Search results for " Modeling"
showing 10 items of 2411 documents
Monte Carlo studies of adsorbed monolayers: Lattice-gas models with translational degrees of freedom
1998
Standard lattice-gas models for the description of the phase behavior of adsorbed monolayers are generalized to ``elastic lattice gases'' which allow for translational degrees of freedom of the adsorbate atoms but have the substrate lattice structure built into the adsorbate-adsorbate interaction. For such models, we derive a simple and efficient grand-canonical Monte Carlo algorithm, which treats the occupied and empty sites in precisely the same way. Using this method, we calculate the phase diagram of a simple model for the adsorption of hydrogen on palladium (100); this model includes only pairwise interactions and exhibits an ordered $c(2\ifmmode\times\else\texttimes\fi{}2)$ structure.…
Monte Carlo Methods: a powerful tool of statistical physics
1998
Statistical mechanics of condensed matter systems (solids, fluids) tries to express macroscopic equilibrium properties of matter as averages computed from a Hamiltonian that expresses interactions of an atomistic many body system. While analytic methods for most problems involve crude and uncontrolled approximations, the Monte Carlo computer simulation method allows a numerically exact treatment of this problem, apart from “statistical errors” which can be made as small as desired, and the systematic problem that a system of finite size is treated rather than the thermodynamic limit. However, the simulations of phase transitions then elucidate how a symmetry breaking arises via breaking of …
Dynamics of star polymers in a good solvent: A Kramers potential treatment
1994
The ‘‘effective’’ relaxation time τ of isolated star polymers with excluded volume interactions in the Rouse model limit (i.e., disregarding hydrodynamic interactions present in real solvents) is studied varying both the number of arms f and the number of monomers per arm l. Here τ is defined from the response of the gyration radius of the star polymer to a Kramers potential that describes the effect of shear flow in lowest order in the shear rate. Monte Carlo simulations are performed with two different techniques (simple sampling with enrichment or dynamic Monte Carlo, respectively) for two different models (simple self‐avoiding walks with an extended core or the bond fluctuation model, r…
Monte Carlo simulation of crystalline polyethylene
1996
Abstract We consider here the problem of constructing an efficient algorithm for a classical Monte Carlo simulation of crystalline polyethylene with unconstrained bond lengths and angles. This macromolecular crystal presents a particular example of a system with many different energy scales, ranging from soft ones represented by nonbonded van der Waals interactions, to stiff ones, represented in particular by bond stretching. A proper sampling of all the energy scales poses a problem and it is shown that a standard Metropolis algorithm employing just local moves is not very efficient at low temperatures. As a solution it is proposed to employ also global moves consisting of displacements of…
Chain length dependence of the state diagram of a single stiff-chain macromolecule: Theory and Monte Carlo simulation
2003
We present a Monte Carlo computer simulation and theoretical results for the dependence of the state diagram of a single semiflexible chain on the chain length. The calculated transition lines between different structures in the state diagrams for both studied chain lengths N=40 and N=80 can be described by theoretical predictions which include chain length dependence explicitly. The stability criteria of different structures are discussed. The theoretically predicted exponent in the dependence of the toroid size on the chain length is compatible with computer simulation results.
Effective kink-kink interaction in a one-dimensional model mediated by phonon exchange
1994
The general 1D double-well model with anharmonic interaction is considered in the displacive limit. Expansion of the Hamiltonian around a multikink state results in a phonon-kink Hamiltonian. It is shown that at rather low temperatures and short wave lengths the phonon-kink interaction can be treated in Born approximation, leading to a decomposition of the multikink-phonon Hamiltionian. Elimination of the phonons results in an effective potential for the kink-kink interaction, which corresponds to the one-dimensional analog of the RKKY interaction. This long-range interaction is inherent only for models with anharmonic on-site potentials and not in case of a double-parabola model.
Wilsonʼs momentum shell renormalization group from Fourier Monte Carlo simulations
2011
Abstract Previous attempts to accurately compute critical exponents from Wilsonʼs momentum shell renormalization prescription suffered from the difficulties posed by the presence of an infinite number of irrelevant couplings. Taking the example of the 1d long-ranged Ising model , we calculate the momentum shell renormalization flow in the plane spanned by the coupling constants ( u 0 , r 0 ) for different values of the momentum shell thickness parameter b by simulation using our recently developed Fourier Monte Carlo algorithm. We report strong anomalies in the b-dependence of the fixed point couplings and the resulting exponents y τ and ω in the vicinity of a shell parameter b ⁎ 1 characte…
Simulation of skin reflectance images using 3D tissue modeling and multispectral Monte Carlo light propagation.
2008
In this work we propose a method to simulate the expected, i.e. seen by a camera, multispectral reflectance images of a large skin surface area by combining Monte Carlo light propagation model and realistic tissue modeling based on three dimensional data acquisition of human body areas. In particular, we aim to simulate more accurately light transport in biological tissue by taking into account the geometrical topography of the skin surface, the structure and optical properties of the skin layers, and the subcutaneous veins in presence. We describe our computation method in detail and present simulated reflectance images results.
The Heating of the Solar Corona
2021
The solar corona, the outer atmosphere of the Sun, is heated to millions of Kelvin. This is several orders of magnitude hotter than the photosphere, the optical surface of the Sun, below, and a mystery that has baffled scientists for centuries. The answer to the question of how the solar corona is heated lies in the crucial magnetic connection through the atmosphere of the Sun. The magnetic field that threads the corona extends below the solar photosphere, where convective motions drag the magnetic field footpoints, tangling and twisting them. The chromosphere is the atmospheric layer above the photosphere, and the magnetic field provides an important connection between these layers. The ex…
QUANTUM MODELING OF LOVE AFFAIRS
2010
We adopt the so-called number representation, originally used in quantum me- chanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relation. We present a simple model, involv- ing two actors (Alice and Bob), and we consider either a linear model or a nonlinear model.