Simulation of a Single Polymer Chain in Solution by Combining Lattice Boltzmann and Molecular Dynamics

In this paper we establish a new efficient method for simulating polymer-solvent systems which combines a lattice Boltzmann approach for the fluid with a continuum molecular dynamics (MD) model for the polymer chain. The two parts are coupled by a simple dissipative force while the system is driven by stochastic forces added to both the fluid and the polymer. Extensive tests of the new method for the case of a single polymer chain in a solvent are performed. The dynamic and static scaling properties predicted by analytical theory are validated. In this context, the influence of the finite size of the simulation box is discussed. While usually the finite size corrections scale as L^{-1} (L denoting the linear dimension of the box), the decay rate of the Rouse modes is only subject to an L^{-3} finite size effect. Furthermore, the mapping to an existing MD simulation of the same system is done so that all physical input values for the new method can be derived from pure MD simulation. Both methods can thus be compared quantitatively, showing that the new method allows for much larger time steps. Comparison of the results for both methods indicates systematic deviations due to non-perfect match of the static chain conformations.Comment: 17 pages, 12 figures, submitted to J. Chem. Phy

Markov Chain Modeling of Polymer Translocation Through Pores

We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition probabilities which satisfy a specific balance constraint provide a refinement of the Chuang-Kantor-Kardar relaxation picture of translocation, allowing us to investigate finite size effects in the evaluation of dynamical scaling exponents. We find that (i) previous Langevin simulation results can be recovered only if corrections to the polymer mobility exponent are taken into account and that (ii) the dynamical scaling exponents have a slow approach to their predicted asymptotic values as the polymer's length increases. We also address, along with strong support from additional numerical simulations, a critical discussion which points in a clear way the viability of the Markov chain approach put forward in this work.Comment: 17 pages, 5 figure

Universal low-temperature tricritical point in metallic ferromagnets and ferrimagnets

An earlier theory of the quantum phase transition in metallic ferromagnets is revisited and generalized in three ways. It is shown that the mechanism that leads to a fluctuation-induced first-order transition in metallic ferromagnets with a low Curie temperature is valid, (1) irrespective of whether the magnetic moments are supplied by the conduction electrons or by electrons in another band, (2) for ferromagnets in the XY and Ising universality classes as well as for Heisenberg ferromagnets, and (3) for ferrimagnets as well as for ferromagnets. This vastly expands the class of materials for which a first-order transition at low temperatures is expected, and it explains why strongly anisotropic ferromagnets, such as UGe2, display a first-order transition as well as Heisenberg magnets.Comment: 11pp, 2 fig

Metastable tight knots in a worm-like polymer

Based on an estimate of the knot entropy of a worm-like chain we predict that the interplay of bending energy and confinement entropy will result in a compact metastable configuration of the knot that will diffuse, without spreading, along the contour of the semi-flexible polymer until it reaches one of the chain ends. Our estimate of the size of the knot as a function of its topological invariant (ideal aspect ratio) agrees with recent experimental results of knotted dsDNA. Further experimental tests of our ideas are proposed.Comment: 4 pages, 3 figure

Non-ideal behavior of intramolecular structure factor of dilute polymers in a theta solvent

We study the configurational properties of single polymers in a theta solvent by Monte Carlo simulation of the bond fluctuation model. The intramolecular structure factor at the theta point is found to be distinctively different from that of the ideal chain. The structure factor shows a hump around $q\sim 5/R_g$ and a dip around $q\sim 10/R_g$ in the Kratky plot with $R_g$ being the radius of gyration. This feature is apparently similar to that in a melt. The theoretical expression by the simple perturbation expansion to the first order in terms of the Mayer function can be fitted to the obtained structure factor quite well, but the second virial coefficient cannot be set to zero.Comment: 8 pages, 7figure

Pair Connectedness and Shortest Path Scaling in Critical Percolation

We present high statistics data on the distribution of shortest path lengths between two near-by points on the same cluster at the percolation threshold. Our data are based on a new and very efficient algorithm. For $d=2$ they clearly disprove a recent conjecture by M. Porto et al., Phys. Rev. {\bf E 58}, R5205 (1998). Our data also provide upper bounds on the probability that two near-by points are on different infinite clusters.Comment: 7 pages, including 4 postscript figure

Suppression of Spontaneous Supercurrents in a Chiral p-Wave Superconductor

The superconducting state of SRO is widely believed to have chiral p-wave order that breaks time reversal symmetry. Such a state is expected to have a spontaneous magnetization, both at sample edges and at domain walls between regions of different chirality. Indeed, muon spin resonance experiments are interpreted as evidence of spontaneous magnetization due to domain walls or defects in the bulk. However, recent magnetic microscopy experiments place upper limits on the magentic fields at the sample edge and surface which are as much as two orders of magnitude smaller than the fields predicted theoretically for a somewhat idealized chiral p-wave superconductor. We investigate the effects on the spontaneous supercurrents and magnetization of rough and pair breaking surfaces for a range of parameters within a Ginzburg-Landau formalism. The effects of competing orders nucleated at the surface are also considered. We find the conditions under which the edge currents are significantly reduced while leaving the bulk domain wall currents intact, are quite limited. The implications for interpreting the existing body of experimental results on superconducting SRO within a chiral p-wave model are discussed.Comment: Changes to section 3, typos remove

Nematic cells with defect-patterned alignment layers

Using Monte Carlo simulations of the Lebwohl--Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of $\pm 1$ point topological defects of lattice spacing $a$. We find that the nematic order depends crucially on the ratio of the height of the cell $H$ to $a$. When $H/a \gtrsim 0.9$ the system is very well--ordered and the frustration induced by the lattice of defects is relieved by a network of half--integer defect lines which emerge from the point defects and hug the top and bottom surfaces of the cell. When $H/a \lesssim 0.9$ the system is disordered and the half--integer defect lines thread through the cell joining point defects on the top and bottom surfaces. We present a simple physical argument in terms of the length of the defect lines to explain these results. To facilitate eventual comparison with experimental systems we also simulate optical textures and study the switching behavior in the presence of an electric field

Columnar Fluctuations as a Source of Non-Fermi-Liquid Behavior in Weak Metallic Magnets

It is shown that columnar fluctuations, in conjunction with weak quenched disorder, lead to a T^{3/2} temperature dependence of the electrical resistivity. This is proposed as an explanation of the observed non-Fermi-liquid behavior in the helimagnet MnSi, with one possible realization of the columnar fluctuations provided by skyrmion lines that have independently been proposed to be present in this material.Comment: 4pp, 4 figure

Ginzburg-Landau Vortex Lattice in Superconductor Films of Finite Thickness

The Ginzburg-Landau equations are solved for ideally periodic vortex lattices in superconducting films of arbitrary thickness in a perpendicular magnetic field. The order parameter, current density, magnetic moment, and the 3-dimensional magnetic field inside and outside the film are obtained in the entire ranges of the applied magnetic field, Ginzburg Landau parameter kappa, and film thickness. The superconducting order parameter varies very little near the surface (by about 0.01) and the energy of the film surface is small. The shear modulus c66 of the triangular vortex lattice in thin films coincides with the bulk c66 taken at large kappa. In thin type-I superconductor films with kappa < 0.707, c66 can be positive at low fields and negative at high fields.Comment: 12 pages including 14 Figures, corrected, Fig.14 added, appears in Phys. Rev. B 71, issue 1 (2005