The analytic form of the daylight locus.

2013 ◽  
pp. 57-72
Author(s):  
Geoffrey Iverson ◽  
Charles Chubb
Keyword(s):  
Analytic Form

Incipient Separation Near Corners

2018 ◽  
Author(s):  
Anatoly I. Ruban
Keyword(s):  
Corner Point ◽  
Analytic Form ◽  
The Body ◽  
Recirculation Region ◽  
Body Contour ◽  
Concave Corner ◽  
Attached Flow ◽  
Surface Deflection ◽  
Interaction Problem ◽  
Incipient Separation

Chapter 4 analyses the transition from an attached flow to a flow with local recirculation region near a corner point of a body contour. It considers both subsonic and supersonic flow regimes, and shows that the flow near a corner can be studied in the framework of the triple-deck theory. It assumes that the body surface deflection angle is small, and formulates the linearized viscous-inviscid interaction problem. Its solution is found in an analytic form. It also presents the results of the numerical solution of the full nonlinear problem. It shows how, and when, the separation region forms in the boundary layer. In conclusion, it suggests that in the subsonic flow past a concave corner, the solution is not unique.

scholarly journals Structure factors for generalized grey Browinian motion

2019 ◽  
Vol 22 (2) ◽  
pp. 396-411
Author(s):  
José L. da Silva ◽  
Ludwig Streit
Keyword(s):  
Gaussian Processes ◽  
Form Factors ◽  
Analytic Form ◽  
Debye Function ◽  
Asymptotic Decay ◽  
Structure Factors ◽  
Closed Analytic Form ◽  
Non Gaussian

Abstract In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

scholarly journals A theory of giant vortices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Alexander A. Penin ◽  
Quinten Weller
Keyword(s):  
Asymptotic Expansion ◽  
Analytic Form ◽  
Scalar Fields ◽  
Winding Number ◽  
Asymptotic Results ◽  
Convergence Region ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Neutral Scalar ◽  
Vortex Solutions

Abstract We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number n. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-n corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.

An Overall Approach for Microcrack and Inhomogeneity Toughening in Brittle Solids

1999 ◽  
Vol 15 (2) ◽  
pp. 57-68
Author(s):  
Huang Hsing Pan
Keyword(s):  
Poisson Ratio ◽  
Crack Density ◽  
Mean Field ◽  
Analytic Form ◽  
Density Parameter ◽  
Brittle Solids ◽  
The Matrix ◽  
Microcrack Toughening ◽  
Average Quantity ◽  
The Mean

ABSTRACTBased on the weight function theory and Hutchinson's technique, the analytic form of the toughness change near a crack-tip is derived. The inhomogeneity toughening is treated as an average quantity calculated from the mean-field approach. The solutions are suitable for the composite materials with moderate concentration as compared with Hutchinson's lowest order formula. The composite has the more toughened property if the matrix owns the higher value of the Poisson ratio. The composite with thin-disc inclusions obtains the highest toughening and that with spheres always provides the least effective one. For the microcrack toughening, the variations of the crack shape do not significantly affect the toughness change if the Budiansky and O'Connell crack density parameter is used. The explicit forms for three types of the void toughening and two types of the microcrack toughening are also shown.

The interaction between dark energy and dark matter and its connection to the modified gravity

2015 ◽  
Vol 30 (28n29) ◽  
pp. 1545012
Author(s):  
Jian-Hua He ◽  
Bin Wang
Keyword(s):  
Analytic Form ◽  
Rate Function ◽  
Einstein Frame ◽  
Linear Perturbation ◽  
Jordan Frame ◽  
Expansion Of The Universe ◽  
Text Model ◽  
Conformal Equivalence ◽  
The Universe ◽  
Dilation Rate

We review the conformal equivalence in describing the background expansion of the universe by [Formula: see text] gravity both in the Jordan frame and the Einstein frame. In the Jordan frame, we present the general analytic expression for [Formula: see text] models that have the same expansion history as the [Formula: see text]CDM model. This analytic form can provide further insights on how cosmology can be used to test the [Formula: see text] gravity at the largest scales. Moreover we present a systematic and self-consistent way to construct the viable [Formula: see text] model in Jordan frame using the mass dilation rate function from the Einstein frame through the conformal transformation. In addition, we extend our study to the linear perturbation theories and we further exhibit the equivalence of the [Formula: see text] gravity presented in the Jordan frame and Einstein frame in the perturbed space–time. We argue that this equivalence has solid physics root.

Parametric Description of Vibration Using the Autocorrelation Function

2009 ◽  
Vol 147-149 ◽  
pp. 606-611
Author(s):  
Adam Kotowski
Keyword(s):  
Autocorrelation Function ◽  
Curve Fitting ◽  
Vibration Signal ◽  
Analytic Form ◽  
Parametric Representation ◽  
Rotating Machine ◽  
Fitting Procedure ◽  
Power Spectral ◽  
Parametric Description ◽  
Harmonic Components

The paper presents the use of the autocorrelation function for the description of vibrations and the problems connected with. The proposed method is based on the analysis of vibration signal recorded for machine during its operations using an analytic form of the autocorrelation function. The parameters are obtained using a curve fitting procedure. To keep a quality of parametric representation of considered vibration, only the curve fitting causes a determination coefficient over 0.90 is taken into consideration. Therefore, the autocorrelation functions are submitted for the fast Fourier transform to be helped, in determination of number of the dominant harmonic components. Also, the analytic form and parameters of power spectral density has been also calculated. Finally, the set of parameters has been collected to describe the selected fragment of vibration of the simple rotating machine. The influence of duration of analyzed vibration on the parameters values is also examined in this work.

scholarly journals On the analytic form of the discrete Kramer sampling theorem

2001 ◽  
Vol 25 (11) ◽  
pp. 709-715 ◽  
Author(s):  
Antonio G. García ◽  
Miguel A. Hernández-Medina ◽  
María J. Muñoz-Bouzo
Keyword(s):  
Orthogonal Polynomials ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Analytic Form ◽  
Sampling Theorem ◽  
Discrete Version ◽  
Moment Problems ◽  
Sturm Liouville ◽  
The Subject ◽  
Sampling Expansions

The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems. In this paper a discrete version of the analytic Kramer sampling theorem is proved. Orthogonal polynomials arising from indeterminate Hamburger moment problems as well as polynomials of the second kind associated with them provide examples of Kramer analytic kernels.

Mathematical Hull Design for Sailing Yachts

1981 ◽  
Author(s):  
John S. Letcher
Keyword(s):  
Historical Perspective ◽  
Analytic Form ◽  
Surface Shape ◽  
Analytic Geometry ◽  
Representation System ◽  
Construction Methods ◽  
Small Craft ◽  
Hull Design ◽  
Basic Concepts ◽  
Mathematical Design

Mathematical representations of hull surface shape have largely supplanted graphical fairing and lofting of lines in the shipbuilding and aircraft industries, but have had little application so far to small craft. Past methods of hull design are surveyed to put mathematical design into historical perspective and point up its many advantages. The basic concepts of analytic geometry of surfaces needed for yacht hull design are briefly introduced with references. Several special aspects of the geometry of yacht hulls, arising from considerations of aesthetics, hydrodynamics, and construction methods are discussed and cast into analytic form for inclusion in a hull design scheme. The paper explains in detail a particular representation system called FAIRLINE/1, simple enough to fit into the program and memory limitations of a TI-59 calculator, yet extremely versatile. A program listing and several example hull designs created with this program are presented.

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