Search results for "canonical"
showing 10 items of 221 documents
Phase transitions in nonadditive hard disc systems: a Gibbs ensemble Monte Carlo Study
2007
we study the properties of a model fluid in two dimensions with Gibbs ensemble Monte Carlo (GEMC) techniques, in particular we analyze the entropy-driven phase separation in case of a nonadditive symmetric hard disc fluid. By a combination of GEMC with finite size scaling techniques we locate the critical line of nonadditivities as a function of the system density, which separates the mixing/demixing regions and compare with a simple analytical approximation.
Isotropic–isotropic phase separation in mixtures of rods and spheres: Some aspects of Monte Carlo simulation in the grand canonical ensemble
2008
Abstract In this article we consider mixtures of non-adsorbing polymers and rod-like colloids in the isotropic phase, which upon the addition of polymers show an effective attraction via depletion forces. Above a certain concentration, the depletant causes phase separation of the mixture. We performed Monte Carlo simulations to estimate the phase boundaries of isotropic–isotropic coexistence. To determine the phase boundaries we simulated in the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120 (2004) 10925]. The location of the critical point was estimated by a finite size scaling analysis. In order to equilibrate the system efficiently, we used a cluster move…
How Do Droplets Depend on the System Size? Droplet Condensation and Nucleation in Small Simulation Cells
2003
Using large scale grandcanonical Monte Carlo simulations in junction with a multicanonical reweighting scheme we investigate the liquid-vapor transition of a Lennard—Jones fluid. Particular attention is focused on the free energy of droplets and the transition between different system configurations as the system tunnels between the vapor and the liquid state as a function of system size. The results highlight the finite size dependence of droplet properties in the canonical ensemble and free energy barriers along the path from the vapor to the liquid in the grandcanonical ensemble.
How do droplets on a surface depend on the system size?
2002
Abstract We investigate the thermodynamics of inhomogeneous polymer melts in the framework of a coarse grained off-lattice model. Properties of the liquid–vapour interface and the packing of the melt in contact with an attractive wall are considered. We employ Monte Carlo simulations in the grand canonical ensemble to determine excess free energies, the wetting temperature and the pre-wetting line, as well as the pre-wetting critical point. Having determined the wetting properties and the phase diagram of the model polymer, we perform canonical Monte Carlo simulations of small droplets on a surface. This allows us to study the dependence of droplet size on the wetting properties. It is foun…
On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
2023
In this paper we investigate canonical extensions of conditional probabilities to Boolean algebras of conditionals. Before entering into the probabilistic setting, we first prove that the lattice order relation of every Boolean algebra of conditionals can be characterized in terms of the well-known order relation given by Goodman and Nguyen. Then, as an interesting methodological tool, we show that canonical extensions behave well with respect to conditional subalgebras. As a consequence, we prove that a canonical extension and its original conditional probability agree on basic conditionals. Moreover, we verify that the probability of conjunctions and disjunctions of conditionals in a rece…
Path integral quantization for massive vector bosons
2010
A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown that the self-consistency condition of this system with the second-class constraints in combination with the perturbative renormalizability leads to an SU(2) Yang-Mills theory with an additional mass term.
Sign and Rank Covariance Matrices: Statistical Properties and Application to Principal Components Analysis
2002
In this paper, the estimation of covariance matrices based on multivariate sign and rank vectors is discussed. Equivariance and robustness properties of the sign and rank covariance matrices are described. We show their use for the principal components analysis (PCA) problem. Limiting efficiencies of the estimation procedures for PCA are compared.
Tensor decomposition of EEG signals: A brief review
2015
Electroencephalography (EEG) is one fundamental tool for functional brain imaging. EEG signals tend to be represented by a vector or a matrix to facilitate data processing and analysis with generally understood methodologies like time-series analysis, spectral analysis and matrix decomposition. Indeed, EEG signals are often naturally born with more than two modes of time and space, and they can be denoted by a multi-way array called as tensor. This review summarizes the current progress of tensor decomposition of EEG signals with three aspects. The first is about the existing modes and tensors of EEG signals. Second, two fundamental tensor decomposition models, canonical polyadic decomposit…
Computing Sum of Products about the Mean with Pairwise Algorithms
1997
We discuss pairwise algorithms, a kind of computational algorithm which can be useful in dynamically updating statistics as new samples of data are collected. Since test data are usually collected through time as individual data sets, these algorithms would be profitably used in computer programs to treat this situation. Pair-wise algorithms are presented for calculating the sum of products of deviations about the mean for adding a sample of data (or removing one) to the whole data set.
Heisenberg Uncertainty Relation in Quantum Liouville Equation
2009
We consider the quantum Liouville equation and give a characterization of the solutions which satisfy the Heisenberg uncertainty relation. We analyze three cases. Initially we consider a particular solution of the quantum Liouville equation: the Wigner transformf(x,v,t) of a generic solutionψ(x;t) of the Schrödinger equation. We give a representation ofψ(x,t) by the Hermite functions. We show that the values of the variances ofxandvcalculated by using the Wigner functionf(x,v,t) coincide, respectively, with the variances of position operatorX^and conjugate momentum operatorP^obtained using the wave functionψ(x,t). Then we consider the Fourier transform of the density matrixρ(z,y,t) =ψ∗(z,t)…