Diffusion with random traps: Transient one-dimensional kinetics in a linear potential

The problem of one-dimensional diffusion with random traps is solved without and with a constant field of force. Using an eigenvalue expansion for long times and the method of images for short times we give an exact, straightforward solution for the time dependence of the mean survival probability and the mean probability density for returning to the origin. Using the backward equation approach, we determine the mean survival time and the mean residence time density at the origin. We comment on the relation between these solutions and those for one-dimensional diffusion with random reflectors.     

Effects of co-solutes on the hydrogen bonding structure and dynamics in aqueous N-methylacetamide solution: a molecular dynamics simulations study

The effects of trimethylamine-N-oxide (TMAO), urea and tetramethyl urea (TMU) on the hydrogen bonding structure and dynamics of aqueous solution of N-methylacetamide (NMA) are investigated by classical molecular dynamics simulations. The modification of the water's hydrogen bonding structure and interactions is calculated in presence of these co-solutes. It is observed that the number of four-hydrogen-bonded water molecules in the solution decreases significantly in the presence of TMAO rather than urea and TMU. The lifetime and structural relaxation time of water–water and NMA–water hydrogen bonds show a strong increase with the addition of TMAO and TMU in the solution, whereas the change is nominal in case of urea solution. It is also found that the translational and rotational dynamics of water and NMA slowdown with increasing the concentration of these osmolytes. The slower dynamics of water and NMA is more pronounced in case of TMAO and TMU solution, as these co-solutes strengthen the average hydrogen bond energies between water–water and NMA–water, whereas urea has a little effect on the hydrogen bonding structure and dynamics of aqueous NMA solution. The calculated self-diffusion coefficient values for water and these co-solutes are in similar pattern with experimental observations.     

The linearized Boltzmann equation: a concise and accurate solution of the temperature-jump problem

Polynomial expansion procedures, along with an analytical discrete-ordinates method, are used to solve the temperature-jump problem based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, the temperature and density perturbations and the temperature-jump coefficient are obtained (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented for general values of the accommodation coefficient to yield numerical results that can be considered a new standard of reference.     

Application of statistical mechanics to combinatorial optimization problems: The chromatic number problem andq-partitioning of a graph

Methods of statistical mechanics are applied to two important NP-complete combinatorial optimization problems. The first is the chromatic number problem, which seeks the minimal number of colors necessary to color a graph such that no two sites connected by an edge have the same color. The second is partitioning of a graph intoq equal subgraphs so as to minimize intersubgraph connections. Both models are mapped into a frustrated Potts model, which is related to theq- state Potts spin glass. For the first problem, we obtain very good agreement with numerical simulations and theoretical bounds using the annealed approximation. The quenched model is also discussed. For the second problem we obtain analytic and numerical results by evaluating the groundstate energy of theq=3 and 4 Potts spin glass using Parisi's replica symmetry breaking. We also perform some numerical simulations to test the theoretical result and obtain very good agreement.