arXiv subjects

C. B. Muratov

Publications and source records attributed to C. B. Muratov.

23 records · Page 2Linked to original sources

arXiv1996

Instabilities and disorder of the domain patterns in the systems with competing interactions

The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at certain temperatures the ordered hexagonal pattern becomes unstable with respect to the two types of instabilities: the radially-nonsymmetric distortions of the domains and the repumping of the order parameter between the neighbors. Both these instabilities may lead to the transformation of the regular hexagonal pattern into a disordered pattern.

cond-mat↗

arXiv1996

Synchronization, chaos, and breakdown of collective domain oscillations in reaction-diffusion systems

The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary $d$-dimensional reaction-diffusion system of the activator-inhibitor type are asymptotically derived. It is shown that not far from the instability leading to the formation of the pulsating multidomain pattern the oscillations of different domains synchronize. In one dimension standing and traveling waves of the oscillation phase are realized. In addition to these, in two dimensions target and spiral waves of the oscillation phase, as well as spatio-temporal chaos of domain oscillations, are feasible. Further inside the unstable region the collective oscillations break down, so the pulsating multidomain pattern transforms into an irregular pulsating pattern, the uniform self-oscillations, or turbulence. The parameter regions where these effects occur are analyzed. The effects of the pattern's disorder are also studied. The conclusions of the analysis are supported by the numerical simulations of a concrete model. The obtained results explain the dynamics of Turing patterns observed in the experiments on chlorite-iodide-malonic acid reaction.

patt-sol↗

arXiv1996

Scenarios of domain pattern formation in a reaction-diffusion system

We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as a result of Turing instability. In the stable homogeneous system with the fast inhibitor one can excite both localized and extended patterns by applying a localized stimulus. Depending on the parameters and the excitation level of the system stripes, spots, wriggled stripes, or labyrinthine patterns form. The labyrinthine patterns may be both connected and disconnected. In the the stable homogeneous system with the slow inhibitor one can excite self-replicating spots, breathing patterns, autowaves and turbulence. The parameter regions in which different types of patterns are realized are explained on the basis of the asymptotic theory of instabilities for patterns with sharp interfaces developed by us in Phys. Rev. E. 53, 3101 (1996). The dynamics of the patterns observed in our simulations is very similar to that of the patterns forming in the ferrocyanide-iodate-sulfite reaction.

patt-sol↗

arXiv1996

Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor

An asymptotic equation of motion for the pattern interface in the domain-forming reaction-diffusion systems is derived. The free boundary problem is reduced to the universal equation of non-local contour dynamics in two dimensions in the parameter region where a pattern is not far from the points of the transverse instabilities of its walls. The contour dynamics is studied numerically for the reaction-diffusion system of the FitzHugh-Nagumo type. It is shown that in the asymptotic limit the transverse instability of the localized domains leads to their splitting and formation of the multidomain pattern rather than fingering and formation of the labyrinthine pattern.

patt-sol↗

arXiv1996

General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems

An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is carried out. It is shown that in the considered class of systems the criteria for different types of instabilities are universal. The specific nonlinearities enter the criteria only via three numerical constants of order one. The performed analysis explains the self-organization scenarios observed in the recent experiments and numerical simulations of some concrete reaction-diffusion systems.

patt-sol↗