Scaling laws for localised states in a nonlocal amplitude equation

It is well known that, although a uniform magnetic field inhibits the onset of small amplitude thermal convection in a layer of fluid heated from below, isolated convection cells may persist if the fluid motion within them is sufficiently vigorous to expel magnetic flux. Such fully nonlinear(‘‘convecton’’) solutions for magnetoconvection have been investigated by several authors. Here we explore a model amplitude equation describing this separation of a fluid layer into a vigorously convecting part and a magnetically-dominated part at rest. Our analysis elucidates the origin of the scaling laws observed numerically to form the boundaries in parameter space of the region of existence of these localised states, and importantly, for the lowest thermal forcing required to sustain them.

‘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.

An Application of 3-D Kinematical Conservation Laws: Propagation of a 3-D Wavefront

Three-dimensional (3-D) kinematical conservation laws (KCL) are equations of evolution of a propagating surface Omega(t) in three space dimensions. We start with a brief review of the 3-D KCL system and mention some of its properties relevant to this paper. The 3-D KCL, a system of six conservation laws, is an underdetermined system to which we add an energy transport equation for a small amplitude 3-D nonlinear wavefront propagating in a polytropic gas in a uniform state and at rest. We call the enlarged system of 3-D KCL with the energy transport equation equations of weakly nonlinear ray theory (WNLRT). We highlight some interesting properties of the eigenstructure of the equations of WNLRT, but the main aim of this paper is to test the numerical efficacy of this system of seven conservation laws. We take several initial shapes for a nonlinear wavefront with a suitable amplitude distribution on it and let it evolve according to the 3-D WNLRT. The 3-D WNLRT is a weakly hyperbolic 7 x 7 system that is highly nonlinear. Here we use the staggered Lax-Friedrichs and Nessyahu-Tadmor central schemes and have obtained some very interesting shapes of the wavefronts. We find the 3-D KCL to be suitable for solving many complex problems for which there presently seems to be no other method capable of giving such physically realistic features.

Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: stability and moving-horizon approximations

Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and movinghorizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.

A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.

Australian property investment advice : an unregulated industry and the need for better consumer protection laws

Currently, consumers have no means of protecting themselves when they are looking for property investment advice in Australia. There is no uniform national or State regulation in the property investment advice and marketeering industry. The only protection and remedies currently available are those under the general consumer protection laws scattered in various Acts, and even so, these have numerous problems. This paper highlights what those problems are under the general consumer protection laws and suggests some changes to the current system. The paper also argues that a national co-operative approach is the only way to move forward in this area and suggests that the constitutional difficulty can be overcome by using the legislative conferral of state powers provision, which has often been overlooked. The paper also argues that a new regulator be set up to administer and enforce the new proposed laws on property investment advice.

An argument for uniform Australian sentencing law

Sentencing law and practice impacts on fundamental individual interests, both from the perspective of offenders and victims. It also affects community safety and security The scope of sentencing law and its principal objectives are broadly similar throughout Australia. However, there are many important differences, especially in relation to sentencing practice, with some jurisdictions appearing to impose considerably heavier penalties for certain offence types. This article argues that uniform sentencing law should be implemented throughout Australia. The likely benefits would extend beyond achieving greater consistency in sentencing outcomes. A move toward uniform national sentencing laws would provide the catalyst for an objective, evidence-based review of sentencing policy and practice, thereby providing a vehicle for harmonising the law with a wealth of empirical data regarding the objectives that can be achieved through a system of state-imposed sanctions. It would also present a meaningful opportunity for a normative assessment of the justifiable operation of sentencing law. The main impediment to uniform sentencing laws is likely to come from state and territory governments seeking to maintain control over this often socially controversial area as a means of securing and maintaining community support. However, this obstacle is not necessarily insurmountable. It is not clear whether sentencing policy is, in fact, a main driver of voter preferences. Some politicians may prefer to have ·national uniformity' as a buffer to counteract reflexive calls for tougher sentencing that often occur following particularly serious crimes or seemingly light sentences handed down by courts.

Driver licensing laws affecting handicapped drivers.

National Highway Traffic Safety Administration, Washington, D.C.

State laws on mopeds and motorized bicycles.

National Highway Traffic Safety Administration, Washington, D.C.

Laws requiring helmets and eye protection for motorcylists.

National Highway Traffic Safety Administration, Washington, D.C.

State laws on reexamining drivers.

National Highway Traffic Safety Administration, Washington, D.C.

Los Angeles County buildings laws;

"1962 Edition".

Task Force on a Uniform Building Code : final report.

"April 2006."

Uniform arbitration act; proceedings in Committee of the Whole.

Mode of access: Internet.

Bank deposits and collections (under the Uniform commercial code, October 1955)

Bibliographical footnotes