Perspectives for Monte Carlo simulations on the CNN Universal Machine

Possibilities for performing stochastic simulations on the analog and fully parallelized Cellular Neural Network Universal Machine (CNN-UM) are investigated. By using a chaotic cellular automaton perturbed with the natural noise of the CNN-UM chip, a realistic binary random number generator is built. As a specific example for Monte Carlo type simulations, we use this random number generator and a CNN template to study the classical site-percolation problem on the ACE16K chip. The study reveals that the analog and parallel architecture of the CNN-UM is very appropriate for stochastic simulations on lattice models. The natural trend for increasing the number of cells and local memories on the CNN-UM chip will definitely favor in the near future the CNN-UM architecture for such problems.Comment: 14 pages, 6 figure

Evidences of a consolute critical point in the Phase Separation regime of La(5/8-y)Pr(y)Ca(3/8)MnO(3) (y = 0.4) single crystals

We report on DC and pulsed electric field sensitivity of the resistance of mixed valent Mn oxide based La(5/8-y)Pr(y)Ca(3/8)MnO(3) (y = 0.4) single crystals as a function of temperature. The low temperature regime of the resistivity is highly current and voltage dependent. An irreversible transition from high (HR) to a low resistivity (LR) is obtained upon the increase of the electric field up to a temperature dependent critical value (V_c). The current-voltage characteristics in the LR regime as well as the lack of a variation in the magnetization response when V_c is reached indicate the formation of a non-single connected filamentary conducting path. The temperature dependence of V_c indicates the existence of a consolute point where the conducting and insulating phases produce a critical behavior as a consequence of their separation.Comment: 5 pages, 6 figures, corresponding author: C. Acha ([email protected]

Numerical Study of Natural Convection in Square Tilted Solar Cavity Considering Extended Domain

This work presents a numerical investigation on heat transfer and fluid-dynamic aspects for a solar open cavities in an extended fluid flow domain. The vertical wall inside the open cavities facing the aperture is assumed to be isothermal while the other walls are kept insulated. Heat transfer steady laminar natural convection is studied by solving the non-dimensional governing equations of mass, momentum and energy in the framework of a finite volume method. The analysis are carried out under Rayleigh number range of 9.41×105 to 3.76×106, inclination 0° to 90° and opening ratio 0.25, 0.5 and 1. The model results for avaergar Nusselt number evaluation was in good agreement with other published work for similar configuration. The results show that convective average Nusselt number decreases by 93% when the inclination angle increased from 0° to 90° due to the trapped vortices that limit the airflow throughout the cavity. The air flowing through the cavit is maximum when the the inclination angle is zero even at higher values of Raylight number. Results show also that decreasing the opening ratio from 1 to 0.25 leads to a drop in heat loss by 22.79%. A simple correlation has been developed for calculating the the average Nusselt number as a function of Rayleigh number, opening ratio and inclination angle

Stochastic Light-Cone CTMRG: a new DMRG approach to stochastic models

We develop a new variant of the recently introduced stochastic transfer-matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG (CTMRG), adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process, are studied and compared to exact data and Monte-Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10^5 shows a considerable improvement to the old stochastic TMRG algorithm.Comment: 15 pages, uses IOP styl

Directed Percolation with a Wall or Edge

We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface critical phenomena and field theory. The results of previous numerical work for a wall can thus be interpreted in terms of surface exponents satisfying scaling relations generalising those for ordinary directed percolation. New exponents for edge directed percolation are also introduced. They are calculated in mean-field theory and measured numerically in 2+1 dimensions.Comment: 14 pages, submitted to J. Phys.

Rooted Spiral Trees on Hyper-cubical lattices

We study rooted spiral trees in 2,3 and 4 dimensions on a hyper cubical lattice using exact enumeration and Monte-Carlo techniques. On the square lattice, we also obtain exact lower bound of 1.93565 on the growth constant $\lambda$. Series expansions give $\theta=-1.3667\pm 0.001$ and $\nu = 1.3148\pm0.001$ on a square lattice. With Monte-Carlo simulations we get the estimates as $\theta=-1.364\pm0.01$, and $\nu = 1.312\pm0.01$. These results are numerical evidence against earlier proposed dimensional reduction by four in this problem. In dimensions higher than two, the spiral constraint can be implemented in two ways. In either case, our series expansion results do not support the proposed dimensional reduction.Comment: replaced with published versio

Muon Spin Relaxation and Susceptibility Studies of Pure and Doped Spin 1/2 Kagom\'{e}-like system (Cux_xZn1−x_{1-x})3_{3}V2_{2}O7_7(OH)2_{2} 2H2_2O

Muon spin relaxation ($\mu$SR) and magnetic susceptibility measurements have been performed on the pure and diluted spin 1/2 kagom\'{e} system (Cu$_x$Zn$_{1-x}$)$_{3}$V$_{2}$O$_7$(OH)$_{2}$ 2H$_2$O. In the pure $x=1$ system we found a slowing down of Cu spin fluctuations with decreasing temperature towards $T \sim 1$ K, followed by slow and nearly temperature-independent spin fluctuations persisting down to $T$ = 50 mK, indicative of quantum fluctuations. No indication of static spin freezing was detected in either of the pure ($x$=1.0) or diluted samples. The observed magnitude of fluctuating fields indicates that the slow spin fluctuations represent an intrinsic property of kagom\'e network rather than impurity spins.Comment: 4 pges, 4 color figures, Phys. Rev. Lett. in pres

Sliding blocks with random friction and absorbing random walks

With the purpose of explaining recent experimental findings, we study the distribution $A(\lambda)$ of distances $\lambda$ traversed by a block that slides on an inclined plane and stops due to friction. A simple model in which the friction coefficient $\mu$ is a random function of position is considered. The problem of finding $A(\lambda)$ is equivalent to a First-Passage-Time problem for a one-dimensional random walk with nonzero drift, whose exact solution is well-known. From the exact solution of this problem we conclude that: a) for inclination angles $\theta$ less than \theta_c=\tan(\av{\mu}) the average traversed distance \av{\lambda} is finite, and diverges when $\theta \to \theta_c^{-}$ as \av{\lambda} \sim (\theta_c-\theta)^{-1}; b) at the critical angle a power-law distribution of slidings is obtained: $A(\lambda) \sim \lambda^{-3/2}$. Our analytical results are confirmed by numerical simulation, and are in partial agreement with the reported experimental results. We discuss the possible reasons for the remaining discrepancies.Comment: 8 pages, 8 figures, submitted to Phys. Rev.

Variational approach to the scaling function of the 2D Ising model in a magnetic field

The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the remarkable field theory results obtained by Fonseca and Zamolodchikov, as well as with many previously known exact and numerical results for the 2D Ising model. This includes excellent agreement with analytic results for the magnetic susceptibility obtained by Orrick, Nickel, Guttmann and Perk. In general the high precision of the numerical results underlines the potential and full power of the variational corner transfer matrix approach.Comment: 12 pages, 1 figure, 4 tables, v2: minor corrections, references adde

Non-equilibrium Phase Transitions with Long-Range Interactions

This review article gives an overview of recent progress in the field of non-equilibrium phase transitions into absorbing states with long-range interactions. It focuses on two possible types of long-range interactions. The first one is to replace nearest-neighbor couplings by unrestricted Levy flights with a power-law distribution P(r) ~ r^(-d-sigma) controlled by an exponent sigma. Similarly, the temporal evolution can be modified by introducing waiting times Dt between subsequent moves which are distributed algebraically as P(Dt)~ (Dt)^(-1-kappa). It turns out that such systems with Levy-distributed long-range interactions still exhibit a continuous phase transition with critical exponents varying continuously with sigma and/or kappa in certain ranges of the parameter space. In a field-theoretical framework such algebraically distributed long-range interactions can be accounted for by replacing the differential operators nabla^2 and d/dt with fractional derivatives nabla^sigma and (d/dt)^kappa. As another possibility, one may introduce algebraically decaying long-range interactions which cannot exceed the actual distance to the nearest particle. Such interactions are motivated by studies of non-equilibrium growth processes and may be interpreted as Levy flights cut off at the actual distance to the nearest particle. In the continuum limit such truncated Levy flights can be described to leading order by terms involving fractional powers of the density field while the differential operators remain short-ranged.Comment: LaTeX, 39 pages, 13 figures, minor revision