Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSimulation of a directed random-walk model: the effect of pseudo-random-number correlations
130
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in several types of pseudo-random-number sequences. This model provides qualitative understanding of the bias mechanism in a class of cluster Monte Carlo algorithms.
rate research
Read More
By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean number $leftlanglemathcal{N}_mathrm{tot}rightrangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension $d=1+1$, grows exponentially $leftlanglemathcal{N}_mathrm{tot}rightranglesimexp{(r,L)}$ with its length $L$. The growth rate $r$ is found to be directly related to the generalised Lyapunov exponent (GLE) which is a moment-generating function characterising the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schrodinger operator of the 1D Anderson localization problem. For strong confinement, the rate $r$ is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate $r$ is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape topology trivialization phenomenon, we obtain an upper bound for the depinning threshold $f_c$, in the presence of an applied force, for elastic lines and $d$-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.
We investigate the critical properties of the Ising model in two dimensions on {it directed} small-world lattice with quenched connectivity disorder. The disordered system is simulated by applying the Monte Carlo update heat bath algorithm. We calculate the critical temperature, as well as the critical exponents $gamma/ u$, $beta/ u$, and $1/ u$ for several values of the rewiring probability $p$. We find that this disorder system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The Ising model on {it directed} small-world lattices presents in fact a second-order phase transition with new critical exponents which do not dependent of $p$, but are identical to the exponents of the Ising model and the spin-1 Blume-Capel model on {it directed} small-world network.
We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of As takes precedence over that of Bs. The model was originally proposed and analyzed in Maragakis et al., Phys. Rev. E 77, 020103 (2008); here we provide additional results. We solve analytically the diffusion coefficients of the two species in lattices for a number of protocols. In networks, we find that the probability of a B particle to be free decreases exponentially with the node degree. In scale-free networks, this leads to localization of the Bs at the hubs and arrest of their motion. To remedy this, we investigate several strategies to avoid trapping of the Bs: moving an A instead of the hindered B; allowing a trapped B to hop with a small probability; biased walk towards non-hub nodes; and limiting the capacity of nodes. We obtain analytic results for lattices and networks, and discuss the advantages and shortcomings of the possible strategies.
Ising Monte Carlo simulations of the random-field Ising system Fe(0.80)Zn(0.20)F2 are presented for H=10T. The specific heat critical behavior is consistent with alpha approximately 0 and the staggered magnetization with beta approximately 0.25 +- 0.03.
The motion of an artificial micro-scale swimmer that uses a chemical reaction catalyzed on its own surface to achieve autonomous propulsion is fully characterized experimentally. It is shown that at short times, it has a substantial component of directed motion, with a velocity that depends on the concentration of fuel molecules. At longer times, the motion reverts to a random walk with a substantially enhanced diffusion coefficient. Our results suggest strategies for designing artificial chemotactic systems.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
