Evolution in range expansions with competition at rough boundaries.

When a biological population expands into new territory, genetic drift develops an enormous influence on evolution at the propagating front. In such range expansion processes, fluctuations in allele frequencies occur through stochastic spatial wandering of both genetic lineages and the boundaries between genetically segregated sectors. Laboratory experiments on microbial range expansions have shown that this stochastic wandering, transverse to the front, is superdiffusive due to the front's growing roughness, implying much faster loss of genetic diversity than predicted by simple flat front diffusive models. We study the evolutionary consequences of this superdiffusive wandering using two complementary numerical models of range expansions: the stepping stone model, and a new interpretation of the model of directed paths in random media, in the context of a roughening population front. Through these approaches we compute statistics for the times since common ancestry for pairs of individuals with a given spatial separation at the front, and we explore how environmental heterogeneities can locally suppress these superdiffusive fluctuations

Spontaneous emission by rotating objects: A scattering approach

We study the quantum electrodynamics (QED) vacuum in the presence of a body rotating along its axis of symmetry and show that the object spontaneously emits energy if it is lossy. The radiated power is expressed as a general trace formula solely in terms of the scattering matrix, making an explicit connection to the conjecture of Zel'dovich [JETP Lett. 14, 180 (1971)] on rotating objects. We further show that a rotating body drags along nearby objects while making them spin parallel to its own rotation axis

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

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

Thermodynamic Fingerprints of Disorder in Flux Line Lattices and other Glassy Mesoscopic Systems

We examine probability distributions for thermodynamic quantities in finite-sized random systems close to criticality. Guided by available exact results, a general ansatz is proposed for replicated free energies, which leads to scaling forms for cumulants of various macroscopic observables. For the specific example of a planar flux line lattice in a two dimensional superconducting film near H_c1, we provide detailed results for the statistics of the magnetic flux density, susceptibility, heat capacity, and their cross-correlations.Comment: 4 page

Free Energy Self-Averaging in Protein-Sized Random Heteropolymers

Current theories of heteropolymers are inherently macrpscopic, but are applied to folding proteins which are only mesoscopic. In these theories, one computes the averaged free energy over sequences, always assuming that it is self-averaging -- a property well-established only if a system with quenched disorder is macroscopic. By enumerating the states and energies of compact 18, 27, and 36mers on a simplified lattice model with an ensemble of random sequences, we test the validity of the self-averaging approximation. We find that fluctuations in the free energy between sequences are weak, and that self-averaging is a valid approximation at the length scale of real proteins. These results validate certain sequence design methods which can exponentially speed up computational design and greatly simplify experimental realizations.Comment: 4 pages, 3 figure

Modified critical correlations close to modulated and rough surfaces

Correlation functions are sensitive to the presence of a boundary. Surface modulations give rise to modified near surface correlations, which can be measured by scattering probes. To determine these correlations, we develop a perturbative calculation in deformations in height from a flat surface. The results, combined with a renormalization group around four dimensions, are also used to predict critical behavior near a self-affinely rough surface. We find that a large enough roughness exponent can modify surface critical behavior.Comment: 4 pages, 1 figure. Revised version as published in Phys. Rev. Lett. 86, 4596 (2001

Anomalous Dynamics of Forced Translocation

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N^2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (sub-diffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N^2 and N^{1+\nu}, respectively, where \nu is the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N=512).Comment: 13 pages, RevTeX4, 16 eps 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