General mean-field BDSDEs with continuous coefficients

2022 ◽  
Vol 506 (2) ◽  
pp. 125699
Author(s):  
Juan Li ◽  
Chuanzhi Xing
Keyword(s):  
2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.


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

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk

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.


2020 ◽  
Author(s):  
James Sterling ◽  
Wenjuan Jiang ◽  
Wesley M. Botello-Smith ◽  
Yun L. Luo

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.


2019 ◽  
Author(s):  
Jonas Landsgesell ◽  
Oleg Rud ◽  
Pascal Hebbeker ◽  
Raju Lunkad ◽  
Peter Košovan ◽  
...  

We introduce the grand-reaction method for coarse-grained simulations of acid-base equilibria in a system coupled to a reservoir at a given pH and concentration of added salt. It can be viewed as an extension of the constant-pH method and the reaction ensemble, combining explicit simulations of reactions within the system, and grand-canonical exchange of particles with the reservoir. Unlike the previously introduced methods, the grand-reaction method is applicable to acid-base equilibria in the whole pH range because it avoids known artifacts. However, the method is more general, and can be used for simulations of any reactive system coupled to a reservoir of a known composition. To demonstrate the advantages of the grand-reaction method, we simulated a model system: A solution of weak polyelectrolytes in equilibrium with a buffer solution. By carefully accounting for the exchange of all constituents, the method ensures that all chemical potentials are equal in the system and in the multi-component reservoir. Thus, the grand-reaction method is able to predict non-monotonic swelling of weak polyelectrolytes as a function of pH, that has been known from mean-field predictions and from experiments but has never been observed in coarse-grained simulations. Finally, we outline possible extensions and further generalizations of the method, and provide a set of guidelines to enable safe usage of the method by a broad community of users.<br><br>


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