Analysis of shear-induced and extensional-induced associating polymer assemblies: Brownian dynamics simulation.

In order to examine the difference between shear-induced and extensional-induced associating polymer assemblies at the molecular level, Brownian dynamics simulations with the bead-spring model were carried out for model DNA molecules with sticky spots. The radial distribution of molecules overestimates from that in the absence of flow and increases with increasing Weissenberg number in extensional flow, but slightly underestimates without regard to shear rate in shear flow. The fractional extension progresses more rapidly in extensional flow than in shear flow and the distribution of fractional extension at the formation time has a relatively sharper peak and narrower spectrum in extensional flow than in shear flow. In shear flow, the inducement of the assembly mainly results from the progress of the probability distribution of fractional extension. However, in extensional flow, the assembly is induced by both the progress of the probability distribution and increasing the values of the radial distribution.

The mechanism of the self-assembly of associating DNA molecules under shear flow: Brownian dynamics simulation.

A shear flow induces the assembly of DNAs with the sticky spots. In order to strictly interpret the mechanism of shear-induced DNA assembly, Brownian dynamics simulations with the bead-spring model were carried out for these molecules at various ranges of the Weissenberg numbers (We). We calculate a formation time and analyze the radial distribution function of end beads and the probability distribution of fractional extension at the formation time to understand the mechanism of shear-induced assembly. At low Weissenberg number the formation time, which is defined as an elapsed time until a multimer forms for the first time, decreases rapidly, reaching a plateau at We = 1000. A shear flow changes the radial distribution of end beads, which is almost the same regardless of the Weissenberg number. A shear flow deforms and stretches the molecules and generates different distributions between end beads with a stickly spot. The fractional extension progresses rapidly in shear flow from a Gaussian-like distribution to a uniform distribution. The progress of the distribution of fractional extension increases the possibility of meeting of end beads. In shear flow, the inducement of the assembly mainly results from the progress of the probability distribution of fractional extension. We also calculate properties such as the radius of gyration, stretch, and so on. As the Weissenberg number increases, the radius of gyration at the formation time also increases rapidly, reaching a plateau at We = 1000.

Depinning transition of a pattern forming system in a washboard potential.

We investigate numerically the depinning transition of the Kuramoto-Sivashinsky equation in a washboard potential in one dimension, and find three distinct behaviors. For a certain range of parameters, the transition is well described by the mean field exponent of 1/2. The next case is that the critical behavior is dominated by the growth of spatially periodic mode with critical exponent 1. Finally, a parameter range exists in which intermittent movement is observed. "Anchor," which is a spontaneously generated coherent structure, acts as a pinning center. The destruction of anchor is shown to involve a topological change of "unknotting."

Spiral waves in a coupled network of sine-circle maps.

A coupled two-dimensional lattice of sine-circle maps is investigated numerically as a simple model for coupled network of nonlinear oscillators under a spatially uniform, temporally periodic, external forcing. Various patterns, including quasiperiodic spiral waves, periodic, banded spiral waves in several different polygonal shapes, and domain patterns, are observed. The banded spiral waves and domain patterns match well with the results of earlier experimental studies. Several transitions are analyzed. Among others, the source-sink transition of a quasiperiodic spiral wave and the cascade of "side-doubling" bifurcations of polygonal spiral waves are of great interest.

Parametrically forced surface wave with a nonmonotonic dispersion relation.

Surface wave patterns that arise in a mechanically driven ferrofluid system under constant magnetic field are investigated (1) to find out what kind of spatial patterns emerge when the system acquires a nonmonotonic dispersion relation and (2) to compare its surface wave patterns with those produced in the magnetically driven system studied earlier. As the strength of the applied magnetic field increases, the initial subharmonic square lattice formed by the Faraday instability first transforms to rolls, then becomes a rhomboid lattice. The rolls and the rhomboid lattice are found to coexist for a finite range of parameter space forming patterns with mixed domains. Possible underlying mechanisms for the observed rhomboid lattice is discussed. None of the diverse superlattices observed in the magnetically driven ferrofluid system appears in the mechanically driven system studied here.

Subharmonic bifurcations of standing wave lattices in a driven ferrofluid system.

Superlattice standing waves arising on the surface of ferrofluids that are driven by an ac magnetic field are investigated experimentally. Several different types are obtained through successive spatial period doublings, which are mediated by resonant mode interactions. The observed superlattices are quite diverse, depending on the relevant base Fourier modes, the orientation and the number of emerged subharmonic modes, and the phase difference among the involved modes all together. On the other hand, their temporal evolutions are all either period-1 (harmonic) or period-2 (subharmonic).

Unusual spiral wave tip trajectories in a parametrically forced nonequilibrium system.

The effect of parametric modulations on spiral waves that form in a thin layer of liquid crystal under rotating magnetic field is studied in laboratory experiments and numerical simulations. Parametric forcings that are sinusoidal in time make a simply rotating spiral tip to meander, rendering a compound tip trajectory that is composed of a main circular orbit and a satellite orbit with an unusual crescent shape. No evidence of frequency locking is found. The underlying mechanism for the unusual shape of the satellite orbit is elucidated, and the dependence of the rotation frequency of the main circular orbit f(o) on the perturbation parameters are discussed.

Harmonic forcing of an extended oscillatory system: homogeneous and periodic solutions.

In this paper we study the effect of external harmonic forcing on a one-dimensional oscillatory system described by the complex Ginzburg-Landau equation (CGLE). For a sufficiently large forcing amplitude, a homogeneous state with no spatial structure is observed. The state becomes unstable to a spatially periodic "stripe" state via a supercritical bifurcation as the forcing amplitude decreases. An approximate phase equation is derived, and an analytic solution for the stripe state is obtained, through which the asymmetric behavior of the stability border of the state is explained. The phase equation, in particular the analytic solution, is found to be very useful in understanding the stability borders of the homogeneous and stripe states of the forced CGLE.