Dynamic structure factor of a dilute polymer solution: Generalized mean field approximation

1981 ◽  
Vol 74 (2) ◽  
pp. 1495-1498 ◽  
Author(s):  
Jane Jane Ou ◽  
John S. Dahler ◽  
Myung S. Jhon
Keyword(s):  
Polymer Solution ◽  
Structure Factor ◽  
Mean Field ◽  
Dynamic Structure ◽  
Field Approximation ◽  
Dynamic Structure Factor ◽  
Dilute Polymer Solution ◽  
Mean Field Approximation ◽  
Generalized Mean

An attempt to handle the nanopatterning of materials created under ion beam mixing

2013 ◽  
Vol 1514 ◽  
pp. 49-58 ◽  
Author(s):  
D. Simeone ◽  
G. Baldinozzi ◽  
D. Gosset ◽  
G. Demange ◽  
Y. Zhang ◽  
...  
Keyword(s):  
Structure Factor ◽  
Ion Beam ◽  
Mean Field ◽  
Grazing Incidence ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
X Ray Diffraction ◽  
Ion Beam Mixing ◽  
Slowing Down ◽  
Nano Patterning

ABSTRACTIn the past fifty years, experimental works based on TEM or grazing incidence X ray diffraction have clearly shown that alloys and ceramics exhibit a nano pattering under irradiation [1,2,3]. Many works were devoted to study the nano patterning induced by ion beam mixing in solids [17,18,19]. Understanding the nano patterning will provide scientific bases to tailor materials with well-defined microstructures at the nanometric scale. The slowing down of impinging particles in solids leads to a complex distribution of subcascades. Each subcascade will give rise to an athermal diffusion of atoms in the medium. In this work, we focused on this point. Based on the well-known Cahn Hilliard Cook (CHC) equation, we analytically calculate the structure factor describing the nano patterning within the mean field approximation. It has shown that this analytical structure factor mimics the structure factor extracted from direct numerical simulations of the time dependent CHC equation. It appears that this structure factor exhibits a universal feature under irradiation.

scholarly journals Generalized mean-field approximation for the Deffuant opinion dynamics model on networks

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
Susan C. Fennell ◽  
Kevin Burke ◽  
Michael Quayle ◽  
James P. Gleeson
Keyword(s):  
Mean Field ◽  
Opinion Dynamics ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Dynamics Model ◽  
Generalized Mean

Dynamic Structure Factor of Diblock Copolymers Solutions in the Disordered State. 3. The Non-Mean-Field Regime

2003 ◽  
Vol 36 (3) ◽  
pp. 830-838 ◽  
Author(s):  
P. Holmqvist ◽  
S. Pispas ◽  
N. Hadjichristidis ◽  
G. Fytas ◽  
R. Sigel
Keyword(s):  
Structure Factor ◽  
Diblock Copolymers ◽  
Mean Field ◽  
Dynamic Structure ◽  
Dynamic Structure Factor ◽  
Mean Field Regime

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

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.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

scholarly journals Single Chain Dynamic Structure Factor of Linear Polymers in an All-Polymer Nano-Composite

2016 ◽  
Vol 49 (6) ◽  
pp. 2354-2364 ◽  
Author(s):  
Arantxa Arbe ◽  
José A. Pomposo ◽  
Isabel Asenjo-Sanz ◽  
Debsindhu Bhowmik ◽  
Oxana Ivanova ◽  
...  
Keyword(s):  
Structure Factor ◽  
Dynamic Structure ◽  
Dynamic Structure Factor ◽  
Linear Polymers ◽  
Single Chain ◽  
Nano Composite ◽  
Chain Dynamic

Geometrical and Transport Properties of Disordered Fibre Networks: Analytical Results

1997 ◽  
Vol 11 (20) ◽  
pp. 867-875 ◽  
Author(s):  
A. A. Rodríaguez ◽  
E. Medina
Keyword(s):  
Probability Distribution ◽  
Transport Properties ◽  
Geometrical Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Fracture Networks ◽  
Simplified Models ◽  
Fibre Density ◽  
Line Network

We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field approximation to conduction, above the percolation threshold, using the derived results. Relevance of the results to fracture networks will be discussed.

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