Search results for " Modeling"

A Brightening Coronal Loop Observed byTRACE. II. Loop Modeling and Constraints on Heating

2000

This is the second of two papers dedicated to the brightening of a coronal loop observed by the Transition Region and Coronal Explorer (TRACE) on 1998 June 26; it aims at hydrodynamic modeling of the brightening. Since the loop geometry is practically unchanged during the brightening, the evolution of the plasma confined in the loop is described with a one-dimensional hydrodynamic time-dependent numerical model, and from the results the emission along the loop in the TRACE 171 A band is synthesized. The information from Paper I is used to derive the geometry and the initial configuration of the loop as well as for comparison with the results of the model. The modeling is focused to determin…

Balance equation of generalised sub-grid scale (SGS) turbulent kinetic energy in a new tensorial dynamic mixed SGS model

2000

A new dynamic model is proposed in which the eddy viscosity is defined as a symmetric second rank tensor, proportional to the product of a turbulent length scale with an ellipsoid of turbulent velocity scales. The employed definition of the eddy viscosity allows to remove the local balance assumption of the SGS turbulent kinetic energy formulated in all the dynamic Smagorinsky-type SGS models. Furthermore, because of the tensorial structure of the eddy viscosity the alignment assumption between the principal axes of the SGS turbulent stress tensor and the resolved strain-rate tensor is equally removed, an assumption which is employed in the scalar eddy viscosity SGS models. The proposed mod…

Lack of long-range order in confined two-dimensional model colloidal crystals.

2006

We investigate the nature of the ordered phase for a model of colloidal particles confined within a quasi-one-dimensional (Q1D) strip between two parallel boundaries, or walls, separated a distance $D$ in two dimensions (2D). Using Monte Carlo simulations we find that at densities typical of the bulk 2D triangular solid the order in the D1D strip is determined by the nature of the boundaries. While the order is enhanced for a suitably corrugated boundary potential, for a uniformly repulsive smooth boundary potential ordering normal to the walls is enhanced (``layering''), but destroyed parallel to the wall.

Simple sampling Monte Carlo methods

2005

Limits of lateral expansion in two-dimensional materials with line defects

2021

The flexibility of two-dimensional (2D) materials enables static and dynamic ripples that are known to cause lateral contraction, shrinking of the material boundary. However, the limits of 2D materials' \emph{lateral expansion} are unknown. Therefore, here we discuss the limits of intrinsic lateral expansion of 2D materials that are modified by compressive line defects. Using thin sheet elasticity theory and sequential multiscale modeling, we find that the lateral expansion is inevitably limited by the onset of rippling. The maximum lateral expansion $\chi_{max}\approx 2.1\cdot t^2\sigma_d$, governed by the elastic thickness $t$ and the defect density $\sigma_d$, remains typically well belo…

Single-cluster Monte Carlo study of the Ising model on two-dimensional random lattices.

1994

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices with up to 80,000 sites which are linked together according to the Voronoi/Delaunay prescription. In one set of simulations we use reweighting techniques and finite-size scaling analysis to investigate the critical properties of the model in the very vicinity of the phase transition. In the other set of simulations we study the approach to criticality in the disordered phase, making use of improved estimators for measurements. From both sets of simulations we obtain clear evidence that the critical exponents agree with the exactly known exponents for regular latti…

Application of the Monte Carlo coherent-anomaly method to two-dimensional lattice-gas systems with further-neighbor interactions

1990

A Monte Carlo version of the coherent-anomaly method has been used to determine critical properties of a two-dimensional Ising ferromagnet with nearest- and next-nearest-neighbor interactions and of a series of two-dimensional lattice-gas systems of particles interacting via 6-12 Lennard-Jones potential. It has demonstrated that the method leads to quite accurate determination of critical temperature but is less successful when used to determine the values of critical exponents \ensuremath{\gamma} and \ensuremath{\nu}.

Monte Carlo simulation of correlated electrons in disordered systems

1992

Abstract The properties of many-electron states in disordered systems with long-range electron-eletron interaction are investigated by means of a Monte Carlo simulation. Using the Metropolis algorithm, three-dimensional systems up to 512 sites are systematically analysed. The low-lying excitations are investigated in order to distinguish between one-particle and many-particle hopping. In the interesting regime in which disorder and correlation effects are equally important we find that variable-range hopping is insignificant for electron transfer when compared with the contribution from nearest-neighbour one-electron hopping processes as well as variable-number hopping.

Beyond the Vegard's law: solid mixing excess volume and thermodynamic potentials prediction, from end-members

2020

Abstract A method has been developed, herein presented, to model binary solid solutions' volume, enthalpy and Gibbs energy using the energy state functions, E ( V , S ) , of the end-members only. The E ( V , S ) s are expanded around an unknown mixing volume, V Mix , and the fundamental equilibrium equation − ( ∂ E / ∂ V ) S = P is used to determine V Mix . V Mix allows us to model enthalpy, straightforwardly. The same argument holds using Helmholtz energy, F ( V , T ) , in place of E ( V , S ) , and the equilibrium equation becomes − ( ∂ F / ∂ V ) T = P . One can readily determine the Gibbs free energy, too. The method presented remarkably simplifies computing of solid mixings' thermodynam…

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…