protein's sojourn from initial to final state. However, finding even a single pathway, with the detail chronicling of intermediates, is an arduous task. In this work we explore the free energy surface of unfolding pathway through umbrella sampling, for a small globular a-helical protein chicken-villin headpiece (HP-36) when the melting of secondary structures is induced by adding DMSO in aqueous solution. We find that the unfolding proceeds through the initial separation or melting of aggregated hydrophobic core that comprises of three phenylalanine residues (Phe7, Phe11, and Phe18). This separation is accompanied by simultaneous melting of the second helix. Unfolding is found to be a multistage process involving crossing of three consecutive minima and two barriers at the initial stage. At a molecular level, Phe18 is observed to reorient itself towards other hydrophobic grooves to stabilize the intermediate states. We identify the configuration of the intermediates and correlate the intermediates with those obtained in our previous works. We also give an estimate of the barriers for different transition states and observe the softening of the barriers with increasing DMSO concentration. We show that higher concentration of DMSO tunes the unfolding pathway by destabilizing the third minimum and stabilizing the second one, indicating the development of a solvent modified, less rugged pathway. The prime outcome of this work is the demonstration that mixed solvents can profoundly transform the nature of the energy landscape and induce unfolding via a modified route. A successful application of Kramer's rate equation correlating the free energy simulation results shows faster rate of unfolding with increasing DMSO concentration. This work perhaps presents the first systematic theoretical study of the effect of a chemical denaturant on the microscopic free energy surface and rates of unfolding of HP-36. (C) 2014 AIP Publishing LLC.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

Kinetic theory for sheared granular flows

Rapid granular flows are far-from-equilibrium-driven dissipative systems where the interaction between the particles dissipates energy, and so a continuous supply of energy is required to agitate the particles and facilitate the rearrangement required for the flow. This is in contrast to flows of molecular fluids, which are usually close to equilibrium, where the molecules are agitated by thermal fluctuations. Sheared granular flows form a class of flows where the energy required for agitating the particles in the flowing state is provided by the mean shear. These flows have been studied using the methods of kinetic theory of gases, where the particles are treated in a manner similar to molecules in a molecular gas, and the interactions between particles are treated as instantaneous energy-dissipating binary collisions. The validity of the assumptions underlying kinetic theory, and their applicability to the idealistic case of dilute sheared granular flows are first discussed. The successes and challenges for applying kinetic theory for realistic dense sheared granular flows are then summarised. (C) 2014 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

A micropolar peridynamic theory in linear elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. (C) 2015 Elsevier Ltd. All rights reserved.

Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

THEORY OF NEWFORMS OF HALF-INTEGRAL WEIGHT

We set up the theory of newforms of half-integral weight on Gamma(0)(8N) and Gamma(0)(16N), where N is odd and squarefree. Further, we extend the definition of the Kohnen plus space in general for trivial character and also study the theory of newforms in the plus spaces on Gamma(0)(8N), Gamma(0)(16N), where N is odd and squarefree. Finally, we show that the Atkin-Lehner W-operator W-4 acts as the identity operator on S-2k(new)(4N), where N is odd and squarefree. This proves that S-2k(-)(4) = S-2k(4).

Direct measurements of growing amorphous order and non-monotonic dynamic correlations in a colloidal glass-former

The transformation of flowing liquids into rigid glasses is thought to involve increasingly cooperative relaxation dynamics as the temperature approaches that of the glass transition. However, the precise nature of this motion is unclear, and a complete understanding of vitrification thus remains elusive. Of the numerous theoretical perspectives(1-4) devised to explain the process, random first-order theory (RFOT; refs 2,5) is a well-developed thermodynamic approach, which predicts a change in the shape of relaxing regions as the temperature is lowered. However, the existence of an underlying `ideal' glass transition predicted by RFOT remains debatable, largely because the key microscopic predictions concerning the growth of amorphous order and the nature of dynamic correlations lack experimental verification. Here, using holographic optical tweezers, we freeze a wall of particles in a two-dimensional colloidal glass-forming liquid and provide direct evidence for growing amorphous order in the form of a static point-to-set length. We uncover the non-monotonic dependence of dynamic correlations on area fraction and show that this non-monotonicity follows directly from the change in morphology and internal structure of cooperatively rearranging regions(6,7). Our findings support RFOT and thereby constitute a crucial step in distinguishing between competing theories of glass formation.

Improving the Rigor and Consistency of the Thermodynamic Theory for Clathrate Hydrates through Incorporation of Movement of Water Molecules of Hydrate Lattice

Current applications of statistical thermodynamic theories for clathrate hydrates do not incorporate the translational and rotational movement of water molecules of the hydrate lattice,in a rigorous manner. Previous studies have shown that the movement of water molecules has a significant effect on the properties of clathrate hydrates. In this Article, a method is presented to incorporate the effect of water movement with as much rigor as possible. This method is then used to calculate the Langmuir constant of the guest species in a clathrate hydrate. Unlike previous studies on modeling of clathrate hydrate thermodynamics, the method presented in this paper does not regress either the intermolecular potentials or the properties of the empty hydrate from clathrate phase equilibria data. Also the properties of empty hydrate used in the theory do not depend on the nature and composition of the guest molecules. The predicted phase equilibria from the resulting theory are shown to be highly accurate and thermodynamically consistent by comparing them with the phase equilibria computed directly from molecular simulations.

How should biologists engage with controversial mathematical theory?

Mathematics is beautiful and precise and often necessary to understand complex biological phenomena. And yet biologists cannot always hope to fully understand the mathematical foundations of the theory they are using or testing. How then should biologists behave when mathematicians themselves are in dispute? Using the on-going controversy over Hamilton's rule as an example, I argue that biologists should be free to treat mathematical theory with a healthy dose of agnosticism. In doing so biologists should equip themselves with a disclaimer that publicly admits that they cannot entirely attest to the veracity of the mathematics underlying the theory they are using or testing. The disclaimer will only help if it is accompanied by three responsibilities - stay bipartisan in a dispute among mathematicians, stay vigilant and help expose dissent among mathematicians, and make the biology larger than the mathematics. I must emphasize that my goal here is not to take sides in the on-going dispute over the mathematical validity of Hamilton's rule, indeed my goal is to argue that we should refrain from taking sides.

Conformal perturbation theory and higher spin entanglement entropy on the torus

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential mu, the deformation is related at high temperatures to a higher spin black hole in hs0] theory on AdS(3) spacetime. We calculate the order mu(2) corrections to the single interval Renyi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order mu(2) corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Renyi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Renyi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

Correlation Between Decay Rate and Amplitude of Solar Cycles as Revealed from Observations and Dynamo Theory

Using different proxies of solar activity, we have studied the following features of the solar cycle: i) The linear correlation between the amplitude of cycle and its decay rate, ii) the linear correlation between the amplitude of cycle and the decay rate of cycle , and iii) the anti-correlation between the amplitude of cycle and the period of cycle . Features ii) and iii) are very useful because they provide precursors for future cycles. We have reproduced these features using a flux-transport dynamo model with stochastic fluctuations in the Babcock-Leighton effect and in the meridional circulation. Only when we introduce fluctuations in meridional circulation, are we able to reproduce different observed features of the solar cycle. We discuss the possible reasons for these correlations.

Novel Biobjective Clustering (BiGC) Based on Cooperative Game Theory

We propose a new approach to clustering. Our idea is to map cluster formation to coalition formation in cooperative games, and to use the Shapley value of the patterns to identify clusters and cluster representatives. We show that the underlying game is convex and this leads to an efficient biobjective clustering algorithm that we call BiGC. The algorithm yields high-quality clustering with respect to average point-to-center distance (potential) as well as average intracluster point-to-point distance (scatter). We demonstrate the superiority of BiGC over state-of-the-art clustering algorithms (including the center based and the multiobjective techniques) through a detailed experimentation using standard cluster validity criteria on several benchmark data sets. We also show that BiGC satisfies key clustering properties such as order independence, scale invariance, and richness.