Journal articles on the topic 'Known-rotation problem'
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Lian, Yong-sheng, Jun-yi Sun, Zhi-xin Yang, Xiao-ting He, and Zhou-lian Zheng. "Closed-form solution of well-known Hencky problem without small-rotation-angle assumption." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 96, no. 12 (May 27, 2016): 1434–41. http://dx.doi.org/10.1002/zamm.201600059.
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Stebulyanin, M. M., and Ya I. Pimushkin. "Solution of the Rodriguez Equation in Modeling Volumetric Geometric Accuracy of Multi-Coordinate Systems." EPJ Web of Conferences 248 (2021): 04004. http://dx.doi.org/10.1051/epjconf/202124804004.
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The article describes the solution to the Rodrigues equation for determining the volumetric accuracy of multi-axis CNC-controlled systems. An algorithm for calculating the position of the axis of a rotary kinematic pair in problems of volumetric accuracy of mechanical motion of a portal-type system with an additional pair of rotation. The algorithm is based on the analytical solution of the Rodrigues equation in the inverse problem of finding the vector of the final rotation of the known modulus from the known initial and final values of the characteristic vector of the rotated rigid body. In contrast to the well-known direct problem, where based on a finite rotation vector known in direction and magnitude, and the initial value of the characteristic vector of a body, its final value is found, the inverse problem of the Rodrigues equation is not that common due to the nonlinearity and need to solve a nonlinear coupled system of second order equations. The results of this work make it possible to expand the dimension of the space of generalized coordinates of the system analyzed for the volumetric accuracy from three to four. This is expected contribute to the development of ultra-precise systems of controlled mechanical movement. The analytical results of this study were verified by comparing with numerical solutions of the inverse problem in Maple.
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Lian, Yong-sheng, Xiao-ting He, Guang-hui Liu, Jun-yi Sun, and Zhou-lian Zheng. "Application of perturbation idea to well-known Hencky problem: A perturbation solution without small-rotation-angle assumption." Mechanics Research Communications 83 (July 2017): 32–46. http://dx.doi.org/10.1016/j.mechrescom.2017.05.001.
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DALZIEL, STUART B. "The twists and turns of rotating turbulence." Journal of Fluid Mechanics 666 (January 6, 2011): 1–4. http://dx.doi.org/10.1017/s0022112010005409.
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Turbulence is widely considered one of the most important and most difficult unsolved problems in classical physics. It is also the area of fluid mechanics where the greatest effort is exerted, the most papers published and, some would argue, the least progress made. Although direct numerical simulation is becoming an increasingly valuable tool, there remains a need for high-quality experiments to underpin our theoretical and numerical progress. Such statements apply equally to the ‘classical’ problem of homogeneous isotropic turbulence and to turbulence in its many other guises. Of particular interest is turbulence in a rotating system, where it is well known that the influence of rotation leads to the development of anisotropy and the elongation of scales parallel to the rotation axis. Moisy et al. (J. Fluid Mech., 2010, this issue, vol. 666, pp. 5–35) present new experiments in the free decay of grid-generated turbulence in a rotating system. They investigate the emergence of anisotropy from essentially isotropic initial conditions. While it is well known that rotation suppresses velocity gradients parallel to the rotation axis, Moisy et al. (2010) uncover some startling and previously overlooked implications.
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Martin, John, Stefan Weigert, and Olivier Giraud. "Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States." Quantum 4 (June 22, 2020): 285. http://dx.doi.org/10.22331/q-2020-06-22-285.
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Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.
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MATTHEWS, PAUL, and STEPHEN COX. "Linear stability of rotating convection in an imposed shear flow." Journal of Fluid Mechanics 350 (November 10, 1997): 271–93. http://dx.doi.org/10.1017/s0022112097006903.
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In many geophysical and astrophysical contexts, thermal convection is influenced by both rotation and an underlying shear flow. The linear theory for thermal convection is presented, with attention restricted to a layer of fluid rotating about a horizontal axis, and plane Couette flow driven by differential motion of the horizontal boundaries.The eigenvalue problem to determine the critical Rayleigh number is solved numerically assuming rigid, fixed-temperature boundaries. The preferred orientation of the convection rolls is found, for different orientations of the rotation vector with respect to the shear flow. For moderate rates of shear and rotation, the preferred roll orientation depends only on their ratio, the Rossby number.It is well known that rotation alone acts to favour rolls aligned with the rotation vector, and to suppress rolls of other orientations. Similarly, in a shear flow, rolls parallel to the shear flow are preferred. However, it is found that when the rotation vector and shear flow are parallel, the two effects lead counter-intuitively (as in other, analogous convection problems) to a preference for oblique rolls, and a critical Rayleigh number below that for Rayleigh–Bénard convection.When the boundaries are poorly conducting, the eigenvalue problem is solved analytically by means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of the stability problem is found to be qualitatively similar to that for fixed-temperature boundaries.Fully nonlinear numerical simulations of the convection are also carried out. These are generally consistent with the linear stability theory, showing convection in the form of rolls near the onset of motion, with the appropriate orientation. More complicated states are found further from critical.
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Lian, Yong-Sheng, Jun-Yi Sun, Zhi-Hang Zhao, Xiao-Ting He, and Zhou-Lian Zheng. "A Revisit of the Boundary Value Problem for Föppl–Hencky Membranes: Improvement of Geometric Equations." Mathematics 8, no. 4 (April 20, 2020): 631. http://dx.doi.org/10.3390/math8040631.
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In this paper, the well-known Föppl–Hencky membrane problem—that is, the problem of axisymmetric deformation of a transversely uniformly loaded and peripherally fixed circular membrane—was resolved, and a more refined closed-form solution of the problem was presented, where the so-called small rotation angle assumption of the membrane was given up. In particular, a more effective geometric equation was, for the first time, established to replace the classic one, and finally the resulting new boundary value problem due to the improvement of geometric equation was successfully solved by the power series method. The conducted numerical example indicates that the closed-form solution presented in this study has higher computational accuracy in comparison with the existing solutions of the well-known Föppl–Hencky membrane problem. In addition, some important issues were discussed, such as the difference between membrane problems and thin plate problems, reasonable approximation or assumption during establishing geometric equations, and the contribution of reducing approximations or relaxing assumptions to the improvement of the computational accuracy and applicability of a solution. Finally, some opinions on the follow-up work for the well-known Föppl–Hencky membrane were presented.
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HILLS, CHRISTOPHER P., and H. K. MOFFATT. "Rotary honing: a variant of the Taylor paint-scraper problem." Journal of Fluid Mechanics 418 (September 10, 2000): 119–35. http://dx.doi.org/10.1017/s0022112000001075.
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The three-dimensional flow in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighbourhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the ‘Taylor’ streamlines of the well-known ‘paint-scraper’ problem. Three geometrical variants are considered: (i) when the centre of rotation of the lower plate is offset from the contact line; (ii) when both planes rotate with different angular velocities about a vertical axis and Coriolis effects are retained in the analysis; and (iii) when two vertical planes intersecting at an angle 2β are honed by a rotating conical boundary. The last is described by a similarity solution of the first kind (in the terminology of Barenblatt) which incorporates within its structure a similarity solution of the second kind involving corner eddies of a type familiar in two-dimensional corner flows.
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Glybovets, M. M., N. M. Gulayeva, and I. O. Morozov. "Analysis of Genetic Algorithms for solving the 2D Orthogonal Strip Packing Problem." PROBLEMS IN PROGRAMMING, no. 4 (December 2016): 104–16. http://dx.doi.org/10.15407/pp2016.04.104.
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A class of genetic algorithms for solving the 2D Strip Packing Problem is investigated. The theoretical analysis of the complexity of implementing decoders MERA and BLF is done. Original implementations of these MERA and BLF decoders enhanced with a number of heuristic optimizations are proposed. Genetic algorithm for solving the 2D Strip Packing Problem for special cases (allowed/forbidden objects rotation by 90°) with the use of MERA/BLF decoders is proposed. Extensive computational experiments with well-known instances are performed to analyze different configurations of basic parameters of proposed genetic algorithm. The comparison of the obtained algorithm with other known algorithms is given.
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Ziegler, Franz, and Piotr Borejko. "The Method of Generalized Ray-Revisited." Journal of Mechanics 16, no. 2 (June 2000): 125–26. http://dx.doi.org/10.1017/s1727719100001696.
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In Section 2, ROTATION OF COORDINATES, the Authors derived the emittance functions in the Weyl-Sommerfeld representation of the wave potentials for a horizontal instantaneous single force from those known for a vertical force from conditions of invariance of the phase and amplitude of plane waves under coordinate rotation, Eqs. (10) ∼ (13) and (18) ∼ (20). That transformation implies the validity of the commonly applied identity for the (force) vector components when rotating the vector in the opposite sense to the coordinate rotation. Further, in the three-dimensional case, the vertical force poses an axisymmetric problem which is compatible with the Fourier transformation applied to the coordinates in the horizontal plane.
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Lau, Ming G. "Torsional axisymmetric finite element model for problems in elasticity." Canadian Journal of Civil Engineering 13, no. 5 (October 1, 1986): 583–87. http://dx.doi.org/10.1139/l86-085.
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This note describes how the displacements and shear stresses of an axisymmetric elastic component, when loaded in torsion, can be computed by modelling the component with torsional axisymmetric finite elements. The model developed represents only minor modifications of the well-known plane stress or plane strain finite element technique.In the analysis, the model is split into a mesh of triangular annuli. Each node of each element has only one degree of freedom, the tangential displacement. The state of strain in each element is represented by a three-term displacement function, one representing a rigid body rotation, the second representing the state of torsion, and the third representing the state of strain in a hollow thin disc.The model has been applied satisfactorily to three torsional problems with known theoretical solutions. The first problem involves the computation of torsional shear stresses of a uniform shaft subjected to pure torsion. In the second problem, the solution is obtained for a conical shaft. In the third problem, known as the Reissner–Sagoci problem, an elastic semi-infinite medium is subjected to a torsional displacement on a small area of the surface.A typical application of the model to the problem of a shrink-fitted assembly subjected to torsion is discussed. Key words: torsion, finite element, elasticity, axisymmetry.
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Eg Su, Goh, and Ajune Wanis Ismail. "Pre-define Rotation Amplitudes Object Rotation in Handheld Augmented Reality." International Journal of Innovative Computing 11, no. 2 (October 31, 2021): 103–9. http://dx.doi.org/10.11113/ijic.v11n2.315.
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Interaction is one of the important topics to be discussed since it includes the interface where the end-user communicates with the augmented reality (AR) system. In handheld AR interface, the traditional interaction techniques are not suitable for some AR applications due to the different attributes of handheld devices that always refer to smartphones and tablets. Currently interaction techniques in handheld AR are known as touch-based technique, mid-air gesture-based technique and device-based technique that can led to a wide discussion in related research areas. However, this paper will focus to discover the device-based interaction technique because it has proven in the previous studies to be more suitable and robust in several aspects. A novel device-based 3D object rotation technique is proposed to solve the current problem in performing 3DOF rotation of 3D object. The goal is to produce a precise and faster 3D object rotation. Therefore, the determination of the rotation amplitudes per second is required before the fully implementation. This paper discusses the implementation in depth and provides a guideline for those who works in related to device-based interaction.
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Deo, Satya, and Pankaj Shukla. "Creeping flow of Micropolar fluid past a fluid sphere with non-zero spin boundary condition." International Journal of Engineering & Technology 1, no. 2 (May 10, 2012): 67. http://dx.doi.org/10.14419/ijet.v1i2.5.
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Abstract: This paper concerns the problem of creeping flow of an incompressible micropolar fluid past a fluid sphere with non-homogeneous boundary condition for micro rotation vector i.e. the micro rotation on the boundary of the fluid sphere is assumed to be proportional to the rotation rate of the velocity field on the boundary. The stream functions are determined by matching the solution of micropolar field equation for flow outside the fluid sphere with that of the Stokes equation for the flow inside the fluid sphere. The drag force experienced by a fluid sphere is evaluated and its variation is studied with respect to the material parameters. Some well-known results are then deduced.
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Liu, Tianyang, Qiang Sun, Huachun Zhou, and Qi Wei. "Optimization of Network Coding Resources Based on Improved Quantum Genetic Algorithm." Photonics 8, no. 11 (November 8, 2021): 502. http://dx.doi.org/10.3390/photonics8110502.
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The problem of network coding resource optimization with a known topological structure is NP-hard. Traditional quantum genetic algorithms have the disadvantages of slow convergence and difficulty in finding the optimal solution when dealing with this problem. To overcome these disadvantages, this paper proposes an adaptive quantum genetic algorithm based on the cooperative mutation of gene number and fitness (GNF-QGA). This GNF-QGA adopts the rotation angle adaptive adjustment mechanism. To avoid excessive illegal individuals, an illegal solution adjustment mechanism is added to the GNF-QGA. A solid demonstration was provided that the proposed algorithm has a fast convergence speed and good optimization capability when solving network coding resource optimization problems.
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Hori Jr, Houju. "Type 2 Vague Events and Their Applications." Sumerianz Journal of Scientific Research, no. 41 (January 24, 2021): 1–2. http://dx.doi.org/10.47752/sjsr.41.1.2.
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[1] discovered a mapping formula for Type 1 Vague events, and presented an alternative problem as an example of its application. Since it is well known that the alternative problem results in sequential Bayesian inference, the subsequent research flow is to make the mapping formula multidimensional, to derive the Markov (decision) process by introducing the concept of time, and so on. Furthermore, the stochastic differential equation from which it is derived was formulated. [2] This paper refers to Type 2 Vague events based on the secondary mapping formula. This quadratic mapping formula gives a certain rotation to a non-mapping function by transforming it with a relationship between the two mapping functions. Furthermore, here we refer to the derivation of the Type 2 Vague Markov process and the initial and stop conditions for its rotation.
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Hori Jr, Houju. "Type 2 Vague Events and Their Applications." Sumerianz Journal of Scientific Research, no. 41 (January 24, 2021): 1–2. http://dx.doi.org/10.47752/sjsr.41.1.2.
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[1] discovered a mapping formula for Type 1 Vague events, and presented an alternative problem as an example of its application. Since it is well known that the alternative problem results in sequential Bayesian inference, the subsequent research flow is to make the mapping formula multidimensional, to derive the Markov (decision) process by introducing the concept of time, and so on. Furthermore, the stochastic differential equation from which it is derived was formulated. [2] This paper refers to Type 2 Vague events based on the secondary mapping formula. This quadratic mapping formula gives a certain rotation to a non-mapping function by transforming it with a relationship between the two mapping functions. Furthermore, here we refer to the derivation of the Type 2 Vague Markov process and the initial and stop conditions for its rotation.
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Stewart, G. A., and E. W. Laing. "Wave propagation in equal-mass plasmas." Journal of Plasma Physics 47, no. 2 (April 1992): 295–319. http://dx.doi.org/10.1017/s0022377800024247.
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We study linear wave propagation in the case of equal-mass plasmas. We show that the special symmetry of such plasmas simplifies the problem and causes the disappearance of well-known phenomena such as Faraday rotation and whistler wave modes. We exploit the Symmetry of the problem to derive analytical expressions for wave propagation for various fluid models of the plasma. We also find which distribution functions will retain the symmetry properties of the fluid models.
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Crnkić, Aladin, and Zinaid Kapić. "Interpolation on the special orthogonal group with high-dimensional Kuramoto model." IOP Conference Series: Materials Science and Engineering 1208, no. 1 (November 1, 2021): 012037. http://dx.doi.org/10.1088/1757-899x/1208/1/012037.
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Abstract The construction of smooth interpolation trajectories in different non-Euclidean spaces finds application in robotics, computer graphics, and many other engineering fields. This paper proposes a method for generating interpolation trajectories on the special orthogonal group SO(3), called the rotation group. Our method is based on a high-dimensional generalization of the Kuramoto model which is a well-known mathematical description of self-organization in large populations of coupled oscillators. We present the method through several simulations and visualize each simulation as trajectories on unit spheres S2. In addition, we applied our method to the specific problem of object rotation interpolation.
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Tognolatti, Ludovica, Cristina Ponti, Massimo Santarsiero, and Giuseppe Schettini. "An Efficient Computational Technique for the Electromagnetic Scattering by Prolate Spheroids." Mathematics 10, no. 10 (May 21, 2022): 1761. http://dx.doi.org/10.3390/math10101761.
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In this paper we present an efficient Matlab computation of a 3-D electromagnetic scattering problem, in which a plane wave impinges with a generic inclination onto a conducting ellipsoid of revolution. This solid is obtained by the rotation of an ellipse around one of its axes, which is also known as a spheroid. We have developed a fast and ad hoc code to solve the electromagnetic scattering problem, using spheroidal vector wave functions, which are special functions used to describe physical problems in which a prolate or oblate spheroidal reference system is considered. Numerical results are presented, both for TE and TM polarization of the incident wave, and are validated by a comparison with results obtained by a commercial electromagnetic simulator.
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Li, Xue, Jun-Yi Sun, Zhi-Hang Zhao, Shou-Zhen Li, and Xiao-Ting He. "A New Solution to Well-Known Hencky Problem: Improvement of In-Plane Equilibrium Equation." Mathematics 8, no. 5 (April 25, 2020): 653. http://dx.doi.org/10.3390/math8050653.
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In this paper, the well-known Hencky problem—that is, the problem of axisymmetric deformation of a peripherally fixed and initially flat circular membrane subjected to transverse uniformly distributed loads—is re-solved by simultaneously considering the improvement of the out-of-plane and in-plane equilibrium equations. In which, the so-called small rotation angle assumption of the membrane is given up when establishing the out-of-plane equilibrium equation, and the in-plane equilibrium equation is, for the first time, improved by considering the effect of the deflection on the equilibrium between the radial and circumferential stress. Furthermore, the resulting nonlinear differential equation is successfully solved by using the power series method, and a new closed-form solution of the problem is finally presented. The conducted numerical example indicates that the closed-form solution presented here has a higher computational accuracy in comparison with the existing solutions of the well-known Hencky problem, especially when the deflection of the membrane is relatively large.
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Kachoyan, B. J., and P. J. Blennerhassett. "On the finite Dean problem: linear theory." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 30, no. 2 (October 1988): 157–78. http://dx.doi.org/10.1017/s0334270000006135.
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AbstractThe Dean problem of pressure-driven flow between finite-length concentric cylinders is considered. The outer cylinder is at rest and the small-gap approximation is used. In a similar procedure to that of Blennerhassett and Hall [8] in the context of Taylor vortices, special end conditions are imposed in which the ends of the cylinder move with the mean flow, allowing the use of a perturbation analysis from a known basic flow. Difficulties specific to Dean flow (and more generally to non-Taylor-vortex flow) require the use of a parameter α which measures the relative strengths of the velocities due to rotation and the pressure gradient, to trace the solution from Taylor to Dean flow. Asymptotic expansions are derived for axial wavenumbers at a given Taylor number. The calculation of critical Taylor number for a given cylinder height is then carried out. Corresponding stream-function contours clearly show features not evident in infinite flow.
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Denysenko, Viktoriia, Iryna Kovalova, and Dina Lazarieva. "The Dynamic Problem of Torsion by a Rigid Shaft of a Nonhomogeneous Half-Space." Materials Science Forum 968 (August 2019): 396–403. http://dx.doi.org/10.4028/www.scientific.net/msf.968.396.
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An axisymmetric contact problem concerning the torsion of a circular shaft of an orthotropic-nonhomogeneous half-space is considered. By means of the technique of integral transformations of Laplace and Hankel, with the subsequent application of the orthogonal polynomial method, an approximate solution in the transformant space is constructed. Also was performed reverse transformation. Calculated formulas for the angle of rotation of the shaft and the tangential stress acting on the contact area are obtained. Numerical calculations for certain types of heterogeneity have been performed. Comparison of the obtained results with the previously known results is made.
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Dzyuba, Anatolii, Inha Safronova, and Larysa Levitina. "Algorithm for reducing computational costs in problems of calculation of asymmetrically loaded shells of rotation." Strength of Materials and Theory of Structures, no. 105 (November 30, 2020): 99–113. http://dx.doi.org/10.32347/2410-2547.2020.105.99-113.
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The problem of calculating the shells of rotation of a variable along the meridian of rigidity under asymmetric loading is reduced o a set of systems of one-dimensional boundary value problems with respect to the amplitudes of decomposition of the required functions into trigonometric Fourier series.
A method for reducing the number of one-dimensional boundary value problems required to achieve a given accuracy in determining the stress-strain state of the shells of rotation with a variable along the meridian wall thickness under asymmetric load. The idea of the proposed approach is to apply periodic extrapolation (prediction) of the values of the decomposition coefficients of the required functions using the results of calculations of previous coefficients of the corresponding trigonometric series, thus replacing them with some prediction values calculated by simple formulas.
To solve this problem, we propose the joint use of Aitken-Steffens extrapolation dependences and Adams method in the form of incremental component, which is quite effective in solving the Cauchy problem for systems of ordinary differential equations and is based on Lagrange and Newton extrapolation dependences.
The validity of the proposed approach was verified b the results of a systematic numerical experiment by predicting the values of the expansion coefficients in the Fourier series of known functions of one variable.
The approach is quite effective in the calculation of asymmetrically loaded shells of rotation with variable along the meridian thickness, when the coefficients of decomposition of the required functions into Fourier series are functions of the longitudina lcoordinate and are calculated by solving the corresponding boundary value problem. In this case, the approach allows solving solutions of differential equations for the amplitudes of decompositionin to trigonometric series only for individual "reference" harmonics, and the amplitudes for every third harmonic can be calculated by interpolating their values for all node integration points of the corresponding boundary value problem. This significantly reduces the computational cost of obtaining the solution as a whole.
As an example, the results of the calculation of the stress-strain state of a steel annular plate under asymmetric transverse loading are given.
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BIGELOW, STEPHEN, and CLAIRE LEVAILLANT. "AN EXACT ENTANGLING GATE USING FIBONACCI ANYONS." Bulletin of the Australian Mathematical Society 99, no. 2 (November 12, 2018): 319–26. http://dx.doi.org/10.1017/s0004972718001028.
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Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However, there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there is no known ‘leakage-free’ entangling gate made by braiding. In this paper, we provide a remedy to this problem by supplementing braiding with measurement operations in order to produce an exact controlled rotation gate on two qubits.
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Stone, Thomas, Michael Mangan, Antoine Wystrach, and Barbara Webb. "Rotation invariant visual processing for spatial memory in insects." Interface Focus 8, no. 4 (June 15, 2018): 20180010. http://dx.doi.org/10.1098/rsfs.2018.0010.
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Visual memory is crucial to navigation in many animals, including insects. Here, we focus on the problem of visual homing, that is, using comparison of the view at a current location with a view stored at the home location to control movement towards home by a novel shortcut. Insects show several visual specializations that appear advantageous for this task, including almost panoramic field of view and ultraviolet light sensitivity, which enhances the salience of the skyline. We discuss several proposals for subsequent processing of the image to obtain the required motion information, focusing on how each might deal with the problem of yaw rotation of the current view relative to the home view. Possible solutions include tagging of views with information from the celestial compass system, using multiple views pointing towards home, or rotation invariant encoding of the view. We illustrate briefly how a well-known shape description method from computer vision, Zernike moments, could provide a compact and rotation invariant representation of sky shapes to enhance visual homing. We discuss the biological plausibility of this solution, and also a fourth strategy, based on observed behaviour of insects, that involves transfer of information from visual memory matching to the compass system.
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Noor, Khalida Inayat, and Sadia Riaz. "Generalized q-starlike functions." Studia Scientiarum Mathematicarum Hungarica 54, no. 4 (December 2017): 509–22. http://dx.doi.org/10.1556/012.2017.54.4.1380.
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In this paper, we introduce a new concept of q-bounded radius rotation and define the class R*m(q), m ≥ 2, q ∈ (0, 1). The class R*2(q) coincides with S*q which consists of q-starlike functions defined in the open unit disc. Distortion theorems, coefficient result and radius problem are studied. Relevant connections to various known results are pointed out.
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Borisov, Alexey, Ivan Mamaev, and Nadezhda Erdakova. "Dynamics of a body sliding on a rough plane and supported at three points." Theoretical and Applied Mechanics 43, no. 2 (2016): 169–90. http://dx.doi.org/10.2298/tam161130013b.
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This paper is concerned with the problem of a rigid body (tripod) moving with three points in contact with a horizontal plane under the action of dry friction forces. It is shown that the regime of asymptotic motion (final dynamics) of the tripod can be pure rotation, pure sliding, or sliding and rotation can cease simultaneously, which is determined by the position of the tripod?s supports relative to the radius of inertia. In addition, the dependence of the trajectory of the center of mass on the system parameters is investigated. A comparison is made with the well-known theoretical and experimental studies on the motion of bodies with a flat base.
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Hao, Zongbo, Tao Zhang, Mingwang Chen, and Zou Kaixu. "RRL: Regional Rotate Layer in Convolutional Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 1 (June 28, 2022): 826–33. http://dx.doi.org/10.1609/aaai.v36i1.19964.
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Convolutional Neural Networks (CNNs) perform very well in image classification and object detection in recent years, but even the most advanced models have limited rotation invariance. Known solutions include the enhancement of training data and the increase of rotation invariance by globally merging the rotation equivariant features. These methods either increase the workload of training or increase the number of model parameters. To address this problem, this paper proposes a module that can be inserted into the existing networks, and directly incorporates the rotation invariance into the feature extraction layers of the CNNs. This module does not have learnable parameters and will not increase the complexity of the model. At the same time, only by training the upright data, it can perform well on the rotated testing set. These ad-vantages will be suitable for fields such as biomedicine and astronomy where it is difficult to obtain upright samples or the target has no directionality. Evaluate our module with LeNet-5, ResNet-18 and tiny-yolov3, we get impressive results.
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Huré, J.-M. "Nested spheroidal figures of equilibrium I. Approximate solutions for rigid rotations." Monthly Notices of the Royal Astronomical Society 512, no. 3 (April 6, 2022): 4031–46. http://dx.doi.org/10.1093/mnras/stab3388.
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ABSTRACT We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient pressure), approximations can be obtained for configurations involving a small confocal parameter. The problem then admits two families of solutions, depending on the pressure along the common interface (constant or quadratic with the cylindrical radius). We give in both cases the pressure and the rotation rates as a function of the fractional radius, ellipticities, and mass–density jump. Various degrees of flattening are allowed but there are severe limitations for global rotation, as already known from classical theory (e.g. impossibility of confocal and coelliptical solutions, gradient of ellipticity outward). States of relative rotation are much less constrained, but these require a mass–density jump. This analytical approach compares successfully with the numerical solutions obtained from the self-consistent-field method. Practical formula are derived in the limit of small ellipticities appropriate for slowly rotating star/planet interiors.
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JIANG, MINGHUI, YING XU, and BINHAI ZHU. "PROTEIN STRUCTURE–STRUCTURE ALIGNMENT WITH DISCRETE FRÉCHET DISTANCE." Journal of Bioinformatics and Computational Biology 06, no. 01 (February 2008): 51–64. http://dx.doi.org/10.1142/s0219720008003278.
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Matching two geometric objects in two-dimensional (2D) and three-dimensional (3D) spaces is a central problem in computer vision, pattern recognition, and protein structure prediction. In particular, the problem of aligning two polygonal chains under translation and rotation to minimize their distance has been studied using various distance measures. It is well known that the Hausdorff distance is useful for matching two point sets, and that the Fréchet distance is a superior measure for matching two polygonal chains. The discrete Fréchet distance closely approximates the (continuous) Fréchet distance, and is a natural measure for the geometric similarity of the folded 3D structures of biomolecules such as proteins. In this paper, we present new algorithms for matching two polygonal chains in two dimensions to minimize their discrete Fréchet distance under translation and rotation, and an effective heuristic for matching two polygonal chains in three dimensions. We also describe our empirical results on the application of the discrete Fréchet distance to protein structure–structure alignment.
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Noleto, Luciano Gonçalves, Manuel N. D. Barcelos, and Antonio C. P. Brasil. "A Pseudo-Stokes Mesh Motion Algorithm." Advances in Applied Mathematics and Mechanics 5, no. 2 (April 2013): 194–211. http://dx.doi.org/10.4208/aamm.11-m1186.
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AbstractThis work presents a moving mesh methodology based on the solution of a pseudo flow problem. The mesh motion is modeled as a pseudo Stokes problem solved by an explicit finite element projection method. The mesh quality requirements are satisfied by employing a null divergent velocity condition. This methodology is applied to triangular unstructured meshes and compared to well known approaches such as the ones based on diffusion and pseudo structural problems. One of the test cases is an airfoil with a fully meshed domain. A specific rotation velocity is imposed as the airfoil boundary condition. The other test is a set of two cylinders that move toward each other. A mesh quality criteria is employed to identify critically distorted elements and to evaluate the performance of each mesh motion approach. The results obtained for each test case show that the pseudo-flow methodology produces satisfactory meshes during the moving process.
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Rowland, David R. "On claims that general relativity differs from Newtonian physics for self-gravitating dusts in the low velocity, weak field limit." International Journal of Modern Physics D 24, no. 08 (July 2015): 1550065. http://dx.doi.org/10.1142/s0218271815500650.
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Galaxy rotation curves are generally analyzed theoretically using Newtonian physics; however, two groups of authors have claimed that for self-gravitating dusts, general relativity (GR) makes significantly different predictions to Newtonian physics, even in the weak field, low velocity limit. One group has even gone so far as to claim that nonlinear general relativistic effects can explain flat galactic rotation curves without the need for cold dark matter. These claims seem to contradict the well-known fact that the weak field, low velocity, low pressure correspondence limit of GR is Newtonian gravity, as evidenced by solar system tests. Both groups of authors claim that their conclusions do not contradict this fact, with Cooperstock and Tieu arguing that the reason is that for the solar system, we have test particles orbiting a central gravitating body, whereas for a galaxy, each star is both an orbiting body and a contributor to the net gravitational field, and this supposedly makes a difference due to nonlinear general relativistic effects. Given the significance of these claims for analyses of the flat galactic rotation curve problem, this article compares the predictions of GR and Newtonian gravity for three cases of self-gravitating dusts for which the exact general relativistic solutions are known. These investigations reveal that GR and Newtonian gravity are in excellent agreement in the appropriate limits, thus supporting the conventional use of Newtonian physics to analyze galactic rotation curves. These analyses also reveal some sources of error in the referred to works.
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Buchheit, Martin. "Houston, We Still Have a Problem." International Journal of Sports Physiology and Performance 12, no. 8 (September 2017): 1111–14. http://dx.doi.org/10.1123/ijspp.2017-0422.
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Apollo 13 was initially looking like it would be the smoothest flight ever. After the explosion of an oxygen tank, however, the astronauts were close to spending the rest of their lives in rotation around the planet. This well-known incident is used to further discuss the link, or lack thereof, between sport-science research and current field practices. There is a feeling that the academic culture and its publishing requirements have created a bit of an Apollo 13–like orbiting world (eg, journals and conferences) that is mostly disconnected from the reality of elite performance. The author discusses how poor research discredits our profession and provides some examples from the field where the research does not apply. In fact, the reality is that sport scientists often do not have the right answers. Some perspectives to improve translation are finally discussed, including a rethink of the overall publishing process: promotion of relevant submission types (eg, short-paper format, short reports, as provided by IJSPP), improvement of the review process (faster turnaround, reviewers identified to increase accountability, and, in turn, review quality), and media types (eg, free downloads, simplified versions published in coaching journals, book chapters, infographics, dissemination via social media). When it comes to guiding practitioners and athletes, instead of using an evidence-based approach, we should rather promote an “evidence-led” or “informed-practice” approach—one that appreciates context over simple scientific conclusions.
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Ecsedi, István, Ákos József Lengyel, Attila Baksa, and Dávid Gönczi. "Bounds for the electrical resistance for homogeneous conducting body of rotation." Multidiszciplináris tudományok 11, no. 5 (2021): 104–22. http://dx.doi.org/10.35925/j.multi.2021.5.11.
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A mathematical model is developed for the steady-state electric current flow through in a homogeneous isotropic conductor whose shape is a body of rotation. The body of rotation considered is bounded by the coordinate surfaces of an orthogonal curvilinear coordinate system. The equations of the Maxwell’s theory of electric current flow in a homogeneous solid conductor body are used to formulate the corresponding electric boundary value problem. The studied steady-state conduction problem is axisymmetric. The determination of the steady motion of charges is based on the concept of the electrical conductance of the conductors the inverse of which is the electrical resistance. The exact (strict) value of the electrical resistance is known only for bodies with very simple shapes, therefore, the principles and the methods that can be used for creating lower and upper bounds to the numerical value of electrical resistance (electrical conductance) are important. The derivation of the upper and lower bound formulae for the electrical conductance of axisymmetric ring-like conductor is based on the two types of Cauchy–Schwarz inequality. The condition of equality of the derived lower and upper bounds is examined. Several examples illustrate the applications of the derived upper and lower bound formulae.
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Lazányi, J. "SUSTAINABLE RYE PRODUCTION IN THE WESTSIK CROP ROTATION EXPERIMENT." Acta Agronomica Hungarica 48, no. 3 (December 1, 2000): 271–77. http://dx.doi.org/10.1556/aagr.48.2000.3.7.
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The best-known and most remarkable example of continuous production in Hungary is the Westsik crop rotation experiment established in 1929. It is still in use to study the effects of organic manure treatment, to develop models and to predict the likely effects of different cropping systems on soil properties and crop yields. In this respect, the Westsik crop rotation experiment provides data of immediate value to farmers concerning the application of green manure, straw and farmyard manure. The increased demand for food and changes in the ecological requirements of agricultural production have urged scientists to revise the widely used traditional principles and to develop alternative crop production practices. In this respect, they must strive for the adoption of technologies which serve for the simultaneous maintenance of production levels, soil fertility and environmental goals. The Westsik crop rotation experiment provides useful help and a thorough scientific basis for the solution of this problem. It models various possible methods of nutrient management and assists in answering questions on the sustainability of agricultural production. Since 1929, only minor changes have been introduced in some treatments. These changes have made the classical experiment more relevant to current research needs and farming practices.
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Mahmoud, S. R. "An Analytical Solution for Effect of Magnetic Field and Initial Stress on an Infinite Generalized Thermoelastic Rotating Nonhomogeneous Diffusion Medium." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/284646.
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The problem of generalized magneto-thermoelastic diffusion in an infinite rotating nonhomogeneity medium subjected to certain boundary conditions is studied. The chemical potential is also assumed to be a known function of time at the boundary of the cavity. The analytical expressions for the displacements, stresses, temperature, concentration, and chemical potential are obtained. Comparison was made between the results obtained in the presence and absence of diffusion. The results indicate that the effect of nonhomogeneity, rotation, magnetic field, relaxation time, and diffusion is very pronounced.
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Ibrahim, Sharif, Kevin Sonnanburg, Thomas J. Asaki, and Kevin R. Vixie. "Nonasymptotic Densities for Shape Reconstruction." Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/341910.
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In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area of a disk centered on the boundary that is also inside the shape. It is easy to show uniqueness when these densities are known for all radii in a neighborhood ofr=0, but much less straightforward when we assume that we only know the area invariant and its derivatives for only oner>0. We present variations of uniqueness results for reconstruction (modulo translation and rotation) of polygons and (a dense set of) smooth curves under certain regularity conditions.
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Sugiyama, Hiroyuki, Nobuyuki Kobayashi, and Yoshimasa Komaki. "Modeling and Experimental Methods for Dynamic Analysis of the Spaghetti Problem." Journal of Vibration and Acoustics 127, no. 1 (February 1, 2005): 44–51. http://dx.doi.org/10.1115/1.1857919.
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The nonlinear dynamics of a very flexible body with time-variant length encompasses several industrial applications such as high-speed automatic coiling machines and copy machines. Among others, the significant increase in the vibration that occurs when the material length is shortened with time is known as the spaghetti problem. In this paper, the modeling method and the experimental procedure for the analysis of the spaghetti problem are presented. The change in the state of the forces and displacements at the boundary with a clearance is taken into consideration by modeling the mechanical interactions resulting from the clearance. A flexible beam is modeled using the finite segment method to account for the geometric nonlinearities due to the large rotation. The contact forces at the boundary are modeled using a set of springs and dampers. The numerical results obtained using the proposed modeling method agree well with the results obtained using the experiment. The effect of the transport velocity and the clearance are demonstrated, and the cause of the significant increase in the flexible body vibration is discussed from an energy balance viewpoint.
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Levskii, M. V. "Analytical Solving the Optimal Control Problem of Spacecraft’s Slew Maneuver with Minimal Energy of Rotation." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 3 (March 5, 2020): 174–83. http://dx.doi.org/10.17587/mau.21.174-183.
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Dynamic problem of optimal reorientation from an arbitrary initial attitude into the given final angular position with restricted control which minimizes kinetic energy of spacecraft rotation was solved. Termination time of maneuver is known. Quadratic criterion of quality is applied for finding the optimal control program. Use of integral index in special form concerning angular velocity has helped solve the formulated problem by analytical way. Control law was written down in explicit form. Designing the optimal control is based on quaternion variables and models. It is shown that during optimal turn, the controlling moment is parallel to the straight line which is immobile in the inertial space, and direction of spacecraft’s angular momentum in the process of rotation is constant relative to the inertial coordinate system. Special control regime was studied in detail, and conditions of the impossibility of occurrence of this regime are formulated. It is proven that spacecraft rotates by inertia in special control regime if it exists. The formalized equations and computational expressions for determining the optimal rotation program and duration of acceleration and braking were written. A dependence of control variables on phase coordinates is presented also. The proposed control algorithm allows the spacecraft’s reorientation to be carried out within the fixed time period with minimal angular kinetic energy. Analytical expressions for computing the time characteristics of reorientation maneuver are given, and condition for determination of the moment of the beginning of the braking, based on factual kinematic parameters of motion judging by principles of terminal control is formulated, that provides high accuracy of orientation. A comprehensive solution to the control problem is presented for a dynamically symmetric spacecraft: the dependences as explicit functions of time for the control variables are obtained, and relations for calculating the key parameters of the turn maneuver’s control law are given also. A numerical example and the results of mathematical simulation of spacecraft’s motion with optimal control are presented, which demonstrate the practical feasibility of the designed method for controlling the spacecraft attitude. Presence of ready formulas for synthesis of optimal motion program during reorientation maneuver does the executed research as practically significant and suitable for direct use in practice of space flights.
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Tang, Xin Rui, Keiichi Nakamoto, Kazushi Obata, and Yoshimi Takeuchi. "The Effect of Cutting Point Swivel Machining by Using Round Tool with Special Chamfer." Key Engineering Materials 523-524 (November 2012): 119–24. http://dx.doi.org/10.4028/www.scientific.net/kem.523-524.119.
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Recently, in accordance with the technical development and miniaturization of the information equipments, the demand of optic elements with high precision and miniaturization is increased. The mold is used in the manufacture of the optic elements. Thus, it is needed to machine the mold with high efficiency and high precision. As the material of mold, hard material including cemented carbide and ceramics is used. However, it is a problem of the occurrence of severe tool wear when hard material is machined. To solve this problem, the cutting point swivel machining by using the diamond tool with special chamfer was proposed, which has the ability to suppress tool wear and to realize ultraprecise machining. It is confirmed that the cutting point swivel machining has the ability to suppress tool wear by the microgrooving experiment of SiC. This study aims at investigating the effect of the cutting point swivel machining, and making clear the relationship between tool rotation speed and tool wear. As a result, it is known that the actual cutting direction can be changed by using the cutting point swivel machining, and that the chipping of tool becomes conspicuous with increasing tool rotation speed.
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Spruit, H. C. "Angular Momentum Transport and Mixing by Magnetic Fields." Symposium - International Astronomical Union 215 (2004): 356–65. http://dx.doi.org/10.1017/s0074180900195889.
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Magnetic fields can be created in stably stratified (non-convective) layers in a differentially rotating star. A magnetic instability in the toroidal field (wound up by differential rotation) replaces the role of convection in closing the field amplification loop. A dynamo model is developed from these ingredients, and applied to the problem of angular momentum transport in stellar interiors. It produces a predominantly horizontal field. The process is found to be more effective in transporting angular momentum than the known hydrodynamic mechanisms, with the possible exception of transport by internal gravity waves.
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Kusaka, Takashi, and Takayuki Tanaka. "Stateful Rotor for Continuity of Quaternion and Fast Sensor Fusion Algorithm Using 9-Axis Sensors." Sensors 22, no. 20 (October 19, 2022): 7989. http://dx.doi.org/10.3390/s22207989.
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Advances in micro-electro-mechanical systems technology have led to the emergence of compact attitude measurement sensor products that integrate acceleration, magnetometer, and gyroscope sensors on a single chip, making them important devices in the field of three-dimensional (3D) attitude measurement for unmanned aerial vehicles, smartphones, and other devices. Sensor fusion algorithms for posture measurement have become an indispensable technology in cutting-edge research, such as human posture measurement using wearable sensors, and stabilization problems in robot position and posture measurement. We have also developed wearable sensors and powered suits in our previous research. We needed a technology for the real-time measurement of a 3D human body motion. It is known that quaternions can be used to algebraically handle 3D rotations; however, sensor fusion algorithms for three sensors are presently complex. This is because these algorithms deal with the post-rotation attitude (pure quaternions) rather than rotation information (the rotor) to avoid a double covering problem involving the rotor. If we are dealing with rotation, it may be possible to make the algorithm simpler and faster by dealing directly with the rotor. In this study, to solve the double covering problem involving the rotor, we propose a stateful rotor and develop a technique for uniquely determining the time-varying states of the rotor. The proposed stateful rotor guarantees the continuity of the rotor parameters with respect to angular changes, and this paper confirms its effectiveness by simulating two rotations around an arbitrary axis. In addition, we verify experimentally that a fast sensor fusion method using stateful rotor can be used for attitude calculation. Experiments also confirm that the calculated results converge to the desired rotation angle for two spatial rotations around an arbitrary axis. Since the proposed stateful rotor extends and stabilizes the definition of the rotor, it is applicable to any algorithm that deals with time-varying quaternionic rotors. In this research, an algorithm based on a multiply–add operation is designed to reduce computational complexity as a high-speed calculation for embedded systems. This method is theoretically equivalent to other methods, while contributing to power saving and the cost reduction of products.
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Ďurech, J., and J. Hanuš. "Reconstruction of asteroid spin states from Gaia DR2 photometry." Astronomy & Astrophysics 620 (November 30, 2018): A91. http://dx.doi.org/10.1051/0004-6361/201834007.
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Context. In addition to stellar data, Gaia Data Release 2 (DR2) also contains accurate astrometry and photometry of about 14 000 asteroids covering 22 months of observations. Aims. We used Gaia asteroid photometry to reconstruct rotation periods, spin axis directions, and the coarse shapes of a subset of asteroids with enough observations. One of our aims was to test the reliability of the models with respect to the number of data points and to check the consistency of these models with independent data. Another aim was to produce new asteroid models to enlarge the sample of asteroids with known spin and shape. Methods. We used the lightcurve inversion method to scan the period and pole parameter space to create final shape models that best reproduce the observed data. To search for the sidereal rotation period, we also used a simpler model of a geometrically scattering triaxial ellipsoid. Results. By processing about 5400 asteroids with at least 10 observations in DR2, we derived models for 173 asteroids, 129 of which are new. Models of the remaining asteroids were already known from the inversion of independent data, and we used them for verification and error estimation. We also compared the formally best rotation periods based on Gaia data with those derived from dense lightcurves. Conclusions. We show that a correct rotation period can be determined even when the number of observations N is less than 20, but the rate of false solutions is high. For N > 30, the solution of the inverse problem is often successful and the parameters are likely to be correct in most cases. These results are very promising because the final Gaia catalogue should contain photometry for hundreds of thousands of asteroids, typically with several tens of data points per object, which should be sufficient for reliable spin reconstruction.
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Cucci, D. A., and J. Skaloud. "ON RAW INERTIAL MEASUREMENTS IN DYNAMIC NETWORKS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-2/W5 (May 29, 2019): 549–57. http://dx.doi.org/10.5194/isprs-annals-iv-2-w5-549-2019.
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<p><strong>Abstract.</strong> Dynamic Networks have been introduced in the literature to solve multi-sensor fusion problems for navigation and mapping. They have been shown to outperform conventional methods in challenging scenarios, such as corridor mapping or self-calibration. In this work we investigate the problem of how raw inertial readings can be fused with GNSS position observations in Dynamic Networks (DN) with the goal of i) limiting the number of unknowns in the estimation problem and ii) improving the conditioning of the normal equations arising in least-squares adjustments in the absence of spatial constraints (e.g., image observations). For that we propose a modified version of the well known IMU-preintegration method, accounting for a non-constant gravity model, the Earth rotation and the apparent Coriolis force, and we compare it with the conventional DN formulation in a emulated scenario. This consists of a fixed-wing UAV flying four times over a 2&thinsp;km long corridor.</p>
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Sherov, K. T., M. R. Sikhimbayev, B. S. Donenbayev, A. A. Sagitov, and S. S. Ainabekova. "Experimental Research of Rotational-and-Frictional Boring of Big Holes in Large Parts." Journal of Theoretical and Applied Mechanics 47, no. 4 (December 1, 2017): 23–36. http://dx.doi.org/10.1515/jtam-2017-0018.
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Abstract When producing large-dimensional parts of heavy machines, the largest specific weight in the general labour input is made by the operations, connected with machining the main holes, i. e. holes of large diameter. To the holes of large diameter of large-dimensional parts, there are specified high requirements in the aspect of accuracy of the size, shape and arrangement. Machining of holes still remains one of the topical problems of present day mechanical engineering, in particular machine-building enterprises of the Republic of Kazakhstan. Solving the problem of ensuring accuracy and quality of machining large holes of large-dimensional parts requires the development of new resource-saving technologies of machining. In this work there are presented the results of studying a resource-saving method of rotation-friction boring of large diameter holes. There has been achieved good results in providing the quality indicators, when machining by the proposed method of rotation-friction boring with the use of the tool (a disk cutter) made of steel 90CrSi5 in comparison with well-known boring of holes. The diagram of chip formation of cutting and the results of studying the zone of chip formation by the metallographic method is also presented.
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Pittel, Boris. "On a Random Instance of a ‘Stable Roommates’ Problem: Likely Behavior of the Proposal Algorithm." Combinatorics, Probability and Computing 2, no. 1 (March 1993): 53–92. http://dx.doi.org/10.1017/s0963548300000481.
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In a set of even cardinality n, each member ranks all the others in order of preference. A stable matching is a partition of the set into n/2 pairs, with the property that no two unpaired members both prefer each other to their partners under matching. It is known that for some problem instances no stable matching exists. In 1985, Irving found an O(n2) two-phase algorithm that would determine, for any instance, whether a stable matching exists, and if so, would find such a matching. Recently, Tan proved that Irving's algorithm, with a modified second phase, always finds a stable cyclic partition of the members set, which is a stable matching when each cycle has length two. In this paper we study a likely behavior of the algorithm under the assumption that an instance of the ranking system is chosen uniformly at random. We prove that the likely number of basic steps, i.e. the individual proposals in the first phase and the rotation eliminations, involving subsets of members in the second phase, is O(n log n), and that the likely size of a rotation is O((n log n)1/2). We establish a ‘hyperbola law’ analogous to our past result on stable marriages. It states that at every step of the second phase, the product of the rank of proposers and the rank of proposal holders is asymptotic, in probability, to n3. We show that every stable cyclic partition is likely to be almost a stable matching, in the sense that at most O((n log n)1/2) members can be involved in the cycles of length three or more.
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Septanto, Harry, Riyanto T. Bambang, Arief Syaichu-Rohman, Ridanto Eko Poetro, and Adrianto Ravi Ibrahim. "Quaternion-Based Attitude Control System Design of Single and Cooperative Spacecrafts: Boundedness of Solution Approach." Modelling and Simulation in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/652571.
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It is well known that single equilibrium orientation point in matrix rotation is represented by two equilibrium points in quaternion. This fact would imply nonefficient control effort as well as problem in guaranteeing stability of the two equilibrium points in quaternion. This paper presents a solution to design quaternion-based spacecraft attitude control system whose saturation element is in its control law such that those problems are overcome. The proposed feature of methodology is the consideration on boundedness of solution in the control system design even in the presence of unknown external disturbance. The same methodology is also used to design cooperative spacecrafts attitude control system. Through the proposed method, the most relaxed information-state topology requirement is obtained, that is, the directed graph that contains a directed spanning tree. Some numerical simulations demonstrate effectiveness of the proposed feature of methodology.
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Rapstine, Thomas, and Paul Sava. "Removing residual airborne sensor motion for measuring seismic signals from a drone." Journal of Unmanned Vehicle Systems 9, no. 3 (September 1, 2021): 129–48. http://dx.doi.org/10.1139/juvs-2020-0017.
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Acquiring seismic data using drones requires excellent knowledge of the drone’s motion since positional measurements made from an airborne sensor represent a combination of sensor and ground motion. Recent advancements in laser Doppler vibrometry and repeat lidar surveys show that the frequency and resolution of non-contact motion measurements is increasing to the point necessary for measuring seismic signals. We explore the conditions under which separation of sensor motion from ground motion can be accomplished in practice. We assume (i) that the translation and rotation of a stabilized airborne sensor follows an analytic form in time that is either known or can be estimated from the sensor’s measurements, (ii) that the seismic signal we observe has compact support contained within the measurement window, and (iii) that the ground motion can be described by a rigid translation. We analyze the effectiveness of our signal separation problem as a function of peak signal, sensor noise level, sensor rotation angle, and sensor point sampling density by defining a boundary where SNR = 0 dB for various combinations of these parameters. We find that under the set of assumptions, lower rotation angles, lower sensor noise, and denser point samplings on the ground provide better signal separation using our method.
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Noor, Khalida I., and Haila Madifer. "On some classes of analytic functions." International Journal of Mathematics and Mathematical Sciences 10, no. 3 (1987): 495–501. http://dx.doi.org/10.1155/s0161171287000589.
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Letm1,m2be any numbers and letVm1,m2be the class of functions of analytic in the unit discE={z:|z|<1}for whichf′(z)=(S′1(z))m1(S′2(z))m2whereS1andS2are analytic inEwithS′1(0)=(S′2(0))=1. Moulis [1] gave a sufficient condition and a necessary condition on parametersm1andm2for the classVm1,m2to consist of univalent functions ifS1andS2are taken to be convex univalent functions inE. In fact he proved that iff ϵ Vm1,m2whereS1andS2are convex andm1=k+24e−iα(1−ρ)cosα,m2=k−24e−iα(1−ρ)cosα,2|m1+m2|≤1, thenfis univalent inE.In this paper we consider the classVm1,m2in more general way and show that it contains the class of functions with bounded boundary rotation and many other classes related with it. Some coefficient results, arclength problem, radius of convexity and other problems are proved for certain cases. Our results generalize many previously known ones.
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Hård af Segerstad, Per, Staffan Toll, and Ragnar Larsson. "A micropolar theory for the finite elasticity of open-cell cellular solids." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2103 (December 2, 2008): 843–65. http://dx.doi.org/10.1098/rspa.2008.0267.
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A mechanistic model is presented for an open-cell cellular solid consisting of a three-dimensional network of elastic struts. By considering the bending and torsion as well as stretching and buckling of the struts, we allow for length-scale effects in the macroscopic response. Constitutive equations are developed for the force and couple stress tensors, accounting for finite deformations and anisotropy. The consistent tangent stiffness operators are derived and the equations are fully implemented in a nonlinear two-dimensional finite-element solution scheme for the coupled displacement/rotation problem. A boundary-value problem of a shear gap with prescribed boundary rotations is analysed, and the model is shown to predict the well-known gap–size effect. The mechanistic model allows some detailed interpretation of the micropolar behaviour, such as the effects of strut slenderness, strut length and anisotropy.