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Register a new userCrossover from reptation to Rouse dynamics in a one-dimensional model
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A simple one-dimensional model is constructed for polymer motion. It exhibits the crossover from reptation to Rouse dynamics through gradually allowing hernia creation and annihilation. The model is treated by the density matrix technique which permits an accurate finite-size-scaling analysis of the behavior of long polymers.
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The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the renewal time and the diffusion coefficient are calculated as a function of the strength of the barrier crossings. A strong crossover influence of the barrier crossings is found and it is analyzed in terms of effective exponents for a given chain length. The crossover scaling functions and the crossover scaling exponents are calculated.
The competition between reptation and Rouse Dynamics is incorporated in the Rubinstein-Duke model for polymer motion by extending it with sideways motions, which cross barriers and create or annihilate hernias. Using the Density-Matrix Renormalization-Group Method as solver of the Master Equation, the renewal time and the diffusion coefficient are calculated as function of the length of the chain and the strength of the sideways motion. These new types of moves have a strong and delicate influence on the asymptotic behavior of long polymers. The effects are analyzed as function of the chain length in terms of effective exponents and crossover scaling functions.
We discuss the exact solution for the properties of the recently introduced ``necklace model for reptation. The solution gives the drift velocity, diffusion constant and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
A gas composed of a large number of atoms evolving according to Newtonian dynamics is often described by continuum hydrodynamics. Proving this rigorously is an outstanding open problem, and precise numerical demonstrations of the equivalence of the hydrodynamic and microscopic descriptions are rare. We test this equivalence in the context of the evolution of a blast wave, a problem that is expected to be at the limit where hydrodynamics could work. We study a one-dimensional gas at rest with instantaneous localized release of energy for which the hydrodynamic Euler equations admit a self-similar scaling solution. Our microscopic model consists of hard point particles with alternating masses, which is a nonintegrable system with strong mixing dynamics. Our extensive microscopic simulations find a remarkable agreement with Euler hydrodynamics, with deviations in a small core region that are understood as arising due to heat conduction.
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer chain subject to steady driving. We compute the effective dynamics for one of the many monomers by integrating out the rest of the chain. The result is a generalized Langevin dynamics for which we give the memory and noise kernels and the effective force, and we discuss the inherited nonequilibrium aspects.
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