Common Axis Of Symmetry Research Articles

Stabilization of a Reentry Vehicle by a Partial Spin-up during Uncontrolled Descent

Stabilization of a reentry vehicle (RV) by a partial spin-up of it is considered for the case of uncontrolled descent into the atmosphere. In this case, the vehicle is a composite construction consisting of two rigid bodies, a return capsule and a stabilizing block, which is put in rotation. A model is developed for the spatial motion of the reentry vehicle considered as a system of coaxial rigid bodies rotating about a common axis of symmetry. The free motion is studied, and the stability of steady-state regimes is analyzed. The spatial motion of the system is considered for the case of a small asymmetry due to displacement of the axes of dynamic symmetry of the bodies with respect to the spin axis, and approximate solutions for the motion parameters of the free system are found.

A Two Body Benchmark Problem for Transient and Ultrawideband Scattering

In this paper we propose a novel benchmark for numerical solutions of transient and ultrawideband scattering from perfectly conducting targets. The target for the problem comprises two open concentric spherical shells with a common axis of symmetry, which represents the direction of propagation of the incident field. This geometry includes a variety of physical features including surfaces, edges, cavities and an inclusion within a cavity. It provides a range of scattering mechanisms, including multiple body interactions and cavity resonance effects, the relative strength of which can be varied via the parameters of the problem. The time harmonic scattering problem is solved via the method of regularization providing a semi-analytic solution of arbitrary predetermined accuracy with good stability and convergence properties. Solution of this time harmonic problem provides a benchmark for both time domain and frequency domain numerical solutions of Maxwell's equations. An example is given of this benchmark problem, as applied to a time domain integral equation method.

Motion of trains of vortex rings

A numerical experiment on investigation of the dynamics of the interaction of three coaxial vortex rings formed from thermics is performed. As a mathematical model of the phenomenon, the system of Navier–Stokes equations for a compressible heat‐conducting gas in a cylindrical coordinate system is chosen. The calculations are performed using a finite‐difference method based on an explicit three‐step scheme of splitting by physical processes. The influence of the position of the thermics on the common axis of symmetry on the character of their motion and interaction is investigated.

An inhomogeneous Landau equation with application to spherical Couette flow in the narrow gap limit

A nonlinear evolution equation is derived which governs the amplitude modulation of Taylor vortices between two rapidly rotating concentric spheres which bound a narrow gap and almost co-rotate about a common axis of symmetry. In this weakly nonlinear regime the latitudinal vortex width is comparable to the gap between the shells. The vortices are located close to the equator and are modulated on a latitudinal length scale large compared to the gap width but small compared to the shell radius. The tendency for vortices off the equator to oscillate introduces the phenomenon of phase mixing. Steady finite amplitude solutions of the model equation are determined both numerically and analytically. The linear eigensolutions are identified by an ascending sequence of eigenvalues λ=λ n (n=0, 1, …) . Each eigensolution has its own finite amplitude continuation under variation of λ which is a measure of the excess Taylor number. Without phase mixing each vortex amplitude increases monotonically with growing λ and does so indefinitely. In contrast, with phase mixing each pair of linear modes (n=0, 1) , (n=2, 3) , etc. are connected under the finite amplitude continuation; both the mode amplitude and λ remain bounded. Though the small phase mixing results agree with the non-phase mixed ones up to moderately large λ, this range is of limited extent. As phase mixing is increased the solution space shrinks and the amplitude of the remaining solutions is strongly suppressed.

A numerical study of two coaxial axi-symmetric particles undergoing steady equal rotation in the slip regime

The problem of two axi-symmetric particles (separated by a certain distance) that rotate about their common axis of symmetry in an infinite viscous fluid with slip boundary conditions at their surfaces have been studied numerically. Aerosol particles are usually nonspherical with the exception of liquid droplets in certain cases, and the shape of particles has a significant impact on frictional drag (for particle translation) and torque (for particle rotation), and, hence, on Brownian motion, and the deposition, sampling and coagulation of particles. The effects of the rotation of particles prior to their collision and coagulation have usually been ignored in favor of simpler calculations. The study of two-particle systems should give more information about the interaction between particles that cannot be understood from the study of single particles alone. In this work, the Laplace equation (resulting from the steady Stokes equation) with slip boundary conditions is converted into a Fredholm integral equation of the second kind via the use of Green's function. The integral equations are then solved by the singularity subtraction method. The local stresses are calculated at each nodal point and the torques are then calculated from the summation of the local stresses. Explicit numerical results for the local stresses and torques are reported for three systems of two axi-symmetric particles, i.e. sphere-sphere, sphere-spheroid, and spheroid-spheroid. While the formulation of the problem is quite general, the results reported here have been limited to calculations for systems in which both particles have identical angular velocities. The numerical method is, however, valid for arbitrary axi-symmetric particles and its modification to systems containing other shaped particles or differing angular velocities is straightforward. Numerical results of the torques for each system studied show in every case that the presence of slip results in a reduction in the torques. As a consequence, the impact of the slip on the torques and local stresses is substantial and cannot be ignored. The distance between the centers of the particles (the separation distance) also plays an important role in determining the values of the torques and local stresses. In the systems that have been studied here, as the particles get further apart, the torques on both particles increase.

New integrable problems of motion of a rigid body acted upon by nonsymmetric electromagnetic forces

The problem of motion of a rigid body with a spherical dynamical symmetry about a fixed point under the action of a combination of nonsymmetric nonuniform electric, magnetic, gravitational and Lorentz forces is considered. Two systems of equations of motion written in the body system and in the inertial system are shown to have the same structure. Transforming some recently found integrable cases of a nonsymmetric body in an axial combination of fields, we construct two new integrable cases of a body in a nonsymmetric combination of fields. In the latter cases, the body is assumed to have distributions of electric charges, mass and magnetization which exhibit a common axis of symmetry and carries a rotor along that axis. Explicit solution of the equations of motion is discussed.

A Method for Calculating the Ray Paths in Optical Systems Composed of Axially Symmetric Reflecting and Refracting Surfaces

A method for calculating the ray paths in optical systems composed of axially symmetric reflecting and refracting surfaces is outlined. It is assumed that there is no common symmetry axis in the system, so that the ray paths are substantially three-dimensional. For the sake of generality, both the simplest cases admitting of an analytic solution and the more intricate cases when iterative procedure has to be used are considered. Particular attention is given to the computation features which make the algorithm both universal and robust. The method proposed allows for the use of a wide range (five types of the surfaces specified) of optical elements. Furthermore, the approach suggested is universal and, as such, makes it possible also to pass on with relative ease to other cases of specifying the surfaces.

P-SHconversions in a flat-layered medium with anisotropy of arbitrary orientation

SUMMARY P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV-and SH-polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used ‘receiver function’ technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct (P) and converted (Ps) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.

Coulomb drag of coupled cylindrical quantum wells in magnetic field

We investigate the Coulomb drag resistivity between a couple of barrier separated cylindrical δ quantum wells (CDWs) with common rotated symmetry axis ( z-axis) in the presence of external magnetic field along z-direction. We find that in the presence of external magnetic field along z-axis, the characteristic properties of momentum relaxation rate (MRR) in the absence of magnetic field which are originated from the dimensionalities of both CDWs coupled, are still maintained. For example, for the coupled 2D-1D CDWs, the MRR, τ D −1, is approximately proportional to T 4 in the temperature range of 0 to 10 K, while for coupled 2D-2D CDWs, it is proportional to T 2 which is in accord with the characteristic behaviour of MRR in coupled 2D-2D planes. The presence of magnetic field can only change the value of the MRR and the temperature T max at which the MRR divided by T 4 for coupled 2D-1D CDWs (or by T 2 for coupled 2D-2D CDWs) is found to exhibit a maximum. For coupled 2D-2D CDWs, the presence of magnetic field can either raise or reduce the value of MRR, while for coupled 2D-1D CDWs, except the negligible reducing at low strength of magnetic field, the value of MRR is raised significantly in nearly the whole range of external magnetic field strength.

Structure model of a complex between the factor for inversion stimulation (FIS) and DNA: modeling protein-DNA complexes with dyad symmetry and known protein structures.

A method is presented to predict overall conformations of protein-DNA complexes on the basis of the known three-dimensional structures of the proteins. The method is restricted to proteins with a common twofold symmetry axis, which show only minor conformational changes upon binding to DNA. The method uses a numerical finite difference solution of the linearized Poisson-Boltzmann equation and subsequent energy minimization cycles. Structural parameters-the rotation angle of the DNA relative to the protein around the common symmetry axis, the protein-DNA distance, and intermolecular hydrogen-bonding contacts-are presented for two test cases, DNA bound to CAP (catabolite gene activator protein) and to the Cro-repressor of bacteriophage 434. The DNA curvature in the starting model of the docking procedure was chosen as a smoothed approximation of the conformation found in the X-ray structures of these complexes. The method is further used to predict the unknown structure of the complex between the factor for inversion stimulation (FIS) and DNA, which is bent upon binding to FIS. In contrast to the test cases, the unknown curvature of the starting model is derived from a calibration of electrostatic precalculations for different proteins according to crystallographically observed DNA bending. The results of the modeling are in good accordance with the experimentally observed overall structure of protein-DNA complexes for the two test cases; for FIS, they correspond to several of the experimentally proposed protein-DNA contacts.

Structure model of a complex between the factor for inversion stimulation (FIS) and DNA: Modeling protein-DNA complexes with dyad symmetry and known protein structures

A method is presented to predict overall conformations of protein-DNA complexes on the basis of the known three-dimensional structures of the proteins. The method is restricted to proteins with a common twofold symmetry axis, which show only minor conformational changes upon binding to DNA. The method uses a numerical finite difference solution of the linearized Poisson-Boltzmann equation and subsequent energy minimization cycles. Structural parameters—the rotation angle of the DNA relative to the protein around the common symmetry axis, the protein-DNA distance, and intermolecular hydrogen-bonding contacts—are presented for two test cases, DNA bound to CAP (catabolite gene activator protein) and to the Cro-repressor of bacteriophage 434. The DNA curvature in the starting model of the docking procedure was chosen as a smoothed approximation of the conformation found in the X-ray structures of these complexes. The method is further used to predict the unknown structure of the complex between the factor for inversion stimulation (FIS) and DNA, which is bent upon binding to FIS. In contrast to the test cases, the unknown curvature of the starting model is derived from a calibration of electrostatic precalculations for different proteins according to crystallographically observed DNA bending. The results of the modeling are in good accordance with the experimentally observed overall structure of protein-DNA complexes for the two test cases; for FIS, they correspond to several of the experimentally proposed protein-DNA contacts. © 1996 Wiley-Liss, Inc.

Coulomb drag in coupled 2D-2D and 2D-1D cylindrical quantum wells

To study the Coulomb drag resistivity of barrier-coupled 2D-1D and 2D-2D systems as well as the transition behaviour between them, we suggest investigation of a system which is composed of a couple of barrier-separated cylindrical S quantum wells (CDWs) with a common cylindrical symmetry axis. We find that for coupled 2D-1D CDWs, the momentum relaxation rate, tau D-1, is approximately proportional to T4, while for coupled 2D-2D CDWs, it is proportional to T2 which is in accord with the characteristic behaviour of the momentum relaxation rate in coupled 2D-2D planes. In the transition region from coupled 2D-1D to 2D-2D CDWs, tau D-1 is proportional to Tn with n reduced from 4 to 2 gradually. In addition, quite unlike the approximate d(-2.4)-dependence of momentum relaxation rate divided by Tmax2 in coupled 2D-2D planes, due to the quantization of the circular motion round a cylindrical symmetry axis, for coupled 2D-1D CDWs the momentum relaxation rate divided by Tmax4 is approximately proportional to d-3 times a nearly periodic function of d, while for coupled 2D-2D CDWs, the momentum relaxation rate divide by Tmax2 is approximately proportional to d-2.4 times a nearly periodic function of d, where d is the distance between two CDWs.

A quintuple turning-joint to be linked with all sides of a symmetrical hexagon-linkage having parallel running diagonals

Two perspective and symmetrical hexagon-linkages both having parallel running diagonals perpendicular to the common axis of symmetry that contains their center of perspectivity, are to be interconnected by six turning-joints being the intersections of corresponding sides of the hexagons. All six of them join a common line perpendicular to the axis of symmetry. The 12-bar chain, obtained this way, represents an overconstrained linkage with two redundant (i.e. superfluous) turning-joints. The kinematic chain so designed, simultaneously contains three paris of reflected four-bars being folding ones when only one of them is. In case one of the perspective hexagons contracts into the center of perspectivity, a quintuple turning-joint is to be linked with all sides of the other hexagon.

A note on leapfrogging vortex rings

In this paper we provide examples, by numerical simulation using the Navier-Stokes equations for axisymmetric laminar flow, of the ‘leapfrogging’ motion of two, initially identical, vortex rinǧs which share a common axis of symmetry. We show that the number of clear passes that each ring makes through the other increases with Reynolds number, and that as long as the configuration remains stable the two rings ultimately merge to form a single vortex ring.

Unsteady flow in an annulus between two concentric rotating spheres

An analysis is presented for the unsteady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric spheres rotating about a common axis of symmetry. A solution of the Navier-Stokes equations is obtained by employing an iterative technique. The solution is valid for small values of Reynolds numbers and acceleration parameters of the spheres. In applying the results of this analysis to a rotationally accelerating sphere, a virtual moment of inertia is introduced to account for the local inertia of the fluid.

Acoustic scattering from multiple rigid cylinders.

Results are presented for acoustic scattering from multiple rigid, axisymmetric cylinders where all the cylinders have a common axis of symmetry with an acoustic field incident from an arbitrary direction. The boundary-element method is implemented to compute the scattered field from cylinders with hemispherical endcaps where the azimuthal dependence is separated first to reduce computation time. Scattering computations are made for various two- and three-cylinder configurations where the dependence of the scattered field on the distance between the cylinders is examined as well as scattering from a large cylinder in the presence of a smaller cylinder.

Characteristic mechanical impedance of rheometers with axial symmetry. A theoretical and numerical analysis

The strain wave field generated in a linear viscoelastic medium confined between two infinitely large parallel planar surfaces, one fixed and the other oscillating sinusoidally in its own plane, has been well accounted for (Schrag, 1977). Here, we describe the strain wave field generated between a cylinder and a coaxial surrounding tube, both infinitely long. The tube or the cylinder remains stationary while the complementary component undergoes sinusoidal angular displacements around the common symmetry axis. This geometry is frequently used in dynamic rheometers. Both exact analytic expressions for the characteristic mechanical impedance and series expansions valid close to gap loading or surface loading conditions are provided. The exact analysis is valid for arbitrary gap width, cylinder radius, and linear viscoelastic properties of the medium within the rheometer gap. We also show how standard, modern desktop computers can be used to rapidly obtain accurate numerical values of the characteristic mechanical impedance of rheometers with axial symmetry using the exact analytic expressions.

Influence of general rotation on the transfer of torsional vibrations through axisymmetric layers of viscous liquid

A study is made of the motion of a viscous incompressible liquid in a gap between a cylinder of finite length and a jacket that contains it. The motion is due to small torsional vibrations of the jacket, whereas the complete system rotates uniformly around the common symmetry axis. The equation is linearized under the assumption that the Rossby number is small. Three problems are considered: the one-dimensional problem of vibrational motion in the cylindrical gap, the self-similar problem for the flow in the end interdisk gaps, and the two-dimensional problem that describes the flow in the corner region. It is established that the superposition of the general rotation makes the damping properties of the liquid layers between the jacket and the ends of the cylinder much less good. The influence of boundary effects is clarified.

Effects of vibrational intercentre interaction in a trigonal two-centre system with twofold electronic degeneracy at each centre

The two-centre system formed by a pair of electronically degenerate metal ions and their surroundings, interacting via the common vibrational system and electron-electron coupling, is investigated. The centres are assumed to have a common symmetry axis of third order, each centre being in a non-Kramers doubly degenerate electronic state strongly coupled to doubly degenerate nearest-neighbour nuclear displacements of E type. The adiabatic potential-energy surface of the system is shown to have a one-dimensional ring continuum of minima (a trough), and the representative point rotates freely along the trough. This internal rotation corresponds to in-phase rotations of the nearest-neighbour nuclear distortions around the centres. The counterphase motion is reduced to hindered rotations or to localized vibrations at the bottom of the potential well, depending on the value of the intercentre coupling constant. The vibronic energy spectrum is obtained and the nature of the ground singlet vibronic state of the J...

A preliminary comparison of two apparently diverse cementite/austenite orientation relationships

Summary Two reproducible yet apparently dissimilar cementite/austenite ORs have been reported. Both ORs have a common bicrystal symmetry axis which is [010] C ‖ [101] A . Further analysis indicated parallelism of close-packed planes for both ORs. Based on these observations, the statement of both ORs in the form: { 103 } C ∥ { 111 } A 010 > C ∥ 101 > A 301 > C ∥ 121 > A while possibly serving to emphasize good atomic matching which may be responsible for these ORs, does not uniquely describe the crystallographic relationships between the two phases. Similarities between the ORs suggest that comparable nucleation kinetics might be expected.