Diffusion of small light particles in a solvent of large massive molecules

We study diffusion of small light particles in a solvent which consists of large heavy particles. The intermolecular interactions are chosen to approximately mimic a water-sucrose (or water-polysaccharide) mixture. Both computer simulation and mode coupling theoretical (MCT) calculations have been performed for a solvent-to-solute size ratio five and for a large variation of the mass ratio, keeping the mass of the solute fixed. Even in the limit of large mass ratio the solute motion is found to remain surprisingly coupled to the solvent dynamics. Interestingly, at intermediate values of the mass ratio, the self-intermediate scattering function of the solute, F_{s}(k,t) (where k is the wavenumber and t the time), develops a stretching at long time which could be fitted to a stretched exponential function with a k-dependent exponent, \beta. For very large mass ratio, we find the existence of two stretched exponentials separated by a power law type plateau. The analysis of the trajectory shows the coexistence of both hopping and continuous motions for both the solute and the solvent particles. It is found that for mass ratio five, the MCT calculations of the self-diffusion underestimates the simulated value by about 20 %, which appears to be reasonable because the conventional form of MCT does not include the hopping mode. However, for larger mass ratio, MCT appears to breakdown more severely. The breakdown of the MCT for large mass ratio can be connected to a similar breakdown near the glass transition.Comment: RevTex4, 9 pages, 10 figure

Galilean Conformal Algebras and AdS/CFT

Non-relativistic versions of the AdS/CFT conjecture have recently been investigated in some detail. These have primarily been in the context of the Schrodinger symmetry group. Here we initiate a study based on a {\it different} non-relativistic conformal symmetry: one obtained by a parametric contraction of the relativistic conformal group. The resulting Galilean conformal symmetry has the same number of generators as the relativistic symmetry group and thus is different from the Schrodinger group (which has fewer). One of the interesting features of the Galilean Conformal Algebra is that it admits an extension to an {\it infinite} dimensional symmetry algebra (which can potentially be dynamically realised). The latter contains a Virasoro-Kac-Moody subalgebra. We comment on realisations of this extended symmetry in a boundary field theory. We also propose a somewhat unusual geometric structure for the bulk gravity dual to any realisation of this symmetry. This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an $AdS_2$ comprising of the time and radial direction. The infinite dimensional Virasoro extension is identified with the asymptotic isometries of this $AdS_2$.Comment: v2: 26 pages, minor changes, references and comments added v3: a note and references adde

Pair dynamics in a glass-forming binary mixture: simulations and theory

We have carried out molecular dynamics simulations to understand the dynamics of a tagged pair of atoms in a strongly nonideal glass-forming binary Lennard-Jones mixture. Here atom B is smaller than atom A (σBB=0.88σAA , where σAA is the molecular diameter of the A particles) and the AB interaction is stronger than that given by Lorentz-Berthelot mixing rule (εAB = 1.5e AA , where εAA is the interaction energy strength between the A particles). The generalized time-dependent pair distribution function is calculated separately for the three pairs (AA, BB, and AB). The three pairs are found to behave differently. The relative diffusion constants are found to vary in the order DBBR>DABR>DAAR, with DBBR ∼ 2DAAR , showing the importance of the hopping process (B hops much more than A). We introduce a non-Gaussian parameter αP2(t)] to monitor the relative motion of a pair of atoms and evaluate it for all the three pairs with initial separations chosen to be at the first peak of the corresponding partial radial distribution functions. At intermediate times, significant deviation from the Gaussian behavior of the pair distribution functions is observed with different degrees for the three pairs. A simple mean-field MF model, proposed originally by Haan [Phys. Rev. A 20, 2516 (1979)] for one-component liquid, is applied to the case of a binary mixture and compared with the simulation results. While the MF model successfully describes the dynamics of the AA and AB pairs, the agreement for the BB pair is less satisfactory. This is attributed to the large scale anharmonic motions of the B particles in a weak effective potential. Dynamics of the next nearest neighbor pairs is also investigated

Heterogeneous relaxation in supercooled liquids: a density functional theory analysis

Recent time domain experiments which allow selective study of the relaxation of slower subpopulations among the distributions of local, inhomogeneous regions, have shown the existence of a length scale (~2-3 nm) beyond which the liquid behaves like a homogeneous liquid. Here we use the density functional theory to calculate the probability of creating a soft localized density fluctuation (density droplet). Theoretical calculation shows that the free energy penalty for creating a local inhomogeneity of small size is much less than that for a large size and that a dense supercooled system is unlikely to sustain inhomogeneity of a length, lf, which is larger than 5σ, where σ is the molecular diameter. We have calculated both the equilibrium and the nonequilibrium (subsequent to photobleaching) orientational correlation functions with the theoretically obtained inhomogeneous distributions. The nonequilibrium distribution relaxes at a slower rate. A simple two state exchange model has been used to mimic the relaxation of the slow regions to equilibrium; the model shows that the diffusional exchange cannot be the mechanism for the extremely slow relaxation process very near to the glass transition temperature. These results have been compared with recent experimental results

A short note on “Group theoretic approach to rationally extended shape invariant potentials” [Ann. Phys. 359 (2015) 46–54]

It is proved the equivalence of the compatibility condition of Ramos (2011, 2012) with a condition found in Yadav et al. (2015). The link of Shape Invariance with the existence of a Potential Algebra is reinforced for the rationally extended Shape Invariant potentials. Some examples on X1 and Xl Jacobi and Laguerre cases are given

GCA in 2d

We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2d. Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2d CFT, many of the tools for the analysis of the quantum mechanical GCA. These include the representation theory based on GCA primaries, Ward identities for their correlation functions and a nonrelativistic Kac table. In particular, the null vectors of the GCA lead to differential equations for the four point function. The solution to these equations in the simplest case is explicitly obtained and checked to be consistent with various requirements.Comment: 45 pages; v2: 47 pages. Restructured introduction, minor corrections, added references. Journal versio

TANGO: Performance and Fault Management in Cellular Networks through Cooperation between Devices and Edge Computing Nodes

Cellular networks have become an essential part of our lives. With increasing demands on its available bandwidth, we are seeing failures and performance degradations for data and voice traffic on the rise. In this paper, we propose the view that fog computing, integrated in the edge components of cellular networks, can partially alleviate this situation. In our vision, some data gathering and data analytics capability will be developed at the edge of the cellular network and client devices and the network using this edge capability will coordinate to reduce failures and performance degradations. We also envisage proactive management of disruptions including prediction of impending events of interest (such as, congestion or call drop) and deployment of appropriate mitigation actions. We show that a simple streaming media pre-caching service built using such device-fog cooperation significantly expands the number of streaming video users that can be supported in a nominal cellular network of today