Topological Theory of Entanglement: A Polymer Chain and a Fixed Barrier. I. Diffusion Equation

1974 ◽  
Vol 37 (5) ◽  
pp. 1413-1422 ◽  
Author(s):  
Kazuyoshi Iwata
Keyword(s):  
Diffusion Equation ◽  
Polymer Chain ◽  
Topological Theory

scholarly journals A non-local diffusion equation arising in terminally attached polymer chains

1990 ◽  
Vol 1 (4) ◽  
pp. 311-326 ◽  
Author(s):  
Xinfu Chen ◽  
Avner Friedman
Keyword(s):  
Field Theory ◽  
Diffusion Equation ◽  
Polymer Chain ◽  
Mean Field Theory ◽  
Mean Field ◽  
Polymer Melt ◽  
Polymer Chains ◽  
Number Density ◽  
Non Local ◽  
Local Diffusion

We consider a polymer melt in a domain Ω whereby each polymer chain is attached at one endpoint to a fixed surface S contained in ∂Ω. Denote by G(x, t;y) the normalized number density of all subchains from x to y of length t. Then, according to the selfconsistent mean field theory, G satisfies, for each y: Gt - Δ2G + σϕG = 0, where σ is a real parameter, and ϕ is a functional of G(·, ·; ·) both non-local and nonlinear. We establish the existence of G and C∞ regularity of ϕ, as a function of x.

scholarly journals THE STEADY STATE CONFIGURATIONAL DISTRIBUTION DIFFUSION EQUATION OF THE STANDARD FENE DUMBBELL POLYMER MODEL: EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR ARBITRARY VELOCITY GRADIENTS

2009 ◽  
Vol 19 (11) ◽  
pp. 2039-2064 ◽  
Author(s):  
IONEL SORIN CIUPERCA ◽  
LIVIU IULIAN PALADE
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Polymer Chain ◽  
Viscoelastic Flows ◽  
Uniqueness Of Solutions ◽  
Outer Flow ◽  
Function Solution ◽  
Velocity Gradients ◽  
Nonlinear Elastic ◽  
Arbitrary Velocity

The configurational distribution function, solution of an evolution (diffusion) equation of the Fokker–Planck–Smoluchowski type, is (at least part of) the corner stone of polymer dynamics: it is the key to calculating the stress tensor components. This can be reckoned from Ref. 1, where a wealth of calculation details is presented regarding various polymer chain models and their ability to accurately predict viscoelastic flows. One of the simplest polymer chain idealization is the Bird and Warner's model of finitely extensible nonlinear elastic (FENE) chains. In this work we offer a proof that the steady state configurational distribution equation has unique solutions irrespective of the (outer) flow velocity gradients (i.e. for both slow and fast flows).

Conformation of Polymer Chain in the Bulk

1976 ◽  
Vol 1 ◽  
pp. 112-121
Author(s):  
J. P. Cotton ◽  
D. Decker ◽  
H. Benoit ◽  
B. Farnoux ◽  
J. Higgins ◽  
...  
Keyword(s):  
Polymer Chain

Undulations of a Straight Polymer Chain Embedded in a Membrane

1996 ◽  
Vol 6 (12) ◽  
pp. 1743-1757
Author(s):  
M. Singh-Zocchi ◽  
M. M. Kozlov ◽  
W. Helfrich
Keyword(s):  
Polymer Chain

PARTIAL HOMOGENIZATION OF THE DIFFUSION EQUATION WITH A DIRAC-LIKE POTENTIAL

2020 ◽  
Vol 18 (5) ◽  
pp. 507-518
Author(s):  
Latifa Ait Mahiout ◽  
Gregory P. Panasenko ◽  
Vitaly Volpert
Keyword(s):  
Diffusion Equation
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