Fold analysis of crumpled sheets using microcomputed tomography.

Hand-crumpled paper balls involve intricate structure with a network of creases and vertices, yet show simple scaling properties, which suggests self-similarity of the structure. We investigate the internal structure of crumpled papers by the microcomputed tomography (micro-CT) without destroying or unfolding them. From the reconstructed three-dimensional (3D) data, we examine several power laws for the crumpled square sheets of paper of the sizes L=50-300 mm and obtain the mass fractal dimension D_{M}=2.7±0.1 by the relation between the mass and the radius of gyration of the balls and the fractal dimension 2.5≲d_{f}≲2.8 for the internal structure of each crumpled paper ball by the box counting method in the real space and the structure factors in the Fourier space. The data for the paper sheets are consistent with D_{M}=d_{f}, suggesting that the self-similarity in the structure of each crumpled ball gives rise to the similarity among the balls with different sizes. We also examine the cellophane sheets and the aluminium foils of the size L=200 mm and obtain 2.6≲d_{f}≲2.8 for both of them. The micro-CT also allows us to reconstruct 3D structure of a line drawn on the crumpled sheets of paper. The Hurst exponent for the root-mean-square displacement along the line is estimated as H≈0.9 for the length scale shorter than the scale of the radius of gyration, beyond which the line structure becomes more random with H∼0.5.

Different Synchrony in Rhythmic Movement Caused by Morphological Difference between Five- and Six-armed Brittle Stars.

Physiological experiments and mathematical models have supported that neuronal activity is crucial for coordinating rhythmic movements in animals. On the other hand, robotics studies have suggested the importance of physical properties made by body structure, i.e. morphology. However, it remains unclear how morphology affects movement coordination in animals, independent of neuronal activity. To begin to understand this issue, our study reports a rhythmic movement in the green brittle star Ophiarachna incrassata. We found this animal moved five radially symmetric parts in a well-ordered unsynchronized pattern. We built a phenomenological model where internal fluid flows between the five body parts to explain the coordinated pattern without considering neuronal activity. Changing the number of the body parts from five to six, we simulated a synchronized pattern, which was demonstrated also by an individual with six symmetric parts. Our model suggests a different number in morphology makes a different fluid flow, leading to a different synchronization pattern in the animal.

Compressive response and helix formation of a semiflexible polymer confined in a nanochannel.

Configurations of a single semiflexible polymer is studied when it is pushed into a nanochannel in the case where the polymer persistence length l_{p} is much longer than the channel diameter D:l_{p}/D≫1. Using numerical simulations, we show that the polymer undergoes a sequence of recurring structural transitions upon longitudinal compression: random deflection along the channel, a helix going around the channel wall, double-fold random deflection, double-fold helix, etc. We find that the helix transition can be understood as buckling of deflection segments, and the initial helix formation takes place at very small compression with no appreciable weak compression regime of the random deflection polymer.

Pattern formation in phase separating binary mixtures.

We experimentally investigate the interplay of thermodynamics with hydrodynamics during phase separation of (quasi-) binary mixtures. Well defined patterns emerge while slowly crossing the cloud point curve. Depending on the material parameters of the experimental system, two distinct scenarios are observed. In quasi-binary mixtures of methanol-hexane patterns appear before macroscopic phase separation sets in. In course of time the patterns turn faint while the overall turbidity of the sample increases until the mixtures become completely turbid. We attribute this pattern formation to a latent heat induced instability resembling a Rayleigh-Bénard instability. This is confirmed by calorimetric data and an estimate of its Rayleigh number. Mixtures of C(4)E(1)-water doped with decane phase separate under heating. After passing the cloud point curve these mixtures first become homogenously turbid. While clearing up, pattern formation is observed. We attribute this type of pattern formation to an interfacial tension induced Bénard-Marangoni instability. The occurrence of the two scenarios is supported by the relevant dimensionless numbers.

Asymmetric oscillations during phase separation under continuous cooling: A simple model.

We investigate the phase separation of binary mixtures under continuous cooling using the Cahn-Hilliard equation including the effect of gravity. In our simple model, sedimentation is accounted for by instantaneously "removing" droplets from the supersaturated mixture into the coexisting phase once the droplets have reached a defined maximum size. Our model predicts an oscillatory variation of turbidity. Depending on the composition, either both phases oscillate (symmetric oscillations) or only one of the phases oscillates (asymmetric oscillations). In the asymmetric case, droplet sedimentation from the majority phase into the minority phase reduces supersaturation in the minority phase. This inhibits droplet formation in the minority phase. The cooling rate dependence of the period agrees with experimental results.

The Gray-Scott model under the influence of noise: reentrant spatiotemporal intermittency in a reaction-diffusion system.

We investigate the influence of noise on the spatiotemporal behavior of the Gray-Scott model, a prototype for a simple reaction-diffusion system. In the parameter regime studied it is characterized deterministically by a stable fixed point. As the noise increases a regular periodic pattern is replaced first by an irregularly oscillating periodic pattern and then by spatiotemporal intermittency. With further increasing noise strength the spatiotemporal intermittency is first replaced by a low amplitude noisy regime followed by spatiotemporal intermittency (STI) embedded into a noisy background. At sufficiently high noise intensity high amplitude noise prevails. We point out that the transition from spatiotemporal intermittency to low amplitude noise can be traced back to the fact that the spatially homogeneous state is a global attractor. As the noise strength grows further the "noisy" fixed point starts to communicate with STI leading to noise-induced spatiotemporal intermittency as an excitable state. At high enough noise strength high amplitude noise is left over wiping out all details of the underlying deterministic dynamical system.

Coexistence of stable particle and hole solutions for fixed parameter values in a simple reaction diffusion system.

We present a simple autocatalytic reaction-diffusion model for two variables, which shows for fixed parameter values the simultaneous stable coexistence of particle solutions as well of two types of hole solutions. The associated spatially homogeneous system is characterized by the coexistence of one stable fixed point and a stable limit cycle solution. We compare our results to other dissipative systems which have for fixed parameters either stable particle or stable hole solutions including the quintic complex Ginzburg-Landau equation and the envelope equation for optical bistability as well as other reaction-diffusion models.

External noise imposed on the reaction-diffusion system CO+O2-->CO2 on Ir(111) surfaces: experiment and theory.

We study experimentally and theoretically the influence of noise on the fractions of CO and oxygen in the constant gas flow directed at an Ir(111) surface during CO oxidation. Depending on the noise strength and the fraction Y of CO we observe in the deterministically bistable region a large variety of different types of behavior. These include bistable behavior for small noise intensities, transitions from the upper to the lower branch of the bistable loop and vice versa, island nucleation and growth and noise-induced switching. Near the boundary of the bistable region and in the presence of noise the transition between the two branches takes place via very slow domain wall motion with time scales of the order of 10(4)-10(5) s. The experiments were carried out in an UHV system for which the mass flow could be controlled very precisely. The modeling was using the reaction-diffusion system underlying the reaction studied for which all the kinetic coefficients are known rather precisely. Our numerical analysis was performed for one and two spatial dimensions showing qualitatively similar behavior. The comparison between the experimental results and the modeling shows semiquantitative to quantitative agreement.

Analytical approach to localized structures in a simple reaction-diffusion system.

We study from an analytical point of view a simple reaction-diffusion model, which admits stable oscillating localized structures as a consequence of the coexistence between a stable limit cycle and a stable fixed point. Using a generalized matching approach we are able to find approximate analytical expressions for localized oscillating structures in this reaction-diffusion model capturing all the essential ingredients of these breathing particlelike solutions.

Self-replication of a pulse in excitable reaction-diffusion systems.

We investigate self-replication of a pulse in Bonhoffer-van der Pol type reaction-diffusion systems in one dimension. The interface dynamics of front and back of a pulse developed for a bistable system is extended to a monostable case, which is useful to clarify the mechanism of the self-replication. We shall show that the threshold parameter for excitability plays the central role for self-replication. The present theory can be applied not only to a symmetric pulse, but also to a propagating asymmetric pulse.