Blade loss transient dynamics analysis, volume 2. Task 2: TETRA 2 user's manual

This is the user's manual for the TETRA 2 Computer Code, a program developed in the NASA-Lewis Blade Loss Program. TETRA 2 calculates a turbine engine's dynamic structural response from applied stimuli. The calculation options are: (1) transient response; and (2) steady state forced response. Based on the method of modal syntheses, the program allows the use of linear, as well as nonlinear connecting elements. Both transient and steady state options can include: flexible Bladed Disk Module, and Nonlinear Connecting Elements (including deadband, hardening/softening spring). The transient option has the additional capability to calculate response with a squeeze film bearing module. TETRA 2 output is summarized in a plotfile which permits post processing such as FFT or graphical animation with the proper software and computer equipment

Muon Dynamics in a Toroidal Sector Magnet

We present a Hamiltonian formulation of muon dynamics in toroidal sector solenoids (bent solenoids)Comment: format aipproc.cls; aipproc.sty; 7 pages, two figures (*.ps). Submitted to the Proceedings of the 4th International Conference on Physics Potential and Development of mu-mu Colliders, San Francisco, Dec. 199

A hyperbolic universal operator commuting with a compact operator

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a non-trivial, quasinilpotent, injective, compact operator with dense range, but unlike other examples, it acts on the Bergman space instead of the Hardy space and this operator is associated with a `hyperbolic' composition operator

A new proof of a Nordgren, Rosenthal and Wintrobe Theorem on universal operators

A striking result by Nordgren, Rosenthal and Wintrobe states that the Invariant Subspace Problem is equivalent to the fact that any minimal invariant subspace for a composition operator Cφ induced by a hyperbolic automorphism φ of the unit disc D acting on the classical Hardy space H² is one dimensional. We provide a completely different proof of Nordgren, Rosenthal and Wintrobe’s Theorem based on analytic Toeplitz operators

Inverse Neutrino-less Double Beta Decay Revisited: Neutrinos, Higgs Triplets and a Muon Collider

We revisit the process of inverse neutrino-less double beta decay (e e -> W W) at future linear colliders. The cases of Majorana neutrino and Higgs triplet exchange are considered. We also discuss the processes e mu -> W W and mu mu -> W W, which are motivated by the possibility of muon colliders. For heavy neutrino exchange and center-of-mass energies larger than 1 TeV, we show that masses up to 10^6 (10^5) GeV could be probed for e-e and e-mu machines, respectively. The stringent limits for mixing of heavy neutrinos with muons render mu mu -> W W less promising, even though this process is not constrained by limits from neutrino-less double beta decay. If Higgs triplets are responsible for inverse neutrino-less double beta decay, observable signals are only possible if a very narrow resonance is met. We also consider unitarity aspects of the process in case both Higgs triplets and neutrinos are exchanged. An exact see-saw relation connecting low energy data with heavy neutrino and triplet parameters is found.Comment: 19 pages, 6 figure

High Energy Colliders

We consider the high energy advantages, disadvantages and luminosity requirements of hadrons, leptons and photon-photon colliders. Technical problems in obtaining increased energy in each type of machine are presented. The machines relative size are also discussed.Comment: LaTeX, 27 pages, 8 figures (eps, ps). Submitted to the Proceedings of the Princeton's 250th Anniversary Conference on Critical Problems in Physic

Future Colliders

The high energy physics advantages, disadvantages and luminosity requirements of hadrons, of leptons and photon-photon colliders are considered. Technical arguments for increased energy in each type of machine are presented. Their relative size, and the implications of size on cost are discussed.Comment: LaTeX, 10 pages, 10figure

High Luminosity Muon Collider Design

Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadrons and electron machines. They should be regarded as complementary. Parameters are given of a 4 TeV high luminosity muon-muon collider, and of a 0.5 TeV demonstration machine. We discuss the various systems in such muon collider.Comment: LaTeX 5 pages 4 figure

Blade loss transient dynamics analysis, volume 1. Task 2: TETRA 2 theoretical development

The theoretical development of the forced steady state analysis of the structural dynamic response of a turbine engine having nonlinear connecting elements is discussed. Based on modal synthesis, and the principle of harmonic balance, the governing relations are the compatibility of displacements at the nonlinear connecting elements. There are four displacement compatibility equations at each nonlinear connection, which are solved by iteration for the principle harmonic of the excitation frequency. The resulting computer program, TETRA 2, combines the original TETRA transient analysis (with flexible bladed disk) with the steady state capability. A more versatile nonlinear rub or bearing element which contains a hardening (or softening) spring, with or without deadband, is also incorporated