Search results for "mean field"
showing 10 items of 191 documents
Pressure-Induced Formation of Diblock Copolymer "Micelles" in Supercritical Fluids. A Combined Study by Small Angle Scattering Experiments and Mean-F…
2004
We developed a simple mean-field theory to describe polymer and AB diblock copolymer phase separation in supercritical (SC) fluids. The highly compressible SC fluid has been described by using a phenomenological hole theory, properly extended to consider the solvent/polymer/vacancy pseudoternary mixture. The model has been applied to describe the phase behavior of AB-diblock copolymers under the assumption of a strong solvent selectivity for just one copolymer chain. In our model the solvent selectivity is a strong function of the external pressure because in compressible fluids vacancies reduce the number of favorable solvent-polymer contacts. The combined effect of the pressure on the ave…
Simulation of Copolymer Bottle-Brushes
2007
The structure of bottle-brush polymers with a rigid backbone and flexible side chains is studied in three dimensions, varying the grafting density, the side chain length, and the solvent quality. Some preliminary results of theoretical scaling considerations for one-component bottle-brush polymers in a good solvent are compared with Monte Carlo simulations of a simple lattice model. For the simulations a variant of the pruned-enriched Rosenbluth method (PERM) allowing for simultaneous growth of all side chains in the Monte Carlo sampling is employed. For a symmetrical binary (A,B) bottle-brush polymer, where two types (A,B) of flexible side chains are grafted with one chain end to the backb…
Pressure-induced cooperative spin transition in ironII 2D coordination polymers: room-temperature visible spectroscopic study.
2011
For the 2D coordination polymers [Fe(3-Fpy)(2)M(II)(CN)(4)] (M(II) = Ni, Pd, Pt), the pressure-induced spin crossover behavior has been investigated at 298 K by monitoring the distinct optical properties associated with each spin state. Cooperative first-order spin transition characterized by a piezohysteresis loop ca. 0.1 GPa wide was observed for the three derivatives. Application of the mean field regular solution theory has enabled estimation of the cooperative parameter, Γ(p), and the enthalpy, ΔH(HL)(p), associated with the spin transition for each derivative. These values, found in the intervals 6.8-7.9 and 18.6-20.8 kJ mol(-1), respectively, are consistent with those previously repo…
Nonlinear Relaxation in Population Dynamics
2001
We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the i-th population and on the distribution of the population and of the local field.
Opinion dynamics and stubbornness through mean-field games
2013
This paper provides a mean field game theoretic interpretation of opinion dynamics and stubbornness. The model describes a crowd-seeking homogeneous population of agents, under the influence of one stubborn agent. The game takes on the form of two partial differential equations, the Hamilton-Jacobi-Bellman equation and the Kolmogorov-Fokker-Planck equation for the individual optimal response and the population evolution, respectively. For the game of interest, we establish a mean field equilibrium where all agents reach epsilon-consensus in a neighborhood of the stubborn agent's opinion.
Density flow over networks: A mean-field game theoretic approach
2014
A distributed routing control algorithm for dynamic networks has recently been presented in the literature. The networks were modeled using time evolution of density at network edges and the routing control algorithm allowed edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We borrow the idea and rearrange the density model to recast the problem within the framework of mean-field games. The contribution of this paper is three-fold. First, we provide a mean-field game formulation of the problem at hand. Second, we illustrate an extended state space solution approach. Third, we study the stochastic case where the density …
Flat bands, Dirac cones, and atom dynamics in an optical lattice
2010
We study atoms trapped with a harmonic confinement in an optical lattice characterized by a flat band and Dirac cones. We show that such an optical lattice can be constructed which can be accurately described with the tight binding or Hubbard models. In the case of fermions the release of the harmonic confinement removes fast atoms occupying the Dirac cones while those occupying the flat band remain immobile. Using exact diagonalization and dynamics we demonstrate that a similar strong occupation of the flat band does not happen in bosonic case and furthermore that the mean field model is not capable for describing the dynamics of the boson cloud.
Opinion dynamics, stubbornness and mean-field games
2014
This paper studies opinion dynamics and stubbornness using mean-field game theory. Assuming an initial exponential density function and affine control policies we analyze under what conditions the Fokker-Planck equation returns an exponential density function over the horizon. Consensus and clusters formation are also studied.
One‐magnon Raman scattering in Ni c Mg 1–c O solid solutions
2005
The one-magnon Raman scattering was studied for the first time in antiferromagnetic NicMg1–cO solid solutions as a function of temperature and composition. We found that (i) the one-magnon frequency extrapolated to T = 0 K experiences an abrupt change between c = 0.99 and c = 0.9 and (ii) the one-magnon energy for highly diluted nickel oxide vanishes significantly below the Neel temperature. The obtained dependences are compared to the theoretical predictions within the mean field approximation. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Saddle index properties, singular topology, and its relation to thermodynamic singularities for aϕ4mean-field model
2004
We investigate the potential energy surface of a ${\ensuremath{\phi}}^{4}$ model with infinite range interactions. All stationary points can be uniquely characterized by three real numbers ${\ensuremath{\alpha}}_{+},{\ensuremath{\alpha}}_{0},{\ensuremath{\alpha}}_{\ensuremath{-}}$ with ${\ensuremath{\alpha}}_{+}+{\ensuremath{\alpha}}_{0}+{\ensuremath{\alpha}}_{\ensuremath{-}}=1$, provided that the interaction strength $\ensuremath{\mu}$ is smaller than a critical value. The saddle index ${n}_{s}$ is equal to ${\ensuremath{\alpha}}_{0}$ and its distribution function has a maximum at ${n}_{s}^{\mathrm{max}}=1∕3$. The density $p(e)$ of stationary points with energy per particle $e$, as well as…