Angular Profile Research Articles

Analytical Solution of the Dynamics Equations for a Wave Solid-State Gyroscope Using the Angular Rate Linear Approximation

The exact solution is provided of the dynamics equation for an elastic inextensible ring being the basic model of a wave solid-state gyroscope with the linear law of the base angular rotation rate alteration. This solution is presented in terms of the parabolic cylinder functions (Weber function). Asymptotic approximations are used in the device certain operating modes. On the basis of the solution obtained, the analytical solution to the equation of the ring dynamics in case of piecewise linear approximation of the angular rate arbitrary profile on a time grid is derived. This significantly expands the class of angular rate dependences, for which the solution could be written down analytically. Earlier, in addition to the simplest case of constant angular rate, solutions were obtained for angular rate varying according to the square root law with time (Airy function), as well as according to the harmonic law (Mathieu function). Error dependence of such approximation on the discretization step in time is estimated numerically. Results obtained make it possible to reduce the number of operations, when it is necessary to study long-term evolutions of the dynamic system oscillations, as well as to quantitatively and qualitatively control convergence of finite-difference schemes in solving dynamics equations for a wave solid-state gyroscope with the ring resonator

A slim disc approach to external photoevaporation of discs

ABSTRACT The photoevaporation of protoplanetary discs by nearby massive stars present in their birth cluster plays a vital role in their evolution. Previous modelling assumes that the disc behaves like a classical Keplerian accretion disc out to a radius where the photoevaporative outflow is launched. There is then an abrupt change in the angular velocity profile, and the outflow is modelled by forcing the fluid parcels to conserve their specific angular momenta. Instead, we model externally photoevaporating discs using the slim disc formalism. The slim disc approach self-consistently includes the advection of radial and angular momentum as well as angular momentum redistribution by internal viscous torques. Our resulting models produce a smooth transition from a rotationally supported Keplerian disc to a photoevaporative driven outflow, where this transition typically occurs over ∼4–5 scale heights. The penetration of ultraviolet photons predominately sets the radius of the transition and the viscosity’s strength plays a minor role. By studying the entrainment of dust particles in the outflow, we find a rapid change in the dust size and surface density distribution in the transition region due to the steep gas density gradients present. This rapid change in the dust properties leaves a potentially observable signature in the continuum spectral index of the disc at mm wavelengths. Using the slim disc formalism in future evolutionary calculations will reveal how both the gas and dust evolve in their outer regions and the observable imprints of the external photoevaporation process.

A novel methodology to measure the film thickness profile based on current stimulation for two-phase flow

The film thickness of a two-phase flow is a parameter of interest since it is of importance to the heat and mass transfer phenomena. A novel method is proposed based on electrical impedance tomography (EIT) and conductance sensors to measure this quantity. An analytical equation is developed to relate the differential voltage associated with a current injection on the domain and the angular film thickness profile. A characteristic of the measuring procedure is that it presents a high sensitivity when the thickness is small, with the possibility of adjustment using different magnitudes of current. This model is compared experimentally and by the complete electrode model (CEM), solved by finite elements method (FEM). Results presented a good agreement with the FEM simulations, and the experimental results presented systematic error caused by the fringe effect.

Optimization of a convex pattern surface for sliding wear reduction based on a definitive screening design and discrete element method

A previous study revealed that a convex pattern surface can reduce sliding wear of a transfer chute. A convex pattern surface is a flat surface outfitted with a pattern of convexes defined by five parameters. A three-level definitive screening design (DSD) method combined with discrete element method (DEM) is used to investigate the influence of the five parameters and two operational conditions on the sliding wear. Two flow regimes are distinguished, namely continuous and discontinuous flow regimes, and both flow regimes can significantly reduce the sliding wear. The particle velocity and angular velocity profiles verify the guiding and rolling effect of the convex pattern on the motion of particles. A regression model fitted based on the DSD indicates that three main factors and one interaction have significant influence on the sliding wear.

The role of the deposited charge in tailoring ion beams by nanocapillaries in mica

The shaping and focusing of a Ne7+ ion beam by transmission through an array of nanocapillaries of rectangular cross section in mica is studied both by experiments and simulations. The transmitted angular profiles of the beam are measured as they develop with charging-up the rectangular capillaries by ion impact and compared with rhombic capillaries of different parameters in mica. Thereby it is found that the profiles after transmission through rectangular capillaries degrade with charging them up. This is in contrast to our previous findings [Phys. Rev. A.86, 022,901 (2012)] with rhombic capillaries, where the transmitted angular profiles only shift by charging-up. The reasons for that and the features of the tailored shapes of the transmitted ion beams will be discussed here, supported by simulations.

Jupiter and Saturn Multi-layer Models Rotating Differentially

In a past work, models for Jupiter were constructed in base to a set of concentric distorted spheroids (“spheroidals”) rotating differentially—whose semi-axes are independent of one another—a task that was achieved with a law of rotation deduced from a generalization of Bernoulli’s theorem, and which holds exclusively for axial-symmetric masses. The shape of the mass is that of a spheroid whose surface equation contains an extra term, d/z4, where d is a parameter which measures the degree of distortion. Each layer rotates with its own profile of angular velocity. The rotation law has a simple dependence on the derivative of the gravitational potential. No magnetic fields or equations of state were involved. The multi- structures were demanded, firstly, to reproduce the gravitational moments of the planets, as surveyed by space missions; and, secondly, to be equilibrium figures. For the calculation of the gravitational moments, a minimization procedure was employed. Paying attention on the outermost laye—the relevant one in the present context—of the formerly reported models for Jupiter, we became aware that they all share an angular velocity profile that decreases from the pole towards the equator, an event that, so far, has not been verified observationally. Since figures with profiles of the opposite tendency turned out to be also possible, they should be included as candidates for our purpose, as effectively they are herein as a complement of that work. The same procedure is here entailed to Saturn, for which figures to show one or the other tendencies are as well obtained. The dual behavior of the rotation profiles may be explained by arguments involving the centripetal force. According to this standpoint, the double behavior is a consequence of the algebraic sign assigned to d: if positive, so that the surface is more bloated than that of a spheroid, the decreasing tendency results; whereas if negative, so that the surface is more depressed, the increasing tendency shows up. This, in turn, is because for d negative the radial force increases more rapidly from pole to the equator than for d positive. We point out that the rotation profiles of the current figures are determined from their equilibrium, rather than being imposed ad initio.

Micropolar fluid past a convectively heated surface embedded with nth order chemical reaction and heat source/sink

The objective of the present article is to investigate an incompressible micropolar Prandtl fluid flowing over a porous stretching sheet with the inclusion of effects like exponential temperature-dependent heat source, higher-order chemical reaction viscous dissipation, nonlinear thermal radiation, and multiple convective surface boundary conditions. The nonlinear partial differential equations (PDEs) for momentum, energy, micro-rotation, and concentration are discussed. These PDEs are converted into ordinary differential equations (ODEs) by utilizing suitable variables and then tackled with the utilization of the nonlinear shooting method. For the numerical assessment of upcoming results comparison with already existing literature has been taken. It is canvassed that by augmenting the microrotation parameter, a boost in the angular velocity profile is seen. Moreover, The higher order of reactivity upsurges the heat transmission rate, whilst the mass convection enhances the concentration size. This gives the current model potency as a potential application in clean engine lubricants and coolant industrial liquids under the same constraints.

Commissioning and quality assurance of HalcyonTM 2.0 linear accelerator.

BackgroundVarian Medical Systems has introduced a new medical linear accelerator called HalcyonTM 2.0, which is based on the ring delivery system (RDS). It is a true IGRT machine having 6MV FFF photon energy. In addition to the planar and MV-CBCT imaging techniques it also has an option of ultra-fast kV-iCBCT which enhances the image reconstruction and improves the visualization of soft tissue. The field portals are shaped by a unique dual layer MLC with special stacked and staggered design which enables high modulation with low radiation leakage. Recently, we have commissioned our first Halcyon 2.0 machine. The aim of this work was to systematically investigate various parameters of a newly installed HalcyonTM 2.0 linear accelerator.Materials and methodsDetailed measurements were conducted as per various guidelines. Also, the measurements were performed to fulfil the national regulatory requirements. Commissioning data of Halcyon 6 MV-FFF beam was performed in a water tank. For absolute measurements, a 0.6-cc waterproof Farmer chamber and electrometer were used. All relative measurements (PDDs, in-line, cross-line and angular profiles) were performed with 0.0125 cc point chamber.ResultsAll the tests were within the acceptable limit. Measured data were compared with factory data as well as the existing medical linear accelerator of the same category. The obtained results were quite satisfactory.ConclusionsThis study summarizes the commissioning experience with Halcyon linear accelerator. Evaluation of mechanical, radiation safety and dosimetric parameters were performed. The obtained parameters were well below the specified tolerance limits.

The flow of a micropolar nanofluid past a stretched and shrinking wedge surface with absorption

This research is examining, a continuous, laminar, flow of a micropolar nanofluid through a stretched and shrinking wedge in the presence of heat generation or absorption and applied magnet field over a wedge surface. A number of governing parameters are employed to assess the results. The governing partial differential equations were transformed into ordinary differential equations which were solved numerically by using the Runge Kutta Gill and shooting methods. The steady-state velocity, temperature, and angular velocity profiles are shown graphically. The result showed the effects of nanoparticle concentration, wedge angle, suction and material parameter on velocity, temperature and angular velocity fields.

Slant type taper profiling and prediction of profiling speed for a circular profile during in wire electric discharge machining using Hastelloy-X

Hastelloy-X a nickel-based alloy used in nozzles, flame holders, turbine blades, turbocharges, jet engine tailpipes, afterburner components etc. having complex tapering profiles. Wire electric discharge machining proves to be the most beneficial machining technique as it provides required accuracy for the components. In the present research, a slant type taper fixture is employed for achieving taper angles as convention tapering have many hindrances like wire bend, angular inaccuracy, guide wear, insufficient flushing and wire breakage etc. and machining a simple circular profile on Hastelloy-X. The behaviour of different output parameters like profiling speed, surface roughness, profile areas, microhardness and recast layer were investigated for various input parameters for machined taper components at 0°, 15° and 30°. The cutting speed override parameter influenced most on the profiling speed and surface roughness. The wire offset parameter was found to be the most significant factor in the case of circular profile areas that were machined. The variation of different output parameters to profiling/cutting speed and taper angle was also highlighted. It is found the recast layer decreased which indicated lesser thermal degradation at higher taper angles at different profiling parameters. This is also validated by the microhardness where the machined surface hardness of taper angular profiles was found to be greater than the 0° profiles. The artificial neural networks and adaptive neuro-fuzzy interference system were used for the prediction of profiling speed. The adaptive neuro-fuzzy interference system was found better in prediction as the percentage error varies between 0–5 per cent. In conclusion, the profiling speed influences both on the accuracy and surface of machined taper circular profiles.

CPSM Simulation of the Variable Properties’ Role in MHD Non-Newtonian Micropolar Nanofluid Flow Over a Stretching Porous Sheet (Flow Filtration)

In this manuscript, to modify the fluid thermophysical properties, the alumina suspended nanoparticles were immersed in two different kinds of base fluids, ethylene glycol with Prandtl number (Pr = 204) and water with (Pr = 6.785). The combination between Powell–Eyring model and micropolar fluid was utilized to describe a 2D steady nanofluid flow along a stretching permeable sheet. An inconvenience through a porous material was illustrated by Darcy–Forchheimer (D–F) expression. As it is known, the nanofluid thermophysical properties are not constants especially in the presence of heat transfer; hence, the viscosity and thermal conductivity were employed as variable functions of the temperature and nanoparticle concentration. As well as in the present work, the microrotation and spin gradient viscosities, which were always constant in all the above studies, have been employed as variable functions of the temperature. The governing mathematical equations have been calculated numerically via the Chebyshev pseudospectral method/Mathematica code. A perfect agreement was obtained between some numerical outcomes and previous published data. Also, the present numerical outcomes for the distributions of temperature, concentration, velocities, skin friction, wall couple stress, Nusselt and Sherwood numbers are represented in tabular form and by drawing against different controlling parameters in the ranges $$ \phi (0 - 20\% ),A(0.01 - 1),\,n(0 - 5),\,\beta_{1} ,\,\beta_{1} ,\,\beta_{3} \,(0 - 0.7),\,$$ $$ {\text{Fr}},\,{\text{Da,}}\,K_{c} ,\,{\text{Sc}}\,(0.1 - 2),\,\Delta \,(0.1 - 10),S\,( - 1\, - \,1)$$ , and $$ M(0 - 20)$$ . In this article, it is confirmed that utilizing the nanofluid viscosity/thermal conductivity as a variable function of both the nanoparticle concentration and the temperature had a great importance and is a vital factor to reinforce the rate of heat transfer. Finally, a new result was gotten in this work; when the variable microrotation viscosity parameter rose, the angular velocity profile raised.

A lateral ankle sprain during a lateral backward step in badminton: A case report of a televised injury incident

BackgroundThis study presents a kinematic analysis of an acute lateral ankle sprain incurred during a televised badminton match. The kinematics of this injury were compared to those of 19 previously reported cases in the published literature. MethodsFour camera views of an acute lateral ankle sprain incurred during a televised badminton match were synchronized and rendered in 3-dimensional animation software. A badminton court with known dimensions was built in a virtual environment, and a skeletal model scaled to the injured athlete's height was used for skeletal matching. The ankle joint angle and angular velocity profiles of this acute injury were compared to the summarized findings from 19 previously reported cases in the published literature. ResultsAt foot strike, the ankle joint was 2° everted, 33° plantarflexed, and 18° internally rotated. Maximum inversion of 114° and internal rotation of 69° was achieved at 0.24 s and 0.20 s after foot strike, respectively. After the foot strike, the ankle joint moved from an initial position of plantarflexion to dorsiflexion—from 33° plantarflexion to 53° dorsiflexion (range = 86°). Maximum inversion, dorsiflexion, and internal rotation angular velocity were 1262°/s, 961°/s, and 677°/s, respectively, at 0.12 s after foot strike. ConclusionA forefoot landing posture with a plantarflexed and internally rotated ankle joint configuration could incite an acute lateral ankle sprain injury in badminton. Prevention of lateral ankle sprains in badminton should focus on the control and stability of the ankle joint angle during forefoot landings, especially when the athletes perform a combined lateral and backward step.

Impact of Angular Irradiation Profiles on Performance of Silicon PV Modules Using Light Scattering Films

Light trapping strategies, such as light scattering films (LSFs) present an opportunity to increase the power generated by Si photovoltaic modules. Evaluation of the benefits of these strategies for manufacturing decisions currently relies on current-voltage measurements performed using solar simulators under standard test conditions, with uncertainties representing expected variations due to different angles of incidence that result from the light sources of solar simulators. The practical achievement of normal incidence is challenging and consequently the angular irradiation profile varies between different solar simulators. In this article, we show that use of LSFs can enhance the short circuit current density, J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SC</sub> , of modules by 2.5% under normal incidence as compared to enhancements of 2.33%, 2.12%, and 1.56% measured using three different solar simulators (two short-tunnel and one table). This variation is due to the less effective light trapping of LSFs under more diffuse light. The angular response of these LSF modules on electricity yield is demonstrated through simulations using the angular matrix framework and SunCalculator software. The average J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SC</sub> enhancement varies from 1.46% (Cologne) to 1.63% (Alice Springs) corresponding to a decrease in diffuse irradiation at Alice Springs. Differences in measured J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SC</sub> from three solar simulators can result in the predicted average J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SC</sub> enhancements varying from -0.07% to 0.87% absolute, with the table simulator more closely predicting the average J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SC</sub> enhancement. This highlights the importance of considering the angular profiles of solar simulators if electricity yield and hence returns on investment for PV deployments is to be more accurately predicted.

Solving the Coriolis Vibratory Gyroscope Motion Equations by Means of the Angular Rate B-Spline Approximation

The exact solution of the movement equation of the Coriolis vibratory gyroscope (CVG) with a linear law of variation of the angular rate of rotation of the base is given. The solution is expressed in terms of the Weber functions (the parabolic cylinder functions) and their asymptotic representations. On the basis of the obtained solution, an analytical solution to the equation of the ring dynamics in the case of piecewise linear approximation of an arbitrary angular velocity profile on a time grid is derived. The piecewise linear solution is compared with the more rough piecewise constant solution and the dependence of the error of such approximations on the sampling step in time is estimated numerically. The results obtained make it possible to significantly reduce the number of operations when it is necessary to study long-range dynamics of oscillations of the system, as well as quantitatively and qualitatively control the convergence of finite-difference schemes for solving the movement equations of the Coriolis vibratory gyroscope.

Rotating Filament in Orion B: Do Cores Inherit Their Angular Momentum from Their Parent Filament?

Abstract Angular momentum is one of the most important physical quantities that governs star formation. The initial angular momentum of a core may be responsible for its fragmentation, and can have an influence on the size of the protoplanetary disk. To understand how cores obtain their initial angular momentum, it is important to study the angular momentum of filaments where they form. While theoretical studies on filament rotation have been explored, there exist very few observational measurements of the specific angular momentum in star-forming filaments. We present high-resolution N2D+ ALMA observations of the LBS 23 (HH24-HH26) region in Orion B, which provide one of the most reliable measurements of the specific angular momentum in a star-forming filament. We find the total specific angular momentum (4 × 1020 cm2 s−1), the dependence of the specific angular momentum with radius (j(r) ∝ r 1.83), and the ratio of rotational energy to gravitational energy (β rot ∼ 0.04) comparable to those observed in rotating cores with sizes similar to our filament width (∼0.04 pc) in other star-forming regions. Our filament angular momentum profile is consistent with rotation acquired from ambient turbulence and with simulations that show cores and their host filaments develop simultaneously due to multi-scale growth of nonlinear perturbation generated by turbulence.

Dimensionless parameter scaling of intrinsic torque in C-Mod enhanced confinement plasmas

A dimensionless parameter dependence study of intrinsic torque has been performed on a database of H- and I-mode plasmas from the Alcator C-Mod tokamak. The torque was determined by comparing intrinsic angular momentum density profiles just before and just after L–H and L–I transitions. The intrinsic torque has been found to scale as , with the parameter ranges 0.3 ⩽ β N ⩽ 1.5, 0.004 ⩽ ρ * ⩽ 0.011 and 0.04 ⩽ ν * ⩽ 0.9. Comparison with results from JET and DIII-D suggests that the intrinsic torque should be normalized by some measure of the device size. Depending upon this normalization, the estimated total intrinsic torques for ITER, SPARC and ARC are ∼20, ∼4 and ∼8 Nm, respectively.

Polarization resolved radiation angular patterns of orientationally ordered nanorods

We combine the transfer matrix based algebraic approach with the Green’s function method to theoretically study polarization resolved far-field angular distributions of photoluminescence from quantum nanorods (NRs) embedded in an optically anisotropic film. The emission and excitation properties of NRs are described by the emission and excitation anisotropy tensors. These tensors and the solution of the emission problem expressed in terms of the evolution operators are used to derive the orientationally averaged coherency matrix of the emitted wavefield. For the case of in-plane alignment and unpolarized excitation, we estimate the emission anisotropy parameter and compute the angular profiles for the photoluminescence polarization parameters such as the degree of linear polarization, the Stokes parameter s1, the ellipticity and the polarization azimuth. We show that the alignment order parameter has a profound effect on the angular profiles.

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.

Electron impact single ionization of hydrogen molecule by twisted electron beam

In this communication, we present the results of the five-fold differential cross-section (5DCS) and triple differential cross-section (TDCS) for the (e, 2e) process on molecular hydrogen (H2) by the plane wave and the twisted electron beam impact. The formalism is developed within the first Born approximation using the plane wave and the twisted wave for the incident electron beam. We describe the plane wave, Heitler–London type wave function, Coulomb wave for the scattered electron, the H2 molecular state, and the ejected electron. We compare the angular profiles of the 5DCS and TDCS for the different values of orbital angular momentum (OAM) number m of the twisted electron beam with that of the plane wave beam. We also present the 5DCS for different molecular orientations and study the effect of m on the 5DCS. We further investigate the influence of the twisted electron beam on the (e,2e) process on the H2 molecule from the perspective of the ‘Young-type’ interference of the scattered waves, emanating from the two atomic centers of the H2 molecule. We also study the TDCS for macroscopic H2 target to explore the effect of opening angle (θ p) of the twisted electron beam on the TDCS. Our results clearly show the effect of the twisted electron’s OAM number (m) and the opening angle (θ p) on the 5DCS and TDCS of the molecular hydrogen.

The application of a reflected non-axisymmetric torsional guided wave model for imaging crack-like defects in small-diameter pipes

Crack imaging of a pipe can provide detailed information about defects within the pipe such as the circumferential and axial position of the defect and its circumferential coverage. Due to the complicated propagation characteristics of a non-axisymmetric guided wave within a small pipe and the limited surface area available to install the transducer, crack imaging within a small-diameter pipe is difficult. This paper reports a reflected non-axisymmetric torsional guided wave model for imaging a crack in a small pipe. First, the reflected non-axisymmetric torsional guided wave model was proposed based on the theory of the normal mode expansion method. Then, the crack imaging algorithm was determined based on the theoretical reflected non-axisymmetric torsional guided wave model. Subsequently, the relationships between the angular profiles of the reflected T(M,1) and the axial distance of the cracks, the relationships between the angular profiles of the reflected T(M,1) and the circumferential length of the cracks predicted by the theoretical model were supported by the simulation results and the experimental data. Next, the crack imaging based on the proposed reflected non-axisymmetric torsional guided wave model was carried out for four pipes to verify its practicability. The axial position and circumferential range of the cracks within the four pipes were different. The experimental and numerical results demonstrated that the reflected non-axisymmetric torsional guided wave model has the potential to image cracks within a small pipe.