Transport of Single Molecules Along the Periodic Parallel Lattices with Coupling

General discrete one-dimensional stochastic models to describe the transport of single molecules along coupled parallel lattices with period $N$ are developed. Theoretical analysis that allows to calculate explicitly the steady-state dynamic properties of single molecules, such as mean velocity $V$ and dispersion $D$, is presented for N=1 and N=2 models. For the systems with $N>2$ exact analytic expressions for the large-time dynamic properties are obtained in the limit of strong coupling between the lattices that leads to dynamic equilibrium between two parallel kinetic pathways.Comment: Submitted to J. Chem. Phy

Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model

The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly different low-temperature behavior. The structure of the spin-glass overlap distribution for the Edwards-Anderson model suggests that its low-temperature phase has only a single pair of pure states.Comment: 4 pages, 6 figures, 2 table

Reply to "Comment on Evidence for the droplet picture of spin glasses"

Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation (MKA), Marinari et al. study in their comment on our paper the link overlap between two replicas of a three-dimensional Ising spin glass in the presence of a coupling between the replicas. They claim that the results of the MCS indicate replica symmetry breaking (RSB), while those of the MKA are trivial, and that moderate size lattices display the true low temperature behavior. Here we show that these claims are incorrect, and that the results of MCS and MKA both can be explained within the droplet picture.Comment: 1 page, 1 figur

Velocity Distribution of Topological Defects in Phase-Ordering Systems

The distribution of interface (domain-wall) velocities ${\bf v}$ in a phase-ordering system is considered. Heuristic scaling arguments based on the disappearance of small domains lead to a power-law tail, $P_v(v) \sim v^{-p}$ for large v, in the distribution of $v \equiv |{\bf v}|$. The exponent p is given by $p = 2+d/(z-1)$, where d is the space dimension and 1/z is the growth exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to conserved case (model B). The nonconserved result is exemplified by an approximate calculation of the full distribution using a gaussian closure scheme. The heuristic arguments are readily generalized to systems described by a vector order parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear in Physical Review E (May 1, 1997

Spin-resolved electron-impact ionization of lithium

Electron-impact ionization of lithium is studied using the convergent close-coupling (CCC) method at 25.4 and 54.4 eV. Particular attention is paid to the spin-dependence of the ionization cross sections. Convergence is found to be more rapid for the spin asymmetries, which are in good agreement with experiment, than for the underlying cross sections. Comparison with the recent measured and DS3C-calculated data of Streun et al (1999) is most intriguing. Excellent agreement is found with the measured and calculated spin asymmetries, yet the discrepancy between the CCC and DS3C cross sections is very large

Non-equilibrium Phase-Ordering with a Global Conservation Law

In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising model leads to an asymptotic length-scale $L \sim (\rho t)^{1/2} \sim t^{1/3}$ at $T=0$ because the kinetic coefficient is renormalized by the broken-bond density, $\rho \sim L^{-1}$. For $T>0$, activated kinetics recovers the standard asymptotic growth-law, $L \sim t^{1/2}$. However, at all temperatures, infinite-range energy-transport is allowed by the spin-exchange dynamics. A better implementation of global conservation, the microcanonical Creutz algorithm, is well behaved and exhibits the standard non-conserved growth law, $L \sim t^{1/2}$, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st

Critical properties of the unconventional spin-Peierls system TiOBr

We have performed detailed x-ray scattering measurements on single crystals of the spin-Peierls compound TiOBr in order to study the critical properties of the transition between the incommensurate spin-Peierls state and the paramagnetic state at Tc2 ~ 48 K. We have determined a value of the critical exponent beta which is consistent with the conventional 3D universality classes, in contrast with earlier results reported for TiOBr and TiOCl. Using a simple power law fit function we demonstrate that the asymptotic critical regime in TiOBr is quite narrow, and obtain a value of beta_{asy} = 0.32 +/- 0.03 in the asymptotic limit. A power law fit function which includes the first order correction-to-scaling confluent singularity term can be used to account for data outside the asymptotic regime, yielding a more robust value of beta_{avg} = 0.39 +/- 0.05. We observe no evidence of commensurate fluctuations above Tc1 in TiOBr, unlike its isostructural sister compound TiOCl. In addition, we find that the incommensurate structure between Tc1 and Tc2 is shifted in Q-space relative to the commensurate structure below Tc1.Comment: 12 pages, 8 figures. Submitted to Physical Review

No many-scallop theorem: Collective locomotion of reciprocal swimmers

To achieve propulsion at low Reynolds number, a swimmer must deform in a way that is not invariant under time-reversal symmetry; this result is known as the scallop theorem. We show here that there is no many-scallop theorem. We demonstrate that two active particles undergoing reciprocal deformations can swim collectively; moreover, polar particles also experience effective long-range interactions. These results are derived for a minimal dimers model, and generalized to more complex geometries on the basis of symmetry and scaling arguments. We explain how such cooperative locomotion can be realized experimentally by shaking a collection of soft particles with a homogeneous external field

Real space analysis of inherent structures

We study a generalization of the one-dimensional disordered Potts model, which exhibits glassy properties at low temperature. The real space properties of inherent structures visited dynamically are analyzed through a decomposition into domains over which the energy is minimized. The size of these domains is distributed exponentially, defining a characteristic length scale which grows in equilibrium when lowering temperature, as well as in the aging regime at a given temperature. In the low temperature limit, this length can be interpreted as the distance between `excited' domains within the inherent structures.Comment: 7 pages, 8 figures, final versio

Phase Ordering Kinetics with External Fields and Biased Initial Conditions

The late-time phase-ordering kinetics of the O(n) model for a non-conserved order parameter are considered for the case where the O(n) symmetry is broken by the initial conditions or by an external field. An approximate theoretical approach, based on a `gaussian closure' scheme, is developed, and results are obtained for the time-dependence of the mean order parameter, the pair correlation function, the autocorrelation function, and the density of topological defects [e.g. domain walls ($n=1$), or vortices ($n=2$)]. The results are in qualitative agreement with experiments on nematic films and related numerical simulations on the two-dimensional XY model with biased initial conditions.Comment: 35 pages, latex, no figure