Electroconvection in a homeotropic bent-rod nematic liquid crystal beyond the dielectric inversion frequency

We characterize the structural transitions in an initially homeotropic bent-rod nematic liquid crystal excited by ac fields of frequency f well above the dielectric inversion point f(i). From the measured principal dielectric constants and electrical conductivities of the compound, the Carr-Helfrich conduction regime is anticipated to extend into the sub-megahertz region. Periodic patterned states occur through secondary bifurcations from the Freedericksz distorted state. An anchoring transition between the bend Freedericksz (1317) and degenerate planar (DP) states is detected. The BF state is metastable well above the Freedericksz threshold and gives way to the DP state, which persists in the field-off condition for several hours. Numerous +1 and -1 umbilics form at the onset of BF distortion, the former being largely of the chiral type. They survive in the DP configuration as linear defects, nonsingular in the core. In the BF regime, not far from fi, periodic Williams-like domains form around the umbilics; they drift along the director easy axis right from their onset. With increasing f, the wave vector of the periodic domains switches from parallel to normal disposition with respect to the c vector. Well above fi, a broadband instability is found.

Stability and dynamical behavior in a lake-model and implications for regime shifts in real lakes

A modified abstract version of the Comprehensive Aquatic Simulation Model (CASM) is found to exhibit three types of folded bifurcations due to nutrient loading. The resulting bifurcation diagrams account for nonlinear dynamics such as regime shifts and cyclic changes between clear-water state and turbid state that have actually been observed in real lakes. In particular, pulse-perturbation simulations based on the model presented suggest that temporal behaviors of real lakes after biomanipulations can be explained by pulse-dynamics in complex ecosystems, and that not only the amplitude (manipulated abundance of organisms) but also the phase (timing) is important for restoring lakes by biomanipulation. Ecosystem management in terms of possible irreversible changes in ecosystems induced by regime shifts is also discussed. (c) 2007 Elsevier B.V All rights reserved.

Standing wave oscillations in an electrocatalytic reaction

Experimental standing wave oscillations of the interfacial potential across an electrode have been observed in the electrocatalytic oxidation of formic acid on a Pt ring working electrode. The instantaneous potential distribution was monitored by means of equispaced potential microprobes along the electrode. The oscillatory standing waves spontaneously arose from a homogeneous stationary state prior to a Hopf bifurcation if the reference electrode was placed close to the working electrode. Reduced electrolyte concentrations resulted in aperiodic potential patterns, while the presence of a sufficiently large ohmic resistance completely suppressed spatial inhomogeneities. The experimental findings confirm numerical predictions of a reaction-migration formalism: under the chosen geometry, a long-range negative potential coupling between distant points across the ring electrode can lead to oscillatory potential domains of distinct phase. It is further shown that the occurrence of oscillatory standing waves can be rationalized as the electrochemical equivalent of Turing's second bifurcation (wave bifurcation). In the presence of an external resistance, the coupling becomes positive throughout and leads to spatial synchronization.

A review of topographic controls on moraine distribution

Ice-marginal moraines are often used to reconstruct the dimensions of former ice masses, which are then used as proxies for palaeoclimate. This approach relies on the assumption that the distribution of moraines in the modern landscape is an accurate reflection of former ice margin positions during climatically controlled periods of ice margin stability. However, the validity of this assumption is open to question, as a number of additional, nonclimatic factors are known to influence moraine distribution. This review considers the role played by topography in this process, with specific focus on moraine formation, preservation, and ease of identification (topoclimatic controls are not considered). Published literature indicates that the importance of topography in regulating moraine distribution varies spatially, temporally, and as a function of the ice mass type responsible for moraine deposition. In particular, in the case of ice sheets and ice caps ( > 1000 km2), one potentially important topographic control on where in a landscape moraines are deposited is erosional feedback, whereby subglacial erosion causes ice masses to become less extensive over successive glacial cycles. For the marine-terminating outlets of such ice masses, fjord geometry also exerts a strong control on where moraines are deposited, promoting their deposition in proximity to valley narrowings, bends, bifurcations, where basins are shallow, and/or in the vicinity of topographic bumps. Moraines formed at the margins of ice sheets and ice caps are likely to be large and readily identifiable in the modern landscape. In the case of icefields and valley glaciers (10–1000 km2), erosional feedback may well play some role in regulating where moraines are deposited, but other factors, including variations in accumulation area topography and the propensity for moraines to form at topographic pinning points, are also likely to be important. This is particularly relevant where land-terminating glaciers extend into piedmont zones (unconfined plains, adjacent to mountain ranges) where large and readily identifiable moraines can be deposited. In the case of cirque glaciers (< 10 km2), erosional feedback is less important, but factors such as topographic controls on the accumulation of redistributed snow and ice and the availability of surface debris, regulate glacier dimensions and thereby determine where moraines are deposited. In such cases, moraines are likely to be small and particularly susceptible to post-depositional modification, sometimes making them difficult to identify in the modern landscape. Based on this review, we suggest that, despite often being difficult to identify, quantify, and mitigate, topographic controls on moraine distribution should be explicitly considered when reconstructing the dimensions of palaeoglaciers and that moraines should be judiciously chosen before being used as indirect proxies for palaeoclimate (i.e., palaeoclimatic inferences should only be drawn from moraines when topographic controls on moraine distribution are considered insignificant).

Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.

The Reliability of the Arc-Length Method in the Analysis of Mode-Jumping Problems

The Arc-Length Method is a solution procedure that enables a generic non-linear problem to pass limit points. Some examples are provided of mode-jumping problems solutions using a commercial nite element package, and other investigations are carried out on a simple structure of which the numerical solution can be compared with an analytical one. It is shown that Arc-Length Method is not reliable when bifurcations are present in the primary equilibrium path; also the presence of very sharp snap-backs or special boundary conditions may cause convergence diÆculty at limit points. An improvement to the predictor used in the incremental procedure is suggested, together with a reliable criteria for selecting either solution of the quadratic arc-length constraint. The gap that is sometimes observed between the experimantal load level of mode-jumping and its arc-length prediction is explained through an example.