Search results for "statistical mechanics"
showing 10 items of 706 documents
Ab initioquality neural-network potential for sodium
2010
An interatomic potential for high-pressure high-temperature (HPHT) crystalline and liquid phases of sodium is created using a neural-network (NN) representation of the ab initio potential energy surface. It is demonstrated that the NN potential provides an ab initio quality description of multiple properties of liquid sodium and bcc, fcc, cI16 crystal phases in the P-T region up to 120 GPa and 1200 K. The unique combination of computational efficiency of the NN potential and its ability to reproduce quantitatively experimental properties of sodium in the wide P-T range enables molecular dynamics simulations of physicochemical processes in HPHT sodium of unprecedented quality.
A tool for filtering information in complex systems
2005
We introduce a technique to filter out complex data-sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation based graphs giving filtered graphs which preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0) triangular loops and 4 element cliques are formed. The application of this filtering procedure to 100 stocks in the USA equity markets shows that such loops and cliqu…
Mean Escape Time in a System with Stochastic Volatility
2007
We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be considered as a generalization of the Heston model, where the geometric Brownian motion is replaced by a random walk in the presence of a cubic nonlinearity. We investigate the statistical properties of the escape time of the returns, from a given interval, as a function of the three parameters of the model. We find that the noise can have a stabilizing effect on the system, as long as the global noise is not too high with respect to the effective potential barr…
A Diffusive Strategic Dynamics for Social Systems
2010
We propose a model for the dynamics of a social system, which includes diffusive effects and a biased rule for spin-flips, reproducing the effect of strategic choices. This model is able to mimic some phenomena taking place during marketing or political campaigns. Using a cost function based on the Ising model defined on the typical quenched interaction environments for social systems (Erdos-Renyi graph, small-world and scale-free networks), we find, by numerical simulations, that a stable stationary state is reached, and we compare the final state to the one obtained with standard dynamics, by means of total magnetization and magnetic susceptibility. Our results show that the diffusive str…
The Boltzmann Probability as a Unifying Approach to Different Phenomena
2010
We discuss a pedagogical approach to the role of the Boltzmann probability in describing the temperature dependence of three simple experimental situations. The approach has been experimented in an introductory course on statistical mechanics for undergraduate engineering students at University of Palermo.
Problems of Clustering of Radiogalaxies
2012
We present the preliminary analysis of clustering of a sample of 1157 radio-identified galaxies from Machalski & Condon (1999). We found that for separations $2-15 h^{-1}$Mpc their redshift space autocorrelation function $\xi(s)$ can be approximated by the power law with the correlation length $\sim 3.75h^{-1}$Mpc and slope $\gamma \sim 1.8$. The correlation length for radiogalaxies is found to be lower and the slope steeper than the corresponding parameters of the control sample of optically observed galaxies. Analysis the projected correlation function $\Xi(r)$ displays possible differences in the clustering properties between active galactic nuclei (AGN) and starburst (SB) galaxies.
Excitation levels and magic numbers of small parahydrogen clusters (N⩽40)
2008
The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies the partition function has been obtained, thus allowing for an estimate of thermal e…
The relaxation dynamics of a viscous silica melt: II The intermediate scattering functions
2001
We use molecular dynamics computer simulations to study the relaxation dynamics of a viscous melt of silica. The coherent and incoherent intermediate scattering functions, F_d(q,t) and F_s(q,t), show a crossover from a nearly exponential decay at high temperatures to a two-step relaxation at low temperatures. Close to the critical temperature of mode-coupling theory (MCT) the correlators obey in the alpha-regime the time temperature superposition principle (TTSP) and show a weak stretching. We determine the wave-vector dependence of the stretching parameter and find that for F_d(q,t) it shows oscillations which are in phase with the static structure factor. The temperature dependence of the…
Evidence against a glass transition in the 10-state short range Potts glass
2002
We present the results of Monte Carlo simulations of two different 10-state Potts glasses with random nearest neighbor interactions on a simple cubic lattice. In the first model the interactions come from a \pm J distribution and in the second model from a Gaussian one, and in both cases the first two moments of the distribution are chosen to be equal to J_0=-1 and Delta J=1. At low temperatures the spin autocorrelation function for the \pm J model relaxes in several steps whereas the one for the Gaussian model shows only one. In both systems the relaxation time increases like an Arrhenius law. Unlike the infinite range model, there are only very weak finite size effects and there is no evi…
Critical Dynamics in a Binary Fluid: Simulations and Finite-Size Scaling
2006
We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories {\it provided} finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.