These notes supplement Robert Kohn’s Lecture 3 at the 2014 PCMI Graduate Summer School. For background and heuristic arguments, see the pdf of that lecture. For physicsoriented discussions of this topic see [4] and [3]. For upper and lower energy bounds similar to those presented here but using nonlinear elasticity and a rather general membrane model see [1]. We want to study deformations of a ...

Submitted for the DPP09 Meeting of The American Physical Society Self-Similar Decay of Enstrophy in an Electron Plasma DOUGLAS RODGERS, SERGIO SERVIDIO, WILLIAM MATTHAEUS, TRAVIS MITCHELL, Department of Physics and Astronomy, University of Delaware, Newark, DE 19716 — The similarity solution for energy decay in 3D hydrodynamic turbulence, due to Taylor and von Karman [1], based on the self pres...

We perform numerical experiments with a novel cellularautomaton fluid model. The model has simple pair-interaction rules and works in arbitrarily many dimensions; here we consider the twodimensional case. By observing the smoothing-out of the velocity profile of a shear flow and the relaxation of a shear wave, we measure the kinematic shear viscosity and obtain a value of :::::: 0.5. To demonst...

In this thesis, a new method for calculating the electronic structure of polymer molecules is developed. The polymer is assumed to be quasiinfinite, fully extended, rigid, and translationally symmetric, and Born-von Karman cyclic boundary conditions are applied. The molecular orbitals are expanded in terms of Bloch functions formed from linear combinations of atomic orbitals. The Hartree-Fock e...

The problem of large deflections of thin flat plates is mderived here using a novel integral equation approach. These plate deformations arc governed by the von Karman plate theory. The numerical solution that is implemented combines both boundary and interior elements in the discretization of the continuum. The formulation also illustrates the adaptability of the boundary element technique to ...

The Colorado State University standard mesoscale model is used to evaluate the sensitivity of one-dimensional (1D) and two-dimensional (2D) fields to differences in surface-layer parameterization “constants”. Such differences reflect the range in the published values of the von Karman constant, Monin-Obukhov stability functions and the temperature roughness length at the surface. The sensitivit...

in Shock Waves by means of a Spectral-Lagrangian Boltzmann Solver Alessandro Munafò∗, Jeffrey R. Haack, Irene M. Gamba∗∗ and Thierry E. Magin∗ ∗Aeronautics/Aerospace department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640 Rhode-Saint-Genèse, Belgium Department of Mathematics, The University of Texas at Austin, 201 E. 24th Street, Austin, TX 78712, USA ∗∗Department of ...

We study the influence on steady turbulent states of the forcing in a von Karman flow, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities to low-dimensional systems. We suggest that this forcing dependence may be applicable to other turbulent ...

In this paper, transverse and longitudinal vibration of nonlinear plate under exciting of orbiting mass is considered based on first-order shear deformation theory. The nonlinear governing equation of motion are discretized by the finite element method in combination with Newmark’s time integration scheme under von Karman strain-displacement assumptions. For validation of method and formulation...

Using differential quadrature method (DQM), this study investigated pull-in instability of beam-type nano-switches under the effects of small-scale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nano-switches, electrostatic forces served as the driving force, and von-Karman type nonlinear strain was used to examine nonlinear geometric effects. To de...