Enhanced diffusion by reciprocal swimming

Purcell's scallop theorem states that swimmers deforming their shapes in a time-reversible manner ("reciprocal" motion) cannot swim. Using numerical simulations and theoretical calculations we show here that in a fluctuating environment, reciprocal swimmers undergo, on time scales larger than that of their rotational diffusion, diffusive dynamics with enhanced diffusivities, possibly by orders of magnitude, above normal translational diffusion. Reciprocal actuation does therefore lead to a significant advantage over non-motile behavior for small organisms such as marine bacteria

Are Simple Real Pole Solutions Physical?

We consider exact solutions generated by the inverse scattering technique, also known as the soliton transformation. In particular, we study the class of simple real pole solutions. For quite some time, those solutions have been considered interesting as models of cosmological shock waves. A coordinate singularity on the wave fronts was removed by a transformation which induces a null fluid with negative energy density on the wave front. This null fluid is usually seen as another coordinate artifact, since there seems to be a general belief that that this kind of solution can be seen as the real pole limit of the smooth solution generated with a pair of complex conjugate poles in the transformation. We perform this limit explicitly, and find that the belief is unfounded: two coalescing complex conjugate poles cannot yield a solution with one real pole. Instead, the two complex conjugate poles go to a different limit, what we call a ``pole on a pole''. The limiting procedure is not unique; it is sensitive to how quickly some parameters approach zero. We also show that there exists no improved coordinate transformation which would remove the negative energy density. We conclude that negative energy is an intrinsic part of this class of solutions.Comment: 13 pages, 3 figure

Levy Flights in Inhomogeneous Media

We investigate the impact of external periodic potentials on superdiffusive random walks known as Levy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Levy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Levy index $\mu$. Our analysis is based on a novel generalization of the Fokker-Planck equation suitable for systems in thermal equilibrium. Thus, the results presented are applicable to the large class of situations in which superdiffusion is caused by topological complexity, such as diffusion on folded polymers and scale-free networks.Comment: 4 pages, 4 figure

Multicanonical Recursions

The problem of calculating multicanonical parameters recursively is discussed. I describe in detail a computational implementation which has worked reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded Z-compressed .tar file created by uufiles), figure file corrected

Testing Error Correcting Codes by Multicanonical Sampling of Rare Events

The idea of rare event sampling is applied to the estimation of the performance of error-correcting codes. The essence of the idea is importance sampling of the pattern of noises in the channel by Multicanonical Monte Carlo, which enables efficient estimation of tails of the distribution of bit error rate. The idea is successfully tested with a convolutional code

Shaking a Box of Sand

We present a simple model of a vibrated box of sand, and discuss its dynamics in terms of two parameters reflecting static and dynamic disorder respectively. The fluidised, intermediate and frozen (`glassy') dynamical regimes are extensively probed by analysing the response of the packing fraction to steady, as well as cyclic, shaking, and indicators of the onset of a `glass transition' are analysed. In the `glassy' regime, our model is exactly solvable, and allows for the qualitative description of ageing phenomena in terms of two characteristic lengths; predictions are also made about the influence of grain shape anisotropy on ageing behaviour.Comment: Revised version. To appear in Europhysics Letter

Our Administrative System of Criminal Justice

To commemorate our founding in 1914, the Board of Editors has selected six influential pieces published by the Law Review over the past 100 years and will republish one piece in each issue. The fourth piece selected by the Board is Our Administrative System of Criminal Justice, an article written by Gerard E. Lynch that is among the most cited works in the Law Review’s history. This article illustrates how the practice of plea bargaining blurs the boundaries between adversarial and inquisitorial criminal justice systems. Judge Lynch now sits on the Second Circuit having eventually succeeded the late Judge Joseph M. McLaughlin, who also is honored in the pages of this book for the permanent mark he left on Fordham Law School and the Law Review. We think it is fitting that the Law Review feature two of the many contributions that judges of the Second Circuit have made to legal education and scholarship in this issue

Evidence for the double degeneracy of the ground-state in the 3D ±J\pm J spin glass

A bivariate version of the multicanonical Monte Carlo method and its application to the simulation of the three-dimensional $\pm J$ Ising spin glass are described. We found the autocorrelation time associated with this particular multicanonical method was approximately proportional to the system volume, which is a great improvement over previous methods applied to spin-glass simulations. The principal advantage of this version of the multicanonical method, however, was its ability to access information predictive of low-temperature behavior. At low temperatures we found results on the three-dimensional $\pm J$ Ising spin glass consistent with a double degeneracy of the ground-state: the order-parameter distribution function $P(q)$ converged to two delta-function peaks and the Binder parameter approached unity as the system size was increased. With the same density of states used to compute these properties at low temperature, we found their behavior changing as the temperature is increased towards the spin glass transition temperature. Just below this temperature, the behavior is consistent with the standard mean-field picture that has an infinitely degenerate ground state. Using the concept of zero-energy droplets, we also discuss the structure of the ground-state degeneracy. The size distribution of the zero-energy droplets was found to produce the two delta-function peaks of $P(q)$.Comment: 33 pages with 31 eps figures include

On the Tail of the Overlap Probability Distribution in the Sherrington--Kirkpatrick Model

We investigate the large deviation behavior of the overlap probability density in the Sherrington--Kirkpatrick model from several analytical perspectives. First we analyze the spin glass phase using the coupled replica scheme. Here generically $\frac1N \log P_N(q)$ $\approx$ $- {\cal A}$ $((|q|-q_{EA})^3$, and we compute the first correction to the expansion of \A in powers of $T_c-T$. We study also the $q=1$ case, where $P(q)$ is know exactly. Finally we study the paramagnetic phase, where exact results valid for all $q$'s are obtained. The overall agreement between the various points of view is very satisfactory. Data from large scale numerical simulations show that the predicted behavior can be detected already on moderate lattice sizes.Comment: 18 pages including ps figure