SELF-CONSISTENT MEAN FIELD MODEL OF HYDROGEL AND ITS NUMERICAL SIMULATION

2013 ◽  
Vol 12 (06) ◽  
pp. 1350048 ◽  
Author(s):  
CHAOHUI YUAN ◽  
HUI ZHANG
Keyword(s):  
Numerical Simulation ◽  
Volume Fraction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Chains ◽  
Model Parameters ◽  
Micro Structure ◽  
Mean Field Model ◽  
Self Consistent ◽  
Micro Structures

A model to describe the micro-structure of macromolecular microsphere composite (MMC) hydrogel is proposed in the framework of self-consistent mean field theory (SCMFT),1 which is usually used to investigate copolymer. Based on the SCMFT approximation, a system of equations associated with the complex topology of MMC hydrogel is derived and solved by a new kind of relaxation algorithm successfully. From the numerical simulation of the model, we find that the two model parameters play important roles in describing the micro-structure of MMC hydrogel, the interactions between two species (polymer chains and MMS spheres) and the volume fraction of MMS spheres. The role of other model parameters on the structure of the MMC hydrogel is also discussed. The numerical results are consistent with the observation from the chemical experiments. Moreover, we also show some new micro-structures obtained by using the SCMFT model, but discovered in chemical experiments.

scholarly journals Applications of the relativistic mean-field model to finite nuclei.

2020 ◽  
Vol 9 ◽  
pp. 256
Author(s):  
G. A. Lalazissis
Keyword(s):  
Body Problem ◽  
Field Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Many Body ◽  
Mean Field Model ◽  
Consistent System ◽  
Relativistic Mean Field ◽  
Self Consistent ◽  
Finite Nuclei

The relativistic mean-field theory (RMF) provides a framework in which the nuclear many-body problem is described as a self-consistent system of nucléons and mesons. We review recent applications of the RMF theory to the structure of finite nuclei.

scholarly journals Calorimetric glass transition in a mean-field theory approach

2015 ◽  
Vol 112 (8) ◽  
pp. 2361-2366 ◽  
Author(s):  
Manuel Sebastian Mariani ◽  
Giorgio Parisi ◽  
Corrado Rainone
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Supercooled Liquid ◽  
Analytic Solutions ◽  
Theory Approach ◽  
Mean Field Model ◽  
Thermalization Time ◽  
Glass Forming ◽  
Heating And Cooling ◽  
Spatial Dimensions

The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean-field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions; on the experimental and numerical side, the study of the properties of metastable glassy states requires thermalizing the system in the supercooled liquid phase, where the thermalization time may be extremely large. We consider here a hard-sphere mean-field model that is solvable in any number of spatial dimensions; moreover, we easily obtain thermalized configurations even in the glass phase. We study the 3D version of this model and we perform Monte Carlo simulations that mimic heating and cooling experiments performed on ultrastable glasses. The numerical findings are in good agreement with the analytical results and qualitatively capture the features of ultrastable glasses observed in experiments.

scholarly journals Mean-field model of interacting quasilocalized excitations in glasses

2021 ◽  
Vol 4 (2) ◽  
Author(s):  
Corrado Rainone ◽  
Pierfrancesco Urbani ◽  
Francesco Zamponi ◽  
Edan Lerner ◽  
Eran Bouchbinder
Keyword(s):  
Elastic Medium ◽  
Density Of States ◽  
Field Model ◽  
Mean Field ◽  
Mean Square Displacement ◽  
Decisive Role ◽  
Future Research ◽  
Model Parameters ◽  
Mean Field Model ◽  
Structural Glasses

Structural glasses feature quasilocalized excitations whose frequencies \omegaω follow a universal density of states {D}(\omega)\!\sim\!\omega^4D(ω)∼ω4. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff \kappa_0κ0) in the absence of interactions, interact among themselves through random couplings (characterized by a strength JJ) and with the surrounding elastic medium (an interaction characterized by a constant force hh). We first show that the model gives rise to a gapless density of states {D}(\omega)\!=\!A_{g}\,\omega^4D(ω)=Agω4 for a broad range of model parameters, expressed in terms of the strength of the oscillators’ stabilizing anharmonicity, which plays a decisive role in the model. Then — using scaling theory and numerical simulations — we provide a complete understanding of the non-universal prefactor A_{g}(h,J,\kappa_0)Ag(h,J,κ0), of the oscillators’ interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that A_{g}(h,J,\kappa_0)Ag(h,J,κ0) is a non-monotonic function of JJ for a fixed hh, varying predominantly exponentially with -(\kappa_0 h^{2/3}\!/J^2)−(κ0h2/3/J2) in the weak interactions (small JJ) regime — reminiscent of recent observations in computer glasses — and predominantly decays as a power-law for larger JJ, in a regime where hh plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.

scholarly journals Calculation of the T-P phase diagrams for the halogenomethane compounds (CCl-=SUB=-4-n-=/SUB=-Br-=SUB=-n-=/SUB=-, n=0, 1, 2, 4) using the mean field theory -=SUP=-*-=/SUP=-

2019 ◽  
Vol 61 (2) ◽  
pp. 339
Author(s):  
H. Yurtseven ◽  
S.B. Isik ◽  
E. Kilit Dogan
Keyword(s):  
Phase Diagrams ◽  
Mean Field Theory ◽  
Mean Field ◽  
Face Centered Cubic ◽  
Mean Field Model ◽  
Phase Line ◽  
Component Systems ◽  
Two Component Systems ◽  
The Mean ◽  
Face Centered

AbstractThe T – P phase diagrams of the halogenomethane compounds (CCl_4 – _ n Br_ n , n = 0, 1, 2, 4) are calculated using a mean field model. By expanding the free energy in terms of the order parameters for the transitions of the liquid (L), rhombohedral (R), face-centered cubic (FCC) and monoclinic (M) phases in those compounds, the phase line equations are derived and they are fitted to the experimental data from the literature. This method of calculating the T – P phase diagram is satisfactory to explain the T – P measurements for the halogenomethane compounds and it can also be applied to two-component systems.

Study of electron-phonon coupling and its effect on electrical resistivity in HF systems

2019 ◽  
Vol 33 (04) ◽  
pp. 1950012
Author(s):  
P. C. Baral
Keyword(s):  
Electrical Resistivity ◽  
Mean Field Theory ◽  
Tight Binding ◽  
Harmonic Approximation ◽  
Mean Field ◽  
Graphical Analysis ◽  
Kondo Lattice ◽  
Model Parameters ◽  
Binding Model ◽  
Model Hamiltonian

In this work, we report on theoretical study of the effect of electron-phonon (EP) interaction in THz frequency and temperature dependence of the electrical resistivity in heavy fermion (HF) systems. For this purpose, a model Hamiltonian is considered which consists of the Heisenberg type exchange interaction between localized moments and a tight binding model called the Kondo lattice model (KLM). The effect of EP coupling on electrical resistivity is presented by considering phonon interaction to bare f-electrons, band electrons and to the hybridization between band and f-electrons as a perturbed term. The phonon Hamiltonian in harmonic approximation is also included. The model Hamiltonian is solved by employing the mean-field theory (MFT) along with the Hubbard model of approximation. The temperature- and frequency-dependent electrical resistivity exhibits change in slopes at T[Formula: see text] as well as at T[Formula: see text]. The theoretical findings from the graphical analysis by varying the model parameters g[Formula: see text], g[Formula: see text] and g[Formula: see text] are compared to some of the experimental results in HF systems.

Phase Behavior and Microdomain Structure in Perfluorosulfonated Ionomers via Self-Consistent Mean Field Theory

2002 ◽  
Vol 35 (14) ◽  
pp. 5630-5639 ◽  
Author(s):  
Jeffrey J. Krueger ◽  
Philip P. Simon ◽  
Harry J. Ploehn
Keyword(s):  
Field Theory ◽  
Phase Behavior ◽  
Mean Field Theory ◽  
Mean Field ◽  
Self Consistent ◽  
Microdomain Structure
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