Influence of deflection angles on flow behaviours in openchannel bends

The deflection angle of a river bend plays an important role on behaviours of the flow within it, and a clear understanding of the angle's influence is significant in both theoretical study and engineering application. This paper presents a systematic numerical investigation on effects of deflection angles(30°, 60°, 90°, 120°, 150°, and 180°) on flow phenomena and their evolution in open-channel bends using a Re-Normalization Group(RNG) κ-ε model and a volume of fluid(VOF) method. The numerical results indicate that the deflection angle is a key factor for flows in bends. It is shown that the maximum transverse slope of water surface occurs at the middle cross section of a bend, and it increases with the deflection angle. Besides a major vortex, or, the primary circulation cell near the channel bottom, a secondary vortex, or, an outer bank cell, may also appear above the former and near the outer bank when the deflection angle is sufficiently large, and it will gradually migrate towards the inner bank and evolve into an inner bank cell. The strength of the secondary circulations increases with the deflection angle. The simulation demonstrates that there is alow-stress zone on the bed near the outer bank and a high-stress zone on the bed near the inner bank, and both of them increase in size with the deflection angle. The maximum of shear stress on the inner bank increases nonlinearly with the angle, and its maximums on the outer bank and on the bed take place when the deflection angle becomes 120°.

Spherically Symmetric Wormhole Gravitational Lens Deflection Angle Signifying Braneworld Cosmology

Previously, the gravitational lens of a wormhole was introduced by various researchers. Their treatment was focused basically on the lens signature that describes wormhole geometrical character such as the differences from a black hole or between any various types of wormhole models. The braneworld scenario provides the idea of spacetime with underlying extra-dimensions. The inclusion of extra-dimensional terms in the lens object spacetime line element will result in some variation in the expression for its gravitational lens deflection angle. Thus in this paper we investigate such variation by deriving this deflection angle expression. As such, this paper not only shows the existence of such variation but also suggests the potential utilization of gravitational lensing to prove the existence of extra dimensions by studying the deflection angle characteristic in accordance with the spacetime expansion rate of the universe.

Thermal fluctuations,deflection angle,and greybody factor of a high-dimensional Schwarzschild black hole in scalar-tensor-vector gravity

In this study,we examined the thermal fluctuations,deflection angle,and greybody factor of a high-dimensional Schwarzschild black hole in scalar-tensor-vector gravity(STVG).We calculated some thermodynamic quantities related to the correction of the black hole entropy caused by thermal fluctuations and discussed the effect of the correction parameters on these quantities.By analyzing the changes in the corrected specific heat,we found that thermal fluctuations made the small black hole more stable.It is worth noting that the STVG parameter did not affect the thermodynamic stability of this black hole.Additionally,by utilizing the Gauss-Bonnet theorem,the deflection angle was obtained in the weak field limit,and the effects of the two parameters on the results were visualized.Finally,we calculated the bounds on the greybody factor of a massless scalar field.We observed that as the STVG parameter around the black hole increased,the weak deflection angle became larger,and more scalar particles can reach infinity.However,the spacetime dimension has the opposite effect on the STVG parameter on the weak deflection angle and greybody factor.

Massless Dirac perturbations of black holes in f(Q)gravity:quasinormal modes and a weak deflection angle

This article considers a static and spherical black hole(BH)in f(Q)gravity.f(Q)gravity is the extension of symmetric teleparallel general relativity,where both curvature and torsion are vanishing and gravity is described by nonmetricity.In this study,we investigate the possible implications of quasinormal mode(QNM)modified Hawking spectra and deflection angles generated by the model.The Wentzel–Kramers–Brillouin method is used to solve the equations of motion for massless Dirac perturbation fields and explore the impact of the nonmetricity parameter(Q_(0)).Based on the QNM computation,we can ensure that the BH is stable against massless Dirac perturbations and as Q_(0)increases the oscillatory frequency of the mode decreases.We then discuss the weak deflection angle in the weak field limit approximation.We compute the deflection angle up to the fourth order of approximation and show how the nonmetricity parameter affects it.We find that the Q_(0)parameter reduces the deflection angle.

Effect of the Wick Deflection Angles on Heat Transfer Characteristics for the Flat LHP

Loop Heat Pipe(LHP)is an efficient two-phase heat transfer device,which can be used in waste heat recovery,electronics cooling,aerospace and other fields.The wick,the core component of LHP,plays an important role in its start-up and operation.In this paper,the wick fabricated by 3D printing technology had uniform and interconnected pores.In the experiment,the position of the parallel vapor removal grooves was always fixed towards the vapor outlet.When the cylindrical wick was placed in the evaporator,the rotation angle relative to its central axis could be changed,thus changing the number and shape of the pores facing the vapor removal grooves.The wick deflection angle represented its change in spatial position relative to the fixed vapor removal grooves.The effect of the wick deflection angles on the heat transfer characteristics of the flat LHP was experimentally investigated.It was found that with the change of deflection angle,the number of pores in the evaporation-oriented zone would also change,which had a significant impact on the start-up process and heat transfer performance of LHP.When the deflection angle was 30°,LHP could start fastest at a low heat load of 20 W and operate stable at a high heat load of 180 W.

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma

In this study,the gravitational deflection angle of photons in the weak field limit(or the weak deflection angle)and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole(BH)in the string cloud background are investigated.The influences of the BH charge Q,quintessence parameterγ,and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem.in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the chargedKiselev BH in string clouds.Moreover,we study the effects of plasma(uniform and non-uniform)on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings.In the presence of a uniform/nonuniform plasma medium,an increase in the string cloud parameter a increases the deflection angleα.In contrast,a decrease in the BH charge Q decreases the deflection angle.Further,we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH.We notice that,with an increase in the values of the parametersγand a,the size of the BH shadow increases,and therefore,the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases.Thus,the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH.Moreover,we use the data released by the Event Horizon Telescope(EHT)collaboration,for the supermassive BHs M87*and Sgr A*,to obtain constraints on the values of the parametersγand a.

Quantum effects on the black hole shadow and deflection angle in the presence of plasma

In this study,the optical properties of a renormalization group improved(RGI)Schwarzschild black hole(BH)are investigated in a plasma medium.Beginning with the equations of motion in a plasma medium,we aim to present the modifications in the shadow radius of the RGI BH.To this end,we compute the deflection angle of light in the weak gravity regime for uniform and non-uniform plasma media.Importantly,owing to the plasma media,we discover that the equations of motion for light obtained from the radiating and infalling/rest gas have to be modified.This,in turn,changes and modifies the expression for the intensity observed far away from the BH.Finally,we obtain the shadow images for the RGI BH for different plasma models.Although quantum effects change the background geometry,such effects are minimal,and practically detecting these effects using the current technology based on supermassive BH shadows is impossible.The parameterΩencodes the quantum effects,and in principle,one expects such quantum effects to play significant roles only for very small BHs.However,the effects of plasma media can play an important role in the optical appearance of BHs,as they affect and modify the equations of motion.

Deflection angle switching with a metasurface based on phase-change nanorods [Invited]

We propose the active metasurface using phase-change material Ge2Sb2Te5（GST）, which has two distinct phases so called amorphous and crystalline phases, for an ultrathin light path switching device. By arranging multiple anisotropic GST nanorods, the gradient metasurface, which has opposite directions of phase gradients at the two distinct phases of GST, is demonstrated theoretically and numerically. As a result, in the case of normal incidence of circularly polarized light at the wavelength of 1650 nm, the cross-polarized light deflects to-55.6° at the amorphous phase and ＋55.6° at the crystalline phase with the signal-to-noise ratio above 10 dB.

Angle measurement technology based on magnetization vector for narrow space applications

With the wide application of laser in the field of skin plastic surgery, micro laser galvanometer scanner has made great progress in this field with its portability. However, the measurement method used to measure the deflection angle of laser galvanometer in the narrow space of scanner with high precision remains to be studied. In this paper, an angle measurement method based on magnetic field is proposed, and the effect of the shapes of permanent magnets(PMs) on the measurement is studied by theoretical and experimental study under the condition that the maximum available space for the PMs is a 10 mm side cube. An angle measuring experimental device is set up, and the contrast experiment is carried out with different PMs which are the same as simulation. The experimental results show that cylindrical PM is more suitable than other PMs, which is consistent with the simulation results, and the maximum nonlinearity error is 0.562%. This method has the advantages of small volume,non-contact measurement, small moment of inertia, good dynamic response and no external excitation for the PMs, so it has a broad application prospect in micro laser galvanometer scanner.

Study of bending angle and shadow in a new Schwarzschild-like black hole affected by plasma and non-plasma mediums

In this study,we analyze the models of the deflection angle of a new Schwarzschild-like black hole(BH)and employ the optical metric of the BH.To achieve this,we use the Gaussian curvature of the optical metric and the Gauss-Bonnet theorem,known as the Gibbons-Werner technique,to determine the deflection angle.Furthermore,we examine the deflection angle in the presence of a plasma medium and the effect of the plasma medium on the deflection angle.The deflection angle of the BH solution in the gauged super-gravity is computed using the Keeton-Petters approach.Utilizing the ray-tracing technique,we investigate the shadow of the corresponding BH and analyze the plots of the deflection angle and shadow to verify the influence of the plasma and algebraic thermodynamic parameters on the deflection angle and shadow.

Evolution of light deflection and shadow from a gauge-potential-like AdS black hole under the influence of a non-magnetic plasma medium

We investigate the light deflection in the weak field approximation from the accelerating charged AdS black hole.For this purpose,we apply the Gauss–Bonnet theorem to calculate the light deflection in the weak field area and use the Gibbons–Werner approach to analyze the optical geometry of the accelerating charged AdS black hole in the non-magnetic plasma absence/presence of a non-magnetic medium.We also represent the graphical behavior of the light deflection angle w.r.t.the impact parameter.We also compute the light deflection angle using Keeton and Petters approximations under the impact of accelerating charged AdS black hole geometry.Furthermore,by using the ray-tracing approach,we determine the shadow in the nonmagnetic plasma presence and also demonstrate that graphical shadow has an impact on the gauge potential,non-magnetic plasma frequencies and charge.

Imprints of a gravitational wave through the weak field deflection of photons

In this study,we investigate the novel phenomenon of gravitational lensing experienced by gravitational waves traveling past a Schwarzschild black hole perturbed by a specific,first-order,polar gravitational wave.We apply the Gauss-Bonnet theorem,finding a topological contribution to the deflection of light rays passing near the black hole.We demonstrate that the deflection angle can be determined by analyzing a region entirely outside the path of the light ray,leading to a calculation based solely on the parameters of the perturbing wave(Legendre polynomial order,l;frequency,σ).This approach offers a unique perspective on gravitational lensing and expands our understanding of black hole interactions with gravitational waves.

A Compact Low Energy Electron Microscope for Surface Analysis

The description and function characterization of a flange-on type low energy electron mi- croscope are given. In this microscope a magnetic beam separator with 10° deflection angle is used in order to facilitate compacting the instrument on a single 10 in. flange. Mean- while some correcting elements in the electron optical system are simplified to reduce the complexities of construction and operation. The sample is set close to ground potential, so that all the electrostatic lenses are easily to float at high voltages. The performance of the microscope in typical low energy electron microscopy, low energy electron diffraction and photoemission electron microscopy modes is demonstrated through several experiments. A lateral resolution of 51 nm is estimated for low energy electron microscopy imaging. With femtosecond laser as light source, the consequent nonlinear photoemission makes this micro-scope also suitable for the observation of optical near field phenomena and a lateral resolution of 110 nm is obtained.

Deflection of cavitation bubble near the rigid wall with a gas-containing hole

The presence of a rigid wall causes a microjet of the cavitation bubble to collapse to move toward the wall,while a free surface does the opposite.When a rigid wall surface is combined with a free surface,it may affect the direction of the microjet.The motive of this study is to find out the influence of the dynamic behavior of a laser-induced bubble near the rigid wall with a gas-containing hole.Evolutions of the bubble at different distances from the gas-containing hole in the horizontal and vertical directions were recorded by a high-speed camera(2.3×10^(5) fps).When the bubble collapse near the boundary,the bubble will produce two situations:away from or toward the boundary.It focuses on the direction of the bubble,the oscillation period of a bubble,and reflection angle,and quantitative analysis of the results.It was found that the boundary not only changes the morphologic of the bubble and the overall direction of movement but also affects the oscillation period.In addition,it can control the deflection of the bubble.

A simple plume model induced by stack effect in a vertical shaft

After comparing the mechanism of tilted plume under stack effect with that of spill plume,the tilted plume model induced by stack effect in a vertical shaft is developed simply based on the theoretical results and a series of full-scale tests. It is shown that the two sides of plume are symmetrical and have an accordant regulation that the plume radius has a linear relation to the height z. The profile of fire plume under stack effect is similar to the windblown flame in wind tunnel,and the range of flame deflection angle is about from 50 to 60 degree.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Numerical analysis of deflection control of a gas plasma jet based on magnetohydrodynamic staggered electrode configuration

To control the deflection of the gas plasma jet, a new analytical method is proposed based on the Magnetohydrodynamic(MHD) technique. Based on the typical MHD power generation model, the applied voltage is applied to the staggered electrodes, that is, a pair of electrodes on the same side wall are connected to generate an axial current in the channel. Under the action of the magnetic field perpendicular to the direction of the flow, the plasma is subjected to electromagnetic forces perpendicular to these two directions, and the jet is deflected. The computational model including the Navier-Stokes equations coupled with electromagnetic source terms, the electric potential equation and Ohm’s law is solved. The deflection of the gas jet under the action of an electromagnetic field is observed, and the maximum deflection angle is about 14.8°. The influences of the electric field, magnetic field, and conductivity on the jet deflection are studied. Results show that although the influences of these three factors on the deflection are similar, and the effect of increasing the electric field strength is slightly greater, priority should be given to increasing the magnetic field strength from the perspective of reducing energy consumption. The Stuart number is introduced to assess the ability of electromagnetic force to control jet deflection. When the electromagnetic parameters are constant, this solution provides better control of low-density and low-speed fluid flows. The calculation results show that using the staggered electrode method configuration is feasible in terms of controlling the deflection of a plasma jet deflection.

Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole.Here,we have extended the prior work of Chen and Jing(S.Chen and J.Jing,JCAP,10:002(2015))for a Schwarzschild black hole to a Kiselev black hole.For this purpose,the equation of motion for the photons coupled to the Weyl tensor,null geodesic,and equation of photon sphere in a Kiselev black hole spacetime have been formulated.It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor,but also on the polarization direction of the photons.There is a critical value of the coupling parameter,α,for the existence of the marginally circular photon orbit outside the event horizon,which depends on the parameters of the black hole and the polarization direction of the photons.Further,the polarization directions of the coupled photons and the coupling parameter,α;both modify the features of the photon sphere,angle of deflection,and functions(^ˉa and^ˉb)owing to the strong gravitational lensing in the Kiselev black hole spacetime.In addition to this,the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.

Actual wellbore tortuosity evaluation using a new quasi-three-dimensional approach

The irregular wellbore trajectory caused by the wellbore deviation and fluctuation makes a significant effect on the torque and drag in extending and direction drilling,especially for wellbore trajectory with obvious deviation in the drilling direction.As a consequence,a new quasi-three-dimensional wellbore tortuosity evaluation method is developed.The new method incorporates the effect of fluctuation frequency and amplitude of oscillating wellbore trajectory;a weight coefficient index that quantifies the effect of tortuosity of one segment trajectory to the entire trajectory;a‘Peak-Valley’principle that can decompose the irregular wellbore trajectory in various scale lengths.The studies show that the deflection angle between the segments of tortuous wellbore increases the torque and drag by strengthening the contact behaviors between the drillstring and borehole.Therefore,the deflection angle is introduced to quantify the effect of deviation in the drilling direction on wellbore tortuosity.The evaluation results of two field cases demonstrate the new method which is adapted to the wellbore trajectory fluctuating with various characteristics and can reflect the actual state of wellbore tortuosity with severe oscillation more effectively and accurately.