scholarly journals Mean-Field Theory Revives in Self-Oscillatory Fields with Non-Local Coupling

2006 ◽  
Vol 161 ◽  
pp. 127-143 ◽  
Author(s):  
Yoshiki Kuramoto ◽  
Shin-ichiro Shima ◽  
Dorjsuren Battogtokh ◽  
Yuri Shiogai
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Non Local ◽  
Local Coupling

scholarly journals A non-local diffusion equation arising in terminally attached polymer chains

1990 ◽  
Vol 1 (4) ◽  
pp. 311-326 ◽  
Author(s):  
Xinfu Chen ◽  
Avner Friedman
Keyword(s):  
Field Theory ◽  
Diffusion Equation ◽  
Polymer Chain ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Melt ◽  
Polymer Chains ◽  
Number Density ◽  
Non Local ◽  
Local Diffusion

We consider a polymer melt in a domain Ω whereby each polymer chain is attached at one endpoint to a fixed surface S contained in ∂Ω. Denote by G(x, t;y) the normalized number density of all subchains from x to y of length t. Then, according to the selfconsistent mean field theory, G satisfies, for each y: Gt - Δ2G + σϕG = 0, where σ is a real parameter, and ϕ is a functional of G(·, ·; ·) both non-local and nonlinear. We establish the existence of G and C∞ regularity of ϕ, as a function of x.

scholarly journals Motivation and challenge to capture both large-scale and local transport in next generation accretion theory

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
Eric G. Blackman ◽  
Farrukh Nauman
Keyword(s):  
Field Theory ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Next Generation ◽  
Dynamo Theory ◽  
Non Local ◽  
Local Transport

Accretion disc theory is less developed than stellar evolution theory although a similarly mature phenomenological picture is ultimately desired. While the interplay of theory and numerical simulations has amplified community awareness of the role of magnetic fields in angular momentum transport, there remains a long term challenge to incorporate the insights gained from simulations into improving practical models for comparison with observations. What has been learned from simulations that can lead to improvements beyond SS73 in practical models? Here, we emphasize the need to incorporate the role of non-local transport more precisely. To show where large-scale transport would fit into the theoretical framework and how it is currently missing, we review why the wonderfully practical approach of Shakura & Sunyaev (Astron. Astrophys., vol. 24, 1973, pp. 337–355, SS73) is necessarily a mean field theory, and one which does not include large-scale transport. Observations of coronae and jets, combined with the interpretation of results from shearing box simulations, of the magnetorotational instability (MRI) suggest that a significant fraction of disc transport is indeed non-local. We show that the Maxwell stresses in saturation are dominated by large-scale contributions and that the physics of MRI transport is not fully captured by a viscosity. We also clarify the standard physical interpretation of the MRI as it applies to shearing boxes. Computational limitations have so far focused most attention toward local simulations, but the next generation of global simulations should help to inform improved mean field theories. Mean field accretion theory and mean field dynamo theory should in fact be unified into a single theory that predicts the time evolution of spectra and luminosity from separate disc, corona and outflow contributions. Finally, we note that any mean field theory, including that of SS73, has a finite predictive precision that needs to be quantified when comparing the predictions to observations.

scholarly journals The AbinitioDΓA Project v1.0: Non-local correlations beyond and susceptibilities within dynamical mean-field theory

2019 ◽  
Vol 245 ◽  
pp. 106847 ◽  
Author(s):  
Anna Galler ◽  
Patrik Thunström ◽  
Josef Kaufmann ◽  
Matthias Pickem ◽  
Jan M. Tomczak ◽  
...  
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Dynamical Mean Field Theory ◽  
Local Correlations ◽  
Non Local

Mean field theory of n-layer unbinding

1993 ◽  
Vol 3 (3) ◽  
pp. 385-393 ◽  
Author(s):  
W. Helfrich
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models

scholarly journals Intrinsic dissipative Floquet superconductors beyond mean-field theory

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Qinghong Yang ◽  
Zhesen Yang ◽  
Dong E. Liu
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field
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