Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

Sampling phylogenetic tree space with the generalized Gibbs sampler

The generalized Gibbs sampler (GGS) is a recently developed Markov chain Monte Carlo (MCMC) technique that enables Gibbs-like sampling of state spaces that lack a convenient representation in terms of a fixed coordinate system. This paper describes a new sampler, called the tree sampler, which uses the GGS to sample from a state space consisting of phylogenetic trees. The tree sampler is useful for a wide range of phylogenetic applications, including Bayesian, maximum likelihood, and maximum parsimony methods. A fast new algorithm to search for a maximum parsimony phylogeny is presented, using the tree sampler in the context of simulated annealing. The mathematics underlying the algorithm is explained and its time complexity is analyzed. The method is tested on two large data sets consisting of 123 sequences and 500 sequences, respectively. The new algorithm is shown to compare very favorably in terms of speed and accuracy to the program DNAPARS from the PHYLIP package.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

Isotopes, wool, and rangeland monitoring: Let the sheep do the sampling

Stable carbon isotope analyses of wool staples provided insight into the vegetation consumed by sheep at a temporal resolution not previously studied. Contemporary Australian and historic South African samples dating back to 1916 were analyzed for their stable carbon isotope ratio, a proxy for the proportion of C-3 and C-4 plant species consumed by animals. Sheep sample vegetation continuously throughout a year, and as their wool grows it integrates and stores information about their diet. In subtropical and tropical rangelands the majority of grass species are C-4. Since sheep prefer to graze, and their wool is an isotopic record of their diet, we now have the potential to develop a high resolution index to the availability of grass from a sheep's perspective. Isotopic analyses of wool suggest a new direction for monitoring grazing and for the reconstruction of past vegetation changes, which will make a significant contribution to traditional rangeland ecology and management. It is recommended that isotopic and other analyses of wool be further developed for use in rangeland monitoring programs to provide valuable feedback for land managers.

Experimentally tracking unstable steady states by large periodic modulation

Experimental suppression of chaos has been achieved in an optically pumped far-infrared (NH3)-N-15 laser which displays Lorenz-like chaos. The method of control involves the application of a large amplitude slow (i.e., nonresonant) modulation of the pump power. This may be related to a delayed bifurcation to chaos observed when the pump power is ramped at a constant late.

Bacteria in shrimp pond sediments: their role in mineralizing nutrients and some suggested sampling strategies

Strategies for sampling sediment bacteria were examined in intensive shrimp, Penaeus monodon (Fabricius), ponds in tropical Australia. Stratified sampling of bacteria at the end of the production season showed that the pond centre, containing flocculated sludge, had significantly higher bacterial counts (15.5 X 10(9) g(-1) dw) than the pond periphery (8.1 X 10(9) g(-1) dw), where the action of aerators had swept the pond floor. The variation in bacterial counts between these two zones within a pond was higher than that between sites within each zone or between ponds. Therefore, sampling effort should be focused within these zones: for example, sampling two ponds at six locations within each of the two zones resulted in a coefficient of variation of approximate to 5%. Bacterial numbers in the sediment were highly correlated with sediment grain size, probably because eroded soil particles and organic waste both accumulated in the centre of the pond. Despite high inputs of organic matter added to the ponds, principally as pelleted feeds, the mean bacterial numbers and nutrient concentrations (i.e. organic carbon, nitrogen and phosphorus) in the sediment were similar to those found in mangrove sediments. This suggests that bacteria are rapidly remineralizing particulates into soluble compounds. Bacterial numbers were highly correlated with organic carbon and total kjeldahl nitrogen in the sediment, suggesting that these were limiting factors to bacterial growth.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

Periodic orbit resonances in layered metals in tilted magnetic fields

The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field that is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur when the frequency is a harmonic of the frequency at which the magnetic field causes the electrons to oscillate on the Fermi surface within the layers. The intensity of the different harmonic resonances varies significantly with the direction of the field. The resonances occur for both coherent and weakly incoherent interlayer transport and so their observation does not imply the existence of a three-dimensional Fermi surface. [S0163-1829(99)51240-X].

Semiochemicals and social signaling in the wild European rabbit in Australia: II. Variations in chemical composition of chin gland secretion across sampling sites

The volatile components of the chin gland secretion of the wild European rabbit, Oryctolagus cuniculus (L.), were investigated with the use of gas chromatography. Studies of the chemical nature of this secretion by previous workers demonstrated that it was important in the maintenance of social structure in this species. This study identified 34 different volatile components that consist primarily of aromatic and aliphatic hydrocarbons. Especially common are a series of alkyl-substituted benzene derivatives that provide most of the compound diversity in the secretion. Samples of chin gland secretion collected from animals at three different geographical locations, separated by more than 100 km, showed significant differences in composition. This work suggests that variation among populations needs to be considered when undertaking semiochemical research. Alternate nonparametric methods are also used for the analysis of chromatographic data.

Periodic electric field enhanced transport through membranes

We examine the mean flux across a homogeneous membrane of a charged tracer subject to an alternating, symmetric voltage waveform. The analysis is based on the Nernst-Planck flux equation, with electric field subject to time dependence only. For low frequency electric fields the quasi steady-state flux can be approximated using the Goldman model, which has exact analytical solutions for tracer concentration and flux. No such closed form solutions can be found for arbitrary frequencies, however we find approximations for high frequency. An approximation formula for the average flux at all frequencies is also obtained from the two limiting approximations. Numerical integration of the governing equation is accomplished by use of the numerical method of lines and is performed for four different voltage waveforms. For the different voltage profiles, comparisons are made with the approximate analytical solutions which demonstrates their applicability. (c) 2005 Elsevier B.V. All rights reserved.

A continuum model for periodic two-dimensional block structures

A continuum model for regular block structures is derived by replacing the difference quotients of the discrete equations by corresponding differential quotients. The homogenization procedure leads to an anisotropic Cosserat Continuum. For elastic block interactions the dispersion relations of the discrete and the continuous models are derived and compared. Yield criteria for block tilting and sliding are formulated. An extension of the theory for large deformation is proposed. (C) 1997 by John Wiley & Sons, Ltd.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.