Dynamics of a strongly driven two-component Bose-Einstein condensate

We consider a two-component Bose-Einstein condensate in two spatially localized modes of a double-well potential, with periodic modulation of the tunnel coupling between the two modes. We treat the driven quantum field using a two-mode expansion and define the quantum dynamics in terms of the Floquet Operator for the time periodic Hamiltonian of the system. It has been shown that the corresponding semiclassical mean-field dynamics can exhibit regions of regular and chaotic motion. We show here that the quantum dynamics can exhibit dynamical tunneling between regions of regular motion, centered on fixed points (resonances) of the semiclassical dynamics.

Breeding dynamics of koalas in open woodlands

The spatial and breeding dynamics of koalas in sub-tropical woodlands at Blair Athol in central Queensland were intensively monitored between 1993 and 1998. Genetic relationships among koalas at this locality were studied to determine the breeding dynamics of males, including whether 'resident' or 'transient' males dominate as sires. Males and females were radio-collared and tracked periodically throughout each year of the study. Genotypes from hypervariable microsatellite loci identified uniquely all individuals and were used to analyse parentage as well as to determine population genetic parameters when compared with other regional localities. Koalas at Blair Athol comprise a population in genetic equilibrium. Gene diversity estimates show the population to be similar to other populations found in similar habitat in the region, and estimates of genetic differentiation among four regional populations showed that gene flow conforms to a model of isolation by distance. Analysis of parentage found that both resident and transient males sired about equal numbers of offspring. Familial DNA analysis revealed multiple paternities of successive young in this population. The conclusion from this study is that 'resident' status among males does not confer any advantage for parentage.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Nutrient dynamics in Queensland savannas: Implications for the sustainability of land clearing for pasture production

Eucalyptus savannas on low nutrient soils are being extensively cleared in Queensland. In this paper we provide background information relevant to understanding nutrient (particularly nitrogen) dynamics in sub/tropical savanna, and review the available evidence relevant to understanding the potential impact of clearing Eucalyptus savanna on nutrient relations. The limited evidence presently available can be used to argue for the extreme positions that: (i) woody vegetation competes with grasses Cor resources. and tree/shrub clearing improves pasture production, (ii) woody vegetation benefits pasture production. At present, the lack of fundamental knowledge about Australian savanna nutrient relations makes accurate predictions about medium- and long-term effects of clearing on nutrient relations in low nutrient savannas difficult. The future of cleared savannas will differ if herbaceous species maintain all functions that woody vegetation has previously held, or if woody species have functions distinct from those of herbaceous vegetation. Research suggests that savanna soils are susceptible to nitrate leaching, and that trees improve the nutrient status of savanna soils in some situations. The nitrogen capital of cleared savanna is at risk if mobile ions are not captured efficiently by the vegetation. and nitrogen input via N-2 fixation from vegetation and microbiotic crusts is reduced. In order to predict clearing effects on savanna nutrient relations, research should be directed to answering (i) how open or closed nutrient cycles are in natural and cleared savanna, (ii) which functions are performed by savanna constituents such as woody and herbaceous vegetation, native and exotic plant species. termites, and microbiotic 7 crusts in relation to nutrient cycles. In the absence of detailed knowledge about savanna functioning, clearing carries the risk of promoting continuous nutrient depiction.

The politics of reintegrating Australian Aboriginal and American Indian indigenous knowledge into resource management: The dynamics of resource appropriation and cultural revival

As the United States and Australia struggle with contemporary crises over competing uses of rapidly depleting natural resources, there are striking parallels between American Indian and Australian Aboriginal communities demanding a place at the management table and offering culturally based understandings of and solutions for the ecosystems at risk. These efforts to integrate indigenous knowledge into mainstream natural resource management are part of larger legal and political debates over land tenure, the locus of control, indigenous self-governance, and holistic ecosystems management.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Probing the time course of nonlinear discriminations during human electrodermal conditioning

Animal-based theories of Pavlovian conditioning propose that patterning discriminations are solved using unique cues or immediate configuring. Recent studies with humans, however, provided evidence that in positive and negative patterning two different rules are utilized. The present experiment was designed to provide further support for this proposal by tracking the time course of the allocation of cognitive resources. One group was trained in a positive patterning; schedule (A-, B-, AB+) and a second in a negative patterning schedule (A+, B+, AB-). Electrodermal responses and secondary task probe reaction time were measured. In negative patterning, reaction times were slower during reinforced stimuli than during non-reinforced stimuli at both probe positions while there were no differences in positive patterning. These results support the assumption that negative patterning is solved using a rule that is more complex and requires more resources than does the rule employed to solve positive patterning. (C) 2001 Elsevier Science (USA).

Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Tillering in grain sorghum over a wide range of population densities: Modelling dynamics of tiller fertility

The prediction of tillering is poor or absent in existing sorghum crop models even though fertile tillers contribute significantly to grain yield. The objective of this study was to identify general quantitative relationships underpinning tiller dynamics of sorghum for a broad range of assimilate availabilities. Emergence, phenology, leaf area development and fertility of individual main calms and tillers were quantified weekly in plants grown at one of four plant densities ranging from two to 16 plants m(-2). On any given day, a tiller was considered potentially fertile (a posteriori) if its number of leaves continued to increase thereafter. The dynamics of potentially fertile tiller number per plant varied greatly with plant density, but could generally be described by three determinants, stable across plant densities: tiller emergence rate aligned with leaf ligule appearance rate; cessation of tiller emergence occurred at a stable leaf area index; and rate of decrease in potentially fertile tillers was linearly related to the ratio of realized to potential leaf area growth. Realized leaf area growth is the measured increase in leaf area, whereas potential leaf area growth is the estimated increase in leaf area if all potentially fertile tillers were to continue to develop. Procedures to predict this ratio, by estimating realized leaf area per plant from intercepted radiation and potential leaf area per plant from the number and type of developing axes, are presented. While it is suitable for modelling tiller dynamics in grain sorghum, this general framework needs to be validated by testing it in different environments and for other cultivars. (C) 2002 Annals of Botany Company.

A partial velocity approach to subcycling structural dynamics

Subcycling, or the use of different timesteps at different nodes, can be an effective way of improving the computational efficiency of explicit transient dynamic structural solutions. The method that has been most widely adopted uses a nodal partition. extending the central difference method, in which small timestep updates are performed interpolating on the displacement at neighbouring large timestep nodes. This approach leads to narrow bands of unstable timesteps or statistical stability. It also can be in error due to lack of momentum conservation on the timestep interface. The author has previously proposed energy conserving algorithms that avoid the first problem of statistical stability. However, these sacrifice accuracy to achieve stability. An approach to conserve momentum on an element interface by adding partial velocities is considered here. Applied to extend the central difference method. this approach is simple. and has accuracy advantages. The method can be programmed by summing impulses of internal forces, evaluated using local element timesteps, in order to predict a velocity change at a node. However, it is still only statistically stable, so an adaptive timestep size is needed to monitor accuracy and to be adjusted if necessary. By replacing the central difference method with the explicit generalized alpha method. it is possible to gain stability by dissipating the high frequency response that leads to stability problems. However. coding the algorithm is less elegant, as the response depends on previous partial accelerations. Extension to implicit integration, is shown to be impractical due to the neglect of remote effects of internal forces acting across a timestep interface. (C) 2002 Elsevier Science B.V. All rights reserved.