Blade loss transient dynamics analysis. Volume 3: User's manual for TETRA program

The users manual for TETRA contains program logic, flow charts, error messages, input sheets, modeling instructions, option descriptions, input variable descriptions, and demonstration problems. The process of obtaining a NASTRAN 17.5 generated modal input file for TETRA is also described with a worked sample

Blade loss transient dynamics analysis, volume 1. Task 1: Survey and perspective

An analytical technique was developed to predict the behavior of a rotor system subjected to sudden unbalance. The technique is implemented in the Turbine Engine Transient Rotor Analysis (TETRA) computer program using the component element method. The analysis was particularly aimed toward blade-loss phenomena in gas turbine engines. A dual-rotor, casing, and pylon structure can be modeled by the computer program. Blade tip rubs, Coriolis forces, and mechanical clearances are included. The analytical system was verified by modeling and simulating actual test conditions for a rig test as well as a full-engine, blade-release demonstration

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Blade loss transient dynamics analysis, volume 2. Task 2: Theoretical and analytical development. Task 3: Experimental verification

The component element method was used to develop a transient dynamic analysis computer program which is essentially based on modal synthesis combined with a central, finite difference, numerical integration scheme. The methodology leads to a modular or building-block technique that is amenable to computer programming. To verify the analytical method, turbine engine transient response analysis (TETRA), was applied to two blade-out test vehicles that had been previously instrumented and tested. Comparison of the time dependent test data with those predicted by TETRA led to recommendations for refinement or extension of the analytical method to improve its accuracy and overcome its shortcomings. The development of working equations, their discretization, numerical solution scheme, the modular concept of engine modelling, the program logical structure and some illustrated results are discussed. The blade-loss test vehicles (rig full engine), the type of measured data, and the engine structural model are described

Statistics and Nos\'e formalism for Ehrenfest dynamics

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics.Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.149

Magnetization in AIIIBV semiconductor heterostructures with the depletion layer of manganese

The magnetic moment and magnetization in GaAs/Ga$_{0.84}$In$_{0.16}$As/GaAs heterostructures with Mn deluted in GaAs cover layers and with atomically controlled Mn $\delta$-layer thicknesses near GaInAs-quantum well ($\sim$3 nm) in temperature range T=(1.8-300)K in magnetic field up to 50 kOe have been investigated. The mass magnetization all of the samples of GaAs/Ga$_{0.84}$In$_{0.16}$As/GaAs with Mn increases with the increasing of the magnetic field that pointed out on the presence of low-dimensional ferromagnetism in the manganese depletion layer of GaAs based structures. It has been estimated the manganese content threshold at which the ferromagnetic ordering was found.Comment: 8 pages, 3 figure

The RFOFO Ionization Cooling Ring for Muons

Practical ionization cooling rings could lead to lower cost or improved performance in neutrino factory or muon collider designs. The ring modeled here uses realistic three-dimensional fields. The performance of the ring compares favorably with the linear cooling channel used in the second US Neutrino Factory Study. The normalized 6D emittance of an ideal ring is decreased by a factor of approximately 240, compared with a factor of only 15 for the linear channel. We also examine such \textit{real-world} effects as windows on the absorbers and rf cavities and leaving empty lattice cells for injection and extraction. For realistic conditions the ring decreases the normalized 6D emittance by a factor of 49.Comment: 27 pages, 18 figures and 5 tables. Submitted to Phys. Rev. ST-A

Optimal mesh design methodology considering geometric parameters for rock fragmentation in open-pit mining in the Southern Andes of Peru

Blasting is one of the most important stages in the productive process of a mine due to its direct impact on rock fragmentation, which determines the degree of productivity of operations and the extraction costs generated. In this scenario, an optimized methodology is presented for designing blasting meshes by using mathematical models that help calculate the geometric parameters of a blasting mesh, such as burden, considering the variables of the rock mass and the type of explosive to measure its impact on rock fragmentation and loading productivity (tons/hour). The main advantage of this method is the reliability of the design, which takes into account a greater number of variables that influence fragmentation and uses the principle of distribution and amount of energy in an optimal way. The results obtained in the case of application show that a change in design (2.7 x 2.7 square mesh to 2.2 x 2.5 triangular mesh) reduces P80 by 65%, from 17 to 6 inches, approximately. Additionally, the results show that greater operational efficiency was achieved by increasing excavator productivity by approximately 15.6%

The order parameter-entropy relation in some universal classes: experimental evidence

The asymptotic behaviour near phase transitions can be suitably characterized by the scaling of $\Delta s/Q^2$ with $\epsilon=1-T/T_c$, where $\Delta s$ is the excess entropy and $Q$ is the order parameter. As $\Delta s$ is obtained by integration of the experimental excess specific heat of the transition $\Delta c$, it displays little experimental noise so that the curve $\log(\Delta s/Q^2)$ versus $\log\epsilon$ is better constrained than, say, $\log\Delta c$ versus $\log\epsilon$. The behaviour of $\Delta s/Q^2$ for different universality classes is presented and compared. In all cases, it clearly deviates from being a constant. The determination of this function can then be an effective method to distinguish asymptotic critical behaviour. For comparison, experimental data for three very different systems, Rb2CoF4, Rb2ZnCl4 and SrTiO3, are analysed under this approach. In SrTiO3, the function $\Delta s/Q^2$ does not deviate within experimental resolution from a straight line so that, although Q can be fitted with a non mean-field exponent, the data can be explained by a classical Landau mean-field behaviour. In contrast, the behaviour of $\Delta s/Q^2$ for the antiferromagnetic transition in Rb2CoF4 and the normal-incommensurate phase transition in Rb2ZCl4 is fully consistent with the asymptotic critical behaviour of the universality class corresponding to each case. This analysis supports, therefore, the claim that incommensurate phase transitions in general, and the A$_2$BX$_4$ compounds in particular, in contrast with most structural phase transitions, have critical regions large enough to be observable.Comment: 13 pp. 9 ff. 2 tab. RevTeX. Submitted to J. Phys.: Cond. Matte