Search results for "Random walk"
showing 10 items of 132 documents
Many-body quantum dynamics by adiabatic path-integral molecular dynamics: Disordered Frenkel Kontorova models
2005
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent ), there is one regime in which the chain is pinned (large masses of chain particles) and one in which it is unpinned (small ). If the embedding potential can be classified as a random walk on large length scales ( ), then the chain is always pinned irrespective of the value of . For , two phonon-like branches appear in the spectra.
Multibondic cluster algorithm for Monte Carlo simulations of first-order phase transitions.
1995
Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for $q$-state Potts models a combination of cluster updates with reweighting of the bond configurations in the Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests for the two-dimensional models with $q=7, 10$ and $20$ show that the autocorrelation times of this algorithm grow with the system size $V$ as $\tau \propto V^\alpha$, where the exponent takes the optimal random walk value of $\alpha \approx 1$.
Quantum Search with Multiple Walk Steps per Oracle Query
2015
We identify a key difference between quantum search by discrete- and continuous-time quantum walks: a discrete-time walk typically performs one walk step per oracle query, whereas a continuous-time walk can effectively perform multiple walk steps per query while only counting query time. As a result, we show that continuous-time quantum walks can outperform their discrete-time counterparts, even though both achieve quadratic speedups over their corresponding classical random walks. To provide greater equity, we allow the discrete-time quantum walk to also take multiple walk steps per oracle query while only counting queries. Then it matches the continuous-time algorithm's runtime, but such …
Random walks with short memory in a disordered environment
1991
Etude du modele du saut en arriere pour le cas d'un reseau desordonne. Le modele du saut en arriere est un modele de la marche aleatoire de proches voisins correlee dans lequel le marcheur possede une probabilite de transition differente pour les sauts vers le site qu'il a visite anterieurement, par rapport aux sauts vers tous les autres sites proches voisins. La formulation standard de ce modele doit etre modifiee si le desordre est introduit au niveau de l'equation directrice habituelle. On discute des difficultes rencontrees avec la formulation standard. L'equation maitresse du premier ordre pour le modele du saut en arriere desordonne est etablie, et a partir d'elle, on derive une equat…
Diffusion of magnetotactic bacterium in rotating magnetic field
2011
Swimming trajectory of a magnetotactic bacterium in a rotating magnetic field is a circle. Random reversals of the direction of the bacterium motion induces a random walk of the curvature center of the trajectory. In assumption of the distribution of the switching events according to the Poisson process the diffusion coefficient is calculated in dependence on the frequency of the rotating field and the characteristic time between the switching events. It is confirmed by the numerical simulation of the random walk of the bacterium in the rotating magnetic field.
Geometry and time scale of the rotational dynamics in supercooled toluene
1998
Multidimensional deuteron NMR provides powerful tools for studying molecular reorientation in supercooled liquids. We present results on selectively deuterated toluene-${d}_{5},$ which may be one of the molecularly most simple van der Waals glass formers. From two-time correlation functions the time scale of reorientation was obtained slightly above the calorimetric glass transition temperature. The applied stimulated echo method provides a geometry parameter that, in analogy to $q$-dependent scattering experiments, allows one to investigate the geometry of the elementary rotational process. Continuous time random walk computer simulations were used for the interpretation of the data. It is…
Fractal dimension of superfluid turbulence : A random-walk toy model
2021
This paper deals with the fractal dimension of a superfluid vortex tangle. It extends a previous model [J. Phys. A: Math. Theor. {\bf 43}, 205501 (2010)] (which was proposed for very low temperature), and it proposes an alternative random walk toy model, which is valid also for finite temperature. This random walk model combines a recent Nemirovskii's proposal, and a simple modelization of a self-similar structure of vortex loops (mimicking the geometry of the loops of several sizes which compose the tangle). The fractal dimension of the vortex tangle is then related to the exponents describing how the vortex energy per unit length changes with the length scales, for which we take recent pr…
A Monte Carlo Study of Knots in Long Double-Stranded DNA Chains.
2016
We determine knotting probabilities and typical sizes of knots in double-stranded DNA for chains of up to half a million base pairs with computer simulations of a coarse-grained bead-stick model: Single trefoil knots and composite knots which include at least one trefoil as a prime factor are shown to be common in DNA chains exceeding 250,000 base pairs, assuming physiologically relevant salt conditions. The analysis is motivated by the emergence of DNA nanopore sequencing technology, as knots are a potential cause of erroneous nucleotide reads in nanopore sequencing devices and may severely limit read lengths in the foreseeable future. Even though our coarse-grained model is only based on …
Distributed learning automata-based scheme for classification using novel pursuit scheme
2020
Learning Automata (LA) is a popular decision making mechanism to “determine the optimal action out of a set of allowable actions” (Agache and Oommen, IEEE Trans Syst Man Cybern-Part B Cybern 2002(6): 738–749, 2002). The distinguishing characteristic of automata-based learning is that the search for the optimising parameter vector is conducted in the space of probability distributions defined over the parameter space, rather than in the parameter space itself (Thathachar and Sastry, IEEE Trans Syst Man Cybern-Part B Cybern 32(6): 711–722, 2002). Recently, Goodwin and Yazidi pioneered the use of Ant Colony Optimisation (ACO) for solving classification problems (Goodwin and Yazidi 2016). In th…
Coalescing directed random walks on the backbone of a 1 +1-dimensional oriented percolation cluster converge to the Brownian web
2018
We consider the backbone of the infinite cluster generated by supercritical oriented site percolation in dimension 1 +1. A directed random walk on this backbone can be seen as an "ancestral line" of an individual sampled in the stationary discrete-time contact process. Such ancestral lineages were investigated in [BCDG13] where a central limit theorem for a single walker was proved. Here, we consider infinitely many coalescing walkers on the same backbone starting at each space-time point. We show that, after diffusive rescaling, the collection of paths converges in distribution to the Brownian web. Hence, we prove convergence to the Brownian web for a particular system of coalescing random…