The Spatial-Temporal Lamellar Structures in the Confined Ideal Polymer Blends

Krasnyuk, I. B.; Taranets, Roman M.

doi:10.1007/s10955-011-0378-5

Cited by 4 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…τ τ = = . Now, instead of diffusion Equation (19) and Equation 20, we consider the diffusion equations with delay arguments: O τ can be written as:…”

Section: Nonactive Absorption Centers (On Frequency ω ) Are Not Accommentioning

confidence: 99%

“…α is an absorption coefficient, β is an emission coefficient; n D and I D are diffusion coefficient. Such approach previously applied to the study of binary alloys on the example of Kahn-Hilliard equation with delay argument to applications to binary mixtures [13]- [16] and to binary polymer blends [17]- [19]. Such problem describes by hyperbolic equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Impulse Spatial-Temporal Domains in Semiconductor Laser with Feedback

Krasnyuk¹

2016

JAMP

Self Cite

View full text Add to dashboard Cite

An initial value boundary problem for system of diffusion equations with delay arguments and dynamic nonlinear boundary conditions is considered. The problem describes evolution of the carrier density and the radiation density in the semiconductor laser or laser diodes with "memory" and with feedback. It is shown that the boundary problem can be reduced to a system of difference equations with continuous time. For large times, solutions of these equations tend to piecewise constant asymptotic periodic wave functions which represent chain of shock waves with finite or infinite points of discontinuities on a period. Applications to the optical systems with linear media and nonlinear surface optical properties with feedback have been done. The results are compared with the experiment.

show abstract

“…τ τ = = . Now, instead of diffusion Equation (19) and Equation 20, we consider the diffusion equations with delay arguments: O τ can be written as:…”

Section: Nonactive Absorption Centers (On Frequency ω ) Are Not Accommentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Impulse Spatial-Temporal Domains in Semiconductor Laser with Feedback

Krasnyuk¹

2016

JAMP

Self Cite

View full text Add to dashboard Cite

show abstract

“…An asymptotic behaviour of the corresponding solutions was studied in Refs. [16,31,15,18] when the maps F 0 , G 0 are hyperbolic and structurally stable.…”

Section: Examplementioning

confidence: 99%

“…For structures of turbulent type, a set of corresponding points Γ is uncountable and there is a homeomorphism φ which transforms the set Γ to the well-known Cantor set K by the rule Γ • φ = φ • K (see, Refs. [16][17][18]). In Ref.…”

Section: Introductionmentioning

confidence: 99%

The surface-induced spatial–temporal structures in confined binary alloys

Krasnyuk

Taranets

Chugunova

2014

Physica A: Statistical Mechanics and its Applications

Self Cite

View full text Add to dashboard Cite

Spatial-Temporal Oscillations of the Order Parameter in Confined Diblock Copolymer Mixtures

Krasnyuk

2013

Int. J. Comp. Mat. Sci. Eng.

View full text Add to dashboard Cite

The mathematical model describing the evolution of the order parameter in confined polymer melts is under consideration. The corresponding equation is derived from a special energy functional introduced by Fredrickson and Binder to describe the behavior of polymer chains in block copolymer melts. This equation is modified to take into account the "memory" of correlated blends. The resulting hyperbolic partial differential equation is of order six in space variable. The Puri–Binder dynamical boundary conditions with "feedback" describe processes of cyclic surface crystallization and melting. Two types of polymer mixtures (ideal and non-ideal) are studied. In the case of the ideal mixture, the attractor of the boundary problem consists of asymptotically periodic piecewise constant functions with finite or infinite number of discontinuities per period (spatial-temporal structures of relaxation or turbulent type). In the non-ideal case, the attractor contains quasi-periodic functions or it is so-called strange chaotic or strange non-chaotic. The bifurcation diagram is constructed.

show abstract

The Spatial-Temporal Lamellar Structures in the Confined Ideal Polymer Blends

Cited by 4 publications

References 29 publications

Impulse Spatial-Temporal Domains in Semiconductor Laser with Feedback

Impulse Spatial-Temporal Domains in Semiconductor Laser with Feedback

The surface-induced spatial–temporal structures in confined binary alloys

Spatial-Temporal Oscillations of the Order Parameter in Confined Diblock Copolymer Mixtures

Contact Info

Product

Resources

About