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.

Drifting periodic structures in a degenerate-planar bent-rod nematic liquid crystal beyond the dielectric inversion frequency

We report on the electric-field-generated effects in the nematic phase of a twin mesogen formed of bent-core and calamitic units, aligned homeotropically in the initial ground state and examined beyond the dielectric inversion point. The bend-Freedericksz (BF) state occurring at the primary bifurcation and containing a network of umbilics is metastable; we focus here on the degenerate planar (DP) configuration that establishes itself at the expense of the BF state in the course of an anchoring transition. In the DP regime, normal rolls, broad domains, and chevrons (both defect-mediated and defect-free types) form at various linear defect-sites, in different regions of the frequency-voltage plane. A significant novel aspect common to all these patterned states is the sustained propagative instability, which does not seem explicable on the basis of known driving mechanisms.

Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

Part-whole relations between food webs and the validity of local food-web descriptions

This work analyzes the relationship between large food webs describing potential feeding relations between species and smaller sub-webs thereof describing relations actually realized in local communities of various sizes. Special attention is given to the relationships between patterns of phylogenetic correlations encountered in large webs and sub-webs. Based on the current theory of food-web topology as implemented in the matching model, it is shown that food webs are scale invariant in the following sense: given a large web described by the model, a smaller, randomly sampled sub-web thereof is described by the model as well. A stochastic analysis of model steady states reveals that such a change in scale goes along with a re-normalization of model parameters. Explicit formulae for the renormalized parameters are derived. Thus, the topology of food webs at all scales follows the same patterns, and these can be revealed by data and models referring to the local scale alone. As a by-product of the theory, a fast algorithm is derived which yields sample food webs from the exact steady state of the matching model for a high-dimensional trophic niche space in finite time. (C) 2008 Elsevier B.V. All rights reserved.

The top-down mechanism for body-mass-abundance scaling

Scaling relationships between mean body masses and abundances of species in multitrophic communities continue to be a subject of intense research and debate. The top-down mechanism explored in this paper explains the frequently observed inverse linear relationship between body mass and abundance (i.e., constant biomass) in terms of a balancing of resource biomasses by behaviorally and evolutionarily adapting foragers, and the evolutionary response of resources to this foraging pressure. The mechanism is tested using an allometric, multitrophic community model with a complex food web structure. It is a statistical model describing the evolutionary and population dynamics of tens to hundreds of species in a uniform way. Particularities of the model are the detailed representation of the evolution and interaction of trophic traits to reproduce topological food web patterns, prey switching behavior modeled after experimental observations, and the evolutionary adaptation of attack rates. Model structure and design are discussed. For model states comparable to natural communities, we find that (1) the body-mass-abundance scaling does not depend on the allometric scaling exponent of physiological rates in the form expected from the energetic equivalence rule or other bottom-up theories; (2) the scaling exponent of abundance as a function of body mass is approximately -1, independent of the allometric exponent for physiological rates assumed; (3) removal of top-down control destroys this pattern, and energetic equivalence is recovered. We conclude that the top-down mechanism is active in the model, and that it is a viable alternative to bottom-up mechanisms for controlling body-mass-abundance relations in natural communities.

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.

Estimating trophic link density from quantitative but incomplete diet data

The trophic link density and the stability of food webs are thought to be related, but the nature of this relation is controversial. This article introduces a method for estimating the link density from diet tables which do not cover the complete food web and do not resolve all diet items to species level. A simple formula for the error of this estimate is derived. Link density is determined as a function of a threshold diet fraction below which diet items are ignored (

Food webs: Experts consuming families of experts

Food webs of habitats as diverse as takes or desert valleys are known to exhibit common

Observation of stable phase jump lines in convection of a twisted nematic liquid crystal

We report observations of stable, localized, linelike structures in the spatially periodic pattern formed by nematic electroconvection, along which the phase of the pattern jumps by pi. With increasing electric voltage, these lines form a gridlike structure that goes over into a structure indistinguishable from the well-known grid pattern. We present theoretical arguments that suggest that the twisted cell geometry we are using is indirectly stabilizing the phase jump lines, and that the phase jump lines lattice is caused by an interaction of phase jump lines and a zig-zag instability of the surrounding pattern.

Some properties of the speciation model for food-web structure - Mechanisms for degree distributions and intervality

We present a mathematical analysis of the speciation model for food-web structure, which had in previous work been shown to yield a good description of empirical data of food-web topology. The degree distributions of the network are derived. Properties of the speciation model are compared to those of other models that successfully describe empirical data. It is argued that the speciation model unities the underlying ideas of previous theories. In particular, it offers a mechanistic explanation for the success of the niche model of Williams and Martinez and the frequent observation of intervality in empirical food webs. (c) 2005 Elsevier Ltd. All rights reserved.

Lake restoration in terms of ecological resilience: a numerical study of biomanipulations under bistable conditions

An abstract version of the comprehensive aquatic simulation model (CASM) is found to exhibit bistability under intermediate loading of nutrient input, supporting the alternative-stable-states theory and field observations for shallow lakes. Our simulations of biomanipulations under the bistable conditions reveal that a reduction in the abundance of zooplanktivorous fish cannot switch the system from a turbid to a clear state. Rather, a direct reduction of phytoplankton and detritus was found to be most effective to make this switch in the present model. These results imply that multiple manipulations may be effective for practical restorations of lakes. We discuss the present results of biomanipulations in terms of ecological resilience in multivariable systems or natural systems.

An explanatory model for food-web structure and evolution

Food webs are networks describing who is eating whom in an ecological community. By now it is clear that many aspects of food-web structure are reproducible across diverse habitats, yet little is known about the driving force behind this structure. Evolutionary and population dynamical mechanisms have been considered. We propose a model for the evolutionary dynamics of food-web topology and show that it accurately reproduces observed food-web characteristics in the steady state. It is based on the observation that most consumers are larger than their resource species and the hypothesis that speciation and extinction rates decrease with increasing body mass. Results give strong support to the evolutionary hypothesis. (C) 2005 Elsevier B.V. All rights reserved.

Thin film composite optical waveguides for sensor applications: a review

We review the design and fabrication of thin-film composite optical waveguides (OWG) with high refractive index for sensor applications. A highly sensitive optical sensor device has been developed on the basis of thin-film, composite OWG. The thin-film OWG was deposited onto the surface of a potassium-ion-exchanged (K+) glass OWG by sputtering or spin coating (5-9 mm wide, and with tapers at both ends). By allowing an adiabatic transition of the guided light from the secondary OWG to the thin-film OWG, the electric field of the evanescent wave at the thin film was enhanced. The attenuation of the guided light in the thin film layer was small, and the guided light intensity changed sensitively with the refractive index of the cladding layer. Our experimental results demonstrate that thin-film, composite OWG gas sensors or immunosensors are much more sensitive than sensors based on other technologies. (c) 2004 Elsevier B.V. All rights reserved.

A frequency measure robust to linear filtering

It is noted that the determination of an oscillation frequency by used of the power spectrum of measured time series is susceptible to filtering of the signal. Similarly, frequency measurements made by period counting can yield different, results depending on how the signal is filtered for noise reduction. In an attempt to eliminate these ambiguities, a new measure of frequency, based on an approximate reconstruction of the phase-space trajectory of the oscillator from the signal, is introduced. This measure is shown to be invariant under linear filtering. For this reason, it is also inaccessible by spectral methods. The effect of filtering on frequency for weakly nonlinear, noisy oscillators, to which this definition applies only imperfectly, is quantified. This work provides the theoretical basis for frequency measurements employing MIRVA filtering.