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Full-Text Articles in Physical Sciences and Mathematics
Variational Theory Of Balance Systems, Serge Preston
Variational Theory Of Balance Systems, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constitutive relation C of a balance system is realized as a mapping between a (partial) k-jet bundle and the extended dual bundle similar to the Legendre mapping of the Lagrangian Field Theory. Invariant (variational) form of the balance system corresponding to a constitutive relation C is studied. Special cases of balance systems -Lagrangian systems …
A New Elasticity Element Made For Enforcing Weak Stress Symmetry, Bernardo Cockburn, Jay Gopalakrishnan, Johnny Guzmán
A New Elasticity Element Made For Enforcing Weak Stress Symmetry, Bernardo Cockburn, Jay Gopalakrishnan, Johnny Guzmán
Mathematics and Statistics Faculty Publications and Presentations
We introduce a new mixed method for linear elasticity. The novelty is a simplicial element for the approximate stress. For every positive integer k, the row-wise divergence of the element space spans the set of polynomials of total degree k. The degrees of freedom are suited to achieve continuity of the normal stresses. What makes the element distinctive is that its dimension is the smallest required for enforcing a weak symmetry condition on the approximate stress. This is achieved using certain "bubble matrices", which are special divergence-free matrix-valued polynomials. We prove that the approximation error is of order k + …
Multisymplectic Theory Of Balance Systems, I, Serge Preston
Multisymplectic Theory Of Balance Systems, I, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this paper we are presenting the theory of balance equations of the Continuum Thermodynamics (balance systems) in a geometrical form using Poincare-Cartan formalism of the Multisymplectic Field Theory. A constitutive relation C of a balance system BC is realized as a mapping between a (partial) 1-jet bundle of the configurational bundle π : Y ͢ X and the extended dual bundle similar to the Legendre mapping of the Lagrangian Field Theory. Invariant (variational) form of the balance system BC is presented in three different forms and the space of admissible variations is defined and studied. Action of automorphisms …
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
The Indefinite Metric Of R. Mrugala And The Geometry Of The Thermodynamical Phase Space, Serge Preston, James Vargo
Mathematics and Statistics Faculty Publications and Presentations
We study an indefinite metric G which was introduced by R. Mrugala and is defined on the contact phase space (P, θ) of a homogeneous thermodynamical system. We describe the curvature properties and the isometry group of the metric G. We established an isomorphism of the space (P, θ, G) with the Heisenberg Lie group Hn, endowed with the right invariant contact structure and the right invariant indefinite metric. The lift of the metric G to the symplectization of contact space (P, θ) and its properties are studied. Finally we introduce the "hyperbolic projectivization" of the space …