Anomalous diffusion in correlated continuous time random walks

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement ~t^{2/3}. Long-ranged correlations of the waiting times with power-law exponent alpha (0<alpha<=2) give rise to subdiffusion of the form ~t^{alpha/(1+alpha)}. In contrast correlations in the jump lengths are shown to produce superdiffusion. We show that in both cases weak ergodicity breaking occurs. Our results are in excellent agreement with simulations.Comment: 6 pages, 6 figures. Slightly revised version, accepted to J Phys A as a Fast Track Communicatio

Harmonic operation of a free-electron laser

Harmonic operation of a free-electron-laser amplifier is studied. The key issue investigated here is suppression of the fundamental. For a tapered amplifier with the right choice of parameters, it is found that the presence of the harmonic mode greatly reduces the growth rate of the fundamental. A limit on the reflection coefficient of the fundamental mode that will ensure stable operation is derived. The relative merits of tripling the frequency by operating at the third harmonic versus decreasing the wiggler period by a factor of 3 are discussed

Graph-Embedding Empowered Entity Retrieval

In this research, we improve upon the current state of the art in entity retrieval by re-ranking the result list using graph embeddings. The paper shows that graph embeddings are useful for entity-oriented search tasks. We demonstrate empirically that encoding information from the knowledge graph into (graph) embeddings contributes to a higher increase in effectiveness of entity retrieval results than using plain word embeddings. We analyze the impact of the accuracy of the entity linker on the overall retrieval effectiveness. Our analysis further deploys the cluster hypothesis to explain the observed advantages of graph embeddings over the more widely used word embeddings, for user tasks involving ranking entities

Paradoxical diffusion: Discriminating between normal and anomalous random walks

Commonly, normal diffusive behavior is characterized by a linear dependence of the second central moment on time, $\propto t$, while anomalous behavior is expected to show a different time dependence, $\propto t^{\delta}$ with $\delta 1$ for superdiffusive motions. Here we demonstrate that this kind of qualification, if applied straightforwardly, may be misleading: There are anomalous transport motions revealing perfectly "normal" diffusive character ($\propto t$), yet being non-Markov and non-Gaussian in nature. We use recently developed framework \cite[Phys. Rev. E \textbf{75}, 056702 (2007)]{magdziarz2007b} of Monte Carlo simulations which incorporates anomalous diffusion statistics in time and space and creates trajectories of such an extended random walk. For special choice of stability indices describing statistics of waiting times and jump lengths, the ensemble analysis of paradoxical diffusion is shown to hide temporal memory effects which can be properly detected only by examination of formal criteria of Markovianity (fulfillment of the Chapman-Kolmogorov equation).Comment: 8 pages, 7 figure

Topologically Driven Swelling of a Polymer Loop

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius are generated for loops of up to N=3000 segments. Gyration radii of trivially knotted loops are found to follow a power law similar to that of self avoiding walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200

Comparison of pure and combined search strategies for single and multiple targets

We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with L\'evy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a L\'evy searcher.Comment: 16 pages, 12 figure

DNA bubble dynamics as a quantum Coulomb problem

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We demonstrate that the associated Fokker-Planck equation is equivalent to a Coulomb problem. Below the melting temperature the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential, at the melting temperature the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail, above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.Comment: 4 pages, 3 figures, revte

Bubble coalescence in breathing DNA: Two vicious walkers in opposite potentials

We investigate the coalescence of two DNA-bubbles initially located at weak segments and separated by a more stable barrier region in a designed construct of double-stranded DNA. The characteristic time for bubble coalescence and the corresponding distribution are derived, as well as the distribution of coalescence positions along the barrier. Below the melting temperature, we find a Kramers-type barrier crossing behaviour, while at high temperatures, the bubble corners perform drift-diffusion towards coalescence. The results are obtained by mapping the bubble dynamics on the problem of two vicious walkers in opposite potentials.Comment: 7 pages, 4 figure

Anomalous diffusion and generalized Sparre-Andersen scaling

We are discussing long-time, scaling limit for the anomalous diffusion composed of the subordinated L\'evy-Wiener process. The limiting anomalous diffusion is in general non-Markov, even in the regime, where ensemble averages of a mean-square displacement or quantiles representing the group spread of the distribution follow the scaling characteristic for an ordinary stochastic diffusion. To discriminate between truly memory-less process and the non-Markov one, we are analyzing deviation of the survival probability from the (standard) Sparre-Andersen scaling.Comment: 5 pages, 3 figure