GENERALIZATION OF THE MEAN-FIELD METHOD FOR POWER-LAW DISTRIBUTIONS

2006 ◽  
Vol 16 (01) ◽  
pp. 129-135 ◽  
Author(s):  
TARO TOYOIZUMI ◽  
KAZUYUKI AIHARA
Keyword(s):  
Computational Complexity ◽  
Financial Markets ◽  
Mean Field ◽  
Field Method ◽  
World Systems ◽  
Developed Turbulence ◽  
Binary State ◽  
The Mean ◽  
Generalized Mean ◽  
Power Law Distributions

Recently much attention has been paid to the nonextensive canonical distributions: the α-families. Such distributions have been found in many real-world systems such as fully developed turbulence and financial markets. In this paper, a generalized mean-field method to approximate the expectations of the α-families is proposed. We calculate the α′-projection of a probability distribution to find that the computational complexity to approximate the expectations is greatly reduced with a proper choice of the projection-index α′. We apply this method to a simple binary-state system and compare the results with direct numerical calculations.

The Applicability of the Mean Field Method in the Optical Bistability

1986 ◽  
pp. 173-177
Author(s):  
I. M. Popescu ◽  
E. N. Stefanescu ◽  
P. E. Sterian
Keyword(s):  
Optical Bistability ◽  
Mean Field ◽  
Field Method ◽  
The Mean

Superconducting and other phases in organic high polymers of polyacenic carbon skeletons. II. The mean field method

1986 ◽  
Vol 85 (5) ◽  
pp. 3097-3102 ◽  
Author(s):  
M. Kimura ◽  
H. Kawabe ◽  
K. Nishikawa ◽  
S. Aono
Keyword(s):  
Mean Field ◽  
Field Method ◽  
The Mean ◽  
High Polymers

A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

2009 ◽  
Vol 623 ◽  
pp. 283-316 ◽  
Author(s):  
DIRK M. LUCHTENBURG ◽  
BERT GÜNTHER ◽  
BERND R. NOACK ◽  
RUDIBERT KING ◽  
GILEAD TADMOR
Keyword(s):  
High Frequency ◽  
Field Model ◽  
Mean Field ◽  
Low Frequency ◽  
Navier Stokes ◽  
Mean Field Model ◽  
High Lift ◽  
The Mean ◽  
Generalized Mean ◽  
Low Dimensional

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

Modeling and Modifying the Foraging Strategy in Swarm Robots

2011 ◽  
Vol 467-469 ◽  
pp. 269-274 ◽  
Author(s):  
Dong Xu ◽  
Bai Long Liu ◽  
Ru Bo Zhang
Keyword(s):  
Swarm Intelligence ◽  
Cooperative Behavior ◽  
Mean Field ◽  
Foraging Strategy ◽  
Field Method ◽  
Ant System ◽  
Modified Method ◽  
Swarm Robots ◽  
The Mean ◽  
Foraging Task

Swarm Intelligence which emerges from interactions of simple individuals can be used to solve many problems. The foraging task in ant system is often considered as the prototype of cooperative behavior in Swarm Intelligence. The foraging model in swarm robots which considers the random feature of individual robot is built using the mean field method. Then the conflict between robots which influences the performance is observed. To solve this problem, a modified foraging strategy based on pheromone is proposed. From the simulations in Starlogo platform, it is shown that the modified method can reduces the conflict of robots and increase the performance of the system.

scholarly journals Nuclear structure study of some tin isotopes using the self-consistent mean field method

2019 ◽  
Vol 13 (26) ◽  
pp. 112-120
Author(s):  
Mohammed F. Majid
Keyword(s):  
Mean Field ◽  
Nucleon Nucleon ◽  
Field Method ◽  
Structure Study ◽  
Nucleon Interaction ◽  
Skyrme Interaction ◽  
Hartree Fock ◽  
Nuclear Structure Study ◽  
The Mean ◽  
Nucleon Nucleon Interaction

Hartree-Fock calculations for even-even Tin isotopes usingSkyrme density dependent effective nucleon-nucleon interaction arediscussed systematically. Skyrme interaction and the general formulafor the mean energy of a spherical nucleus are described. The chargeand matter densities with their corresponding rms radii and thenuclear skin for Sn isotopes are studied and compared with theexperimental data. The potential energy curves obtained withinclusion of the pairing force between the like nucleons in Hartree-Fock-Bogoliubov approach are also discussed.

scholarly journals Calculation of the Static Properties of Local Moment Systems by the Mean Field Method

1975 ◽  
Vol 28 (6) ◽  
pp. 685 ◽  
Author(s):  
AM Stewart
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Field Method ◽  
Local Moment ◽  
Mean Field Approximation ◽  
Static Properties ◽  
The Past ◽  
The Mean

It is demonstrated that two different methods which have been used in the past to calculate the static properties oflocal moment systems in the mean field approximation are incomplete. A proof is given of the correctness of another method that the author has used in several previous calculations. It is found that some exact and very general relationships exist between the conduction electron magnetization and the local moment magnetization even when it is not valid to treat the interactions between the magnetic atoms by mean field theory.

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