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

Orientational relaxation in a dispersive dynamic medium : Generalization of the Kubo-Ivanov-Anderson jump diffusion model to include fractional environmental dynamics

Ivanov-Anderson (IA) model (and an earlier treatment by Kubo) envisages a decay of the orientational correlation by random but large amplitude molecular jumps, as opposed to infinitesimal small jumps assumed in Brownian diffusion. Recent computer simulation studies on water and supercooled liquids have shown that large amplitude motions may indeed be more of a rule than exception. Existing theoretical studies on jump diffusion mostly assume an exponential (Poissonian) waiting time distribution for jumps, thereby again leading to an exponential decay. Here we extend the existing formalism of Ivanov and Anderson to include an algebraic waiting time distribution between two jumps. As a result, the first and second rank orientational time correlation functions show the same long time power law, but their short time decay behavior is quite different. The predicted Cole-Cole plot of dielectric relaxation reproduces various features of non-Debye behaviour observed experimentally. We also developed a theory where both unrestricted small jumps and large angular jumps coexist simultaneously. The small jumps are shown to have a large effect on the long time decay, particularly in mitigating the effects of algebraic waiting time distribution, and in giving rise to an exponential-like decay, with a time constant, surprisingly, less than the time constant that arises from small amplitude decay alone.Comment: 14 figure

Tracking down localized modes in PT-symmetric Hamiltonians under the influence of a competing nonlinearity

The relevance of parity and time reversal (PT)-symmetric structures in optical systems is known for sometime with the correspondence existing between the Schrodinger equation and the paraxial equation of diffraction where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrodinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation charaterized by the parameter of perturbative growth rate passing through zero where a transition to imaginary eigenvalues occurs.Comment: 10pages, To be published in Acta Polytechnic

Orientational relaxation in a discotic liquid crystal

We investigate orientational relaxation of a model discotic liquid crystal, consists of disc-like molecules, by molecular dynamics simulations along two isobars starting from the high temperature isotropic phase. The two isobars have been so chosen that (A) the phase sequence isotropic (I)-nematic (N)-columnar (C) appears upon cooling along one of them and (B) the sequence isotropic (I)-columnar (C) along the other. While the orientational relaxation in the isotropic phase near the I-N phase transition in system (A) shows a power law decay at short to intermediate times, such power law relaxation is not observed in the isotropic phase near the I-C phase boundary in system (B). In order to understand this difference (the existence or the absence of the power law decay), we calculated the the growth of the orientational pair distribution functions (OPDF) near the I-N phase boundary and also near the I-C phase boundary. We find that OPDF shows a marked growth in long range correlation as the I-N phase boundary is approached in the I-N-C system (A), but such a growth is absent in the I-C system, which appears to be consistent with the result that I-N phase transition in the former is weakly first order while the the I-C phase transition in the later is not weak. As the system settles into the nematic phase, the decay of the single-particle second-rank orientational OTCF follows a pattern that is similar to what is observed with calamitic liquid crystals and supercooled molecular liquids.Comment: 16 pages and 4 figure

Truncated Harmonic Osillator and Parasupersymmetric Quantum Mechanics

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary order p can also be rewritten in terms of p supercharges (i.e. all of which obey $Q_i^{2} = 0$). However, the Hamiltonian cannot be expressed in a simple form in terms of the p supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, the p supercharges, the p conformal supercharges along with Hamiltonian H, conformal generator K and dilatation generator D form a closed algebra.Comment: 9 page

The Adaptation and Variability of Response of the Human Brain

Electrical potentials have been recorded from the brain of five normal human subjects by means of needle electrodes inserted about half a centimeter through the scalp, one near the external occipital protuberance and another about three inches forward and an inch to the side from the median line. The high time-constant of the amplifier, which was about a second, made it possible to obtain an almost distortionless recording of the low frequency waves. The amplifier was connected to the oscillograph element. The oscillation of the light beam projected from the element was photographed on sensitized paper

Providing Information Feedback to Bidders in Online Multi-unit Combinatorial Auctions

Bidders in online multi-unit combinatorial auctions face the acute problem of estimating the valuations of an immense number of packages. Can the seller guide the bidders to avoid placing bids that are too high or too low? In the single unit case, fast methods are now available for incrementally computing, for each package at each time instant, the recommended lower bound (Deadness Level) and upper bound (Winning Level) on the next bid. But when there are multiple units of items, it becomes difficult to compute the Deadness Level of a package accurately. An upper bound on this quantity can be derived however, and a bid that stays within this bound and the Winning Level is “safe”, in the sense that it is not wasted and has the potential to become a winning bid. What is now needed is an incremental procedure for speeding up the computation of this bound