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Статті в журналах з теми "Spherical part"

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Автор: Grafiati

Опубліковано: 30 травня 2022

Оновлено: 31 травня 2022

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1

Papadakis, Stavros Argyrios, and Bart Van Steirteghem. "Equivariant Degenerations of Spherical Modules: Part II." Algebras and Representation Theory 19, no. 5 (May 12, 2016): 1135–71. http://dx.doi.org/10.1007/s10468-016-9614-7.

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2

Boardman, Richard P., Hans Fangohr, Simon J. Cox, Alexander V. Goncharov, Alexander A. Zhukov, and Peter A. J. de Groot. "Micromagnetic simulation of ferromagnetic part-spherical particles." Journal of Applied Physics 95, no. 11 (June 2004): 7037–39. http://dx.doi.org/10.1063/1.1688639.

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3

Schapery, R. A. "Elastomeric bearing sizing analysis Part 1: Spherical bearing." International Journal of Solids and Structures 152-153 (November 2018): 118–39. http://dx.doi.org/10.1016/j.ijsolstr.2018.03.010.

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4

Lombardini, M., D. I. Pullin, and D. I. Meiron. "Turbulent mixing driven by spherical implosions. Part 2. Turbulence statistics." Journal of Fluid Mechanics 748 (April 28, 2014): 113–42. http://dx.doi.org/10.1017/jfm.2014.163.

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Анотація:

AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number $\approx $1.2, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of 3 %): the incident shock travels from the lighter fluid to the heavy one, or inversely, from the heavy to the light fluid. In Part 1 (Lombardini, M., Pullin, D. I. & Meiron, D. I., J. Fluid Mech., vol. 748, 2014, pp. 85–112), we described the computational problem and presented results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. In particular, it was shown that both configurations reach similar convergence ratios $\approx $2. Here, turbulent mixing is studied through various turbulence statistics. The mixing activity is first measured through two mixing parameters, the mixing fraction parameter $\varTheta $ and the effective Atwood ratio $A_e$, which reach similar late time values in both light–heavy and heavy–light configurations. The Taylor-scale Reynolds numbers attained at late times are estimated at approximately 2000 in the light–heavy case and 1000 in the heavy–light case. An analysis of the density self-correlation $b$, a fundamental quantity in the study of variable-density turbulence, shows asymmetries in the mixing layer and non-Boussinesq effects generally observed in high-Reynolds-number Rayleigh–Taylor (RT) turbulence. These traits are more pronounced in the light–heavy mixing layer, as a result of its flow history, in particular because of RT-unstable phases (see Part 1). Another measure distinguishing light–heavy from heavy–light mixing is the velocity-to-scalar Taylor microscales ratio. In particular, at late times, larger values of this ratio are reported in the heavy–light case. The late-time mixing displays the traits some of the traits of the decaying turbulence observed in planar Richtmyer–Meshkov (RM) flows. Only partial isotropization of the flow (in the sense of turbulent kinetic energy (TKE) and dissipation) is observed at late times, the Reynolds normal stresses (and, thus, the directional Taylor microscales) being anisotropic while the directional Kolmogorov microscales approach isotropy. A spectral analysis is developed for the general study of statistically isotropic turbulent fields on a spherical surface, and applied to the present flow. The resulting angular power spectra show the development of an inertial subrange approaching a Kolmogorov-like $-5/3$ power law at high wavenumbers, similarly to the scaling obtained in planar geometry. It confirms the findings of Thomas & Kares (Phys. Rev. Lett., vol. 109, 2012, 075004) at higher convergence ratios and indicates that the turbulent scales do not seem to feel the effect of the spherical mixing-layer curvature.

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5

ONODA, Yui, and Ayaka SHIMIZU. "The Reductivity of Spherical Curves Part II: 4-gons." Tokyo Journal of Mathematics 41, no. 1 (June 2018): 51–63. http://dx.doi.org/10.3836/tjm/1502179266.

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6

Yamaguchi, H., and B. Nishiguchi. "Spherical Couette flow of a viscoelastic fluid – Part III." Journal of Non-Newtonian Fluid Mechanics 84, no. 1 (July 1999): 45–64. http://dx.doi.org/10.1016/s0377-0257(98)00143-8.

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7

Dincer, Ibrahim, and Osman F. Genceli. "Cooling of spherical products: Part I—effective process parameters." International Journal of Energy Research 19, no. 3 (April 1995): 205–18. http://dx.doi.org/10.1002/er.4440190304.

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8

Dincer, Ibrahim, and Osman F. Genceli. "Cooling of spherical products: Part II—heat transfer parameters." International Journal of Energy Research 19, no. 3 (April 1995): 219–25. http://dx.doi.org/10.1002/er.4440190305.

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9

Bostwick, J. B., and P. H. Steen. "Coupled oscillations of deformable spherical-cap droplets. Part 1. Inviscid motions." Journal of Fluid Mechanics 714 (January 2, 2013): 312–35. http://dx.doi.org/10.1017/jfm.2012.483.

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AbstractA spherical drop is constrained by a solid support arranged as a latitudinal belt. This belt support splits the drop into two deformable spherical caps. The edges of the support are given by lower and upper latitudes yielding a ‘spherical belt’ of prescribed extent and position: a two-parameter family of constraints. This is a belt-constrained Rayleigh drop. In this paper we study the linear oscillations of the two coupled spherical-cap surfaces in the inviscid case, and the viscous case is studied in Part 2 (Bostwick & Steen, J. Fluid Mech., vol. 714, 2013, pp. 336–360), restricting to deformations symmetric about the axis of constraint symmetry. The integro-differential boundary-value problem governing the interface deformation is formulated as a functional eigenvalue problem on linear operators and reduced to a truncated set of algebraic equations using a Rayleigh–Ritz procedure on a constrained function space. This formalism allows mode shapes with different contact angles at the edges of the solid support, as observed in experiment, and readily generalizes to accommodate viscous motions (Part 2). Eigenvalues are mapped in the plane of constraints to reveal where near-multiplicities occur. The full problem is then approximated as two coupled harmonic oscillators by introducing a volume-exchange constraint. The approximation yields eigenvalue crossings and allows post-identification of mass and spring constants for the oscillators.

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10

Willis, D. M., J. Robin Singh, and J. Comer. "Uncertainties in field-line tracing in the magnetosphere. Part I: the axisymmetric part of the internal geomagnetic field." Annales Geophysicae 15, no. 2 (February 28, 1997): 165–80. http://dx.doi.org/10.1007/s00585-997-0165-4.

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Abstract. The technique of tracing along magnetic field lines is widely used in magnetospheric physics to provide a "magnetic frame of reference'' that facilitates both the planning of experiments and the interpretation of observations. The precision of any such magnetic frame of reference depends critically on the accurate representation of the various sources of magnetic field in the magnetosphere. In order to consider this important problem systematically, a study is initiated to estimate first the uncertainties in magnetic-field-line tracing in the magnetosphere that arise solely from the published (standard) errors in the specification of the geomagnetic field of internal origin. Because of the complexity in computing these uncertainties for the complete geomagnetic field of internal origin, attention is focused in this preliminary paper on the uncertainties in magnetic-field-line tracing that result from the standard errors in just the axisymmetric part of the internal geomagnetic field. An exact analytic equation exists for the magnetic field lines of an arbitrary linear combination of axisymmetric multipoles. This equation is used to derive numerical estimates of the uncertainties in magnetic-field-line tracing that are due to the published standard errors in the axisymmetric spherical harmonic coefficients (i.e. gn0 ± δgn0). Numerical results determined from the analytic equation are compared with computational results based on stepwise numerical integration along magnetic field lines. Excellent agreement is obtained between the analytical and computational methods in the axisymmetric case, which provides great confidence in the accuracy of the computer program used for stepwise numerical integration along magnetic field lines. This computer program is then used in the following paper to estimate the uncertainties in magnetic-field-line tracing in the magnetosphere that arise from the published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) geomagnetic field of internal origin. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, calculated here for the axisymmetric part of the internal geomagnetic field, should be regarded as "first approximations'' in the sense that such estimates are only as accurate as the published standard errors in the set of axisymmetric spherical harmonic coefficients. However, all procedures developed in this preliminary paper can be applied to the derivation of more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.

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11

Jallouli, Malika, Wafa Bel Hadj Khélifa, Anouar Ben Mabrouk, and Mohamed Ali Mahjoub. "Toward recursive spherical harmonics issued bi-filters: Part II: an associated spherical harmonics entropy for optimal modeling." Soft Computing 24, no. 7 (August 13, 2019): 5231–43. http://dx.doi.org/10.1007/s00500-019-04274-y.

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12

Benson, Chal, and Gail Ratcliff. "Spaces of bounded spherical functions on Heisenberg groups: part I." Annali di Matematica Pura ed Applicata (1923 -) 194, no. 2 (September 11, 2013): 321–42. http://dx.doi.org/10.1007/s10231-013-0377-z.

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13

Benson, Chal, and Gail Ratcliff. "Spaces of bounded spherical functions on Heisenberg groups: part II." Annali di Matematica Pura ed Applicata (1923 -) 194, no. 2 (November 12, 2013): 533–61. http://dx.doi.org/10.1007/s10231-013-0387-x.

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14

Yun, Zhiwei. "The spherical part of the local and global Springer actions." Mathematische Annalen 359, no. 3-4 (January 22, 2014): 557–94. http://dx.doi.org/10.1007/s00208-013-0994-2.

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15

Pert, G. J. "Models of laser plasma ablation. Part 4. Steadystate theory: collisional absorption flow." Journal of Plasma Physics 49, no. 2 (April 1993): 295–316. http://dx.doi.org/10.1017/s0022377800017001.

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The clarification of models of laser ablation by plasma heating is examined using a general dimensional argument and introducing a set of universal parameters. The regime of laser-plasma interaction in which collisional absorption and thermal conduction dominate is examined for spherical systems. Detailed scaling relations are derived for uninhibited and flux-limited thermal conduction. The complete set of regimes for steady spherical flow are examined, and it is found that the most important flows are thin collisional and thick local absorption.

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16

Zheng, Lu, Zhaohui Ma, Chong Geng, and Qingfeng Yan. "Polymer Particle: Solvent-Assisted Interfacial Tension Deformation of Spherical Particles for the Fabrication of Non-Spherical Particle Arrays (Part. Part. Syst. Charact. 9/2013)." Particle & Particle Systems Characterization 30, no. 9 (September 2013): 820. http://dx.doi.org/10.1002/ppsc.201370037.

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17

WANG, Q. X., and J. R. BLAKE. "Non-spherical bubble dynamics in a compressible liquid. Part 2. Acoustic standing wave." Journal of Fluid Mechanics 679 (May 24, 2011): 559–81. http://dx.doi.org/10.1017/jfm.2011.149.

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This paper investigates the behaviour of a non-spherical cavitation bubble in an acoustic standing wave. The study has important applications to sonochemistry and in understanding features of therapeutic ultrasound in the megahertz range, extending our understanding of bubble behaviour in the highly nonlinear regime where jet and toroidal bubble formation may be important. The theory developed herein represents a further development of the material presented in Part 1 of this paper (Wang & Blake, J. Fluid Mech. vol. 659, 2010, pp. 191–224) to a standing wave, including repeated topological changes from a singly to a multiply connected bubble. The fluid mechanics is assumed to be compressible potential flow. Matched asymptotic expansions for an inner and outer flow are performed to second order in terms of a small parameter, the bubble-wall Mach number, leading to weakly compressible flow formulation of the problem. The method allows the development of a computational model for non-spherical bubbles by using a modified boundary-integral method. The computations show that the bubble remains approximately of a spherical shape when the acoustic pressure is small or is initiated at the node or antinode of the acoustic pressure field. When initiated between the node and antinode at higher acoustic pressures, the bubble loses its spherical shape at the end of the collapse phase after only a few oscillations. A high-speed liquid bubble jet forms and is directed towards the node, impacting the opposite bubble surface and penetrating through the bubble to form a toroidal bubble. The bubble first rebounds in a toroidal form but re-combines to a singly connected bubble, expanding continuously and gradually returning to a near spherical shape. These processes are repeated in the next oscillation.

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18

Bostwick, J. B., and P. H. Steen. "Coupled oscillations of deformable spherical-cap droplets. Part 2. Viscous motions." Journal of Fluid Mechanics 714 (January 2, 2013): 336–60. http://dx.doi.org/10.1017/jfm.2012.480.

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AbstractA spherical drop is constrained by a solid support arranged as a latitudinal belt. The spherical belt splits the drop into two deformable spherical caps. The edges of the belt support are given by lower and upper latitudes, yielding a support of prescribed extent and position: a two-parameter family of geometrical constraints. In this paper we study the linear oscillations of the two coupled surfaces in the viscous case, the inviscid case having been dealt with in Part 1 (Bostwick & Steen, J. Fluid Mech., vol. 714, 2013, pp. 312–335), restricting to axisymmetric disturbances. For the viscous case, limiting geometries are the spherical-bowl constraint of Strani & Sabetta (J. Fluid Mech., vol. 189, 1988, pp. 397–421) and free viscous drop of Prosperetti (J. Méc., vol. 19, 1980b, pp. 149–182). In this paper, a boundary-integral approach leads to an integro-differential boundary-value problem governing the interface disturbances, where the constraint is incorporated into the function space. Viscous effects arise due to relative internal motions and to the no-slip boundary condition on the support surface. No-slip is incorporated using a modified set of shear boundary conditions. The eigenvalue problem is then reduced to a truncated set of algebraic equations using a spectral method in the standard way. Limiting cases recover literature results to validate the proposed modification. Complex frequencies, as they depend upon the viscosity parameter and the support geometry, are reported for both the drop and bubble cases. Finally, for the drop, an approximate boundary between over- and under-damped motions is mapped over the constraint parameter plane.

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19

Gille, Wilfried. "Small-angle scattering analysis of the spherical half-shell." Journal of Applied Crystallography 40, no. 2 (March 12, 2007): 302–4. http://dx.doi.org/10.1107/s0021889806053854.

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For a spherical half-shell (SHS) of diameter D, analytic expressions of the small-angle scattering correlation function \gamma_0(r), the chord length distribution (CLD) and the scattering intensity are analyzed. The spherically averaged pair correlation function p_0(r)\simeq r^2\gamma_0(r) of the SHS is identical to the cap part of the CLD of a solid hemisphere of the same diameter. The surprisingly simple analytic terms in principle allow the determination of the size distribution of an isotropic diluted SHS collection from its scattering intensity.

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20

Jeng, M. C., G. R. Zhou, and A. Z. Szeri. "A Thermohydrodynamic Solution of Pivoted Thrust Pads: Part II—Static Loading." Journal of Tribology 108, no. 2 (April 1, 1986): 208–13. http://dx.doi.org/10.1115/1.3261163.

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This is Part II, of a three-part sequence of papers on pivoted thrust pads. In this paper we apply the thermohydrodynamic theory of Part I to statically loaded, sector shaped pivoted thrust pads. The film shape is arbitrary and pad deformation can be specified once the geometry of the pad and the geometry of its support system are known. Presently we assume spherical crowning of the pad: crowning presents us with an opportunity to discuss film cavitation and its effects. Spherical-crowning is advantageous to employ, because it can be represented by a single parameter and because it yields the approximate shape of a loaded pivoted pad.

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21

Li, Shaofan, Roger A. Sauer, and Gang Wang. "The Eshelby Tensors in a Finite Spherical Domain—Part I: Theoretical Formulations." Journal of Applied Mechanics 74, no. 4 (June 13, 2006): 770–83. http://dx.doi.org/10.1115/1.2711227.

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This work is concerned with the precise characterization of the elastic fields due to a spherical inclusion embedded within a spherical representative volume element (RVE). The RVE is considered having finite size, with either a prescribed uniform displacement or a prescribed uniform traction boundary condition. Based on symmetry and group theoretic arguments, we identify that the Eshelby tensor for a spherical inclusion admits a unique decomposition, which we coin the “radial transversely isotropic tensor.” Based on this notion, a novel solution procedure is presented to solve the resulting Fredholm type integral equations. By using this technique, exact and closed form solutions have been obtained for the elastic disturbance fields. In the solution two new tensors appear, which are termed the Dirichlet–Eshelby tensor and the Neumann–Eshelby tensor. In contrast to the classical Eshelby tensor they both are position dependent and contain information about the boundary condition of the RVE as well as the volume fraction of the inclusion. The new finite Eshelby tensors have far-reaching consequences in applications such as nanotechnology, homogenization theory of composite materials, and defects mechanics.

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22

Zhou, J., E. Pan, and M. Bevis. "A point dislocation in a layered, transversely isotropic and self-gravitating Earth – Part III: internal deformation." Geophysical Journal International 223, no. 1 (June 27, 2020): 420–43. http://dx.doi.org/10.1093/gji/ggaa319.

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SUMMARY In this paper, we derive analytical solutions for the dislocation Love numbers (DLNs) and the corresponding Green's functions (GFs) within a layered, spherical, transversely isotropic and self-gravitating Earth. These solutions are based on the spherical system of vector functions (or the vector spherical harmonics) and the dual variable and position matrix method. The GFs for displacements, strains, potential and its derivatives are formulated in terms of the DLNs and the vector spherical harmonics. The vertical displacement due to a vertical strike-slip dislocation and the potential change (nΦ) due to a vertical dip-slip dislocation are found to be special, with an order O(1/n) on the source level and O(n) elsewhere. Numerical results are presented to illustrate how the internal fields depend on the particular type of dislocation. It is further shown that the effect of Earth anisotropy on the strain field can be significant, about 10 per cent in a layered PREM model and 30 per cent in a homogeneous earth model.

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23

Tönnis, D., F. Tewes, and A. Heinecke. "Noncontainment of the Deformed Anterior Part, Containment of the Spherical Posterior Part of the Femoral Head." Journal of Pediatric Orthopaedics B 1, no. 2 (1992): 184. http://dx.doi.org/10.1097/01202412-199201020-00076.

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24

Koyama, Masahiro, Hisaya Tanaka, and Hideto Ide. "Locating the Part Evoking SEP by Dipole Tracing Method." Journal of Robotics and Mechatronics 13, no. 3 (June 20, 2001): 314–18. http://dx.doi.org/10.20965/jrm.2001.p0314.

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This study separated MRCP (Movement-related Cortical Potential) from SEP (Somatosensory Evoked Potential) by locating the part that evokes SEP with Dipole Tracing, assuming the dipoles in the spherical model of a head, and to describe the results on 3 planes, X-Y, X-Z and Y-Z, analyzing dipoles.

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25

Vercammen, Martijn. "Sound Reflections from Concave Spherical Surfaces. Part I: Wave Field Approximation." Acta Acustica united with Acustica 96, no. 1 (January 1, 2010): 82–91. http://dx.doi.org/10.3813/aaa.918259.

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26

Qaiser, Darakhshan, Anurag Srivastava, Piyush Ranjan, and Kamal Kataria. "Physics for Surgeons Part 3: Why Cyst Is Spherical in Shape?" Indian Journal of Surgery 79, no. 2 (January 7, 2017): 143–47. http://dx.doi.org/10.1007/s12262-016-1586-7.

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27

Mahmoudi, A. H., M. Ghanbari-Matloob, and A. Gomar. "Spherical Indentation, Part II: Experimental Validation for Measuring Equibiaxial Residual Stresses." Journal of Testing and Evaluation 44, no. 6 (November 10, 2015): 20150252. http://dx.doi.org/10.1520/jte20150252.

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28

Warnica, W. D., M. Renksizbulut, and A. B. Strong. "Drag coefficients of spherical liquid droplets Part 1: Quiescent gaseous fields." Experiments in Fluids 18, no. 4 (February 1995): 258–64. http://dx.doi.org/10.1007/bf00195096.

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29

Warnica, W. D., M. Renksizbulut, and A. B. Strong. "Drag coefficients of spherical liquid droplets Part 2: Turbulent gaseous fields." Experiments in Fluids 18, no. 4 (February 1995): 265–76. http://dx.doi.org/10.1007/bf00195097.

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30

Jallouli, Malika, Makerem Zemni, Anouar Ben Mabrouk, and Mohamed Ali Mahjoub. "Toward recursive spherical harmonics-issued bi-filters: Part I: theoretical framework." Soft Computing 23, no. 20 (October 26, 2018): 10415–28. http://dx.doi.org/10.1007/s00500-018-3596-9.

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31

Maggelakis, Sophia A. "Mathematical model of prevascular growth of a spherical carcinoma—part II." Mathematical and Computer Modelling 17, no. 10 (May 1993): 19–29. http://dx.doi.org/10.1016/0895-7177(93)90114-e.

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32

ERDIN, SERKAN, and VALERYC L. POKROVSKY. "OSCILLATIONS OF SPHERICAL AND CYLINDRICAL SHELLS." International Journal of Modern Physics B 15, no. 23 (September 20, 2001): 3099–105. http://dx.doi.org/10.1142/s021797920100721x.

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Анотація:

We have found the complete spectrum and eigenstates for harmonic oscillations of ideal spherical and cylindrical shells, both being infinetely thin. The spectrum of the cylindrical shell has an infinite number of Goldstone modes corresponding to folding deformations. This infrared catastrophe is overcome by accounting for curvature-dependent part of energy.

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33

Lombardini, M., D. I. Pullin, and D. I. Meiron. "Turbulent mixing driven by spherical implosions. Part 1. Flow description and mixing-layer growth." Journal of Fluid Mechanics 748 (April 28, 2014): 85–112. http://dx.doi.org/10.1017/jfm.2014.161.

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AbstractWe present large-eddy simulations (LES) of turbulent mixing at a perturbed, spherical interface separating two fluids of differing densities and subsequently impacted by a spherically imploding shock wave. This paper focuses on the differences between two fundamental configurations, keeping fixed the initial shock Mach number ${\approx }1.2$, the density ratio (precisely $|A_0|\approx 0.67$) and the perturbation shape (dominant spherical wavenumber $\ell _0=40$ and amplitude-to-initial radius of $3\, \%$): the incident shock travels from the lighter fluid to the heavy fluid or, inversely, from the heavy to the light fluid. After describing the computational problem we present results on the radially symmetric flow, the mean flow, and the growth of the mixing layer. Turbulent statistics are developed in Part 2 (Lombardini, M., Pullin, D. I. & Meiron, D. I. J. Fluid Mech., vol. 748, 2014, pp. 113–142). A wave-diagram analysis of the radially symmetric flow highlights that the light–heavy mixing layer is processed by consecutive reshocks, and not by reverberating rarefaction waves as is usually observed in planar geometry. Less surprisingly, reshocks process the heavy–light mixing layer as in the planar case. In both configurations, the incident imploding shock and the reshocks induce Richtmyer–Meshkov (RM) instabilities at the density layer. However, we observe differences in the mixing-layer growth because the RM instability occurrences, Rayleigh–Taylor (RT) unstable scenarios (due to the radially accelerated motion of the layer) and phase inversion events are different. A small-amplitude stability analysis along the lines of Bell (Los Alamos Scientific Laboratory Report, LA-1321, 1951) and Plesset (J. Appl. Phys., vol. 25, 1954, pp. 96–98) helps quantify the effects of the mean flow on the mixing-layer growth by decoupling the effects of RT/RM instabilities from Bell–Plesset effects associated with geometric convergence and compressibility for arbitrary convergence ratios. The analysis indicates that baroclinic instabilities are the dominant effect, considering the low convergence ratio (${\approx } 2$) and rather high ($\ell >10$) mode numbers considered.

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34

Zhong, Z., and S. A. Meguid. "On the Imperfectly Bonded Spherical Inclusion Problem." Journal of Applied Mechanics 66, no. 4 (December 1, 1999): 839–46. http://dx.doi.org/10.1115/1.2791787.

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An exact solution is developed for the problem of a spherical inclusion with an imperfectly bonded interface. The inclusion is assumed to have a uniform eigenstrain and a different elastic modulus tensor from that of the matrix. The displacement discontinuity at the interface is considered and a linear interfacial condition, which assumes that the displacement jump is proportional to the interfacial traction, is adopted. The elastic field induced by the uniform eigenstrain given in the imperfectly bonded inclusion is decomposed into three parts. The first part is prescribed by a uniform eigenstrain in a perfectly bonded spherical inclusion. The second part is formulated in terms of an equivalent nonuniform eigenstrain distributed over a perfectly bonded spherical inclusion which models the material mismatch between the inclusion and the matrix, while the third part is obtained in terms of an imaginary Somigliana dislocation field which models the interfacial sliding and normal separation. The exact form of the equivalent nonuniform eigenstrain and the imaginary Somigliana dislocation are fully determined using the equivalent inclusion method and the associated interfacial condition. The elastic fields are then obtained explicitly by means of the superposition principle. The resulting solution is then used to evaluate the average Eshelby tensor and the elastic strain energy.

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35

LE, MINH-QUY, JIN-WO YI, and SEOCK-SAM KIM. "NUMERICAL INVESTIGATION ON CERAMIC COATINGS UNDER SPHERICAL INDENTATION WITH METALLIC INTERLAYER- PART I: UNCRACKED COATINGS." International Journal of Modern Physics B 20, no. 25n27 (October 30, 2006): 4395–400. http://dx.doi.org/10.1142/s0217979206041410.

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Radial stress distribution and plastic damage zones evolution in ceramic coating/metallic interlayer/ductile substrate systems under spherical indentation were investigated numerically by axisymmetric finite element analysis (FEA) for a typical ceramic coating deposited on carbon steel with various indenter radius-coating thickness ratios and interlayer thickness-coating thickness ratios. The results showed that the suitable metallic interlayer could improve resistance of ceramic coating systems through reducing the peak tensile radial stress on the surface and interface of ceramic coatings and plastic damage zone size in the substrate under spherical indentation.

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36

Pelekasis, Nikolaos A., and John A. Tsamopoulos. "Bjerknes forces between two bubbles. Part 1. Response to a step change in pressure." Journal of Fluid Mechanics 254 (September 1993): 467–99. http://dx.doi.org/10.1017/s0022112093002228.

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It is well known from experiments in acoustic cavitation that two bubbles pulsating in a liquid may attract or repel each other depending on whether they oscillate in or out of phase, respectively. The forces responsible for this phenomenon are called ‘Bjerknes’ forces. When attractive forces are present the two bubbles are seen to accelerate towards each other and coalesce (Kornfeld & Suvorov 1944) and occasionally even breakup in the process. In the present study the response of two initially equal and spherical bubbles is examined under a step change in the hydrostatic pressure at infinity. A hybrid boundary–finite element method is used in order to follow the shape deformation and change in the potential of the two interfaces. Under the conditions mentioned above the two bubbles are found to attract each other always, with a force inversely proportional to the square of the distance between them when this distance is large, a result known to Bjerknes. As time increases the two bubbles continue accelerating towards each other and often resemble either the spherical-cap shapes observed by Davies & Taylor (1950), or the globally deformed shapes observed by Kornfeld & Suvorov (1944). Such shapes occur for sufficiently large or small values of the Bond number respectively (based on the average acceleration). It is also shown here that spherical-cap shapes arise through a Rayleigh–Taylor instability, whereas globally deformed shapes occur as a result of subharmonic resonance between the volume oscillations of the two bubbles and certain non-spherical harmonics (Hall & Seminara 1980). Eventually, in both cases the two bubbles break up due to severe surface deformation.

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37

Saka, Takashi. "A note on X-ray spherical wavefields in the Laue case for perfect crystals." Acta Crystallographica Section A Foundations and Advances 73, no. 6 (October 26, 2017): 474–79. http://dx.doi.org/10.1107/s2053273317014140.

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Spherical wavefields in the Laue case are obtained when the real part of the crystal structure factor is zero or small compared with the imaginary part. The results are the same as in the conventional case where the real part is large. Through this work, it is shown that virtual wavefields on the vacuum side should be taken into account to explain the obtained results. It is also shown that, to obtain the virtual wavefields, a modification of the conventional spherical wave theory is necessary.

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38

Batomunkuev, Yury, and Alexandra Dianova. "CALCULATION OF THE ACHROMATIC DIFFRACTION SYSTEM WITH CORRECTED SPHERICAL ABERRATION (Part 1)." Interexpo GEO-Siberia 8 (2019): 41–46. http://dx.doi.org/10.33764/2618-981x-2019-8-41-46.

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The fifth order axial spherical aberration of a thick diffractive optical element on the example of a hologram optical element (HOE) is analyzed in the paper. Three-component achromatic diffraction system based on the calculated HOE is proposed.

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39

PETRONIO, CARLO. "Spherical splitting of 3-orbifolds." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 2 (March 2007): 269–87. http://dx.doi.org/10.1017/s0305004106009807.

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AbstractThe famous Haken–Kneser–Milnor theorem states that every 3-manifold can be expressed in a unique way as a connected sum of prime 3-manifolds. The analogous statement for 3-orbifolds has been part of the folklore for several years, and it was commonly believed that slight variations on the argument used for manifolds would be sufficient to establish it. We demonstrate in this paper that this is not the case, proving that the apparently natural notion of “essential” system of spherical 2-orbifolds is not adequate in this context. We also show that the statement itself of the theorem must be given in a substantially different way. We then prove the theorem in full detail, using a certain notion of “efficient splitting system.”

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40

Liu, Zhi Wei, Ming Zhe Li, Qi Gang Han, Zhou Sui, and He Li Peng. "Numerical Investigation on the Process of Multi-Point Holder Forming for Titanium Mesh Sheet." Applied Mechanics and Materials 161 (March 2012): 72–76. http://dx.doi.org/10.4028/www.scientific.net/amm.161.72.

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Multi-point holder forming (MPHF) adopts series of coupled holder punches, arranged between forming punches, to clamp the whole sheet in the forming zone. The multi-point holder forming processes of spherical parts of titanium mesh plate were simulated by finite element code, and the results were compared with those of multi-point die forming (MPDF). The influence of holder punch load on the deformation of spherical part in multi-point holder forming was investigated. The shape error analysis of titanium mesh formed by MPHF was performed in finial. The results showed that the spherical part had more excellent performance in multi-point holder forming, and the more deformation the titanium mesh was, the larger force of holder punch would be needed. In addition, there was a small shape error for titanium mesh part formed by MPHF before springback.

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41

Mbadjoun, B. Tchana, J. M. Ema’a Ema’a, Jean Yomi, P. Ele Abiama, G. H. Ben-Bolie, and P. Owono Ateba. "Factorization method for exact solution of the non-central modified Killingbeck potential plus a ring-shaped-like potential." Modern Physics Letters A 34, no. 10 (March 28, 2019): 1950072. http://dx.doi.org/10.1142/s021773231950072x.

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In this paper, we study the Schrödinger equation with non-central modified Killingbeck potential plus a ring-shaped-like potential problem, which is not spherically symmetric. The factorization method is used to solve the hypergeometric equation types which lead to solutions with the associate Laguerre function for the radial part and Jacobi polynomial for the polar part. We introduce the raising and lowering operators to calculate the energies eigenvalues, which show that the lack of spherical symmetry removes the degeneracy of second quantum number m which is completely expected. These obtained energies are better to explain the superposition of the energy levels of the atoms in the crystalline structure of molecules.

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42

WANG, Q. X., and J. R. BLAKE. "Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave." Journal of Fluid Mechanics 659 (July 27, 2010): 191–224. http://dx.doi.org/10.1017/s0022112010002430.

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Micro-cavitation bubbles generated by ultrasound have wide and important applications in medical ultrasonics and sonochemistry. An approximate theory is developed for nonlinear and non-spherical bubbles in a compressible liquid by using the method of matched asymptotic expansions. The perturbation is performed to the second order in terms of a small parameter, the bubble-wall Mach number. The inner flow near the bubble can be approximated as incompressible at the first and second orders, leading to the use of Laplace's equation, whereas the outer flow far away from the bubble can be described by the linear wave equation, also for the first and second orders. Matching between the two expansions provides the model for the non-spherical bubble behaviour in a compressible fluid. A numerical model using the mixed Eulerian–Lagrangian method and a modified boundary integral method is used to obtain the evolving bubble shapes. The primary advantage of this method is its computational efficiency over using the wave equation throughout the fluid domain. The numerical model is validated against the Keller–Herring equation for spherical bubbles in weakly compressible liquids with excellent agreement being obtained for the bubble radius evolution up to the fourth oscillation. Numerical analyses are further performed for non-spherical oscillating acoustic bubbles. Bubble evolution and jet formation are simulated. Outputs also include the bubble volume, bubble displacement, Kelvin impulse and liquid jet tip velocity. Bubble behaviour is studied in terms of the wave frequency and amplitude. Particular attention is paid to the conditions if/when the bubble jet is formed and when the bubble becomes multiply connected, often forming a toroidal bubble. When subjected to a weak acoustic wave, bubble jets may develop at the two poles of the bubble surface after several cycles of oscillations. A resonant phenomenon occurs when the wave frequency is equal to the natural oscillation frequency of the bubble. When subjected to a strong acoustic wave, a vigorous liquid jet develops along the direction of wave propagation in only a few cycles of the acoustic wave.

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43

Wang, Shi Huan, Zhi Gang Cai, and Li Fang Lin. "Research on Surface Machining System for Light Metal Thin-Walled Parts Based on Spherical Coordinate." Advanced Materials Research 97-101 (March 2010): 1841–44. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.1841.

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Surface machining system based on spherical coordinate is present for the large thin-walled director sphere part turning, to improve the efficiency and quality of part machining. In this system, a thickness surface B-spline model is set up based on spherical coordinates, the space spiral path generation method is planned, row spacing angle is determined by scallop height and blunt radius of cutting tool, and back cutting depth optimization treatment and space spiral interpolation algorithm are present.

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44

Batomunkuev, Yury Ts, and Alexandra A. Pechenkina. "CALCULATION OF THE ACHROMATIC DIFFRACTION SYSTEM WITH CORRECTED SPHERICAL ABERRATION (part 2)." Interexpo GEO-Siberia 8, no. 1 (July 8, 2020): 127–33. http://dx.doi.org/10.33764/2618-981x-2020-8-1-127-133.

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Achromatization of a three-component diffraction system consisting of one thick and two thin hologram optical elements is considered in the work. Analytical expressions are obtained for correcting the chromatic aberration of the position of a thick focusing hologram optical element by two scattering thin hologram optical elements in a given spectrum range. It is shown that achromatization is achieved for such a three-component system using two thin hologram elements located symmetrically on both sides of the thick element and having a value of the working diffraction order greater than the ratio of the focal length to the distance from the thin element to the image plane (at a given wavelength). The proposed three-component holographic system can be used to convert both an imaginary image into a real image and a real into an imaginary image in predetermined spectral regions of the visible, ultraviolet or infrared ranges of the spectrum.

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45

Davis, A. W. "Spherical functions on the Grassmann manifold and generalized Jacobi polynomials — part 1." Linear Algebra and its Applications 289, no. 1-3 (March 1999): 75–94. http://dx.doi.org/10.1016/s0024-3795(98)10178-7.

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46

Davis, A. W. "Spherical functions on the Grassmann manifold and generalized Jacobi polynomials — Part 2." Linear Algebra and its Applications 289, no. 1-3 (March 1999): 95–119. http://dx.doi.org/10.1016/s0024-3795(98)10179-9.

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47

JONES, M. N. "Electromagnetic theory of anisotropic media in spherical geometries Part 1. Transverse isotropy." International Journal of Electronics 66, no. 3 (March 1989): 457–67. http://dx.doi.org/10.1080/00207218908925403.

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48

YANOH, Toshinobu, Masahiro MAENO, Sadayoshi MAEDA, Hiromichi KIMURA, Takashi HAYASHI, and Shigemi KOUTA. "Study on the micro silicas. (Part 1). Properties of reinforcing spherical silicas." NIPPON GOMU KYOKAISHI 64, no. 10 (1991): 605–11. http://dx.doi.org/10.2324/gomu.64.605.

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49

Makarov, Prof Dr A. N. "Laws of Heat Radiation from Spherical Gas Volumes. Part I. Laws Formulation." International Journal of Advanced Engineering Research and Science 4, no. 3 (2017): 74–79. http://dx.doi.org/10.22161/ijaers.4.3.11.

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50

Rieutord, Michel. "Linear theory of rotating fluids using spherical harmonics part I: Steady flows." Geophysical & Astrophysical Fluid Dynamics 39, no. 3 (October 1987): 163–82. http://dx.doi.org/10.1080/03091928708208811.

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