Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.

Water use studies and implications for management of subtropical C4 turfgrasses in dryland and irrigated urban open space

A 2000-03 study to improve irrigation efficiency of grassed urban public areas in northern Australia found it would be difficult to grow most species in dry areas without supplementary watering. Sporoboulus virginicus and sand couch, Zoysia macrantha, were relatively drought-tolerant. Managers of sporting fields, parks and gardens could more than halve their current water use by irrigating over a long cycle, irrigating according to seasonal conditions and using grasses with low water use and sound soil management practices that encourage deep rooting. The use of effluent water provides irrigation and fertiliser cost savings and reduced nitrogen and phosphorus discharge to local waterways. Projected savings are $8000/ha/year in water costs for a typical sporting field.

Characterization of the mitochondrial active-site serine protein LACTB: filaments in the mitochondrial intermembrane space

Mitochondria have evolved from endosymbiotic alpha-proteobacteria. During the endosymbiotic process early eukaryotes dumped the major component of the bacterial cell wall, the peptidoglycan layer. Peptidoglycan is synthesized and maintained by active-site serine enzymes belonging to the penicillin-binding protein and the β-lactamase superfamily. Mammals harbor a protein named LACTB that shares sequence similarity with bacterial penicillin-binding proteins and β-lactamases. Since eukaryotes lack the synthesis machinery for peptidoglycan, the physiological role of LACTB is intriguing. Recently, LACTB has been validated in vivo to be causative for obesity, suggesting that LACTB is implicated in metabolic processes. The aim of this study was to investigate the phylogeny, structure, biochemistry and cell biology of LACTB in order to elucidate its physiological function. Phylogenetic analysis revealed that LACTB has evolved from penicillin binding-proteins present in the bacterial periplasmic space. A structural model of LACTB indicates that LACTB shares characteristic features common to all penicillin-binding proteins and β-lactamases. Recombinat LACTB protein expressed in E. coli was recovered in significant quantities. Biochemical and cell biology studies showed that LACTB is a soluble protein localized in the mitochondrial intermembrane space. Further analysis showed that LACTB preprotein underwent proteolytic processing disclosing an N-terminal tetrapeptide motif also found in a set of cell death-inducing proteins. Electron microscopy structural studies revealed that LACTB can polymerize to form stable filaments with lengths ranging from twenty to several hundred nanometers. These data suggest that LACTB filaments define a distinct microdomain in the intermembrane space. A possible role of LACTB filaments is proposed in the intramitochondrial membrane organization and microcompartmentation. The implications of these findings offer novel insight into the evolution of mitochondria. Further studies of the LACTB function might provide a tool to treat mitochondria-related metabolic diseases.

Meaning of public space and sense of community: The case of new neighbourhoods in the Kathmandu Valley

This paper examines the meaning of public space and sense of community among neighbourhood residents in the changing urban context of the Kathmandu Valley in Nepal. Two new neighbourhoods were selected for the purpose of this study with data collected from interviews with the residents. The study has found that most residents of the new neighbourhoods have an understanding of the significance of public space in community life. However, such understandings are based less on the actual use of public space. The existing public spaces in these neighbourhoods are less successful in offering a meaning to the residents, due to their poor development and the lack of active use. Despite these changes, some residents believe they have developed a sense of community, which is an outcome of other individual factors than the use of public space. It is argued that the role of contemporary neighbourhood public space in fostering a sense of community appears to be less significant in the valley’s present context.

Finite-amplitude love-waves on an isotropic layered half-space

A pair of semi-linear hyperbolic partial differential equations governing the slow variations in amplitude and phase of a quasi-monochromatic finite-amplitude Love-wave on an isotropic layered half-space is derived using the method of multiple-scales. The analysis of the exact solution of these equations for a signalling problem reveals that the amplitude of the wave remains constant along its characteristic and that the phase of the wave increases linearly behind the wave-front.

Dynamic Space Warping Of Strokes For Recognition Of Online Handwritten Characters

This paper suggests a scheme for classifying online handwritten characters, based on dynamic space warping of strokes within the characters. A method for segmenting components into strokes using velocity profiles is proposed. Each stroke is a simple arbitrary shape and is encoded using three attributes. Correspondence between various strokes is established using Dynamic Space Warping. A distance measure which reliably differentiates between two corresponding simple shapes (strokes) has been formulated thus obtaining a perceptual distance measure between any two characters. Tests indicate an accuracy of over 85% on two different datasets of characters.

Searching for common threads in threadfins: phylogeography of Australian polynemids in space and time

Proper management of marine fisheries requires an understanding of the spatial and temporal dynamics of marine populations, which can be obtained from genetic data. While numerous fisheries species have been surveyed for spatial genetic patterns, temporally sampled genetic data is not available for many species. We present a phylogeographic survey of the king threadfin Polydactylus macrochir across its species range in northern Australia and at a temporal scale of 1 and 10 yr. Spatially, the overall AMOVA fixation index was Omega(st) = 0.306 (F-st' = 0.838), p < 0.0001 and isolation by distance was strong and significant (r(2) = 0.45, p < 0.001). Temporally, genetic patterns were stable at a time scale of 10 yr. However, this did not hold true for samples from the eastern Gulf of Carpentaria, where populations showed a greater degree of temporal instability and lacked spatial genetic structure. Temporal but not spatial genetic structure in the Gulf indicates demographic interdependence but also indicates that fishing pressure may be high in this area. Generally, genetic patterns were similar to another co-distributed threadfin species Eleutheronema tetradactylum, which is ecologically similar. However, the historical demography of both species, evaluated herein, differed, with populations of P. macrochir being much younger. The data are consistent with an acute population bottleneck at the last glacio-eustatic low in sea level and indicate that the king threadfin may be sensitive to habitat disturbances.

Continuously equivalent networks in state space

Schoeffler has derived continuously equivalent networks in the nodal-admittance domain. The letter derives a corresponding result in state space that combines the usefulness of Schoeffler's result and the power of the state-variable approach.

A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Dwelling house in a sacred space: reused synagogues in Germany.

Contribution to the Congress " Sacred and Secular Buildings," Washington, May 1999, describing a project of the Institute of Architecture at the Technical University of Braunschweig in cooperation with the Center for Jewish Art in Jerusalem, which has been working on a documentation of synagogues, cemetery chapels, and ritual baths in Germany since 1994.

Samoa’s education policy: Negotiating a hybrid space for values

This paper analyses the education policy of Samoa to examine the values that are presented within as relevant to the education system. Drawing on the theory of postcolonialism and globalization, we illustrate how the global and local interact within the education policy to create a hybrid, heterogeneous mix of values and, while the policy acknowledges the significance of Samoan values, it is principally directed towards universal values being incorporated into the education system. We undertake a critical policy analysis to illustrate how the hybrid set of values are indicative of a neo-colonial discourse and argue that universal values are required, however, these need to be equally matched with local Samoan values for the education policy to be highly relevant, authentic and applicable to the Samoan education context.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

Effective earth and space science analogies

There are several good reasons why Earth and Space Science should be a part of any science curriculum. Nearly everything we do each day is connected in some way to the Earth: to its land, oceans, atmosphere, plants and animals. By 2025, eight billion people will live on Earth. If we are to continue extracting resources to maintain a high quality of life, then it is important that our children are scientifically literate in a way that allows them to exploit the Earth’s resources in a sustainable way. People who understand how earth systems work can make informed decisions and may be able to help resolve issues surrounding clean water, urban planning and development, global climate change and the use and management of natural resources.

Semi-Classical Mechanics in Phase Space: A Study of Wigner's Function

We explore the semi-classical structure of the Wigner functions ($\Psi $(q, p)) representing bound energy eigenstates $|\psi \rangle $ for systems with f degrees of freedom. If the classical motion is integrable, the classical limit of $\Psi $ is a delta function on the f-dimensional torus to which classical trajectories corresponding to ($|\psi \rangle $) are confined in the 2f-dimensional phase space. In the semi-classical limit of ($\Psi $ ($\hslash $) small but not zero) the delta function softens to a peak of order ($\hslash ^{-\frac{2}{3}f}$) and the torus develops fringes of a characteristic 'Airy' form. Away from the torus, $\Psi $ can have semi-classical singularities that are not delta functions; these are discussed (in full detail when f = 1) using Thom's theory of catastrophes. Brief consideration is given to problems raised when ($\Psi $) is calculated in a representation based on operators derived from angle coordinates and their conjugate momenta. When the classical motion is non-integrable, the phase space is not filled with tori and existing semi-classical methods fail. We conjecture that (a) For a given value of non-integrability parameter ($\epsilon $), the system passes through three semi-classical regimes as ($\hslash $) diminishes. (b) For states ($|\psi \rangle $) associated with regions in phase space filled with irregular trajectories, ($\Psi $) will be a random function confined near that region of the 'energy shell' explored by these trajectories (this region has more than f dimensions). (c) For ($\epsilon \neq $0, $\hslash $) blurs the infinitely fine classical path structure, in contrast to the integrable case ($\epsilon $ = 0, where $\hslash $ )imposes oscillatory quantum detail on a smooth classical path structure.