Local Solutions for Generic Multidimensional Resonant Wave Conversion

In more than one spatial dimension, resonant linear conversion from one wave type to another can have a more complex geometry than the familiar 'avoided crossing' of one-dimensional problems. In previous work we have shown that helical ray shapes are generic in a mathematical sense. Here we briefly describe how the local field structure can be computed.Comment: 4 pages, to appear in the AIP Proceedings of the 15th Topical Conference on RF Power in Plasma

Cyclic structural analysis of air-cooled gas turbine blades and vanes

The creep fatigue behavior of a fully impingement cooled blade for four cyclic cases was analyzed by using the Elas 55, finite element, nonlinear structural computer program. Expected cyclic lives were calculated by using the method of strainrange partitioning for reversed inelastic strains and time fractions for ratcheted tensile creep strains. Strainrange partitioning was also applied to previous results from a one dimensional cyclic analysis of a film impingement cooled vane. The analyses indicated that strainrange partitioning is more applicable to a constrained airfoil such as the film impingement cooled vane than to the relatively unconstrained fully impingement cooled airfoil

Nonlinear, three-dimensional finite-element analysis of air-cooled gas turbine blades

Cyclic stress-strain states in cooled turbine blades were calculated for a simulated mission of an advanced-technology commercial aircraft engine. The MARC, nonlinear, finite-element computer program was used for the analysis of impingement-cooled airfoils, with and without leading-edge film cooling. Creep was the predominant damage mode (ignoring hot corrosion), particularly artund film-cooling holes. Radially angled holes exhibited less creep than holes with axes normal to the surface. Beam-theory analyses of all-impingement-cooled airfoils gave fair agreement with MARC results for initial creep

Engine cyclic durability by analysis and material testing

The problem of calculating turbine engine component durability is addressed. Nonlinear, finite-element structural analyses, cyclic constitutive behavior models, and an advanced creep-fatigue life prediction method called strainrange partitioning were assessed for their applicability to the solution of durability problems in hot-section components of gas turbine engines. Three different component or subcomponent geometries are examined: a stress concentration in a turbine disk; a louver lip of a half-scale combustor liner; and a squealer tip of a first-stage high-pressure turbine blade. Cyclic structural analyses were performed for all three problems. The computed strain-temperature histories at the critical locations of the combustor linear and turbine blade components were imposed on smooth specimens in uniaxial, strain-controlled, thermomechanical fatigue tests of evaluate the structural and life analysis methods

Geometric phases in electric dipole searches with trapped spin-1/2 particles in general fields and measurement cells of arbitrary shape with smooth or rough walls

The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins and investigated in detail by Pendlebury et al. Their analysis was based on the Bloch equations. In subsequent work using the spin density matrix Lamoreaux and Golub showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently we presented a solution of the Schr\"odinger equation for spin-$1/2$ particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [Steyerl et al.] Here we extend this work to show how the Redfield theory follows directly from the Schr\"odinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., Nicholas et al.] Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and non-stochastic systems and thus we can illustrate the transient spin dynamics, i.e. the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schr\"odinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.Comment: 20 pages, 8 figure

Potts-Percolation-Gauss Model of a Solid

We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookian springs. If the energy is larger than a threshold the "spring" is more likely to fail, while if the energy is lower than the threshold the spring is more likely to be alive. The phase diagram and thermodynamic quantities, such as free energy, numbers of bonds and clusters, and their fluctuations, are determined using renormalization-group and Monte-Carlo techniques.Comment: 10 pages, 12 figure

Post-modernism's use and abuse of Nietzsche

I focus on Nietzsche's architectural metaphor of self-construction in arguing for the claim that postmodern readings of Nietzsche misunderstand his various attacks on dogmatic philosophy as paving the way for acceptance of a self characterized by fundamental disunity. Nietzsche's attack on essentialist dogmatic metaphysics is a call to engage in a purposive self-creation under a unifying will, a will that possesses the strength to reinterpret history as a pathway to "the problem that we are". Nietzsche agrees with the postmodernists that unity is not a pre-given, however he would disavow their rejection of unity as a goal. Where the postmodernists celebrate "the death of the subject" Nietzsche rejects this valorization of disunity as a form of Nihilism and prescribes the creation of a genuine unified subjectivity to those few capable of such a goal. Postmodernists are nearer Nietzsche's idea of the Last Man than his idea of the Overman.Articl

Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\"odinger equation

Pendlebury $\textit{et al.}$ [Phys. Rev. A $\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schr\"odinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.Comment: 11 pages, 4 figure