Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Thermodynamic scaling theory for impurities in metals

A perturbative scaling theory for calculating static thermodynamic properties of arbitrary local impurity degrees of freedom interacting with the conduction electrons of a metal is presented. The basic features are developments of the ideas of Anderson and Wilson, but the precise formulation is new and is capable of taking into account band-edge effects which cannot be neglected in certain problems. Recursion relations are derived for arbitrary interaction Hamiltonians up to third order in perturbation theory. A generalized impurity Hamiltonian is defined and its scaling equations are derived up to third order. The strategy of using such perturbative scaling equations is delineated and the renormalization-group aspects are discussed. The method is illustrated by applying it to the single-impurity Kondo problem whose static properties are well understood.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Thermodynamic scaling theory for the two-impurity Anderson model

We present results of a study of the two-impurity Anderson model using a thermodynamic scaling theory developed recently. The model is characterized by the Coulomb energy U, the orbital energy epsilond, the d-level width Gamma, and the separation between impurities R. If Gamma<<−epsilond<~Gamma. Here we find that the single-impurity physics dominates the low-temperature behavior, and impurity-impurity interactions are perturbative. The qualitative features of the temperature-dependent susceptibility are discussed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

‘Lemon Laws’: an inquiry into consumer protections and remedies for buyers of new motor vehicles

1. Under the Terms of Reference for the Committee’s Inquiry, ‘lemons’ are defined as ‘new motor vehicles with numerous, severe defects that re-occur despite multiple repair attempts or where defects have caused a new motor vehicle to be out of service for a prolonged period of time’. Consumers are currently protected in relation to lemon purchases by the Australian Consumer Law (ACL) located in Schedule 2 of the Competition and Consumer Act 2010 (Cth) (CCA). The ACL applies as a law of Queensland pursuant to the Fair Trading Act 1989 (Qld). The voluntary recall and consumer guarantees law took effect on 1 January 2011. 2. In 2006, the Government of Victoria made a commitment to introduce a lemon law into the provisions of the then Fair Trading Act 1999 (Vic). The public consultation process on the proposal to introduce a lemon law for motor vehicle purchases in Victoria was conducted by Ms Janice Munt MP, with the assistance of Consumer Affairs Victoria (CAV). CAV released an Issues Paper to canvas with industry and the community options for the development and introduction of a motor vehicle lemon law.(Consumer Affairs Victoria, Introducing Victorian motor vehicle lemon laws, Issues Paper, (September, 2007). 3. A CAV report prepared by Janice Munt MP was released in July, 2008 (Consumer Affairs Victoria, Motor Cars: A report on the motor vehicle lemon law consultations (July 2008) (Victorian Lemon Law Report). However, the Victorian proposal was overtaken by events leading to the adoption of a uniform consumer protection law in all Australian jurisdictions, the ACL. 4. The structure of this submission is to consider first the three different bases upon which consumers can obtain relief for economic loss arising from defects in motor vehicles. The second part of the submission considers the difficulties encountered by consumers in litigating motor vehicle disputes in the courts and tribunals. The third part of the submission examines the approach taken in other jurisdictions to resolving motor vehicle disputes. The final part of the submission considers a number of possible reforms that could be made to the existing law and its enforcement to reduce consumer detriment arising from the purchase of ‘lemon’ motor vehicles. 5. There are three principal bases upon which a consumer can obtain redress for defects in new motor vehicles under the ACL. The first is where the manufacturer admits liability and initiates the voluntary recall procedure provided for in s 128 of the ACL. Under this basis the manufacturer generally repairs or replaces the part subject to the recall free of charge. The second basis is where the manufacturer or dealer denies liability and the consumer is initiates proceedings in the court or tribunal seeking a statutory remedy under the ACL, the nature of which will depend on whether the failure to comply with the consumer guarantee was major or not. The third basis upon which a consumer can obtain redress is pursuant to public enforcement by the ACCC. Each basis will be considered in this part. What all three bases have in common is the need to conduct an investigation to identify the nature of the defect and how it arose.

Scaling results up from a plot and paddock scale to a property - a case study from a long-term grazing experiment in northern Australia

Grazing experiments are usually used to quantify and demonstrate the biophysical impact of grazing strategies, with the Wambiana grazing experiment being one of the longest running such experiments in northern Australia. Previous economic analyses of this experiment suggest that there is a major advantage in stocking at a fixed, moderate stocking rate or in using decision rules allowing flexible stocking to match available feed supply. The present study developed and applied a modelling procedure to use data collected at the small plot, land type and paddock scales at the experimental site to simulate the property-level implications of a range of stocking rates for a breeding-finishing cattle enterprise. The greatest economic performance was achieved at a moderate stocking rate of 10.5 adult equivalents 100 ha(-1). For the same stocking rate over time, the fixed stocking strategy gave a greater economic performance than strategies that involved moderate changes to stocking rates each year in response to feed supply. Model outcomes were consistent with previous economic analyses using experimental data. Further modelling of the experimental data is warranted and similar analyses could be applied to other major grazing experiments to allow the scaling of results to greater scales.

Theoretical results of QoS-guaranteed resource scaling for cloud-based MapReduce

Quality of Service (QoS) is a new issue in cloud-based MapReduce, which is a popular computation model for parallel and distributed processing of big data. QoS guarantee is challenging in a dynamical computation environment due to the fact that a fixed resource allocation may become under-provisioning, which leads to QoS violation, or over-provisioning, which increases unnecessary resource cost. This requires runtime resource scaling to adapt environmental changes for QoS guarantee. Aiming to guarantee the QoS, which is referred as to hard deadline in this work, this paper develops a theory to determine how and when resource is scaled up/down for cloud-based MapReduce. The theory employs a nonlinear transformation to define the problem in a reverse resource space, simplifying the theoretical analysis significantly. Then, theoretical results are presented in three theorems on sufficient conditions for guaranteeing the QoS of cloud-based MapReduce. The superiority and applications of the theory are demonstrated through case studies.

Downstream processing of reverse osmosis brine: Characterisation of potential scaling compounds

Reverse osmosis (RO) brine produced at a full-scale coal seam gas (CSG) water treatment facility was characterized with spectroscopic and other analytical techniques. A number of potential scalants including silica, calcium, magnesium, sulphates and carbonates, all of which were present in dissolved and non-dissolved forms, were characterized. The presence of spherical particles with a size range of 10–1000 nm and aggregates of 1–10 microns was confirmed by transmission electron microscopy (TEM). Those particulates contained the following metals in decreasing order: K, Si, Sr, Ca, B, Ba, Mg, P, and S. Characterization showed that nearly one-third of the total silicon in the brine was present in the particulates. Further, analysis of the RO brine suggested supersaturation and precipitation of metal carbonates and sulphates during the RO process should take place and could be responsible for subsequently capturing silica in the solid phase. However, the precipitation of crystalline carbonates and sulphates are complex. X-ray diffraction analysis did not confirm the presence of common calcium carbonates or sulphates but instead showed the presence of a suite of complex minerals, to which amorphous silica and/or silica rich compounds could have adhered. A filtration study showed that majority of the siliceous particles were less than 220 nm in size, but could still be potentially captured using a low molecular weight ultrafiltration membrane.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Scaling for binary liquid systems and ferromagnets under pressure

Scaling relations between the critical indices are derived for two similar systems exhibiting λ lines: binary liquid systems and ferromagnets under pressure. In addition to the usual scaling relations, this procedure gives information about other weakly divergent quantities like isothermal compressibility and thermal expansion. Suggestions for more detailed investigations are made.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Cluster based training for scaling non-linear support vector machines

Support Vector Machines(SVMs) are hyperplane classifiers defined in a kernel induced feature space. The data size dependent training time complexity of SVMs usually prohibits its use in applications involving more than a few thousands of data points. In this paper we propose a novel kernel based incremental data clustering approach and its use for scaling Non-linear Support Vector Machines to handle large data sets. The clustering method introduced can find cluster abstractions of the training data in a kernel induced feature space. These cluster abstractions are then used for selective sampling based training of Support Vector Machines to reduce the training time without compromising the generalization performance. Experiments done with real world datasets show that this approach gives good generalization performance at reasonable computational expense.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Comprehending adverbs of doubt and certainty in health communication: A multidimensional scaling approach

This research explored the feasibility of using multidimensional scaling (MDS) analysis in novel combination with other techniques to study comprehension of epistemic adverbs expressing doubt and certainty (e.g., evidently, obviously, probably) as they relate to health communication in clinical settings. In Study 1, Australian English speakers performed a dissimilarity-rating task with sentence pairs containing the target stimuli, presented as "doctors' opinions". Ratings were analyzed using a combination of cultural consensus analysis (factor analysis across participants), weighted-data classical-MDS, and cluster analysis. Analyses revealed strong within-community consistency for a 3-dimensional semantic space solution that took into account individual differences, strong statistical acceptability of the MDS results in terms of stress and explained variance, and semantic configurations that were interpretable in terms of linguistic analyses of the target adverbs. The results confirmed the feasibility of using MDS in this context. Study 2 replicated the results with Canadian English speakers on the same task. Semantic analyses and stress decomposition analysis were performed on the Australian and Canadian data sets, revealing similarities and differences between the two groups. Overall, the results support using MDS to study comprehension of words critical for health communication, including in future studies, for example, second language speaking patients and/or practitioners. More broadly, the results indicate that the techniques described should be promising for comprehension studies in many communicative domains, in both clinical settings and beyond, and including those targeting other aspects of language and focusing on comparisons across different speech communities.

Investigations of the scaling criteria for a mild combustion burner

In this paper, a new strategy for scaling burners based on "mild combustion" is evolved and adopted to scaling a burner from 3 to a 150 kW burner at a high heat release Late of 5 MW/m(3) Existing scaling methods (constant velocity, constant residence time, and Cole's procedure [Proc. Combust. Inst. 28 (2000) 1297]) are found to be inadequate for mild combustion burners. Constant velocity approach leads to reduced heat release rates at large sizes and constant residence time approach in unacceptable levels of pressure drop across the system. To achieve mild combustion at high heat release rates at all scales, a modified approach with high recirculation is adopted in the present studies. Major geometrical dimensions are scaled as D similar to Q(1/3) with an air injection velocity of similar to 100 m/s (Delta p similar to 600 mm water gauge). Using CFD support, the position of air injection holes is selected to enhance the recirculation rates. The precise role of secondary air is to increase the recirculation rates and burn LIP the residual CO in the downstream. Measurements of temperature and oxidizer concentrations inside 3 kW, 150 kW burner and a jet flame are used to distinguish the combustion process in these burners. The burner can be used for a wide range of fuels from LPG to producer gas as extremes. Up to 8 dB of noise level reduction is observed in comparison to the conventional combustion mode. Exhaust NO emissions below 26 and 3 ppm and temperatures 1710 and 1520 K were measured for LPG and producer gas when the burner is operated at stoichiometry. (c) 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.