scholarly journals The steady aerodynamics of aerofoils with porosity gradients

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170266 ◽  
Author(s):  
Rozhin Hajian ◽  
Justin W. Jaworski
Keyword(s):  
Noise Suppression ◽  
Hilbert Problem ◽  
Practical Interest ◽  
Hölder Condition ◽  
Hölder Continuous ◽  
Porosity Distribution ◽  
Minimal Impact ◽  
Aerodynamic Loads ◽  
Formal Restriction ◽  
Theoretical Predictions

This theoretical study determines the aerodynamic loads on an aerofoil with a prescribed porosity distribution in a steady incompressible flow. A Darcy porosity condition on the aerofoil surface furnishes a Fredholm integral equation for the pressure distribution, which is solved exactly and generally as a Riemann–Hilbert problem provided that the porosity distribution is Hölder-continuous. The Hölder condition includes as a subset any continuously differentiable porosity distributions that may be of practical interest. This formal restriction on the analysis is examined by a class of differentiable porosity distributions that approach a piecewise, discontinuous function in a certain parametric limit. The Hölder-continuous solution is verified in this limit against analytical results for partially porous aerofoils in the literature. Finally, a comparison made between the new theoretical predictions and experimental measurements of SD7003 aerofoils presented in the literature. Results from this analysis may be integrated into a theoretical framework to optimize turbulence noise suppression with minimal impact to aerodynamic performance.

Convergence of derivative free iterative methods

2019 ◽  
Vol 28 (1) ◽  
pp. 19-26
Author(s):  
IOANNIS K. ARGYROS ◽  
◽  
SANTHOSH GEORGE ◽  
Keyword(s):  
Banach Space ◽  
Iterative Methods ◽  
Local Convergence ◽  
Practical Interest ◽  
Systems Of Equations ◽  
Hölder Continuous ◽  
Numerical Examples ◽  
Lipschitz Continuous ◽  
Derivative Free ◽  
Special Cases

We present the local as well as the semi-local convergence of some iterative methods free of derivatives for Banach space valued operators. These methods contain the secant and the Kurchatov method as special cases. The convergence is based on weak hypotheses specializing to Lipschitz continuous or Holder continuous hypotheses. The results are of theoretical and practical interest. In particular the method is compared favorably ¨ to other methods using concrete numerical examples to solve systems of equations containing a nondifferentiable term.

The fractal dimension of quasi-periodic orbits

1998 ◽  
Vol 18 (6) ◽  
pp. 1467-1471
Author(s):  
BRYAN P. RYNNE
Keyword(s):  
Fractal Dimension ◽  
Asymptotic Behaviour ◽  
Periodic Orbits ◽  
Continuous Functions ◽  
Hölder Condition ◽  
Hölder Continuous ◽  
Hölder Continuous Functions

Recently, Naito considered quasi-periodic orbits of Hölder continuous functions and obtained results relating the exponent in the Hölder condition to the asymptotic behaviour of the inclusion lengths of the $\epsilon$-almost periods of these orbits, and also to the fractal dimension of these orbits. In this paper we improve these results.

scholarly journals Modelling density segregation in flowing bidisperse granular materials

2016 ◽  
Vol 472 (2191) ◽  
pp. 20150856 ◽  
Author(s):  
Hongyi Xiao ◽  
Paul B. Umbanhowar ◽  
Julio M. Ottino ◽  
Richard M. Lueptow
Keyword(s):  
Particle Concentration ◽  
Practical Interest ◽  
Industrial Processes ◽  
Dem Simulations ◽  
Granular Mixtures ◽  
Theoretical Predictions ◽  
Local Shear ◽  
Density Ratios ◽  
Kinematic Information ◽  
Modelling Approach

Preventing segregation in flowing granular mixtures is an ongoing challenge for industrial processes that involve the handling of bulk solids. A recent continuum-based modelling approach accurately predicts spatial concentration fields in a variety of flow geometries for mixtures varying in particle size. This approach captures the interplay between advection, diffusion and segregation using kinematic information obtained from experiments and/or discrete element method (DEM) simulations combined with an empirically determined relation for the segregation velocity. Here, we extend the model to include density-driven segregation, thereby validating the approach for the two important cases of practical interest. DEM simulations of density bidisperse flows of mono-sized particles in a quasi-two-dimensional-bounded heap were performed to determine the dependence of the density-driven segregation velocity on local shear rate and particle concentration. The model yields theoretical predictions of segregation patterns that quantitatively match the DEM simulations over a range of density ratios and flow rates. Matching experiments reproduce the segregation patterns and quantitative segregation profiles obtained in both the simulations and the model, thereby demonstrating that the modelling approach captures the essential physics of density-driven segregation in granular heap flow.

scholarly journals Extending the Applicability and Convergence Domain of a Fifth-Order Iterative Scheme under Hölder Continuous Derivative in Banach Spaces

2021 ◽  
pp. 258-270
Author(s):  
Debasis Sharma ◽  
Sanjaya Kumar Parhi ◽  
Shanta Kumari Sunanda
Keyword(s):  
Significant Contribution ◽  
Iterative Scheme ◽  
Local Analysis ◽  
Continuous Derivative ◽  
Hölder Condition ◽  
Convergence Domain ◽  
Hölder Continuous ◽  
Lipschitz Constants ◽  
Fifth Order ◽  
Extra Assumption

The most significant contribution made by this study is that the applicability and convergence domain of a fifth-order convergent nonlinear equation solver is extended. We use Hölder condition on the first Fréchet derivative to study the local analysis, and this expands the applicability of the formula for such problems where the earlier study based on Lipschitz constants cannot be used. This study generalizes the local analysis based on Lipschitz constants. Also, we avoid the use of the extra assumption on boundedness of the first derivative of the involved operator. Finally, numerical experiments ensure that our analysis expands the utility of the considered scheme. In addition, the proposed technique produces a larger convergence domain, in comparison to the earlier study, without using any extra conditions.

Instantaneous Aerodynamic Load Calculations in Rotating Airfoils From Time Resolved PIV Measurements at Low Reynolds Number

2013 ◽  
Author(s):  
Arturo Villegas ◽  
F. Javier Diez
Keyword(s):  
Full Range ◽  
Temporal Variations ◽  
Momentum Equation ◽  
Aerodynamic Load ◽  
Time Resolved ◽  
Unsteady Forces ◽  
Aerodynamic Loads ◽  
Rotating Blade ◽  
Theoretical Predictions ◽  
Stationary Reference Frame

The time-resolved evolution of the instantaneous pressure fields and aerodynamic loads are obtained for rotating airfoils. This method allows evaluating the fluctuations in the instantaneous aerodynamic loads which cannot be evaluated with averaging methods. It also has the ability of capturing high temporal variations such as vortex shedding in the wake of the rotating blade. Briefly, this method obtains the velocity field from time-resolved particle image velocimetry TR-PIV. This is used to calculate the pressure field around the turbine from the Poisson pressure equation. Then, the forces are obtained using the integral momentum equation in a stationary reference frame. These experimental aerodynamic loads are compared to theoretical predictions from the Blade Element Momentum theory (BEM). Accurately determining instantaneous forces in turbines is needed for safety and understanding of their full range of operation. The standard deviation of the instantaneous forces establishes the limits of the forces expected on the turbine. The uncertainty in the measurements is calculated. The method presented may be used to measure unsteady forces in rotating airfoils, providing useful information not just for computational studies, but also for aerodynamics, material and structural optimization and safety purposes.

scholarly journals Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kai Tao
Keyword(s):  
Lyapunov Exponent ◽  
Ergodic Theorem ◽  
Hölder Condition ◽  
Hölder Continuous ◽  
Subharmonic Functions ◽  
Birkhoff Ergodic Theorem ◽  
Special Case ◽  
Coupling Number

<p style='text-indent:20px;'>In this paper, we first prove the strong Birkhoff Ergodic Theorem for subharmonic functions with the irrational shift on the Torus. Then, we apply it to the analytic quasi-periodic Jacobi cocycles and show that for suitable frequency and coupling number, if the Lyapunov exponent of these cocycles is positive at one point, then it is positive on an interval centered at this point and Hölder continuous in <inline-formula><tex-math id="M1">\begin{document}$ E $\end{document}</tex-math></inline-formula> on this interval. What's more, if the coupling number of the potential is large, then the Lyapunov exponent is always positive for all irrational frequencies and Hölder continuous in <inline-formula><tex-math id="M2">\begin{document}$ E $\end{document}</tex-math></inline-formula> for all finite Liouville frequencies. For the Schrödinger cocycles, a special case of the Jacobi ones, its Lyapunov exponent is also Hölder continuous in the frequency and the lengths of the intervals where the Hölder condition of the Lyapunov exponent holds only depend on the coupling number.</p>

ESTIMATION OF FRACTAL DIMENSION OF FRACTIONAL CALCULUS OF THE HÖLDER CONTINUOUS FUNCTIONS

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050123
Author(s):  
YONG-SHUN LIANG
Keyword(s):  
Fractal Dimension ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Continuous Functions ◽  
Box Dimension ◽  
Hölder Condition ◽  
Hölder Continuous ◽  
Lipschitz Continuous ◽  
Liouville Fractional Derivative

In the present paper, fractal dimension and properties of fractional calculus of certain continuous functions have been investigated. Upper Box dimension of the Riemann–Liouville fractional integral of continuous functions satisfying the Hölder condition of certain positive orders has been proved to be decreasing linearly. If sum of order of the Riemann–Liouville fractional integral and the Hölder condition equals to one, the Riemann–Liouville fractional integral of the function will be Lipschitz continuous. If the corresponding sum is strictly larger than one, the Riemann–Liouville fractional integral of the function is differentiable. Estimation of fractal dimension of the derivative function has also been discussed. Finally, the Riemann–Liouville fractional derivative of continuous functions satisfying the Hölder condition exists when order of the Riemann–Liouville fractional derivative is smaller than order of the Hölder condition. Upper Box dimension of the function has been proved to be increasing at most linearly.

Microcalorimeters for X-Ray Spectroscopy

1988 ◽  
Vol 102 ◽  
pp. 41
Author(s):  
E. Silver ◽  
C. Hailey ◽  
S. Labov ◽  
N. Madden ◽  
D. Landis ◽  
...  
Keyword(s):  
High Resolution ◽  
High Efficiency ◽  
Thermal Response ◽  
Low Noise ◽  
High Resolution Spectroscopy ◽  
Superconducting Transition ◽  
Sapphire Substrates ◽  
Laboratory Plasmas ◽  
Adiabatic Demagnetization ◽  
Theoretical Predictions

The merits of microcalorimetry below 1°K for high resolution spectroscopy has become widely recognized on theoretical grounds. By combining the high efficiency, broadband spectral sensitivity of traditional photoelectric detectors with the high resolution capabilities characteristic of dispersive spectrometers, the microcalorimeter could potentially revolutionize spectroscopic measurements of astrophysical and laboratory plasmas. In actuality, however, the performance of prototype instruments has fallen short of theoretical predictions and practical detectors are still unavailable for use as laboratory and space-based instruments. These issues are currently being addressed by the new collaborative initiative between LLNL, LBL, U.C.I., U.C.B., and U.C.D.. Microcalorimeters of various types are being developed and tested at temperatures of 1.4, 0.3, and 0.1°K. These include monolithic devices made from NTD Germanium and composite configurations using sapphire substrates with temperature sensors fabricated from NTD Germanium, evaporative films of Germanium-Gold alloy, or material with superconducting transition edges. A new approache to low noise pulse counting electronics has been developed that allows the ultimate speed of the device to be determined solely by the detector thermal response and geometry. Our laboratory studies of the thermal and resistive properties of these and other candidate materials should enable us to characterize the pulse shape and subsequently predict the ultimate performance. We are building a compact adiabatic demagnetization refrigerator for conveniently reaching 0.1°K in the laboratory and for use in future satellite-borne missions. A description of this instrument together with results from our most recent experiments will be presented.

A crystallographic analysis of the CoSi/Si(111) interface using Transmission Electron Microscopy

1990 ◽  
Vol 48 (4) ◽  
pp. 574-575
Author(s):  
A.C. Daykin ◽  
C.J. Kiely ◽  
R.C. Pond ◽  
J.L. Batstone
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Defect Structure ◽  
Room Temperature ◽  
Theoretical Method ◽  
Crystallographic Analysis ◽  
Si Substrate ◽  
Transmission Electron ◽  
Theoretical Predictions

When CoSi2 is grown onto a Si(111) surface it can form in two distinct orientations. A-type CoSi2 has the same orientation as the Si substrate and B-type is rotated by 180° degrees about the [111] surface normal.One method of producing epitaxial CoSi2 is to deposit Co at room temperature and anneal to 650°C.If greater than 10Å of Co is deposited then both A and B-type CoSi2 form via a number of intermediate silicides .The literature suggests that the co-existence of A and B-type CoSi2 is in some way linked to these intermediate silicides analogous to the NiSi2/Si(111) system. The phase which forms prior to complete CoSi2 formation is CoSi. This paper is a crystallographic analysis of the CoSi2/Si(l11) bicrystal using a theoretical method developed by Pond. Transmission electron microscopy (TEM) has been used to verify the theoretical predictions and to characterise the defect structure at the interface.

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