Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Evaluating business process compliance management frameworks

This research contributes a formal framework to evaluate whether existing CMFs can model and reason about various types of normative requirements. The framework can be used to determine the level of coverage of concepts provided by CMFs, establish mappings between CMF languages and the semantics for the normative concepts and evaluate the suitability of a CMF for issuing a certification of compliance. The developed framework is independent of any specific formalism and it has been formally defined and validated through the examples of such mappings of CMFs.

Evolution of cooperation by reciprocation within structured demes

The iterative two-person Prisoners’ Dilemma game has been generalised to theN-person case. The evolution of cooperation is explored by matching the Tit For Tat (TFT) strategy (Axelrod and Hamilton 1981) against the selfish strategy. Extension of TFT toN-person situations yields a graded set of strategies from the softest TFT, which continues cooperation even if only one of the opponents reciprocates it, to the hardest, which would do so only when all the remaining opponents cooperate. The hardest TFT can go to fixation against the selfish strategy provided it crosses a threshold frequencypc. All the other TFT are invadable by the selfish (D) or the pure defector strategy, while none can invadeD. Yet, provided a thresholdpc is crossed, they can coexist stably withD. AsN, the size of the group increases, the threshold pc also increases, indicating that the evolution of cooperation is more difficult for larger groups. Under certain conditions, only the soft TFT can coexist stably against the selfish strategyD, while the harder ones cannot. An interesting possibility of a complete takeover of the selfish population by successive invasions by harder and harder TFT strategies is also presented.

Depression and its assessment among stroke patients and their caregivers

Approximately one-third of stroke patients experience depression. Stroke also has a profound effect on the lives of caregivers of stroke survivors. However, depression in this latter population has received little attention. In this study the objectives were to determine which factors are associated with and can be used to predict depression at different points in time after stroke; to compare different depression assessment methods among stroke patients; and to determine the prevalence, course and associated factors of depression among the caregivers of stroke patients. A total of 100 consecutive hospital-admitted patients no older than 70 years of age were followed for 18 months after having their first ischaemic stroke. Depression was assessed according to the Diagnostic and Statistical Manual of Mental Disorders (DSM-III-R), Beck Depression Inventory (BDI), Hamilton Rating Scale (HRSD), Visual Analogue Mood Scale (VAMS), Clinical Global Impression (CGI) and caregiver ratings. Neurological assessments and a comprehensive neuropsychological test battery were performed. Depression in caregivers was assessed by BDI. Depressive symptoms had early onsets in most cases. Mild depressive symptoms were often persistent with little change during the 18-month follow-up, although there was an increase in major depression over the same time interval. Stroke severity was associated with depression especially from 6 to 12 months post-stroke. At the acute phase, older patients were at higher risk of depression, and a higher proportion of men were depressed at 18 months post-stroke. Of the various depression assessment methods, none stood clearly apart from the others. The feasibility of each did not differ greatly, but prevalence rates differed widely according to the different criteria. When compared against DSM-III-R criteria, sensitivity and specificity were acceptable for the CGI, BDI, and HRSD. The CGI and BDI had better sensitivity than the more specific HRSD. The VAMS seemed not to be a reliable method for assessing depression among stroke patients. The caregivers often rated patients depression as more severe than did the patients themselves. Moreover, their ratings seemed to be influenced by their own depression. Of the caregivers, 30-33% were depressed. At the acute phase, caregiver depression was associated with the severity of the stroke and the older age of the patient. The best predictor of caregiver depression at later follow-up was caregiver depression at the acute phase. The results suggest that depression should be assessed during the early post-stroke period and that the follow-up of those at risk of poor emotional outcome should be extended beyond the first year post-stroke. Further, the assessment of well-being of the caregivers of stroke patients should be included as a part of a rehabilitation plan for stroke patients.

Proline ring conformations corresponding to a bistable jump model from 13C spin-lattice relaxation times

A formalism for extracting the conformations of a proline ring based on the bistable jump model of R. E. London [(1978) J. Am. Chem. Soc. 100, 2678-2685] from 13C spin-lattice relaxation times (T1) is given. The method is such that the relaxation data are only partially used to generate the conformations; these conformations are constrained to satisfy the rest of the relaxation data and to yield acceptable ring geometry. An alternate equation for T1 of 13C nuclei to that of London is given. The formalism is illustrated through an example.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Vacancy ordered phases and one-dimensional quasiperiodicity

The metastable vacancy ordered phases observed in aluminium transition metal alloys on rapid solidification or vapour deposition can be considered as a periodic arrangement of a truncated quasiperiodic string based on the Fibonacci sequence along the left angle bracket111right-pointing angle bracket stacking direction of the original CsCl cell. Using the projection formalism developed in the context of quasicrystals, the diffraction patterns of the vacancy ordered phases are calculated for both commensurate and incommensurate projection from a periodic cubic cell in four dimensions. These are compared with experimentally observed patterns. It is shown that at increasingly longer periodicity the patterns from commensurate crystals become indistinguishable from the truly quasiperiodic one. It is suggested that there is a strong link between vacancy ordered phases and quasicrystals.

Binary decompositions and acyclic schemes

It is well known that the notions of normal forms and acyclicity capture many practical desirable properties for database schemes. The basic schema design problem is to develop design methodologies that strive toward these ideals. The usual approach is to first normalize the database scheme as far as possible. If the resulting scheme is cyclic, then one tries to transform it into an acyclic scheme. In this paper, we argue in favor of carrying out these two phases of design concurrently. In order to do this efficiently, we need to be able to incrementally analyze the acyclicity status of a database scheme as it is being designed. To this end, we propose the formalism of "binary decompositions". Using this, we characterize design sequences that exactly generate theta-acyclic schemes, for theta = agr,beta. We then show how our results can be put to use in database design. Finally, we also show that our formalism above can be effectively used as a proof tool in dependency theory. We demonstrate its power by showing that it leads to a significant simplification of the proofs of some previous results connecting sets of multivalued dependencies and acyclic join dependencies.

Vibrations of a Beam in Variable Contact With a Flat Surface

We study small vibrations of cantilever beams contacting a rigid surface. We study two cases: the first is a beam that sags onto the ground due to gravity, and the second is a beam that sticks to the ground through reversible adhesion. In both cases, the noncontacting length varies dynamically. We first obtain the governing equations and boundary conditions, including a transversality condition involving an end moment, using Hamilton's principle. Rescaling the variable length to a constant value, we obtain partial differential equations with time varying coefficients, which, upon linearization, give the natural frequencies of vibration. The natural frequencies for the first case (gravity without adhesion) match that of a clamped-clamped beam of the same nominal length; frequencies for the second case, however, show no such match. We develop simple, if atypical, single degree of freedom approximations for the first modes of these two systems, which provide insights into the role of the static deflection profile, as well as the end moment condition, in determining the first natural frequencies of these systems. Finally, we consider small transverse sinusoidal forcing of the first case and find that the governing equation contains both parametric and external forcing terms. For forcing at resonance, w find that either the internal or the external forcing may dominate.

Albert Einstein Portraits; Men

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Preliminary investigation into development of forage budget application and device

Forage budgeting, land condition monitoring and maintaining ground cover residuals are critical management practices for the long term sustainability of the northern grazing industry. The aim of this project is to do a preliminary investigation into industry need, feasibility and willingness to adopt a simple to use hand-held hardware device and compatible, integrated software applications that can be used in the paddock by producers, to assist in land condition monitoring and forage budgeting for better Grazing Land Management and to assist with compliance.

Leading Sheep II

Leading Sheep is an education framework for leading the adoption of new technologies and practices to increase the productivity of the Queensland sheep industry.

Leading Sheep III

Leading Sheep is a framework for supporting decision-making about technologies and practices to increase the profitability and productivity of the Queensland Sheep Businesses. Leading Sheep aims to achieve a high level of engagement with sheep businesses in Queensland to support their ongoing decision making processes about productivity and profitability.

Making More from Sheep Phase II : MMfS State Coordination – Queensland

Making More from Sheep (MMfS) is a majority market extension program funded by Meat & Livestock Australia (MLA) and Australian Wool Innovation (AWI). Phase II of MMfS commenced in Queensland with a business planning process in October 2010 and delivery from November 2010 until November 2013. Mr Tony Hamilton of the Department of Agriculture, Fisheries and Forestry (DAFF) was initially the State Coordinator with responsibility for planning, project implementation, monitoring and evaluation. He was replaced by Ms Nicole Sallur from DAFF towards the end of the project. Delivery involving partner organisations provided best practice management information and tools to sheep producers with target Key Performance Indicators (KPI’s) exceeded across all three tiers of engagement category. 31 events were delivered to 551 participants. Satisfaction and value scores averaged across all events measured 8.7 and 8.2 respectively. Operational recommendations have been included in the report.

Demonstrating recovery of pasture productivity, Mulga Lands - Bollon, South West Queensland

Pasture recovery PDS, Mulga lands.