scholarly journals Deflection angle of a light ray reflected by a general marginally unstable photon sphere in a strong deflection limit

2020 ◽  
Vol 102 (10) ◽  
Author(s):  
Naoki Tsukamoto
Keyword(s):  
Deflection Angle ◽  
Deflection Limit

scholarly journals Strong gravitational lensing of a 4-dimensional Einstein–Gauss–Bonnet black hole in homogeneous plasma

2020 ◽  
Vol 29 (09) ◽  
pp. 2050065 ◽  
Author(s):  
Xing-Hua Jin ◽  
Yuan-Xing Gao ◽  
Dao-Jun Liu
Keyword(s):  
Gravitational Lensing ◽  
Deflection Angle ◽  
Strong Field ◽  
The Novel ◽  
Coupling Constant ◽  
Homogeneous Plasma ◽  
Strong Gravitational Lensing ◽  
Image Separation ◽  
Unmagnetized Plasma ◽  
Deflection Limit

We investigate the strong gravitational lensing of spherically symmetric black holes in the novel Einstein–Gauss–Bonnet (EGB) gravity surrounded by unmagnetized plasma medium. The deflection angle in the strong deflection limit in EGB spacetime with homogeneous plasma is derived. We find that both the coupling constant [Formula: see text] in the novel EGB gravity and the presence of plasma can affect the radius of photon sphere, strong field limit coefficient and other lensing observables significantly, while plasma has little effect on the angular image separation and the relative magnifications as [Formula: see text] and [Formula: see text], respectively.

scholarly journals Strong lensing and observables around 5D Myers–Perry black hole spacetime

2018 ◽  
Vol 33 (23) ◽  
pp. 1850126
Author(s):  
Ravi Shankar Kuniyal ◽  
Hemwati Nandan ◽  
Uma Papnoi ◽  
Rashmi Uniyal ◽  
K. D. Purohit
Keyword(s):  
Black Hole ◽  
Deflection Angle ◽  
Strong Field ◽  
Kerr Black Hole ◽  
Four Dimensions ◽  
Test Particles ◽  
Spin Parameter ◽  
Black Hole Spacetime ◽  
Field Coefficient ◽  
Deflection Limit

We study the motion of massless test particles in a five-dimensional (5D) Myers–Perry black hole spacetime with two-spin parameters. The behavior of the effective potential in view of different values of black hole parameters is discussed in the equatorial plane. The frequency shift of photons is calculated which is found to depend on the spin parameter of black hole and the observed redshift is discussed accordingly. The deflection angle and the strong deflection limit coefficients are also calculated and their behavior with the spin parameters is analyzed in detail. It is observed that the behaviors of both deflection angle and strong field coefficient differs from Kerr black hole spacetime in four dimensions in General Relativity (GR), which is mainly due to the presence of two-spin parameters in higher dimension.

scholarly journals Static Aeroelastic Characteristics of Morphing Trailing-Edge Wing Using Geometrically Exact Vortex Lattice Method

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Sen Mao ◽  
Changchuan Xie ◽  
Lan Yang ◽  
Chao Yang
Keyword(s):  
Vortex Lattice ◽  
Deflection Angle ◽  
Aircraft Design ◽  
Analysis Method ◽  
Lattice Method ◽  
Trailing Edge ◽  
Vortex Lattice Method ◽  
Analysis And Design ◽  
Aeroelastic Analysis ◽  
Typical Model

A morphing trailing-edge (TE) wing is an important morphing mode in aircraft design. In order to explore the static aeroelastic characteristics of a morphing TE wing, an efficient and feasible method for static aeroelastic analysis has been developed in this paper. A geometrically exact vortex lattice method (VLM) is applied to calculate the aerodynamic forces. Firstly, a typical model of a morphing TE wing is chosen and built which has an active morphing trailing edge driven by a piezoelectric patch. Then, the paper carries out the static aeroelastic analysis of the morphing TE wing and corresponding simulations were carried out. Finally, the analysis results are compared with those of a traditional wing with a rigid trailing edge using the traditional linearized VLM. The results indicate that the geometrically exact VLM can better describe the aerodynamic nonlinearity of a morphing TE wing in consideration of geometrical deformation in aeroelastic analysis. Moreover, out of consideration of the angle of attack, the deflection angle of the trailing edge, among others, the wing system does not show divergence but bifurcation. Consequently, the aeroelastic analysis method proposed in this paper is more applicable to the analysis and design of a morphing TE wing.

scholarly journals Design and Optimal Control of a Multistable, Cooperative Microactuator

Actuators ◽  
2021 ◽  
Vol 10 (8) ◽  
pp. 183
Author(s):  
Michael Olbrich ◽  
Arwed Schütz ◽  
Tamara Bechtold ◽  
Christoph Ament
Keyword(s):  
Deflection Angle ◽  
Initial State ◽  
New Concepts ◽  
Vertical Displacements ◽  
State Uncertainty ◽  
Stable Equilibria ◽  
Freely Moving ◽  
Time And Energy ◽  
Multiple Stable Equilibria ◽  
Optimal Trajectory Planning

In order to satisfy the demand for the high functionality of future microdevices, research on new concepts for multistable microactuators with enlarged working ranges becomes increasingly important. A challenge for the design of such actuators lies in overcoming the mechanical connections of the moved object, which limit its deflection angle or traveling distance. Although numerous approaches have already been proposed to solve this issue, only a few have considered multiple asymptotically stable resting positions. In order to fill this gap, we present a microactuator that allows large vertical displacements of a freely moving permanent magnet on a millimeter-scale. Multiple stable equilibria are generated at predefined positions by superimposing permanent magnetic fields, thus removing the need for constant energy input. In order to achieve fast object movements with low solenoid currents, we apply a combination of piezoelectric and electromagnetic actuation, which work as cooperative manipulators. Optimal trajectory planning and flatness-based control ensure time- and energy-efficient motion while being able to compensate for disturbances. We demonstrate the advantage of the proposed actuator in terms of its expandability and show the effectiveness of the controller with regard to the initial state uncertainty.

scholarly journals Quantitative evaluation indexes of the spatial steering effect of directional perforation hydraulic fractures

2021 ◽  
pp. 014459872110102
Author(s):  
Lu Weiyong ◽  
He Changchun
Keyword(s):  
Quantitative Evaluation ◽  
Hydraulic Fracture ◽  
Deflection Angle ◽  
Hydraulic Fractures ◽  
Principal Stress Direction ◽  
Perforation Hole ◽  
Evaluation Indexes ◽  
Initiation Pressure ◽  
The Deflection Angle ◽  
Bending Fracture

To better evaluate the spatial steering effect of directional perforation hydraulic fractures, evaluation indexes for the spatial steering effect are first proposed in this paper. Then, these indexes are used to quantitatively evaluate existing physical experimental results. Finally, with the help of RFPA2D-Flow software, the influence of perforation length and azimuth on the spatial steering process of hydraulic fracture are quantitatively analysed using four evaluation indexes. It is shown by the results that the spatial deflection trajectory, deflection distance, deflection angle and initiation pressure of hydraulic fractures can be used as quantitative evaluation indexes for the spatial steering effect of hydraulic fractures. The deflection paths of directional perforation hydraulic fractures are basically the same. They all gradually deflect to the maximum horizontal principal stress direction from the perforation hole and finally represent a double-wing bending fracture. The deflection distance, deflection angle and initiation pressure of hydraulic fractures increase gradually with increasing perforation azimuth, and the sensitivity of the deflection angle to the perforation azimuth of hydraulic fractures also increases. With increasing perforation length, the deflection distance of hydraulic fractures increases gradually. However, the deflection angle and initiation pressure decrease gradually, as does the sensitivity.

scholarly journals Research on control effectiveness of fluidic thrust vectoring

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042199813
Author(s):  
Fei Xue ◽  
Gu Yunsong ◽  
Yuchao Wang ◽  
Han Qin
Keyword(s):  
High Altitude ◽  
Ground State ◽  
Deflection Angle ◽  
Internal Flow ◽  
Lateral Force ◽  
Control Surface ◽  
Low Density ◽  
Thrust Vectoring ◽  
Density State ◽  
Fluidic Thrust Vectoring

In view of the control effects of fluidic thrust vector technology for low-speed aircraft at high altitude/low density and low altitude/high density are studied. The S-A model of FLUENT software is used to simulate the flow field inside and outside the nozzle with variable control surface parameters, and the relationship between the area of control surface and the deflection effect of main flow at different altitudes is obtained. It is found that the fluidic thrust vectoring nozzle can effectively control the internal flow in the ground state and the high altitude/low density state. and the mainstream deflection angle can be continuously adjusted. The maximum deflection angle of the flow in the ground state is 21.86°, and the maximum deviation angle of the 20 km high altitude/low density state is 18.80°. The deflecting of the inner flow of the nozzle is beneficial to provide more lateral force and lateral torque for the aircraft. The high altitude/low density state is taken as an example. When the internal flow deflects 18.80°, the lateral force is 0.32 times the main thrust. For aircraft with high altitude and low density, sufficient lateral and lateral torque can make the flying aircraft more flexible, which can make up the shortcomings of the conventional rudder failure and even replace the conventional rudder surface.

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