Search results for "modeling"
showing 10 items of 4489 documents
Fractional-order theory of heat transport in rigid bodies
2014
Abstract The non-local model of heat transfer, used to describe the deviations of the temperature field from the well-known prediction of Fourier/Cattaneo models experienced in complex media, is framed in the context of fractional-order calculus. It has been assumed (Borino et al., 2011 [53] , Mongiovi and Zingales, 2013 [54] ) that thermal energy transport is due to two phenomena: ( i ) A short-range heat flux ruled by a local transport equation; ( ii ) A long-range thermal energy transfer proportional to a distance-decaying function, to the relative temperature and to the product of the interacting masses. The distance-decaying function is assumed in the functional class of the power-law …
Modulational stability brought by cubic–quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential
2022
Abstract This work extends to higher-order interactions the results of Ref. Nguetcho (2021), in which we discussed only on modulational instability in one-dimensional chain made of atoms, harmonically coupled to their nearest neighbors and subjected to an external on-site potential. Here we investigate the competition between cubic-quartic nonlinearities interactions of the nearest-neighbor and substrate’s deformability, and mainly discuss its impact on the modulational instability of the system. This makes it possible to adapt the theoretical model to a real physical system such as atomic chains or DNA lattices. The governing equation, derived from the modified Frenkel-Kontorova model, is …
Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class
2014
Abstract The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different para…
On the correlation between phase-locking modes and Vibrational Resonance in a neuronal model
2018
International audience; We numerically and experimentally investigate the underlying mechanism leading to multiple resonances in the FitzHugh-Nagumo model driven by a bichromatic excitation. Using a FitzHugh-Nagumo circuit, we first analyze the number of spikes triggered by the system in response to a single sinusoidal wave forcing. We build an encoding diagram where different phase-locking modes are identified according to the amplitude and frequency of the sinusoidal excitation. Next, we consider the bichromatic driving which consists in a low frequency sinusoidal wave perturbed by an additive high frequency signal. Beside the classical Vibrational Resonance phenomenon, we show in real ex…
Multi-Scale Modeling of Quantum Semiconductor Devices
2006
This review is concerned with three classes of quantum semiconductor equations: Schrodinger models, Wigner models, and fluid-type models. For each of these classes, some phenomena on various time and length scales are presented and the connections between micro-scale and macro-scale models are explained. We discuss Schrodinger-Poisson systems for the simulation of quantum waveguides and illustrate the importance of using open boundary conditions. We present Wigner-based semiconductor models and sketch their mathematical analysis. In particular we discuss the Wigner-Poisson-Focker-Planck system, which is the starting point of deriving subsequently the viscous quantum hydrodynamic model. Furt…
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.