Conservation laws for Z(N) symmetric quantum spin models and their exact ground state energies

We derive an infinite set of conserved charges for some Z(N) symmetric quantum spin models by constructing their Lax pairs. These models correspond to the Potts model, Ashkin-Teller model and the particular set of self-dual Z(N) models solved by Fateev and Zamolodchikov [6]. The exact ground state energy for this last family of hamiltonians is also presented. © 1986.

Conservation laws for liquid bridges

Conservation laws for an inviscid liquid bridge set into motion by conservative forces are given in integral form. These laws provide useful information on the overall motion of the bridge in the presence of unexpected or uncontrolled disturbances and could, in addition, be monitored in a computational solution of the problem as an accuracy check. Many of the resulting conservation laws are familiar to fluiddynamicists. Nevertheless, a systematic approach providing an exhaustive list of these laws reveals the existence of new conserved properties hardly deducible in the classical way. Although the present analysis concerns the case of axial, and constant, gravity it can be applied, with minor refinements, when the gravity field varies with time in both direction and intensity.

Conservation laws and variational principles in general relativity /

"April 23, 1962."

Forest conservation laws ... 1935.

Mode of access: Internet.

The conservation laws in relation to minerals as revised and amended up to the close of the regular session 1930.

At head of title: State of Louisiana.

The conservation laws in relation to minerals.

"This bulletin contains all laws, rules and regulations of the Department of Conservation in relation to minerals from the year 1930 to 1934 inclusive. Laws, rules and regulations prior to 1930 are contained in the edition of 1930."

Conservation laws of Louisiana, controlling the birds, game and fur-bearing animals, mines and minerals, forests, fresh water fish, oysters, sea food, and water bodies and water bottoms.

Mode of access: Internet.

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

On a Limit of Perturbed Conservation Laws with Diffusion and Non-Positive Dispersion

We consider a conservation law perturbed by a linear diffusion and a general form of non-positive dispersion. We prove the convergence of the corresponding solution to the entropy weak solution of the hyperbolic conservation law.

Illegal trade of the guitarfish Rhinobatos horkelii on the coasts of central and southern Brazil: genetic identification to aid conservation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical solutions of the sediment conservation law: A review and improved formulation for coastal morphological modelling

Numerical solutions of the sediment conservation law are reviewed in terms of their application to bed update schemes in coastal morphological models. It is demonstrated that inadequately formulated numerical techniques lead to the introduction of diffusion, dispersion and the bed elevation oscillations previously reported in the literature. Four different bed update schemes are then reviewed and tested against benchmark analytical solutions. These include a first order upwind scheme, two Lax-Wendroff schemes and a non-oscillating centred scheme (NOCS) recently applied to morphological modelling by Saint-Cast [Saint-Cast, F., 2002. Modelisation de la morphodynamique des corps sableux en milieu littoral (Modelling of coastal sand banks morphodynamics), University Bordeaux 1, Bordeaux, 245 pp.]. It is shown that NOCS limits and controls numerical errors while including all the sediment flux gradients that control morphological change. Further, no post solution filtering is required, which avoids difficulties with selecting filter strength. Finally, NOCS is compared to a recent Lax-Wendroff scheme with post-solution filtering for a longer term simulation of the morphological evolution around a trained river entrance. (C) 2006 Elsevier B.V. All rights reserved.

Modelling sea water intrusion in coastal aquifers using heterogeneous computing

The objective of this PhD research program is to investigate numerical methods for simulating variably-saturated flow and sea water intrusion in coastal aquifers in a high-performance computing environment. The work is divided into three overlapping tasks: to develop an accurate and stable finite volume discretisation and numerical solution strategy for the variably-saturated flow and salt transport equations; to implement the chosen approach in a high performance computing environment that may have multiple GPUs or CPU cores; and to verify and test the implementation. The geological description of aquifers is often complex, with porous materials possessing highly variable properties, that are best described using unstructured meshes. The finite volume method is a popular method for the solution of the conservation laws that describe sea water intrusion, and is well-suited to unstructured meshes. In this work we apply a control volume-finite element (CV-FE) method to an extension of a recently proposed formulation (Kees and Miller, 2002) for variably saturated groundwater flow. The CV-FE method evaluates fluxes at points where material properties and gradients in pressure and concentration are consistently defined, making it both suitable for heterogeneous media and mass conservative. Using the method of lines, the CV-FE discretisation gives a set of differential algebraic equations (DAEs) amenable to solution using higher-order implicit solvers. Heterogeneous computer systems that use a combination of computational hardware such as CPUs and GPUs, are attractive for scientific computing due to the potential advantages offered by GPUs for accelerating data-parallel operations. We present a C++ library that implements data-parallel methods on both CPU and GPUs. The finite volume discretisation is expressed in terms of these data-parallel operations, which gives an efficient implementation of the nonlinear residual function. This makes the implicit solution of the DAE system possible on the GPU, because the inexact Newton-Krylov method used by the implicit time stepping scheme can approximate the action of a matrix on a vector using residual evaluations. We also propose preconditioning strategies that are amenable to GPU implementation, so that all computationally-intensive aspects of the implicit time stepping scheme are implemented on the GPU. Results are presented that demonstrate the efficiency and accuracy of the proposed numeric methods and formulation. The formulation offers excellent conservation of mass, and higher-order temporal integration increases both numeric efficiency and accuracy of the solutions. Flux limiting produces accurate, oscillation-free solutions on coarse meshes, where much finer meshes are required to obtain solutions with equivalent accuracy using upstream weighting. The computational efficiency of the software is investigated using CPUs and GPUs on a high-performance workstation. The GPU version offers considerable speedup over the CPU version, with one GPU giving speedup factor of 3 over the eight-core CPU implementation.

Mixed convection in non-Newtonian fluids along a vertical plate in a porous medium

The problem of mixed convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable wall temperature conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5-2.0.

2.5-dimensional solution of the advective accretion disk:a self-similar approach

We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion- induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor.

R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.