WEAK MEAN-FIELD APPROXIMATION FOR DISCRETE EPIDEMIC MODELS IN SCALE-FREE NETWORKS

2011 ◽  
Vol 19 (03) ◽  
pp. 403-416 ◽  
Author(s):  
QINGCHU WU ◽  
XINCHU FU
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Sis Epidemic Model ◽  
The Difference ◽  
Simple Difference ◽  
Previous Approximation

Epidemic dynamics in networks have attracted a great deal of attention from many fields. Based on the previous work, we propose a weak discrete mean-field approximation, and the difference with the previous approximation approach is that it can result in more simple difference equations. We mainly consider the minimal SIS epidemic model in complex networks, and make comparisons amongst two kinds of approximation formulations on the prediction of epidemic prevalence and find that they are effective to model epidemic spreading. Moreover, we investigate its application to the risk feedback case and simulations indicate its effectiveness.

scholarly journals THE INFLUENCE OF THE MAGNETIC FIELD ON THE PROPERTIES OF NEUTRON STAR MATTER

2007 ◽  
Vol 22 (07n10) ◽  
pp. 623-629 ◽  
Author(s):  
WEI CHEN ◽  
PU-QING ZHANG ◽  
LIANG-GANG LIU
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Neutron Star Matter ◽  
Density Region ◽  
High Density Region ◽  
The Difference ◽  
The Magnetic Field

In the mean field approximation of the relativistic σ-ω-ρ model, the magnetic fields are incorporated, and it's influence on the properties of n-p-e neutron star matter are studied. When the strength of the magnetic field is weaker than ~1018G, the particles' fractions and chemical potentials, matter's energy density and pressure hardly change with the magnetic field; when the strength of the magnetic field is stronger than ~1020G, the above quantities change with the magnetic field evidently. Furthermore, the pressure is studied in both thermodynamics and hydrodynamics. The difference between these two ways exits in the high density region, that is, the thermal self-consistency may not be satisfied in this region if the magnetic field is considered.

Monte Carlo Investigation of Cascade Damage Effects in Metals Under Low Temperature Irradiation

1998 ◽  
Vol 540 ◽  
Author(s):  
A.V. Barashev ◽  
D.J. Bacon ◽  
S.I. Golubov
Keyword(s):  
Monte Carlo ◽  
Damage Accumulation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Recoil Energy ◽  
Damage State ◽  
The Difference ◽  
Dynamics Simulations ◽  
Cascade Damage

AbstractThe Monte Carlo (MC) method is used to study cascade damage effects in damage accumulation in pure metals at temperatures below stage III, when vacancies and their clusters are immobile. The irradiation is modelled by sequential introduction of collections of defects representing the primary damage state of cascades placed randomly in the simulation volume. The cascades generated in molecular dynamics simulations for recoil energies from 2 to 20keV are used. Concentrations of point defects as well as defect cluster densities are monitored as a function of dose up to 0.02dpa. The results are compared with those obtained in the mean-field approximation. Factors responsible for the difference in damage accumulation under homogeneous and cascade irradiation conditions are revealed. The effects of temperature and recoil energy are studied. Problems in MC modelling of one-dimensional diffusion of interstitial clusters connected with the limited volume of the simulation box are revealed.

Epidemic Spreading with Feedback Mechanism and Time Delay under Migration in Scale-Free Networks

2013 ◽  
Vol 378 ◽  
pp. 655-661
Author(s):  
Tao Li ◽  
Yuan Mei Wang
Keyword(s):  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Feedback Mechanism ◽  
Critical Threshold ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Epidemic Dynamics ◽  
Scale Free Networks ◽  
The Mean

Taking into account the heterogeneity of the underlying networks, an epidemic model with feedback-mechanism, time delay and migrations of individuals on scale-free networks is presented. First, the epidemic dynamics is analyzed via the mean field theory. The spreading critical threshold and equilibriums are derived. The existence of endemic equilibrium is determined by the spreading threshold. Then, the influences of feedback-mechanism, time delay, migrations of individuals and the heterogeneity of the scale-free networks on the spreading threshold and the epidemic steady-state are studied in detail. Numerical simulations are presented to illustrate the results with the theoretical analysis.

A MEAN FIELD APPROACH FOR ISING MODELS ON SCALE-FREE NETWORKS

2011 ◽  
Vol 25 (07) ◽  
pp. 453-464 ◽  
Author(s):  
G. IANNONE ◽  
ORLANDO LUONGO
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Practical Applications ◽  
Scale Free ◽  
Wide Range ◽  
Scale Free Networks ◽  
The Mean ◽  
Mean Field Approximations

Recently, the study of complex networks led to the analysis of the so-called scale-free models in statistical mechanics. This study has increased its importance, thanks to the wide range of applications in numerous physical contexts; for example, one important question is to understand the behavior of various models on such networks. We start first by investigating the Ising model in the mean field approximation and on scale-free networks, studying especially the Ising model with annealed dilution and Clock model, with particular attention devoted to focusing on similarities between the mean field approximations with or without scale-free statistics. A particular emphasis is given to the possible practical applications of these results in other disciplines such as medicine and social science.

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

Geometrical and Transport Properties of Disordered Fibre Networks: Analytical Results

1997 ◽  
Vol 11 (20) ◽  
pp. 867-875 ◽  
Author(s):  
A. A. Rodríaguez ◽  
E. Medina
Keyword(s):  
Probability Distribution ◽  
Transport Properties ◽  
Geometrical Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Fracture Networks ◽  
Simplified Models ◽  
Fibre Density ◽  
Line Network

We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field approximation to conduction, above the percolation threshold, using the derived results. Relevance of the results to fracture networks will be discussed.

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