Uncertainty Quantification in Helicopter Performance Using Monte Carlo Simulations

The effect of structural and aerodynamic uncertainties on the performance predictions of a helicopter is investigated. An aerodynamic model based on blade element and momentum theory is used to predict the helicopter performance. The aeroelastic parameters, such as blade chord, rotor radius, two-dimensional lift-curve slope, blade profile drag coefficient, rotor angular velocity, blade pitch angle, and blade twist rate per radius of the rotor, are considered as random variables. The propagation of these uncertainties to the performance parameters, such as thrust coefficient and power coefficient, are studied using Monte Carlo Simulations. The simulations are performed with 100,000 samples of structural and aerodynamic uncertain variables with a coefficient of variation ranging from 1 to 5%. The scatter in power predictions in hover, axial climb, and forward flight for the untwisted and linearly twisted blades is studied. It is found that about 20-25% excess power can be required by the helicopter relative to the determination predictions due to uncertainties.

Gibbs’ free energies of formation of Cu2Ln2O5 (Ln = Tb, Dy, Er, Yb) compounds

The standard Gibbs' free energies of formation of compounds of type Cu2L%05 (Ln = Tb,Dy,Er,Yb) were measured using the solid state cell in the temperature range of 970 to 1323 K For formation of Cu2L?O5 compounds from their binary component oxides according to the reaction 2 CUO (s) + L%03 (s) -, Cu,,L%05 (s),the Gibbs' free energy changes can be represented by the following equations:AGO = 13 080 - 13.70 'I" (+80) J mol-' (Ln = Tb)AGq = 11 480 - 13.51 T (260) J mol-I (Ln = Dy)AGO = 10 750 - 13.99 T (260) J mol-I (Ln = Er)AGO = 9 920 - 13.90 T (260) J mol-' (Ln = Yb) Since formation of the compounds is endothermic, the compounds become thermodynamically unstable with respect to their component oxides below 955 K for Cu2Tb205, 850 K for Cu2Dy205, 768 K for Cu2Er205 and 714 K for Cu2Yb2OS When the oxygen partial pressure over Cu2L%05 is lowered, they decompose according to the scheme, 2 CU,L%O, (s) -r 2 L%03 (s) +2 cu20 (s) + 02(g)The equilibrium chemical potentials of oxygen corresponding to the dissociation reactions are computed from the emf data and auxiliary information on Cu20 and CuO. The computed decomposition temperatures at an oxygen partial pressure of 5.0 x ld Pa are compared with those obtained directly from combined thermogravimetric (TGA) and differential thermal analyses (DTA).The free energy, enthalpy and entropy of formation of Cu2Ln205 compounds show systematic variation with the ionic radius of the trivalent lanthanide ion. The trends obtained in this study are compared with information available in the literature. The staZbility of Cu2Ln205 compounds increases with the decrease in ionic radii of the ~ n ion~. +

Relation between Local Structure and Glass Forming Ability of Liquid Alloys

An attempt has been made to describe the glass forming ability (GFA) of liquid alloys, using the concepts of the short range order (SRO) and middle range order (MRO) characterizing the liquid structure.A new approach to obtain good GFA of liquid alloys is based on the following four main factors: (1) formation of new SRO and competitive correlation with two or more kinds of SROs for crystallization, (2) stabilization of dense random packing by interaction between different types of SRO, (3) formation of stable cluster (SC) or middle range order (MRO) by harmonious coupling of SROs, and (4) difference between SRO characterizing the liquid structure and the near-neighbor environment in the corresponding equilibrium crystalline phases. The atomic volume mismatch estimated from the cube of the atomic radius was found to be a close relation with the minimum solute concentration for glass formation. This empirical guideline enables us to provide the optimum solute concentration for good GFA in some ternary alloys. Model structures, denoted by Bernal type and the Chemical Order type, were again tested in the novel description for the glass structure as a function of solute concentration. We illustrated the related energetics of the completion between crystal embryo and different types of SRO. Recent systematic measurements also provide that thermal diffusivity of alloys in the liquid state may be a good indicator of their GFA.

The generalized Onsager model for the secondary flow in a high-speed rotating cylinder

The generalizations of the Onsager model for the radial boundary layer and the Carrier-Maslen model for the end-cap axial boundary layer in a high-speed rotating cylinder are formulated for studying the secondary gas flow due to wall heating and due to insertion of mass, momentum and energy into the cylinder. The generalizations have wider applicability than the original Onsager and Carrier-Maslen models, because they are not restricted to the limit A >> 1, though they are restricted to the limit R e >> 1 and a high-aspect-ratio cylinder whose length/diameter ratio is large. Here, the stratification parameter A = root m Omega(2)R(2)/2k(B)T). This parameter A is the ratio of the peripheral speed, Omega R, to the most probable molecular speed, root 2k(B)T/m, the Reynolds number Re = rho w Omega R(2)/mu, where m is the molecular mass, Omega and R are the rotational speed and radius of the cylinder, k(B) is the Boltzmann constant, T is the gas temperature, rho(w) is the gas density at wall, and mu is the gas viscosity. In the case of wall forcing, analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier-Maslen equation for the velocity potential. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and axial directions for the Onsager equation, and fourth-order and second-order in the axial and radial directions for the Carrier-Maslen equation) are determined. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used `diffuse reflection' boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a `temperature slip' (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity. The predictions of the generalized models are also significantly better than those of the original Onsager and Carrier-Maslen models, which are restricted to thin boundary layers in the limit of high stratification parameter.

The R-x, R2-x Planes; Some New Ideas for the Study of Nonlinear Systems

Use of some new planes such as the R-x, R2-x (where R represents in the n-dimensional phase space, the radius vector from the origin to any point on the trajectory described by the system) is suggested for analysis of nonlinear systems of any kind. The stability conditions in these planes are given. For easy understanding of the method, the transformation from the phase plane to the R-x, R2-x planes is brought out for second-order systems. In general, while these planes serve as useful as the phase plane, they have proved to be simpler in determining quickly the general behavior of certain classes of second-order nonlinear systems. A chart and a simple formula are suggested to evaluate time easily from the R-x and R2-x trajectories, respectively. A means of solving higher-order nonlinear systems is also illustrated. Finally, a comparative study of the trajectories near singular points on the phase plane and on the new planes is made.

Electrical Breakdown of Gases Between Coaxial Cylindrical Electrodes in Crossed Electric and Magnetic Fields

Sparking potentials have been measured in nitrogen and dry air between coaxial cylindrical electrodes for values of n = R2/R1 = approximately 1 to 30 (R1 = inner electrode radius, R2 = outer electrode radius) in the presence of crossed uniform magnetic fields. The magnetic flux density was varied from 0 to 3000 Gauss. It has been shown that the minimum sparking potentials in the presence of the crossed magnetic field can be evaluated on the basis of the equivalent pressure concept when the secondary ionization coefficient does not vary appreciably with B/p (B = magnetic flux density, p = gas pressure). The values of secondary ionization coefficients �¿B in nitrogen in crossed fields calculated from measured values of sparking potentials and Townsend ionization coefficients taken from the literature, have been reported. The calculated values of collision frequencies in nitrogen from minimum sparking potentials in crossed fields are found to increase with increasing B/p at constant E/pe (pe = equivalent pressure). Studies on the similarity relationship in crossed fields has shown that the similarity theorem is obeyed in dry air for both polarities of the central electrode in crossed fields.

3D Acoustic Analysis Of Spherical Chamber Having Single Inlet And Multiple Outlet: An Impedance Matrix Approach

The transmission loss (TL) performance of spherical chambers having single inlet and multiple outlet is obtained analytically through modal expansion of acoustic field inside the spherical cavity in terms of the spherical Bessel functions and Legendre polynomials. The uniform piston driven model based upon the impedance [Z] matrix is used to characterize the multi-port spherical chamber. It is shown analytically that the [Z] parameters are independent of the azimuthal angle (phi) due to the axisymmetric shape of the sphere; rather, they depend only upon the polar angle (theta) and radius of the chamber R(0). Thus, the effects of relative polar angular location of the ports and number of outlet ports are investigated. The analytical results are shown to be in good agreement with the 3D FEA results, thereby validating the procedure suggested in this work.

Structure of DNA-functionalized dendrimer nanoparticles

Atomistic molecular dynamics simulations have been carried out to reveal the characteristic features of ethylenediamine (EDA) cored protonated (corresponding to neutral pH) poly amido amine (PAMAM) dendrimers of generation 3 (G3) and 4 (G4) that are functionalized with single strand DNAs (ssDNAs). The four ssDNA strands that are attached via an alkythiolate [-S(CH(2))(6)-] linker molecule to the free amine groups on the surface of the PAMAM dendrimers are observed to undergo a rapid conformational change during the 25 ns long simulation period. From the RMSD values of ssDNAs, we find relative stability in the case of purine rich (having more adenine and guanine) ssDNA strands than pyrimidine rich (thymine and cytosine) ssDNA strands. The degree of wrapping of ssDNA strands on the dendrimer molecule was found to be influenced by the charge ratio of DNA and the dendrimer. As the G4 dendrimer contains relatively more positive charge than G3 dendrimer, we observe extensive wrapping of ssDNAs on the G4 dendrimer than G3 dendrimer. This might indicate that DNA functionalized G3 dendrimer is more suitable to construct higher order nanostructures. The linker molecule was also found to undergo drastic conformational change during the simulation. During nanosecond long simulation some portion of the linker molecule was found to be lying nearly flat on the surface of the dendrimer molecule. The ssDNA strands along with the linkers are seen to penetrate the surface of the dendrimer molecule and approach closer to the center of the dendrimer indicating the soft sphere nature of the dendrimer molecule. The effective radius of DNA-functionalized dendrimer nanoparticles was found to be independent of base composition of ssDNAs and was observed to be around 19.5 angstrom and 22.4 angstrom when we used G3 and G4 PAMAM dendrimers as the core of the nanoparticle respectively. The observed effective radius of DNA-functionalized dendrimer molecules apparently indicates the significant shrinkage in the structure that has taken place in dendrimer, linker and DNA strands. As a whole our results describe the characteristic features of DNA-functionalized dendrimer nanoparticles and can be used as strong inputs to design effectively the DNA-dendrimer nanoparticle self-assembly for their active biological applications.

Seismic hazard map of Coimbatore using subsurface fault rupture

This study presents the future seismic hazard map of Coimbatore city, India, by considering rupture phenomenon. Seismotectonic map for Coimbatore has been generated using past earthquakes and seismic sources within 300 km radius around the city. The region experienced a largest earthquake of moment magnitude 6.3 in 1900. Available earthquakes are divided into two categories: one includes events having moment magnitude of 5.0 and above, i.e., damaging earthquakes in the region and the other includes the remaining, i.e., minor earthquakes. Subsurface rupture character of the region has been established by considering the damaging earthquakes and total length of seismic source. Magnitudes of each source are estimated by assuming the subsurface rupture length in terms of percentage of total length of sources and matched with reported earthquake. Estimated magnitudes match well with the reported earthquakes for a RLD of 5.2% of the total length of source. Zone of influence circles is also marked in the seismotectonic map by considering subsurface rupture length of fault associated with these earthquakes. As earthquakes relive strain energy that builds up on faults, it is assumed that all the earthquakes close to damaging earthquake have released the entire strain energy and it would take some time for the rebuilding of strain energy to cause a similar earthquake in the same location/fault. Area free from influence circles has potential for future earthquake, if there is seismogenic source and minor earthquake in the last 20 years. Based on this rupture phenomenon, eight probable locations have been identified and these locations might have the potential for the future earthquakes. Characteristic earthquake moment magnitude (M-w) of 6.4 is estimated for the seismic study area considering seismic sources close to probable zones and 15% increased regional rupture character. The city is divided into several grid points at spacing of 0.01 degrees and the peak ground acceleration (PGA) due to each probable earthquake is calculated at every grid point in city by using the regional attenuation model. The maximum of all these eight PGAs is taken for each grid point and the final PGA map is arrived. This map is compared to the PGA map developed based on the conventional deterministic seismic hazard analysis (DSHA) approach. The probable future rupture earthquakes gave less PGA than that of DSHA approach. The occurrence of any earthquake may be expected in near future in these eight zones, as these eight places have been experiencing minor earthquakes and are located in well-defined seismogenic sources.

Impact on spinning discs

The initial local response of a spinning disk subjected to impact is presented to highlight the effect of centrifugal stress. The impact generated deflection falls after reaching a peak unlike in the case of a stationary plate. The peak deflection at a given radius occurs around the time when the membrane wave reaches that location. This paper demonstrates the absorption of impact vibration transients in a spinning disk by the membrane wave action.

Tractable theories for the synthesis of neural networks

The Radius of Direct attraction of a discrete neural network is a measure of stability of the network. it is known that Hopfield networks designed using Hebb's Rule have a radius of direct attraction of Omega(n/p) where n is the size of the input patterns and p is the number of them. This lower bound is tight if p is no larger than 4. We construct a family of such networks with radius of direct attraction Omega(n/root plog p), for any p greater than or equal to 5. The techniques used to prove the result led us to the first polynomial-time algorithm for designing a neural network with maximum radius of direct attraction around arbitrary input patterns. The optimal synaptic matrix is computed using the ellipsoid method of linear programming in conjunction with an efficient separation oracle. Restrictions of symmetry and non-negative diagonal entries in the synaptic matrix can be accommodated within this scheme.

Enhanced photoluminescence of Gd2O3:Eu3+ nanophosphors with alkali (M = Li+, Na+, K+) metal ion co-doping

Gd1.95Eu0.4M0.01O3 (M = Li+ Na+ K+) nanophosphors have been synthesized by a low temperature solution combustion (LSC) method. Powder X-ray diffraction pattern (PXRD), scanning electron microscopy (SEM), UV-vis and photoluminescence (PL) measurements were carried out to characterize their structural and luminescent properties. The excitation and emission spectra indicated that the phosphor could be well excited by UV light (243 nm) and emit red light about 612 nm. The effect of alkali co-dopant on PL properties has been examined. The results showed that incorporation of Li+, Na+ and K+ in to Gd2O3:Eu3+ phosphor would lead to a remarkable increase of photoluminescence. The PL intensity of Gd2O3:Eu3+ phosphor was improved evidently by co-doping with Li+ ions whose radius is less than that of Gd3+ and hardly with Na+, K+ whose radius is larger than that of Gd3+. The effect of co-dopants on enhanced luminescence was mainly regarded as the result of a suitable local distortion of crystal field surrounding the Eu3+ activator. These results will play an important role in seeking some more effective co-dopants. (C) 2011 Published by Elsevier B.V.

Thermal instability and the feedback regulation of hot haloes in clusters, groups and galaxies

We present global multidimensional numerical simulations of the plasma that pervades the dark matter haloes of clusters, groups and massive galaxies (the intracluster medium; ICM). Observations of clusters and groups imply that such haloes are roughly in global thermal equilibrium, with heating balancing cooling when averaged over sufficiently long time- and length-scales; the ICM is, however, very likely to be locally thermally unstable. Using simple observationally motivated heating prescriptions, we show that local thermal instability (TI) can produce a multiphase medium with similar to 104 K cold filaments condensing out of the hot ICM only when the ratio of the TI time-scale in the hot plasma (tTI) to the free-fall time-scale (tff) satisfies tTI/tff? 10. This criterion quantitatively explains why cold gas and star formation are preferentially observed in low-entropy clusters and groups. In addition, the interplay among heating, cooling and TI reduces the net cooling rate and the mass accretion rate at small radii by factors of similar to 100 relative to cooling-flow models. This dramatic reduction is in line with observations. The feedback efficiency required to prevent a cooling flow is similar to 10-3 for clusters and decreases for lower mass haloes; supernova heating may be energetically sufficient to balance cooling in galactic haloes. We further argue that the ICM self-adjusts so that tTI/tff? 10 at all radii. When this criterion is not satisfied, cold filaments condense out of the hot phase and reduce the density of the ICM. These cold filaments can power the black hole and/or stellar feedback required for global thermal balance, which drives tTI/tff? 10. In comparison to clusters, groups have central cores with lower densities and larger radii. This can account for the deviations from self-similarity in the X-ray luminositytemperature () relation. The high-velocity clouds observed in the Galactic halo can be due to local TI producing multiphase gas close to the virial radius if the density of the hot plasma in the Galactic halo is >rsim 10-5 cm-3 at large radii.

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.

Dependence of diffusivity on density and solute diameter in liquid phase: A molecular dynamics study of Lennard-Jones system

Investigations into the variation of self-diffusivity with solute radius, density, and degree of disorder of the host medium is explored. The system consists of a binary mixture of a relatively smaller sized solute, whose size is varied and a larger sized solvent interacting via Lennard-Jones potential. Calculations have been performed at three different reduced densities of 0.7, 0.8, and 0.933. These simulations show that diffusivity exhibits a maximum for some intermediate size of the solute when the solute diameter is varied. The maximum is found at the same size of the solute at all densities which is at variance with the prediction of the levitation effect. In order to understand this anomaly, additional simulations were carried out in which the degree of disorder has been varied while keeping the density constant. The results show that the diffusivity maximum gradually disappears with increase in disorder. Disorder has been characterized by means of the minimal spanning tree. Simulations have also been carried out in which the degree of disorder is constant and only the density is altered. The results from these simulations show that the maximum in diffusivity now shifts to larger distances with decrease in density. This is in agreement with the changes in void and neck distribution with density of the host medium. These results are in excellent agreement with the predictions of the levitation effect. They suggest that the effect of disorder is to shift the maximum in diffusivity towards smaller solute radius while that of the decrease in density is to shift it towards larger solute radius. Thus, in real systems where the degree of disorder is lower at higher density and vice versa, the effect due to density and disorder have opposing influences. These are confirmed by the changes seen in the velocity autocorrelation function, self part of the intermediate scattering function and activation energy. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.3701619]