Application of the Finite Element Method to Rotary Wing Aeroelasticity

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method

Entropic Accelerating Universe

To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann-Lemaitre equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the entropy and temperature intrinsic to the horizon of the universe due to the information holographically stored there. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on the horizon surface screen. We consider an additional quantitative approach inspired by surface terms in general relativity and show that this leads to the entropic accelerating universe.Comment: 14 pages, 1 figure, extended and clarifie

There was movement that was stationary, for the four-velocity had passed around

Is the Doppler interpretation of galaxy redshifts in a Friedmann-Lemaitre-Robertson-Walker (FLRW) model valid in the context of the approach to comoving spatial sections pioneered by de Sitter, Friedmann, Lemaitre and Robertson, i.e. according to which the 3-manifold of comoving space is characterised by both its curvature and topology? Holonomy transformations for flat, spherical and hyperbolic FLRW spatial sections are proposed. By quotienting a simply-connected FLRW spatial section by an appropriate group of holonomy transformations, the Doppler interpretation in a non-expanding Minkowski space-time, obtained via four-velocity parallel transport along a photon path, is found to imply that an inertial observer is receding from herself at a speed greater than zero, implying contradictory world-lines. The contradiction in the multiply-connected case occurs for arbitrary redshifts in the flat and spherical cases, and for certain large redshifts in the hyperbolic case. The link between the Doppler interpretation of redshifts and cosmic topology can be understood physically as the link between parallel transport along a photon path and the fact that the comoving spatial geodesic corresponding to a photon's path can be a closed loop in an FLRW model of any curvature. Closed comoving spatial loops are fundamental to cosmic topology.Comment: 8 pages, 2 figures; v2: missing dot added to Defn 1, minor corrections; submitted to MNRA

Heterotic Cosmic Strings

We show that all three conditions for the cosmological relevance of heterotic cosmic strings, the right tension, stability and a production mechanism at the end of inflation, can be met in the strongly coupled M-theory regime. Whereas cosmic strings generated from weakly coupled heterotic strings have the well known problems posed by Witten in 1985, we show that strings arising from M5-branes wrapped around 4-cycles (divisors) of a Calabi-Yau in heterotic M-theory compactifications, solve these problems in an elegant fashion.Comment: 25 pages, v2: section and references adde

Uncertainty Propagation in Integrated Airframe Propulsion System Analysis for Hypersonic Vehicles

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90676/1/AIAA-2011-2394-420.pd

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multi-component, curvature, and rotation

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a flat background coincide exactly with the ones known in Newton's theory. Here, we present the general relativistic second-order correction terms arising due to (i) pressure, (ii) multi-component, (iii) background curvature, and (iv) rotation. In case of multi-component zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic result again coincides with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order. In the small-scale limit (far inside the horizon), relativistic equations including the rotation coincide with the ones in Newton's gravity.Comment: 41 pages, no figur

Experimental and numerical analysis of mold filling in rotational molding

This work focuses on the development of a numerical mold filling simulation for the rotational molding process. In the rotational molding process, a dry fiber preform is placed in a mold and impregnated with a thermoset matrix under rotation. Additionally, metallic load introduction elements can be inserted into the mold and joined with co-curing or form-fit, resulting in hybrid drive shafts or tie rods. The numerical model can be used to simulate the impregnation of the preform. Based on the resin transfer molding process, an OpenFOAM solver is extended for the rotational molding process. Permeability, kinetic and curing models are selected and adapted to the materials used. A wireless measurement solution with a capacitive sensor is developed to validate the model. Comparisons between measurements and numerically calculated impregnation times to reach the capacitive sensor with the matrix show good quality of the developed model. The average deviation between calculated result and measured mean values in the experiment is 43.8% the maximum deviation is 65.8% . The model can therefore be used to predict the impregnation progress and the curing state

Phases of N=1 USp(2N_c) Gauge Theories with Flavors

We studied the phase structures of N=1 supersymmetric USp(2N_c) gauge theory with N_f flavors in the fundamental representation as we deformed the N=2 supersymmetric QCD by adding the superpotential for adjoint chiral scalar field. We determined the most general factorization curves for various breaking patterns, for example, the two different breaking patterns of quartic superpotential. We observed all kinds of smooth transitions for quartic superpotential. Finally we discuss the intriguing role of USp(0) in the phase structure and the possible connection with observations made recently in hep-th/0304271 (Aganagic, Intriligator, Vafa and Warner) and in hep-th/0307063 (Cachazo).Comment: 61pp; Improved the presentation, references are added and to appear in PR

A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models

Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally, exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a probability space on the set F of compact, comoving, 3-spatial sections of FLRW models, a physically motivated hypothesis is proposed, using the density parameter Omega as a derived rather than fundamental parameter. We assume that the processes that select the 3-manifold also select a global mass-energy and a Hubble parameter. The inferred range in Omega consists of a single real value for any 3-manifold. Thus, the obvious measure over F is the discrete measure. Hence, if the global mass-energy and Hubble parameter are a function of 3-manifold choice among compact FLRW models, then probability spaces parametrised by Omega do not, in general, give a zero probability of a flat model. Alternatively, parametrisation by the injectivity radius r_inj ("size") suggests the Lebesgue measure. In this case, the probability space over the injectivity radius implies that flat models occur almost surely (a.s.), in the sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3: generalisation: m, H functions of

Timing and prediction of CO2 eruptions from Crystal Geyser, UT

Special instruments were deployed at Crystal Geyser, Utah, in August 2005 creating a contiguous 76-day record of eruptions from this cold geyser. Sensors measured temperature and fluid movement at the base of the geyser. Analysis of the time series that contains the start time and duration of 140 eruptions reveals a striking bimodal distribution in eruption duration. About two thirds of the eruptions were short (7-32 min), and about one third were long (98-113 min). No eruption lasted between 32 and 98 min. There is a strong correlation between the duration of an eruption and the subsequent time until the next eruption. A linear least-squares fit of these data can be used to predict the time of the next eruption. The predictions were within one hour of actual eruption time for 90% of the very short eruptions (7-19 min), and about 45% of the long eruptions. Combined with emission estimates from a previous study, we estimate the annual CO{sub 2} emission from Crystal Geyser to be about 11 gigagrams (11,000 tons)