Hopfield Models as Generalized Random Mean Field Models

1998 ◽  
pp. 3-89 ◽  
Author(s):  
Anton Bovier ◽  
Véronique Gayrard
Keyword(s):  
Mean Field ◽  
Mean Field Models

Ion Pairing and Dielectric Decrement in Glycosaminoglycan Brushes

2020 ◽  
Author(s):  
James Sterling ◽  
Wenjuan Jiang ◽  
Wesley M. Botello-Smith ◽  
Yun L. Luo
Keyword(s):  
Molecular Dynamics ◽  
Ion Pairs ◽  
Mean Field ◽  
Salt Bridge ◽  
Ion Pairing ◽  
Donnan Potential ◽  
Mean Field Models ◽  
Ion Exclusion ◽  
Dynamics Simulations ◽  
Contact Ion Pairs

Molecular dynamics simulations of hyaluronic acid and heparin brushes are presented that show important effects of ion-pairing, water dielectric decrease, and co-ion exclusion. Results show equilibria with electroneutrality attained through screening and pairing of brush anionic charges by cations. Most surprising is the reversal of the Donnan potential that would be expected based on electrostatic Boltzmann partitioning alone. Water dielectric decrement within the brush domain is also associated with Born hydration-driven cation exclusion from the brush. We observe that the primary partition energy attracting cations to attain brush electroneutrality is the ion-pairing or salt-bridge energy associated with cation-sulfate and cation-carboxylate solvent-separated and contact ion pairs. Potassium and sodium pairing to glycosaminoglycan carboxylates and sulfates consistently show similar abundance of contact-pairing and solvent-separated pairing. In these crowded macromolecular brushes, ion-pairing, Born-hydration, and electrostatic potential energies all contribute to attain electroneutrality and should therefore contribute in mean-field models to accurately represent brush electrostatics.

scholarly journals PDE limits of stochastic SIS epidemics on networks

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
F Di Lauro ◽  
J-C Croix ◽  
L Berthouze ◽  
I Z Kiss
Keyword(s):  
Network Inference ◽  
Mean Field ◽  
Population Level ◽  
Death Process ◽  
Disease Dynamics ◽  
Epidemic Outbreak ◽  
Numerical Tests ◽  
Mean Field Models ◽  
Stochastic Epidemic ◽  
Fokker Planck Equations

Abstract Stochastic epidemic models on networks are inherently high-dimensional and the resulting exact models are intractable numerically even for modest network sizes. Mean-field models provide an alternative but can only capture average quantities, thus offering little or no information about variability in the outcome of the exact process. In this article, we conjecture and numerically demonstrate that it is possible to construct partial differential equation (PDE)-limits of the exact stochastic susceptible-infected-susceptible epidemics on Regular, Erdős–Rényi, Barabási–Albert networks and lattices. To do this, we first approximate the exact stochastic process at population level by a Birth-and-Death process (BD) (with a state space of $O(N)$ rather than $O(2^N)$) whose coefficients are determined numerically from Gillespie simulations of the exact epidemic on explicit networks. We numerically demonstrate that the coefficients of the resulting BD process are density-dependent, a crucial condition for the existence of a PDE limit. Extensive numerical tests for Regular, Erdős–Rényi, Barabási–Albert networks and lattices show excellent agreement between the outcome of simulations and the numerical solution of the Fokker–Planck equations. Apart from a significant reduction in dimensionality, the PDE also provides the means to derive the epidemic outbreak threshold linking network and disease dynamics parameters, albeit in an implicit way. Perhaps more importantly, it enables the formulation and numerical evaluation of likelihoods for epidemic and network inference as illustrated in a fully worked out example.

scholarly journals Connecting real glasses to mean-field models

2021 ◽  
Vol 154 (9) ◽  
pp. 094506
Author(s):  
Ujjwal Kumar Nandi ◽  
Walter Kob ◽  
Sarika Maitra Bhattacharyya
Keyword(s):  
Mean Field ◽  
Mean Field Models

Hadronic chiral mean field models at extreme temperatures and densities

2001 ◽  
Vol 27 (11) ◽  
pp. 2251-2266 ◽  
Author(s):  
A Delfino ◽  
M Chiapparini ◽  
M E Bracco ◽  
L Castro ◽  
S E Epsztein
Keyword(s):  
Mean Field ◽  
Extreme Temperatures ◽  
Mean Field Models

scholarly journals Parameter counting in relativistic mean-field models

2000 ◽  
Vol 671 (1-4) ◽  
pp. 447-460 ◽  
Author(s):  
R.J. Furnstahl ◽  
Brian D. Serot
Keyword(s):  
Mean Field ◽  
Relativistic Mean Field ◽  
Mean Field Models
Sign in / Sign up

Export Citation Format

Share Document