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Free differential algebras: Their use in field theory and dual formulation (1996)

Castellani, Leonardo ; Perotto, Alberto

Springer

Letters in mathematical physics 38 (1996), S. 321-330

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ISSN: 1573-0530

Keywords: 81R50 ; 16W30 ; 22E70 ; free differential algebras ; antisymmetric tensors ; p-forms ; supergravity theories

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials (p〉1). We study here the algebra of FDA transformations. To every p-form in the FDA, we associate an extended Lie derivative l generating a corresponding ‘gauge’ transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00398356

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Impact of space-time mesh adaptation on solute transport modeling in porous media (2015)

Bahman Esfandiar, Giovanni Porta, Simona Perotto, Alberto Guadagnini

Wiley

In: Water Resources Research

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Publication Date: 2015-01-29

Description: We implement a space-time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of non-reactive transport experiments in laboratory-scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space-time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator which enables us to properly select the size, shape and orientation of the mesh elements. Adaptation of the time step is performed through an ad-hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a non-uniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization. This article is protected by copyright. All rights reserved.

Print ISSN: 0043-1397

Electronic ISSN: 1944-7973

Topics: Architecture, Civil Engineering, Surveying , Geography