Pattern forming instability induced by light in pure and dye-doped nematic liquid crystals

We study theoretically the instabilities induced by a linearly polarized ordinary light wave incident at a small oblique angle on a thin layer of homeotropically oriented nematic liquid crystal with special emphasis on the dye-doped case. The spatially periodic Hopf bifurcation that occurs as the secondary instability after the stationary Freedericksz transition is analyzed.Comment: 8 pages, 7 figures, LaTeX, accepted to Phys. Rev.

Pattern formation of reaction-diffusion system having self-determined flow in the amoeboid organism of Physarum plasmodium

The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pattern in the plasmodium, a reaction-diffusion system having self-determined flow arises. Such a coupling of reaction-diffusion-advection is a characteristic of the biological system, and is expected to relate with control mechanism of amoeboid behaviours. Hence, we have studied effects of the self-determined flow on pattern formation of simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial solution, the envelope dynamics follows the complex Ginzburg-Landau type equation just after bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the equation through the critical wave number squared. Contrary to this, wave number isn't explicitly effective with lack of flow or constant flow. Thus, spatial size of pattern is especially important for regulating pattern formation in the plasmodium. On the other hand, the flow term is negligible in the vicinity of bifurcation at infinitely small wave number, and therefore the pattern formation by simple reaction-diffusion will also hold. A physiological role of pattern formation as above is discussed.Comment: REVTeX, one column, 7 pages, no figur

Self-organized stable pacemakers near the onset of birhythmicity

General amplitude equations for reaction-diffusion systems near to the soft onset of birhythmicity described by a supercritical pitchfork-Hopf bifurcation are derived. Using these equations and applying singular perturbation theory, we show that stable autonomous pacemakers represent a generic kind of spatiotemporal patterns in such systems. This is verified by numerical simulations, which also show the existence of breathing and swinging pacemaker solutions. The drift of self-organized pacemakers in media with spatial parameter gradients is analytically and numerically investigated.Comment: 4 pages, 4 figure

Phase Dynamics of Nearly Stationary Patterns in Activator-Inhibitor Systems

The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The derivation applies to the bistable, excitable, and the Turing unstable regimes. In the bistable case stability thresholds are obtained for the Eckhaus and the zigzag instabilities and for the transition to traveling waves. Neutral stability curves demonstrate the destabilization of stationary planar patterns at low wavenumbers to zigzag and traveling modes. Numerical solutions of the model system support the theoretical findings

Patterning instability on the Mars polar ice caps

We present a mathematical theory to study the origin of large-scale spiral troughs on the Mars residual polar caps, starting with the hypothesis that atmospheric circulation governs the planform of the troughs via an instability that operates in the flow direction of surface winds. This concept can explain why the troughs spiral at each pole in an opposite sense to that expected for Coriolis-deflected winds. The instability arises from interactions on water ice, assumed to contain dust, and depends on how the exchange of atmospheric dust and moisture (H2O) with the polar cap surface controls its albedo and mass and energy balance. Our model predicts spatial patterns to form when moisture is carried by wind over the surface, owing to unstable coupling between the albedo and the H2O-vapor pressure. The resulting albedo pattern causes an alternating "accumulation-ablation'' mass balance, so that an undulating topography develops which resembles the (dark) troughs and their adjacent (bright) smooth terrains on the polar caps. Because the albedo patterning process is fast, whereas topographic evolution is slow, we suggest that an ancient imprint in the surface albedo preconditions today's trough morphology

Inferring the palaeobiology of palorchestid marsupials through analysis of mammalian humeral and femoral shape

The relationship between ecology and morphology of the limbs in living placental mammals is well established and has been used to infer aspects of palaeobiology for many extinct species. However, few studies have applied these principles to extinct marsupials. Palorchestids are a poorly understood extinct family of megafaunal marsupials of particular interest due to their highly robust and unusual limb morphology. Using a comparative sample of humeri and femora from living mammals potentially analogous to palorchestids, we applied three-dimensional geometric morphometric techniques in a phylogenetic comparative framework. We established that humerus and femur shape in living species showed significant associations with size, phylogeny, and substrate use, and found a weak association between humeral shape and diet. We then examined patterns in morphological disparity, modularity, covariance and morphospace occupation in palorchestids relative to comparative living mammals as well as their closest extinct marsupial relatives. We found palorchestid femora to be unremarkable in shape, while their overall and proximal humeral morphology were strongly divergent from all other mammals sampled. Over their evolutionary history, palorchestid distal humeri increasingly resembled those of mammals adapted for tearing and hook-and-pull digging, while other analyses showed various arboreal-like and fossorial-like affinities in humeral shape. Our findings indicate strong asymmetric selection acting on the fore- and hindlimbs in palorchestids, and their unique combination of shape traits suggests they used their forelimbs in a specialised manner that has no direct equivalence either with their extinct relatives or among other mammals alive today.</p