Spiral Defects Research Articles

Control of spiral instabilities in reaction-diffusion systems

Abstract Spiral instabilities and their controls are investigated in a reaction-diffusion system using the Belousov-Zhabotinsky reaction. Two spiral instabilities, the long-wavelength instability and the Doppler instability, are reported, which can lead to spatiotemporal chaos. The long-wavelength instability occurs in an oscillatory regime, while the Doppler instability occurs in an excitable regime. To control these two instabilities, two different strategies are proposed according to their defect-generating mechanisms. For the long-wavelength instability in an oscillatory system, the control can be achieved by introducing a local pacemaker, which emits stable traveling waves to sweep off the unstable spiral defects. For the Doppler instability, the control can be achieved by trapping the spiral tip with a local area of higher diffusion coefficient than its surroundings.

Spatiotemporal chaos control with a target wave in the complex Ginzburg-Landau equation system

An effective method for controlling spiral turbulence in spatially extended systems is realized by introducing a spatially localized inhomogeneity into a two-dimensional system described by the complex Ginzburg-Landau equation. Our numerical simulations show that with the introduction of the inhomogeneity, a target wave can be produced, which will sweep all spiral defects out of the boundary of the system. The effects exist in certain parameter regions where the spiral waves are absolutely unstable. A theoretical explanation is given to reveal the underlying mechanism.

Different embryo-fetal toxicity effects for three VLA-4 antagonists.

VLA-4 (Very late antigen 4, integrin alpha4beta1) plays an important role in cell-cell interactions that are critical for development. Homozygous null knockouts of the alpha4 subunit of VLA-4 or VCAM-1 (cell surface ligand to VLA-4) in mice result in abnormal placental and cardiac development and embryo lethality. Objectives of the current study were to assess and compare the teratogenic potential of three VLA-4 antagonists. IVL745, HMR1031, and IVL984 were each evaluated by the subcutaneous route in standard embryo-fetal developmental toxicity studies in rats and rabbits. IVL984 was also evaluated in mice. Fetuses were examined externally, viscerally, and skeletally. IVL745 did not cause significant maternal or fetal effects at doses up to 100 or 250 mg/kg/day in rats or rabbits, respectively. HMR1031 treatment resulted in marked maternal toxicity and slight fetal toxicity at the highest tested doses of 200 and 75 mg/kg/day in rats and rabbits, respectively. HMR1031 embryo-fetal effects consisted of slightly lower body weight and crown-rump length in rats and minor sternebral defects in rabbits. IVL984 treatment resulted in minimal maternal effects at doses up to 40, 15, and 100 mg/kg/day in rats, rabbits, and mice, respectively (excluding abortions in rabbits). However, marked developmental effects were observed at the lowest tested IVL984 doses, 1, 0.2, and 3 mg/kg/day in rats, rabbits, and mice, respectively. IVL984 embryo-fetal effects consisted of increased total post-implantation loss due to early resorptions and high incidences of cardiac malformations and skeletal malformations and/or variations. Notably, spiral septal defects were observed in up to 76% of rat fetuses and up to 58% of rabbit fetuses. Dramatic differences in teratogenic potential were observed: IVL745 was not teratogenic, HMR1031 caused slight embryo-fetal effects at maternally-toxic doses, and IVL984 was a potent teratogen at doses where direct maternal toxicity was limited to abortions in rabbits. Prominent effects of IVL984 included embryo lethality and cardiac malformations including spiral septal defects in three species.

Nonequilibrium dynamics of the complex Ginzburg-Landau equation: numerical results in two and three dimensions.

This paper is the second of a two-stage exposition, in which we study the nonequilibrium dynamics of the complex Ginzburg-Landau (CGL) equation. We use spiral defects to characterize the system evolution and morphologies. In the first paper of this exposition [S.K. Das, S. Puri, and M.C. Cross, Phys. Rev E 64, 046206 (2001)], we presented analytical results for the correlation function of a single spiral defect, and its short-distance singular behavior. We had also examined the utility of the Gaussian auxiliary field ansatz for characterizing multispiral morphologies. In this paper, we present results from an extensive numerical study of nonequilibrium dynamics in the CGL equation with dimensionality d=2,3. We discuss the behavior of domain growth laws; real-space correlation functions; and momentum-space structure factors. We also compare numerical results for the correlation functions and structure factors with analytical results presented in our first paper.

Nonequilibrium dynamics in the complex Ginzburg-Landau equation

Results from a comprehensive analytical and numerical study of nonequilibrium dynamics in the two-dimensional complex Ginzburg-Landau equation have been presented. In particular, spiral defects have been used to characterize the domain growth law and the evolution morphology. An asymptotic analysis of the single-spiral correlation function shows a sequence of singularities-analogous to those seen for time-dependent Ginzburg-Landau models with O(n) symmetry, where n is even.

Nonequilibrium dynamics of the complex Ginzburg-Landau equation: analytical results.

We present a detailed analytical and numerical study of nonequilibrium dynamics for the complex Ginzburg-Landau equation. In particular, we characterize evolution morphologies using spiral defects. This paper is the first in a two-stage exposition. Here, we present analytical results for the correlation function arising from a single-spiral morphology. We also critically examine the utility of the Gaussian auxiliary field ansatz in characterizing a multispiral morphology. In the next paper of this exposition we will present detailed numerical results.

Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium

The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov dimension density with the average spiral defect density suggests an average dimension per spiral defect varying between 3 and 7. We discuss some implications of these results for experimental studies of excitable media.

Excitation of Spirals and Chiral Symmetry Breaking in Rayleigh-Bénard Convection

Spiral-defect populations in low-Prandtl number Rayleigh-Bénard convection with slow rotation about a vertical axis were measured in carbon dioxide at high pressure. The results indicate that spirals act like "thermally excited" defects and that the winding direction of a spiral is analogous to a magnetic spin. Rotation about a vertical axis, the spiral analog of the magnetic field, breaks the zero-rotation chiral symmetry between clockwise and counterclockwise spiral defects. Many properties of spiral-defect statistics are well described by an effective statistical-mechanical model.

Defect Dynamics for Spiral Chaos in Rayleigh-Bénard Convection

A theory of the novel spiral chaos state recently observed in Rayleigh-Benard convection is proposed in terms of the importance of invasive defects i.e defects that through their intrinsic dynamics expand to take over the system. The motion of the spiral defects is shown to be dominated by wave vector frustration, rather than a rotational motion driven by a vertical vorticity field. This leads to a continuum of spiral frequencies, and a spiral may rotate in either sense depending on the wave vector of its local environment. Results of extensive numerical work on equations modelling the convection system provide some confirmation of these ideas.

Spiral defects in motility assays: A measure of motor protein force.

In a commonly used motility assay, cytoskeletal filaments are observed as they glide over a surface coated with motor proteins. Defects in the motion frequently interrupt the flow of filaments. Examination of one such defect, in which a filament adopts a spiral form and rotates about a fixed point, provides a simple measure of the force exerted by the motor proteins. We demonstrate the universality of this approach by estimating the elementary forces of both myosin and kinesin.

Convection for Prandtl numbers near 1: Dynamics of textured patterns.

Rayleigh-Benard convection in a cylindrical geometry with radius-to-height ratio {Gamma}=40 was studied with the shadowgraph imaging method. The working fluid was CO{sub 2} at 32 bars and at temperatures near 34 {degree}C, with a Prandtl number {sigma}=0.98. The onset pattern of largely straight, parallel rolls went through successive qualitative changes as {epsilon}{equivalent_to}{Delta}{ital T}/{Delta}{ital T}{sub {ital c}}{minus}1 was increased. Quantitative measurements of wave numbers, of spatially averaged roll curvature, and of sidewall roll orientation as functions of {epsilon} are presented. As {epsilon} was increased, pattern dynamics induced by the skewed-varicose instability were first observed at {epsilon}{approx}0.09, and roll-nucleating sidewall foci were seen for {epsilon}{approx_gt}0.15. Spiral defects appeared intermittently at {epsilon}{approx}0.55. The number of spirals fluctuated with time, but the average number increased with {epsilon} until, at {epsilon}{approx}0.8, spirals were present at all times. Coincident with the increase in spiral-defect activity was a decrease in the average wave number, a marked increase in the sidewall-foci roll-nucleation frequency and average roll curvature, and a distinct shape change in the structure factor {ital S}({ital k}). The oscillatory instability was observed at {epsilon}{approx}3.0, in agreement with the stability analysis for straight rolls.

Behavior of focus patterns in low Prandtl number convection.

We present experimental results on the dynamics of concentric roll and textured patterns in a convecting fluid of Prandtl number about 1 and with radius-to-height ratio near 40 and for \ensuremath{\epsilon}==\ensuremath{\Delta}T/\ensuremath{\Delta}${\mathit{T}}_{\mathit{c}}$-1\ensuremath{\le}0.8. At \ensuremath{\epsilon}=0.21, the concentric-roll state was lost by the pattern center moving to the wall while nucleating new rolls which traveled outward. The textured pattern contained sidewall foci which also emitted traveling waves. The average frequency of the emission increased linearly with \ensuremath{\epsilon}, but then increased rapidly by about 40% at \ensuremath{\epsilon}\ensuremath{\approxeq}0.65 where spiral defects appeared.

Dynamics of spiral waves in a spatially inhomogeneous Hopf bifurcation.

We study numerically the behavior of some topological spiral defects, their dynamics being governed by a complex Ginzburg-Landau equation with space-dependent coefficients. We show that the interaction between a spiral and the gradients of the coefficients can counterbalance the repulsion between defects of identical sign and lead to topologically stable patterns. Configurations of several defects with the same topological charge have been observed recently in nonlinear optics experiments.

Analytical description of a state dominated by spiral defects in two-dimensional extended systems

We study the state of a diluted gas of spiral defects observed in a recent simulation of a two-dimensional extended system governed by the Ginzburg-Landau equation with complex coefficients. We show that this state, which is responsible for the disorganization of the system, can be described by an approximate solution in which the new variables are the positions of the spirals and a new global phase. The dynamics of these new variables and the conditions for the existence of the state are determined.

Bursting of line pipe with long external corrosion

Application of AGA NG-18 or CSA-A245.1 recommendations for the evaluation of external corrosion on line pipe appear more conservative for long defects and long spiral defects than for shorter defects. To investigate the burst behaviour of pipe with long defects, a finite element model was developed and the predictions compared with burst tests. The model was used to investigate the effect of the geometry and spiral angle of single long corrosion grooves. Assuming a power hardening material, equations are proposed to predict the reduction in burst pressure of line pipe with long external corrosion defects.

Interaction of defects in two-dimensional systems.

We derive equations of motion for a diluted gas of spiral defects in the two-dimensional complex Ginzburg-Landau equation. The interaction of two defects is treated and our predictions agree with a recent numerical experiment.

Defect Mechanisms in a Noncrystalline Solid

It is proposed that spiral defects originate at torque stress fields in glass and represent variations in localized bond energy. By postulating shear stress couples across flaw lines, extension and annihilation of flaws from neighboring spiral sources were tentatively explained. Distortion or movement within a spiral was indicated on samples subjected to localized stress before etching. Experimentally it was shown that substitution of lead and bismuth for silica in a nonspiral glass produced a rigid, brittle network which ultimately disclosed spirals originating at minute nuclei. Details of structure were quantitatively studied by using the dynamic spherical indenter. Flaw loops were also discovered which originated at random etch pit sources and increased in diameter with applied stress. Rows of etch pits were observed on samples stressed in torque. The conjecture was introduced that the torsion stress caused collapse of flaws into point defect rows. The etch pit rows appeared to be more stable than linear flaws. The minimum length of stability of a void derived from dislocation theory was in agreement with experimental measurements from the point defect rows.

Spiral Dislocations on Glass Fracture Surfaces

Within a certain range of composition spiral defects were observed on etched soda-lime-silica glasses. The patterns described spirals of Archimedes and appeared to originate from interstitial defects in the glass. Mutual stress influence effects were observed. The hypothesis of an existing torque field around the interstitial defects was useful in explaining the spiral mechanism. Application of mechanical torque stresses produced the spiral effect. In some cases it appeared feasible to apply stress energy relationships developed from dislocation theories to these minute flaw patterns. A dynamic spherical indenter technique was developed to study structural variations in these glasses. The lengths of flaws produced by a rolling indenter were found to be sensitive to changes in the silica content of the glasses and less affected by variations in the soda-lime ratio. The effects of heating and crystallization were also studied.