Radu Paul Mondescu

Probability Tree Algorithm for General Diffusion Processes

Motivated by path-integral numerical solutions of diffusion processes, PATHINT, we present a new tree algorithm, PATHTREE, which permits extremely fast accurate computation of probability distributions of a large class of general nonlinear diffusion processes.

Statistics of an ideal polymer in a multistable potential: Exact solutions and instanton approximation

We have considered the stationary state of a one-dimensional Gaussian polymer chain of length Nl (N is number of segments, l is the Kuhn length) subjected to a one-parameter class of exactly solvable, symmetric, repulsive potentials with multiple (two or three) minima. We have calculated analytically and numerically the exact Green’s function G(R|R′;L) and the mean-square end-to-end distance 〈(R−R′)2〉, respectively, of the polymer chain. The instanton approximation is translated in polymer physics language and used to analyze the conformation of the polymer chain in its ground state, by evaluating the average number of folds that connect the potential minima. All quantities are functions of the barrier height and of the separation between wells. Our results show that for a given length N, the polymer expands with increasing barrier width until a maximum value of 〈(R−R′)2〉 is reached. Afterwards, the polymer apparently collapses in one of the wells. This behavior defines a critical length N* and may offer ...

Effective elastic moduli of a composite containing rigid spheres at nondilute concentrations: A multiple scattering approach

Based on the multiple scattering technique [K. F. Freed and M. Muthukumar, J. Chem. Phys. 69, 2657 (1978); 68, 2088 (1978); M. Muthukumar and K. H. Freed, J. Chem. Phys. 70, 5875 (1979)] previously applied to the study of suspensions of spheres and polymers, we propose an approach to the computation of the effective elastic properties of a composite material containing rigid, mono-sized, randomly dispersed, spherical particles. Our method incorporates the many-body, long-range elastic interactions among inclusions. The effective medium equations are constructed and numerically solved self-consistently. We have calculated the effective shear μ′ and Young E′ moduli, as well as the effective Poisson ratio σ′, as functions of the particle volume fraction Φ and of the Poisson ratio σ of the continuous phase. Comparisons with two sets of experimental data—glass beads in a polymer matrix and tungsten carbide particles in a cobalt matrix (Wc/Co)—and to a previous theoretical solution, are also presented. Our mode...

Dynamics of a suspension of spheres and rigid polymers: Effect of geometrical mismatch

An effective medium approach together with a multiple scattering formalism is considered to study the steady‐state dynamics of suspensions of spheres and polymer chains without excluded volume interactions. The polymer chains are assumed to obey rigid‐body dynamics (without rotation) and are taken to be so long that Gaussian statistics is applicable. We have considered the dynamics of probe objects (either a sphere or a polymer) in a solution containing spheres and polymers. The significance of the dimensionless variables appearing when solving the effective medium equations and, in particular, the role of the geometrical parameter t=Rg/a (a is the radius of any sphere and Rg the radius of gyration of a polymer chain) are discussed. The translational diffusion coefficients of the moving probe sphere DS and of the center‐of‐mass of the probe polymer chain DP, and the shear viscosity of the suspensions have been derived. Both the friction coefficient of the probe sphere or that of the probe polymer chain an...