Condensed Matter Theory

Abstract:

The effect of solvent quality on the effective pair potentials of the interacting linear polymers of a solution was investigated. The inversion of c.m. pair distribution function, by using the hypernetted chain closure method, was employed for the derivation of effective pair potentials. The pair potential was found to be strongly dependent on the polymer concentration and temperature.

Abstract:

In this paper, we consider a narrowband point-to-point communication system with nT transmitters and nR receivers. We assume the receiver has perfect knowledge of the channel, while the transmitter has no channel knowledge. We consider the case where the receiving antenna array has uncorrelated elements, while the elements of the transmitting array are arbitrarily correlated. Focusing on the case where nT = 2, we derive simple analytic expressions for the ergodic average and the cumulative distribution function of the mutual information for arbitrary input (transmission) signal covariance. We then determine the ergodic and outage capacities and the associated optimal input signal covariances. We thus show how a transmitter with covariance knowledge should correlate its transmissions to maximize throughput. These results allow us to derive an exact condition (both necessary and sufficient) that determines when beamforming is optimal for systems with arbitrary number of transmitters and receivers.

Abstract:

Solutions of interacting linear polymers are mapped onto a system of "soft" spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only the center of mass (c.m.) of the polymer coils. The effective pair potentials are derived by inverting the c.m. pair distribution function, generated in Monte Carlo simulations, using the hypernetted chain closure. The method, previously devised for the self-avoiding walk model of polymers in good solvent, is extended to the case of polymers in solvents of variable quality by adding a finite nearest-neighbor monomer-monomer attraction to the previous model and varying the temperature. The resulting effective pair potential is found to depend strongly on temperature and polymer concentration. At low concentration the effective interaction becomes increasingly attractive as the temperature decreases, eventually violating thermodynamic stability criteria. However, as polymer concentration is increased at fixed temperature, the effective interaction reverts to mostly repulsive behavior. These issues help to illustrate some fundamental difficulties encountered when coarse-graining complex systems via effective pair potentials.

Abstract:

The slow dynamics of granular flow is studied as an extension of static granular problems, which, as a consequence of shaking or related regimes, can be studied by the methods of statistical mechanics. For packed (i.e. 'jammed'), hard and rough objects, kinetic energy is a minor and ignorable quantity, as is strain. Hence, in the static case, the stress equations need supplementing by 'missing equations' depending solely on configurations. These are in the literature; this paper extends the equilibrium studies to slow dynamics, claiming that the strain rate (which is a consequence of flow, not of elastic strain) takes the place of stress, and as before, the analogue of Stokes's equation has to be supplemented by new 'missing equations' which are derived and which depend only on configurations.