Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics

This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. The present formulation also includes solid-fluid interactions and material interfaces and, in addition, lays the groundwork for a treatment of shocks

Estimates from a Consumer Demand System: Implications for the Incidence of Environmental Taxes

Most studies suggest that environmental taxes are regressive, and thus are unattractive policy options. We consider the distributional effects of a gasoline tax increase using three welfare measures and under three scenarios for gas tax revenue use. To incorporate behavioral responses we use Consumer Expenditure Survey data to estimate a consumer demand system that includes gasoline, other goods, and leisure. We find that the gas tax is regressive, but that returning the revenue through a lump-sum transfer more than offsets this, yielding a net increase in progressivity. We also find that ignoring behavioral changes in distributional calculations overstates both the overall burden of the tax and its regressivity.

Empirical Estimates for Environmental Policy Making in a Second- Best Setting

This study estimates parameters necessary to calculate the optimal second-best gasoline tax, most notably the cross-price elasticity between gasoline and leisure. Prior work indicates that in a second-best setting with distortionary income taxes, both the cost of environmental regulation and the optimal environmental tax rate depend crucially on the cross-price elasticity between a polluting good and leisure. However, no prior study on second-best environmental regulation has estimated this elasticity. Using household data, we find that gasoline is a relative complement to leisure, and thus that the optimal gasoline tax is significantly higher than marginal damages–the opposite of the result suggested by the prior literature. Following this approach to estimate cross-price elasticities with leisure for other major polluting goods could strongly influence estimates of optimal environmental taxes.second-best environmental taxes, optimal taxes, tax interactions, demand system

Variational integrators, the Newmark scheme, and dissipative systems

Variational methods are a class of symplectic-momentum integrators for ODEs. Using these schemes, it is shown that the classical Newmark algorithm is structure preserving in a non-obvious way, thus explaining the observed numerical behavior. Modifications to variational methods to include forcing and dissipation are also proposed, extending the advantages of structure preserving integrators to non-conservative systems

Nonsmooth Lagrangian mechanics and variational collision integrators

Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated

Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra

E_11 and M Theory

We argue that eleven dimensional supergravity can be described by a non-linear realisation based on the group E_{11}. This requires a formulation of eleven dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.Comment: 21 pages, some typos corrected and two references adde