Search results for "statistical [methods]"
showing 10 items of 1664 documents
Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity.
2016
We discuss Onsager's thermodynamic formalism for transport coefficients and apply it to the calculation of the shear modulus and shear viscosity of a monodisperse system of repulsive particles. We focus on the concept of extensive "distance" and intensive "field" conjugated via a Fenchel-Legendre transform involving a thermodynamic(-like) potential, which allows to switch ensembles. Employing Brownian dynamics, we calculate both the shear modulus and the shear viscosity from strain fluctuations and show that they agree with direct calculations from strained and non-equilibrium simulations, respectively. We find a dependence of the fluctuations on the coupling strength to the strain reservoi…
Landau-Zener-Stueckelberg effect in a model of interacting tunneling systems
2003
The Landau-Zener-Stueckelberg (LZS) effect in a model system of interacting tunneling particles is studied numerically and analytically. Each of N tunneling particles interacts with each of the others with the same coupling J. This problem maps onto that of the LZS effect for a large spin S=N/2. The mean-field limit N=>\infty corresponds to the classical limit S=>\infty for the effective spin. It is shown that the ferromagnetic coupling J>0 tends to suppress the LZS transitions. For N=>\infty there is a critical value of J above which the staying probability P does not go to zero in the slow sweep limit, unlike the standard LZS effect. In the same limit for J>0 LZS transition…
STATISTICAL MECHANICS OF NONCLASSIC SOLITONIC STRUCTURES-BEARING DNA SYSTEM
2011
We theoretically investigate the thermodynamic properties of modified oscillator chain proposed by Peyrard and Bishop. This model obtained by adding the quartic anharmonicity term to the coupling in the Peyrard–Bishop model is useful to model the coexistence of various phases of the molecule during the denaturation phenomenon. Within the model, the negative anharmonicity is responsible for the sharpness of calculated melting curves. We perform the transfer integral calculations to demonstrate that the model leads to a good agreement with known experimental results for DNA.
Glassy dynamics in confinement: planar and bulk limits of the mode-coupling theory.
2014
We demonstrate how the matrix-valued mode-coupling theory of the glass transition and glassy dynamics in planar confinement converges to the corresponding theory for two-dimensional (2D) planar and the three-dimensional bulk liquid, provided the wall potential satisfies certain conditions. Since the mode-coupling theory relies on the static properties as input, the emergence of a homogeneous limit for the matrix-valued intermediate scattering functions is directly connected to the convergence of the corresponding static quantities to their conventional counterparts. We show that the 2D limit is more subtle than the bulk limit, in particular, the in-planar dynamics decouples from the motion …
Spline Histogram Method for Reconstruction of Probability Density Functions of Clusters of Galaxies
2003
We describe the spline histogram algorithm which is useful for visualization of the probability density function setting up a statistical hypothesis for a test. The spline histogram is constructed from discrete data measurements using tensioned cubic spline interpolation of the cumulative distribution function which is then differentiated and smoothed using the Savitzky-Golay filter. The optimal width of the filter is determined by minimization of the Integrated Square Error function. The current distribution of the TCSplin algorithm written in f77 with IDL and Gnuplot visualization scripts is available from this http URL
The response field and the saddle points of quantum mechanical path integrals
2021
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…
Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering
2011
By calculating all terms of the high-density expansion of the euclidean random matrix theory (up to second-order in the inverse density) for the vibrational spectrum of a topologically disordered system we show that the low-frequency behavior of the self energy is given by $\Sigma(k,z)\propto k^2z^{d/2}$ and not $\Sigma(k,z)\propto k^2z^{(d-2)/2}$, as claimed previously. This implies the presence of Rayleigh scattering and long-time tails of the velocity autocorrelation function of the analogous diffusion problem of the form $Z(t)\propto t^{(d+2)/2}$.
An inquiry-based approach to Maxwell distribution: a case study with engineering students
2013
The concept of distribution is a fundamental component of statistical thinking. This paper describes a teaching approach for it that uses a specific activity related to the field of statistical mechanics. The concept of the velocity distribution of a particle system is dealt with using an inquiry-based approach involving an experimental examination of Maxwell’s distribution. Some outcomes of a teaching experiment held at the Faculty of Engineering of the University of Palermo, Italy are described.
Quantum Monte Carlo methods
2005
Introduction In most of the discussion presented so far in this book, the quantum character of atoms and electrons has been ignored. The Ising spin models have been an exception, but since the Ising Hamiltonian is diagonal (in the absence of a transverse magnetic field), all energy eigenvalues are known and the Monte Carlo sampling can be carried out just as in the case of classical statistical mechanics. Furthermore, the physical properties are in accord with the third law of thermodynamics for Ising-type Hamiltonians (e.g. entropy S and specific heat vanish for temperature T → 0, etc.) in contrast to the other truly classical models dealt with in previous chapters (e.g. classical Heisenbe…
Monte Carlo studies ofd= 2 Ising strips with long-range boundary fields
2000
A two-dimensional Ising model with nearest-neighbour ferromagnetic exchange confined in a strip of width L between two parallel boundaries is studied by Monte Carlo simulations. `Free' boundaries are considered with unchanged exchange interactions at the boundary but long-range boundary fields of the form H (n ) = ? h [n -3 - (L - n + 1) -3 ], where n = 1, 2, ... ,L labels the rows across the strip. In the case of competing fields and L , the system exhibits a critical wetting transition of a similar type as in the well studied case of short-range boundary fields. At finite L , this wetting transition is replaced by a (rounded) interface localization-delocalization transition at Tc (h , L )…