Collapse of Randomly Linked Polymers

We consider polymers in which M randomly selected pairs of monomers are restricted to be in contact. Analytical arguments and numerical simulations show that an ideal (Gaussian) chain of N monomers remains expanded as long as M<<N. This result is inconsistent with results obtained from free energy considerations by Brygelson and Thirumalai (PRL76, 542 (1996)).Comment: 1 page, 1 postscript figure, LaTe

Energy Barriers to Motion of Flux Lines in Random Media

We propose algorithms for determining both lower and upper bounds for the energy barriers encountered by a flux line in moving through a two-dimensional random potential. Analytical arguments, supported by numerical simulations, suggest that these bounds scale with the length $t$ of the line as $t^{1/3}$ and $t^{1/3}\sqrt{\ln t}$, respectively. This provides the first confirmation of the hypothesis that barriers have the same scaling as the fluctuation in the free energy. \pacs{PACS numbers: 74.60.Ge, 05.70.Ln, 05.40.+j}Comment: 4 pages Revtex, 2 figures, to appear in PRL 75, 1170 (1995

Phase ordering and roughening on growing films

We study the interplay between surface roughening and phase separation during the growth of binary films. Already in 1+1 dimension, we find a variety of different scaling behaviors depending on how the two phenomena are coupled. In the most interesting case, related to the advection of a passive scalar in a velocity field, nontrivial scaling exponents are obtained in simulations.Comment: 4 pages latex, 6 figure

Dynamics of An Underdamped Josephson Junction Ladder

We show analytically that the dynamical equations for an underdamped ladder of coupled small Josephson junctions can be approximately reduced to the discrete sine-Gordon equation. As numerical confirmation, we solve the coupled Josephson equations for such a ladder in a magnetic field. We obtain discrete-sine-Gordon-like IV characteristics, including a flux flow and a ``whirling'' regime at low and high currents, and voltage steps which represent a lock-in between the vortex motion and linear ``phasons'', and which are quantitatively predicted by a simple formula. At sufficiently high anisotropy, the fluxons on the steps propagate ballistically.Comment: 11pages, latex, no figure

Melting of Flux Lines in an Alternating Parallel Current

We use a Langevin equation to examine the dynamics and fluctuations of a flux line (FL) in the presence of an {\it alternating longitudinal current} $J_{\parallel}(\omega)$. The magnus and dissipative forces are equated to those resulting from line tension, confinement in a harmonic cage by neighboring FLs, parallel current, and noise. The resulting mean-square FL fluctuations are calculated {\it exactly}, and a Lindemann criterion is then used to obtain a nonequilibrium `phase diagram' as a function of the magnitude and frequency of $J_{\parallel}(\omega)$. For zero frequency, the melting temperature of the mixed phase (a lattice, or the putative "Bose" or "Bragg Glass") vanishes at a limiting current. However, for any finite frequency, there is a non-zero melting temperature.Comment: 5 pages, 1 figur

A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schroedinger operators on a tubular network built over the graph. If such a manifold has a boundary, Neumann conditions are imposed at it. The procedure involves a local change of graph topology in the vicinity of the vertex; the approximation scheme constructed on the graph is subsequently `lifted' to the manifold. For the corresponding operator a norm-resolvent convergence is proved, with the natural identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added, to appear in CM

Trace formulae for non-equilibrium Casimir interactions, heat radiation and heat transfer for arbitrary objects

We present a detailed derivation of heat radiation, heat transfer and (Casimir) interactions for N arbitrary objects in the framework of fluctuational electrodynamics in thermal non-equilibrium. The results can be expressed as basis-independent trace formulae in terms of the scattering operators of the individual objects. We prove that heat radiation of a single object is positive, and that heat transfer (for two arbitrary passive objects) is from the hotter to a colder body. The heat transferred is also symmetric, exactly reversed if the two temperatures are exchanged. Introducing partial wave-expansions, we transform the results for radiation, transfer and forces into traces of matrices that can be evaluated in any basis, analogous to the equilibrium Casimir force. The method is illustrated by (re)deriving the heat radiation of a plate, a sphere and a cylinder. We analyze the radiation of a sphere for different materials, emphasizing that a simplification often employed for metallic nano-spheres is typically invalid. We derive asymptotic formulae for heat transfer and non-equilibrium interactions for the cases of a sphere in front a plate and for two spheres, extending previous results. As an example, we show that a hot nano-sphere can levitate above a plate with the repulsive non-equilibrium force overcoming gravity -- an effect that is not due to radiation pressure.Comment: 29 pages, 6 figures (v2: Sentence added in Sec. 1

Casimir forces between cylinders at different temperatures

We study Casimir interactions between cylinders in thermal non-equilibrium, where the objects as well as the environment are held at different temperatures. We provide the general formula for the force, in a one reflection approximation, for cylinders of arbitrary radii and optical properties. As is the case for equilibrium, we find that the force for optically diluted cylinders can be obtained by appropriate summation of the corresponding result for spheres. We find that the non-equilibrium forces are generally larger than their equilibrium counterpart at separations greater than the thermal wavelength. They may also exhibit oscillations as function of separation, leading to stable points of zero net force. These effects are particularly pronounced for thin conducting cylinders (e.g. 40nm diameter nano-wires of tungsten) due to their large emissivity.Comment: 10 pages, 5 figure

Anomalous Dynamics of Translocation

We study the dynamics of the passage of a polymer through a membrane pore (translocation), focusing on the scaling properties with the number of monomers $N$. The natural coordinate for translocation is the number of monomers on one side of the hole at a given time. Commonly used models which assume Brownian dynamics for this variable predict a mean (unforced) passage time $\tau$ that scales as $N^2$, even in the presence of an entropic barrier. However, the time it takes for a free polymer to diffuse a distance of the order of its radius by Rouse dynamics scales with an exponent larger than 2, and this should provide a lower bound to the translocation time. To resolve this discrepancy, we perform numerical simulations with Rouse dynamics for both phantom (in space dimensions $d=1$ and 2), and self-avoiding (in $d=2$) chains. The results indicate that for large $N$, translocation times scale in the same manner as diffusion times, but with a larger prefactor that depends on the size of the hole. Such scaling implies anomalous dynamics for the translocation process. In particular, the fluctuations in the monomer number at the hole are predicted to be non-diffusive at short times, while the average pulling velocity of the polymer in the presence of a chemical potential difference is predicted to depend on $N$.Comment: 9 pages, 9 figures. Submitted to Physical Review

Defects in nematic membranes can buckle into pseudospheres

A nematic membrane is a sheet with embedded orientational order, which can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor contractions from differential geometry, we elucidate the elastic terms allowed by symmetry, and indicate differences from hexatic membranes. We find that topological defects in the orientation field can cause the membrane to buckle over a size set by the competition between surface tension and in-plane elasticity. In the absence of bending rigidity the resulting shape is universal, known as a parabolic pseudosphere or a revolved tractrix. Bending costs oppose such buckling and modify the shape in a predictable manner. In particular, the anisotropic rigidities of nematic membranes lead to different shapes for aster and vortex defects, in principle enabling measurement of couplings specific to nematic membranes.Comment: 9 pages, 3 figure