On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

Piggery pond sludge as a nitrogen source for crops. 1. Mineral N supply estimated from laboratory incubations and field application of stockpiled and wet sludge

Piggery pond sludge (PPS) was applied, as-collected (Wet PPS) and following stockpiling for 12 months ( Stockpiled PPS), to a sandy Sodosol and clay Vertosol at sites on the Darling Downs of Queensland. Laboratory measures of N availability were carried out on unamended and PPS-amended soils to investigate their value in estimating supplementary N needs of crops in Australia's northern grains region. Cumulative net N mineralised from the long-term ( 30 weeks) leached aerobic incubation was described by a first-order single exponential model. The mineralisation rate constant (0.057/week) was not significantly different between Control and PPS treatments or across soil types, when the amounts of initial mineral N applied in PPS treatments were excluded. Potentially mineralisable N (N-o) was significantly increased by the application of Wet PPS, and increased with increasing rate of application. Application of Wet PPS significantly increased the total amount of inorganic N leached compared with the Control treatments. Mineral N applied in Wet PPS contributed as much to the total mineral N status of the soil as did that which mineralised over time from organic N. Rates of CO2 evolution during 30 weeks of aerobic leached incubation indicated that the Stockpiled PPS was more stabilised (19-28% of applied organic C mineralised) than the Wet PPS (35-58% of applied organic C mineralised), due to higher lignin content in the former. Net nitrate-N produced following 12 weeks of aerobic non-leached incubation was highly correlated with net nitrate-N leached during 12 weeks of aerobic incubation (R-2 = 0.96), although it was

Simulation of glassy state relaxations in polymers: A static analysis of methyl group and methoxy group rotation in poly(vinyl methyl ether)

We show that the simple quasi-static technique, also called the adiabatic mapping technique, can be used to determine the energetics of rotation of methyl and methoxy groups in amorphous poly(vinyl methyl ether) even though the latter process is too slow to be amenable to direct molecular dynamics simulation. For the methyl group rotation, we find that the mean and standard deviation of the simulated rotational barrier heights agree well with experimental data from quasi-elastic neutron scattering. In the case of the methoxy groups we find that just 4% of the groups contribute more than 90% of the observed dielectric relaxation strength. The groups which make the most contribution are those which, by virtue of their particular conformation and local environment, have two alternative positions of similar energy.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Model for growth hormone receptor activation based on subunit rotation within a receptor dimer

Growth hormone is believed to activate the growth hormone receptor (GHR) by dimerizing two identical receptor subunits, leading to activation of JAK2 kinase associated with the cytoplasmic domain. However, we have reported previously that dimerization alone is insufficient to activate full-length GHR. By comparing the crystal structure of the liganded and unliganded human GHR extracellular domain, we show here that there is no substantial change in its conformation on ligand binding. However, the receptor can be activated by rotation without ligand by inserting a defined number of alanine residues within the transmembrane domain. Fluorescence resonance energy transfer ( FRET), bioluminescence resonance energy transfer (BRET) and coimmunoprecipitation studies suggest that receptor subunits undergo specific transmembrane interactions independent of hormone binding. We propose an activation mechanism involving a relative rotation of subunits within a dimeric receptor as a result of asymmetric placement of the receptor-binding sites on the ligand.

Energy profiles for ketene cyclizations. interconversion of 1,3-oxazin-6-ones, mesoionic 1,3-oxazinium olates and acylketenes, imidoylketenes, oxoketenimines, and cyclization products

The energy surface connecting oxazinium olates 9, several possible conformers of ketenes 10 and 11, and the final cyclization products 12, 13 and 14, as well as the isomeric 1,3-oxazine-6-ones 15, ring opening of the latter to N-acylimidoylketenes 16, and subsequent rearrangement of 16 to oxoketenimines 17, azetinones 18, and the cyclization products 19 and 20 are evaluated computationally at the B3LYP/6-31G* and B3LYP/6-311+G*//B3LYP/6-31G* levels. The cyclizations of ketenes to oxazinium olates 9 and oxazines 15 have the characteristics of pseudopericyclic reactions. Plots of the energy vs internal reaction coordinate for the cyclization of transoid acylketenes such as 10 to 9 (via TS1) and 16 to 15 (via TS7) feature two inflection points and indicate that the part of the energy surface above the lower inflection points describe internal rotation of the acyl function in the ketene moiety, and the part below this point describes the cyclization of the cisoid ketene to the planar mesoionic oxazinium olate 9 or oxazinone 15. The 1,3-shifts of the OR group that interconvert ketenes 16 and ketenimines 17 via four-membered cyclic transition states TS8 behave similarly, the first portion (from the ketenimine side) of the activation barrier being due largely to internal rotation of substituents, and the top part being due to the 1,3-shift proper.

Determination of crystal orientation from micrographs using a MATLAB program

Crys.m is a MATLAB routine that combines a micrograph of a crystal with a scaleable, rotatable three-dimensional cage structure to determine the orientation of the crystal axes. The example presented here uses the morphology of tetragonal lysozyme. Rotation of the cage until it aligns with the crystal in the image yields the orientation of the c axis of the crystal relative to the image normal. This analysis can be used for quantitative determination of crystal orientation effects induced by electric, magnetic and/or gravitational fields.

Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

A numerical method is introduced to determine the nuclear magnetic resonance frequency of a donor (P-31) doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus. In this study, based on the wave functions obtained by the effective-mass theory, we introduce an empirical correction factor to the wave functions at the donor nucleus. Using the corrected wave functions, we formulate a first-order perturbation theory for the perturbed system under the influence of an electric field. In order to calculate the potential distributions inside the silicon and the silicon dioxide layers due to the applied electric field, we use the multilayered Green's functions and solve an integral equation by the moment method. This enables us to consider more realistic, arbitrary shape, and three-dimensional qubit structures. With the calculation of the potential distributions, we have investigated the effects of the thicknesses of silicon and silicon dioxide layers, the relative position of the donor, and the applied electric field on the nuclear magnetic resonance frequency of the donor.

A Constant Torque Micro-Viscometer

We present a technique to measure the viscosity of microscopic volumes of liquid using rotating optical tweezers. The technique can be used when only microlitre (or less) sample volumes are available, for example biological or medical samples, or to make local measurements in complicated micro-structures such as cells. The rotation of the optical tweezers is achieved using the polarisation of the trapping light to rotate a trapped birefringent spherical crystal, called vaterite. Transfer of angular momentum from a circularly polarised beam to the particle causes the rotation. The transmitted light can then be analysed to determine the applied torque to the particle and its rotation rate. The applied torque is determined from the change in the circular polarisation of the beam caused by the vaterite and the rotation rate is used to find the viscous drag on the rotating spherical particle. The viscosity of the surrounding liquid can then be determined. Using this technique we measured the viscosity of liquids at room temperature, which agree well with tabulated values. We also study the local heating effects due to absorption of the trapping laser beam. We report heating of 50-70 K/W in the region of liquid surrounding the particle.

Structure repair of a compacted vertisol with wet-dry cycles and crops

We hypothesized that the four rotation crops: wheat (Triticum aestivum L.), sorghum [Sorghum bicolor (L.) Merr.], lablab [Lablab purpureus (L.) Sweet] and mung bean [ Vigna radiata (L.) R. Wilczek] differ in their ability to repair soil structure. The study was conducted on a Typic Haplustert, Queensland, Australia, locally termed a Black Earth and considered a prime cropping soil. Large (0.5-m depth by 0.3-m diam.) soil cores, collected from compacted wheel furrows in an irrigated cotton (Gossypium hirsutum L.) field, were subjected to three, six, or nine wet-dry cycles that simulated local flood irrigation practices. After each cycle, soil profiles were sampled for clod bulk density, image analysis of soil structure, and evapotranspiration. Generally, all crops improved soil structure over the initial field condition but lablab and mung bean gave improvements to greater depths and more rapidly than wheat and sorghum. Mung bean and lablab caused up to a threefold increase in clod porosity in the 0.1- to 0.4-m soil layer after only three wet-dry cycles, whereas sorghum required nine wet-dry cycles to increase clod porosity in only the 0.2- to 0.3-m layer, and wheat gave no improvement even after nine wet-dry cycles. Image analysis of soil structure showed that lablab and mung bean rapidly (by three wet-dry cycles) produced smaller peds with more interconnected pore space than wheat and sorghum. By nine wet-dry cycles, sorghum achieved deep cracking of the soil but the material between the cracks remained large and dense. Evapotranspiration was double under lablab and mung bean compared with wheat and sorghum. Our results indicate greater cycles of wetting and drying under lablab and mung bean than wheat and sorghum that have led to rapid repair of soil compaction.