3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Rapid internal drainage rates in Ferrosols

Adoption of conservation tillage practices on Red Ferrosol soils in the inland Burnett area of south-east Queensland has been shown to reduce runoff and subsequent soil erosion. However, improved infiltration resulting from these measures has not improved crop performance and there are suggestions of increased loss of soil water via deep drainage. This paper reports data monitoring soil water under real and artificial rainfall events in commercial fields and long-term tillage experiments, and uses the data to explore the rate and mechanisms of deep drainage in this soil type. Soils were characterised by large drainable porosities (≥0.10 m3/m3) in all parts of the profile to depths of 1.50 m, with drainable porosity similar to available water content (AWC) at 0.25 and 0.75 m, but >60% higher than AWC at 1.50 m. Hydraulic conductivity immediately below the tilled layer in both continuously cropped soils and those after a ley pasture phase was shown to decline with increasing soil moisture content, although the rate of decline was much greater in continuously cropped soil. At moisture contents approaching the drained upper limit (pore water pressure = -100cm H2O), estimates of saturated hydraulic conductivity after a ley pasture were 3-5 times greater than in continuously cropped soil, suggesting much greater rates of deep drainage in the former when soils are moist. Hydraulic tensiometers and fringe capacitance sensors monitored during real and artificial rainfall events showed evidence of soils approaching saturation in the surface layers (top 0.30-0.40 m), but there was no evidence of soil moistures exceeding the drained upper limit (i.e. pore water pressures ≤ -100 cm H2O) in deeper layers. Recovery of applied soil water within the top 1.00-1.20 m of the profile during or immediately after rainfall events declined as the starting profile moisture content increased. These effects were consistent with very rapid rates of internal drainage. Sensors deeper in the profile were unable to detect this drainage due to either non-uniformity of conducting macropores (i.e. bypass flow) or unsaturated conductivities in deeper layers that far exceed the saturated hydraulic conductivity of the infiltration throttle at the bottom of the cultivated layer. Large increases in unsaturated hydraulic conductivities are likely with only small increases in water content above the drained upper limit. Further studies with drainage lysimeters and large banks of hydraulic tensiometers are planned to quantify drainage risk in these soil types.

‘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.

Drainage and Irrigation Project Eastern Crimea

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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.

Performance Analysis of Guidance Laws Based on Timescale Gap

An analytical treatment of performance analysis of guidance laws is possible only in simplistic scenarios. As the complexity of the guidance system increases, a search for analytical solutions becomes quite impractical. In this paper, a new performance measure, based upon the notion of a timescale gap that can be computed through numerical simulations, is developed for performance analysis of guidance laws. Finite time Lyapunov exponents are used to define the timescale gap. It is shown that the timescale gap can be used for quantification of the rate of convergence of trajectories to the collision course. Comparisonbetween several guidance laws, based on the timescale gap, is presented. Realistic simulations to study the effect of aerodynamicsand atmospheric variations on the timescale gap of these guidance laws are also presented.

The proposed gun laws are not enough

Argues that as a more effective precuationary measure, it would seem that the firearms revocation threshold should be substantially lowered, or at least further clarified in guidance. Response to public debate in light of school shootings.

Ferrolysis induced soil transformation by natural drainage in Vertisols of sub-humid South India

In sub-humid South India, recent studies have shown that black soil areas (Vertisols and vertic Intergrades), located on flat valley bottoms, have been rejuvenated through the incision of streambeds, inducing changes in the pedoclimate and soil transformation. Joint pedological, geochemical and geophysical investigations were performed in order to better understand the ongoing processes and their contribution to the chemistry of local rivers. The seasonal rainfall causes cycles of oxidation and reduction in a perched watertable at the base of the black soil, while the reduced solutions are exported through a loamy sand network. This framework favours a ferrolysis process, which causes low base saturation and protonation of clay, leading to the weathering of 2:1 then 1:1 clay minerals. Maximum weathering conditions occur at the very end of the wet season, just before disappearance of the perched watertable. Therefore, the by-products of soil transformation are partially drained off and calcareous nodules, then further downslope, amorphous silica precipitate upon soil dehydration. The ferrolysed area is fringing the drainage system indicating that its development has been induced by the streambed incision. The distribution of C-14 ages of CaCO3 nodules suggests that the ferrolysis process started during the late Holocene, only about 2 kyr B.P. at the studied site and about 5 kyr B.P. at the watershed outlet. The results of this study are applied to an assessment of the physical erosion rate (4.8x10(-3) m/kyr) since the recent reactivation of the erosion process. (C) 2010 Elsevier B.V. All rights reserved.

Behaviour of autonomous mobile agents using linear cyclic pursuit laws

In this paper, the behaviour of a group of autonomous mobile agents under cyclic pursuit is studied. Cyclic pursuit is a simple distributed control law, in which the agent i pursues agent i + 1 modulo n.. The equations of motion are linear, with no kinematic constraints on motion. Behaviourally, the agents are identical, but may have different controller gains. We generalize existing results in the literature and show that by selecting these gains, the behavior of the agents can be controlled. They can be made to converge at a point or be directed to move in a straight line. The invariance of the point of convergence with the sequence of pursuit is also shown.

A one point shock capturing kinetic scheme for hyperbolic conservation laws

We have presented a new low dissipative kinetic scheme based on a modified Courant Splitting of the molecular velocity through a parameter φ. Conditions for the split fluxes derived based on equilibrium determine φ for a one point shock. It turns out that φ is a function of the Left and Right states to the shock and that these states should satisfy the Rankine-Hugoniot Jump condition. Hence φ is utilized in regions where the gradients are sufficiently high, and is switched to unity in smooth regions. Numerical results confirm a discrete shock structure with a single interior point when the shock is aligned with the grid.

Studies on removal of metal ions and sulphate reduction using rice husk and Desulfotomaculum nigrificans with reference to remediation of acid mine drainage

The utility of rice husk as an adsorbent for metal ions such as iron, zinc and copper from acid mine water was assessed. The adsorption isotherms exhibited Langmuirian behavior and were endothermic in nature. The free energy values for adsorption of the chosen metal ions onto rice husk were found to be highly negative attesting to favorable interaction. Over 99% Fe3+, 98% of Fe2+ and Zn2+ and 95% Cu2+ uptake was achieved from acid mine water, with a concomitant increase in the pH value by two units using rice husk. The remediation studies carried out on acid mine water and simulated acid mine water pretreated with rice husk indicated successful growth of Desulfotomaculum nigrificans (D. nigrificans). The amount of sulphate bioreduction in acid mine water at an initial pH of 5.3 was enhanced by D. nigrificans from 21% to 40% in the presence of rice husk filtrate supplemented with carbon and nitrogen. In simulated acid mine water with fortified husk filtrate, the sulphate reduction was even more extensive, with an enhancement to 73%. Concurrently, almost 90% Fe2+, 89% Zn2+ and 75% Cu2+ bioremoval was attained from simulated acid mine water. Metal adsorption by rice husk was confirmed in desorption experiments in which almost complete removal of metal ions from the rice husk was achieved after two elutions using 1 M HCl. The possible mechanisms of metal ion adsorption onto rice husk and sulphate reduction using D. nigrificans are discussed.

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.