Local exponential divergence plot and optimal embedding of a chaotic time-series

we propose here a local exponential divergence plot which is capable of providing a new means of characterizing chaotic time series. The suggested plot defines a time dependent exponent LAMBDA and a ''plus'' exponent LAMBDA+ which serves as a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent.

Inhomogeneous behavior of antiplane shear crack in softening material with local unloading

Examined in this work is the anti-plane stress and strain near a crack in a material that softens beyond the elastic peak and unloads on a linear path through the initial state. The discontinuity in the constitutive relation is carried into the analysis such that one portion of the local solution is elliptic in character and the other hyperbolic. Material elements in one region may cross over to another as the loading is increased. Local unloading can thus prevail. Presented are the inhomogeneous character of the asymptotic stress and strain in the elliptic and hyperbolic region, in addition to the region in which the material elements had experienced unloading. No one single stress or strain coefficient would be adequate for describing crack instability.

The motion and the core structure of a geostrophic vortex - one-time scale inner solution and the motion of the vortex

By means of the matched asymptotic expansion method with one-time scale analysis we have shown that the inviscid geostrophic vortex solution represents our leading solution away from the vortex. Near the vortex there is a viscous core structure, with the length scale O(a). In the core the viscous stresses (or turbulent stresses) are important, the variations of the velocity and the equivalent height are finite and dependent of time. It also has been shown that the leading inner solutions of the core structure are the same for two different time scales of S/(ghoo)1/2 and S/a (ghoo)1/2. Within the accuracy of O(a) the velocity of a geostrophic vortex center is equal to the velocity of the local background flow, where the vortex is located, in the absence of the vortex. Some numerical examples demonstrate the contributions of these results.

Theory of local mode excitation in polyatomics by frequency-modulated lasers

that the Stokes-interaction relation is reasonable qualitatively but not correct

Magnetostatic relations including fluctuation fields - the local expansion

Using the approach of local expansion, we analyze the magnetostatic relations in the case of conventional turbulence. The turbulent relations are obtained consisten tly for themomentum equation and induction equation of both the average and fluctuation relations.In comparison with the magnetostatic relations as discussed usually, turbulent fluctuationfields produce forces, one of which 1/(4π)(α1×B0)×B0 may have parallel and perpendicular components in the direction of magnetic field, the other of which 1/(4π)K×B0 is introduced by the boundary value of turbulence and is perpendicular to the magnetic field. In the case of 2-dimensional configuration of magnetic field, the basic equation will be reduced into a second-order elliptic equation, which includes some linear and nonlinear terms introduced by turbulent fluctuation fields. Turbulent fields may change the configuration of magnetic field and even shear it non-uniformly. The study on the influence of turbulent fields is significant since they are observed in many astrophysical environments.

The influence of fluctuation fields on the force-free field .2. The local expansion

In Paper I (Hu, 1982), we discussed the the influence of fluctuation fields on the force-free field for the case of conventional turbulence and demonstrated the general relationships. In the present paper, by using the approach of local expansion, the equation of average force-free field is obtained as (1+b)×B 0=(#x002B;a)B 0#x002B;a (1)×B 0#x002B;K. The average coefficientsa,a (1),b, andK show the influence of the fluctuation fields in small scale on the configurations of magnetic field in large scale. As the average magnetic field is no longer parallel to the average electric current, the average configurations of force-free fields are more general and complex than the usual ones. From the view point of physics, the energy and momentum of the turbulent structures should have influence on the equilibrium of the average fields. Several examples are discussed, and they show the basic features of the fluctuation fields and the influence of fluctuation fields on the average configurations of magnetic fields. The astrophysical environments are often in the turbulent state, the results of the present paper may be applied to the turbulent plasma where the magnetic field is strong.

Activation of violaxanthin cycle in darkness is a common response to different abiotic stresses : a case study in Pelvetia canaliculata

Background: In the violaxanthin (V) cycle, V is de-epoxidized to zeaxanthin (Z) when strong light or light combined with other stressors lead to an overexcitation of photosystems. However, plants can also suffer stress in darkness and recent reports have shown that dehydration triggers V-de-epoxidation in the absence of light. In this study, we used the highly stress-tolerant brown alga Pelvetia canaliculata as a model organism, due to its lack of lutein and its non-photochemical quenching independent of the transthylakoidal-ΔpH, to study the triggering of the V-cycle in darkness induced by abiotic stressors. Results: We have shown that besides desiccation, other factors such as immersion, anoxia and high temperature also induced V-de-epoxidation in darkness. This process was reversible once the treatments had ceased (with the exception of heat, which caused lethal damage). Irrespective of the stressor applied, the resulting de-epoxidised xanthophylls correlated with a decrease in Fv/Fm, suggesting a common function in the down-regulation of photosynthetical efficiency. The implication of the redox-state of the plastoquinone-pool and of the differential activity of V-cycle enzymes on V-de-epoxidation in darkness was also examined. Current results suggest that both violaxanthin de-epoxidase (VDE) and zeaxanthin-epoxidase (ZE) have a basal constitutive activity even in darkness, being ZE inhibited under stress. This inhibition leads to Z accumulation. Conclusion: This study demonstrates that V-cycle activity is triggered by several abiotic stressors even when they occur in an absolute absence of light, leading to a decrease in Fv/Fm. This finding provides new insights into an understanding of the regulation mechanism of the V-cycle and of its ecophysiological roles.