Physical Sciences and Mathematics Commons^™

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 …

Quantum Multiplexers, Parrondo Games, And Proper Quantization, Faisal Shah Khan

Dissertations and Theses

A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary accuracy, via a circuit consisting entirely of variations of the quantum multiplexer, and that certain one player games, the history dependent Parrondo games, can be quantized as games via a particular variation of the quantum multiplexer. However, to date all such quantizations have lacked a certain fundamental game theoretic property.

The main result in this dissertation is the development of quantizations of …

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 + …