We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress-energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient ψ A i. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.
CONTENTS
Although commercially taught systems are effective for managing conflict that arises during public involvement in transportation projects, these systems can be costly and complex. They appear more appropriate for those who can use them frequently. The work described here, by contrast, was focused on finding simple methods for managing less challenging projects and was aimed toward those who may use public involvement only occasionally. The conflict management framework is derived from a distillation of expert opinion, based on discussions of specific projects by Minnesota transportation experts on public involvement. They were interviewed with a standard set of questions about the project, the public involvement process, the reasons for conflict, how the conflict was managed, what worked, and what did not. The interviews encompassed a variety of project types and settings. The framework has two components. The first is a simple organizational scheme for categorizing conflict to assist in determining the appropriate management strategy. The second is the management strategies themselves. An overview of the key elements of these components is given.
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