Generalized Harmonic Functions and the Dewetting of Thin Films

This paper describes the solvability of Dirichlet problems for Laplace's equation when the boundary data is not smooth enough for the existence of a weak solution in H1Ω. Scales of spaces of harmonic functions and of boundary traces are defined and the solutions are characterized as limits of classical harmonic functions in special norms. The generalized harmonic functions, and their norms, are defined using series expansions involving harmonic Steklov eigenfunctions on the domain. It is shown that the usual trace operator has a continuous extension to an isometric isomorphism of specific spaces. This provides a characterization of the generalized solutions of harmonic Dirichlet problems. Numerical simulations of a model problem are described. This problem is related to the dewetting of thin films and the associated phenomenology is describe

The transonic flow problems stability analysis and numerical results

Kloucek, Petr. (1994). The transonic flow problems stability analysis and numerical results. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/2571

On the existence of the entropic solutions for the transonic flow problem

Kloucek, Petr. (1994). On the existence of the entropic solutions for the transonic flow problem. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/2572

The Relaxation of Non-Quasiconvex Variational Integrals

We show that the Steepest Descent Algorithm in connection with wiggly energies yields minimizing sequences that converge to a global minimum of the associated non-quasiconvex variational integrals. We introduce a multi-level infinite dimensional variant of the Steepest Descent Algorithm designed to compute complex microstructures by forming non-smooth minimizers from the smooth initial guess. We apply this multilevel method to the minimization of the variational problems associated with martensitic branching

The Steepest Descent Minimization of Double-Well Stored Energies Does Not Yield Vectorial Microstructures

We prove that the Steepest Descent algorithm applied to the minimization of total stored energies with rank-one related rotationally symmetric energy wells does not produce relaxing vectorial microstructures with non-trivial Young measures

Vibration damping and heat transfer using material phase changes

A method and apparatus wherein phase changes in a material can dampen vibrational energy, dampen noise and facilitate heat transfer. One embodiment includes a method for damping vibrational energy in a body. The method comprises attaching a material to the body, wherein the material comprises a substrate, a shape memory alloy layer, and a plurality of temperature change elements. The method further comprises sensing vibrations in the body. In addition, the method comprises indicating to at least a portion of the temperature change elements to provide a temperature change in the shape memory alloy layer, wherein the temperature change is sufficient to provide a phase change in at least a portion of the shape memory alloy layer, and further wherein the phase change consumes a sufficient amount of kinetic energy to dampen at least a portion of the vibrational energy in the body. In other embodiments, the shape memory alloy layer is a thin film. Additional embodiments include a sensor connected to the material

Three Dimensional Finite Element Modeling of the Earth's Magnetosphere

We demonstrate the feasibility of using a nonconforming finite element method on an unstructured grid in solving a magnetospheric physics problem. We use this approach to construct a global discrete model of the magnetic field of the magnetosphere that includes the effects of shielding currents at the outer boundary (the magnetopause). As in the approach of [17] the internal magnetospheric field model is that of Hilmer and Voigt [3] while the magnetopause shape is based on an empirically-determined approximation [12]. The result is a magnetic field model whose field lines are completely confined within the magnetosphere. The numerical results indicate that the nonconforming discrete model is robust and efficient. Keywords Magnetopause, magnetosphere, Chapman-Ferraro Currents, Nonconforming finite elements, Laplace's equation, Neumann boundary value problem 1991 Mathematical Subject Classification 65M60, 65N50, 65J10, 85A20, 85-08 1 Introduction The Earth's magnetosphere is formed by th..