Polar Angle in Terms of Jacobi Hyperbolic Functions

2012 ◽  
Vol 3 (5) ◽  
pp. 105-106
Author(s):  
Parveen Bawa ◽  
Keyword(s):  
Polar Angle ◽  
Hyperbolic Functions

scholarly journals Tunable multichannel Photonic spin Hall effect in metal-dielectric-metal waveguide

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Li-Ming Zhao ◽  
Yun-Song Zhou
Keyword(s):  
Hall Effect ◽  
Polar Angle ◽  
Spin Hall Effect ◽  
Dipole Source ◽  
Interference Theory ◽  
Wave Interference ◽  
Metal Waveguide ◽  
Component Wave ◽  
Plasmon Polaritons ◽  
Important Progress

AbstractThe discovery of Photonic spin Hall effect (PSHE) on surface plasmon polaritons (SPPs) is an important progress in photonics. In this paper, a method of realizing multi-channel PSHE in two-dimensional metal-air-metal waveguide is proposed. By modulating the phase difference $$\phi$$ ϕ and polar angle $$\theta$$ θ of the dipole source, the SPP can propagate along a specific channel. We further prove that PSHE results from the component wave interference theory. We believe that our findings will rich the application of SPPs in optical devices.

scholarly journals Reminders Regarding Hyperbolic Functions

2021 ◽  
pp. 309-311
Keyword(s):  
Hyperbolic Functions

On the improvement of q-deformed hyperbolic functions

2021 ◽  
Author(s):  
J. Morales ◽  
J. J. Peña ◽  
J. García-Ravelo
Keyword(s):  
Hyperbolic Functions

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

scholarly journals Applications of a duality between generalized trigonometric and hyperbolic functions

2021 ◽  
Vol 502 (1) ◽  
pp. 125241
Author(s):  
Hiroki Miyakawa ◽  
Shingo Takeuchi
Keyword(s):  
Hyperbolic Functions

scholarly journals Study of relativistic magnetized outflows with relativistic equation of state

2019 ◽  
Vol 488 (4) ◽  
pp. 5713-5727
Author(s):  
Kuldeep Singh ◽  
Indranil Chattopadhyay
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Equation Of State ◽  
Polar Angle ◽  
Relativistic Equation ◽  
Azimuthal Velocity ◽  
Astrophysical Jets ◽  
Composition Parameter ◽  
Field Lines ◽  
Flow Experiences

ABSTRACT We study relativistic magnetized outflows using relativistic equation of state having variable adiabatic index (Γ) and composition parameter (ξ). We study the outflow in special relativistic magnetohydrodynamic regime, from sub-Alfvénic to super-fast domain. We showed that, after the solution crosses the fast point, magnetic field collimates the flow and may form a collimation-shock due to magnetic field pinching/squeezing. Such fast, collimated outflows may be considered as astrophysical jets. Depending on parameters, the terminal Lorentz factors of an electron–proton outflow can comfortably exceed few tens. We showed that due to the transfer of angular momentum from the field to the matter, the azimuthal velocity of the outflow may flip sign. We also study the effect of composition (ξ) on such magnetized outflows. We showed that relativistic outflows are affected by the location of the Alfvén point, the polar angle at the Alfvén point and also the angle subtended by the field lines with the equatorial plane, but also on the composition of the flow. The pair dominated flow experiences impressive acceleration and is hotter than electron–proton flow.

scholarly journals Rotor Interaction Noise in Counter-Rotating Propfan Propulsion Systems

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Andreas Peters ◽  
Zoltán S. Spakovszky
Keyword(s):  
Polar Angle ◽  
Secondary Flows ◽  
Tip Vortex ◽  
System Level ◽  
Analysis Tool ◽  
Acoustic Analogy ◽  
Wake Interaction ◽  
Open Rotor ◽  
And Performance ◽  
The Individual

Due to their inherent noise challenge and potential for significant reductions in fuel burn, counter-rotating propfans (CRPs) are currently being investigated as potential alternatives to high-bypass turbofan engines. This paper introduces an integrated noise and performance assessment methodology for advanced propfan powered aircraft configurations. The approach is based on first principles and combines a coupled aircraft and propulsion system mission and performance analysis tool with 3D unsteady, full-wheel CRP computational fluid dynamics computations and aeroacoustic simulations. Special emphasis is put on computing CRP noise due to interaction tones. The method is capable of dealing with parametric studies and exploring noise reduction technologies. An aircraft performance, weight and balance, and mission analysis was first conducted on a candidate CRP powered aircraft configuration. Guided by data available in the literature, a detailed aerodynamic design of a pusher CRP was carried out. Full-wheel unsteady 3D Reynolds-averaged Navier-Stokes (RANS) simulations were then used to determine the time varying blade surface pressures and unsteady flow features necessary to define the acoustic source terms. A frequency domain approach based on Goldstein’s formulation of the acoustic analogy for moving media and Hanson’s single rotor noise method was extended to counter-rotating configurations. The far field noise predictions were compared to measured data of a similar CRP configuration and demonstrated good agreement between the computed and measured interaction tones. The underlying noise mechanisms have previously been described in literature but, to the authors’ knowledge, this is the first time that the individual contributions of front-rotor wake interaction, aft-rotor upstream influence, hub-endwall secondary flows, and front-rotor tip-vortices to interaction tone noise are dissected and quantified. Based on this investigation, the CRP was redesigned for reduced noise incorporating a clipped rear-rotor and increased rotor-rotor spacing to reduce upstream influence, tip-vortex, and wake interaction effects. Maintaining the thrust and propulsive efficiency at takeoff conditions, the noise was calculated for both designs. At the interaction tone frequencies, the redesigned CRP demonstrated an average reduction of 7.25 dB in mean sound pressure level computed over the forward and aft polar angle arcs. On the engine/aircraft system level, the redesigned CRP demonstrated a reduction of 9.2 dB in effective perceived noise (EPNdB) and 8.6 EPNdB at the Federal Aviation Regulations (FAR) 36 flyover and sideline observer locations, respectively. The results suggest that advanced open rotor designs can possibly meet Stage 4 noise requirements.

The q-pell hyperbolic functions

2012 ◽  
Author(s):  
A. Güncan ◽  
Ş. Akduman
Keyword(s):  
Hyperbolic Functions

Nanometer-Scale Composite Structures Formed by Simultaneous Oblique Sputter-Deposition of Two Materials from Different Directions

1990 ◽  
Vol 206 ◽  
Author(s):  
Tomoyoshi Motohiro ◽  
Yasuhiko Takeda ◽  
Yoshihide Watanabe ◽  
Shoji Noda
Keyword(s):  
Composite Structures ◽  
Polar Angle ◽  
Sputter Deposition ◽  
Nanometer Scale ◽  
Metal Insulator ◽  
Host Materials ◽  
Oblique Deposition ◽  
Host Structure ◽  
Optical Applications ◽  
Nonlinear Optical Applications

ABSTRACTOblique depositlon(OD) provides an attractive anisotropic structure In nm-scale as a promising host structure to form anisotropic nm-scale composites(ANSC). Among a variety of possible methods to introduce a guest material Into the host structure of OD, we have attempted simultaneous oblique deposition of a guest and a host material from two different directions. The computer simulation for ballistic deposition, which had greatly contributed to the understanding of the morphology evolution in OD, has been carried out again here to design possible ANSC structures and to survey their variations. A typical ANSC structure obtained here is a composite of slender clusters of the guest and the host materials, which can be regarded as an anisotropic version of the well-known isotropic structures of the metal-insulator or semiconductor-insulator cermets for magneto-optical or nonlinear optical applications. This appears when the host and the guest materials are deposited from the directions of the same polar angle of 70° but from the reverse azimuthal directions. In accordance with this result, a specially designed sputtering apparatus has been constructed. Structures and optical anisotropy of the films of several composites' systems such as ZnTe-SiO2 and Cu-SiO2 formed by this apparatus have indicated that our attempt has hit the mark.

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