Extending the Broad Histogram Method for Continuous Systems

We propose a way of extending the Broad Histogram Monte Carlo method (BHMC) to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model. Our method gives results in excellent agreement with Metropolis and Histogram Monte Carlo simulations and calculates for the whole temperature range 1.2<T<4.7 using only 2 times more computer effort than the Histogram method for the range 2.1<T<2.2. Our way of treatment is general, it can also be applied to other systems with continuous degrees of freedom.Comment: LaTex, 5 pages, 2 eps figure

Broad Histogram Method for Continuous Systems: the XY-Model

We propose a way of implementing the Broad Histogram Monte Carlo method to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model with periodic boundary conditions. We have found an excellent agreement between our method and traditional Metropolis results for the energy, the magnetization, the specific heat and the magnetic susceptibility on a very large temperature range. For the calculation of these quantities in the temperature range 0.7<T<4.7 our method took less CPU time than the Metropolis simulations for 16 temperature points in that temperature range. Furthermore, it calculates the whole temperature range 1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte Carlo method for the range 2.1<T<2.2. Our way of treatment is general, it can also be applied to other systems with continuous degrees of freedom.Comment: 23 pages, 10 Postscript figures, to be published in Int. J. Mod. Phys.

Flux surface shaping effects on tokamak edge turbulence and flows

Shaping of magnetic flux surfaces is found to have a strong impact on turbulence and transport in tokamak edge plasmas. A series of axisymmetric equilibria with varying elongation and triangularity, and a divertor configuration are implemented into a computational gyrofluid turbulence model. The mechanisms of shaping effects on turbulence and flows are identified. Transport is mainly reduced by local magnetic shearing and an enhancement of zonal shear flows induced by elongation and X-point shaping.Comment: 10 pages, 11 figures. Submitted to Physics of Plasma

Diffusion and spectral dimension on Eden tree

We calculate the eigenspectrum of random walks on the Eden tree in two and three dimensions. From this, we calculate the spectral dimension $d_s$ and the walk dimension $d_w$ and test the scaling relation $d_s = 2d_f/d_w$ ($=2d/d_w$ for an Eden tree). Finite-size induced crossovers are observed, whereby the system crosses over from a short-time regime where this relation is violated (particularly in two dimensions) to a long-time regime where the behavior appears to be complicated and dependent on dimension even qualitatively.Comment: 11 pages, Plain TeX with J-Phys.sty style, HLRZ 93/9

Neural network modeling of memory deterioration in Alzheimer's disease

The clinical course of Alzheimer's disease (AD) is generally characterized by progressive gradual deterioration, although large clinical variability exists. Motivated by the recent quantitative reports of synaptic changes in AD, we use a neural network model to investigate how the interplay between synaptic deletion and compensation determines the pattern of memory deterioration, a clinical hallmark of AD. Within the model we show that the deterioration of memory retrieval due to synaptic deletion can be much delayed by multiplying all the remaining synaptic weights by a common factor, which keeps the average input to each neuron at the same level. This parallels the experimental observation that the total synaptic area per unit volume (TSA) is initially preserved when synaptic deletion occurs. By using different dependencies of the compensatory factor on the amount of synaptic deletion one can define various compensation strategies, which can account for the observed variation in the severity and progression rate of AD

Measurement of Indeterminacy in Packings of Perfectly Rigid Disks

Static packings of perfectly rigid particles are investigated theoretically and numerically. The problem of finding the contact forces in such packings is formulated mathematically. Letting the values of the contact forces define a vector in a high-dimensional space enable us to show that the set of all possible contact forces is convex, facilitating its numerical exploration. It is also found that the boundary of the set is connected with the presence of sliding contacts, suggesting that a stable packing should not have more than 2M-3N sliding contacts in two dimensions, where M is the number of contacts and N is the number of particles. These results were used to analyze packings generated in different ways by either molecular dynamics or contact dynamics simulations. The dimension of the set of possible forces and the number of sliding contacts agrees with the theoretical expectations. The indeterminacy of each component of the contact forces are found, as well as the an estimate for the diameter of the set of possible contact forces. We also show that contacts with high indeterminacy are located on force chains. The question of whether the simulation methods can represent a packing's memory of its formation is addressed.Comment: 12 pages, 13 figures, submitted to Phys Rev

Riemann solvers and undercompressive shocks of convex FPU chains

We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space-time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax-shocks are replaced by so called dispersive shocks. For convex-concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave-convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions