Articoli di riviste: "Nonspherical modes"

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Dash, Nehal, e Ganesh Tamadapu. "Nonspherical oscillations of an encapsulated microbubble with interface energy under the acoustic field". Journal of the Acoustical Society of America 155, n. 4 (1 aprile 2024): 2445–59. http://dx.doi.org/10.1121/10.0025390.

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Spherical instability in acoustically driven encapsulated microbubbles (EBs) suspended in a fluid can trigger nonspherical oscillations within them. We apply the interface energy model [N. Dash and G. Tamadapu, J. Fluid Mech. 932, A26 (2022b)] to investigate nonspherical oscillations of smaller radius microbubbles encapsulated with a viscoelastic shell membrane under acoustic field. Using the Lagrangian energy formulation, coupled governing equations for spherical and nonspherical modes are derived, incorporating interface energy effects, shell elasticity, and viscosity. Numerical simulations of governing equations revealed that the parametrically forced even mode excites even modes, while the odd modes excite both even and odd modes. The model demonstrates that finite amplitude nonspherical oscillations are identifiable in smaller radius EBs only when the interface parameters are introduced into the model; otherwise, they are not. Realizing that nonlinear mode coupling is responsible for saturation of instability resulting in stable nonspherical oscillations, we perform a steady-state and stability analysis using the slow-time equations obtained from Krylov–Bogoliubov perturbation method. Analytical expressions for modal amplitudes and stability thresholds are derived in terms of interface and material parameters. The stability curves are invaluable in determining the precise range of excitation pressure and frequency values required for the EB to exhibit finite amplitude nonspherical oscillations.

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Arifi, Fathia F., e Michael L. Calvisi. "Optimal control of the nonspherical oscillations of encapsulated microbubbles". Journal of the Acoustical Society of America 151, n. 4 (aprile 2022): A108. http://dx.doi.org/10.1121/10.0010804.

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Encapsulated microbubbles (EMBs) were originally developed as contrast agents for ultrasound imaging but are more recently emerging as vehicles for intravenous drug and gene delivery. Ultrasound can excite nonspherical oscillations, or shape modes, that can enhance the acoustic signature of an EMB and also incite rupture, which promotes drug and gene delivery at targeted sites. Therefore, the ability to control shape modes can improve the efficacy of both the diagnosis and treatment mediated by EMBs. This work uses optimal control theory to determine the ultrasound input that maximizes a desired nonspherical EMB response (e.g., to enhance scattering or rupture), while minimizing the total acoustic input in order to enhance patient safety and reduce unwanted side effects. The optimal control problem is applied to a model of an EMB that accounts for small amplitude shape deformations. This model is solved subject to a cost function that maximizes the incidence of rupture or acoustic echo while minimizing the acoustic energy input. The optimal control problem is solved numerically through pseudospectral collocation methods using commercial optimization software. Single frequency and broadband acoustic forcing schemes are explored and compared. The results show that broadband forcing significantly reduces the acoustic effort required to incite EMB rupture relative to single frequency schemes. Furthermore, the acoustic effort required depends strongly on the shape mode that is forced to become unstable.

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Pikalov, A. M., e A. V. Dorofeenko. "Magnons and Edge Modes in Chains of Nonspherical Magnetic Particles". Moscow University Physics Bulletin 76, n. 1 (gennaio 2021): 42–46. http://dx.doi.org/10.3103/s0027134921010094.

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Bier, K. D., H. J. Jodl e H. Däufer. "Raman spectroscopy of matrix-isolated hydrogen: I. Influence of matrices on defects". Canadian Journal of Physics 66, n. 8 (1 agosto 1988): 708–15. http://dx.doi.org/10.1139/p88-117.

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The hydrogen molecule is treated as a model substance for matrix-isolation effects. Raman investigations are made concerning the influence of matrix material on the various modes of hydrogen. The opposite interaction, how the defect influences modes of the matrix, is the object of the following paper.For the doublet in the vibrational range of hydrogen in rare-gas solids, an assignment to Q1(0) and Q2(1) is made and well substantiated. In addition to matrix-shift considerations, temperature influences, ortho–para investigations, and aggregation effects, different sites are observable in the nonspherical matrices, N2 and O2, with a restriction of free rotation in nitrogen.

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Kosolapova, L. A., e V. G. Malakhov. "A refined model of nonlinear nonspherical oscillations of a gas bubble in liquid". Proceedings of the Mavlyutov Institute of Mechanics 5 (2007): 241–47. http://dx.doi.org/10.21662/uim2007.1.029.

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A mathematical model of nonlinear oscillations of a gas bubble in a liquid is proposed, in which the change of the bubble surface shape is represented as a series of spherical harmonics, and the equations are accurate up to the third order with respect to the distortion amplitudes of the bubble spherical shape. It is shown that the application of the refined model can lead to modes of oscillation that differ from those obtained using the second-order model.

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Canós Valero, Adrià, Hadi K. Shamkhi, Anton S. Kupriianov, Vladimir R. Tuz, Vjaceslavs Bobrovs, Yuri S. Kivshar e Alexander S. Shalin. "Reaching the superscattering regime with BIC physics". Journal of Physics: Conference Series 2172, n. 1 (1 febbraio 2022): 012003. http://dx.doi.org/10.1088/1742-6596/2172/1/012003.

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Abstract We uncover a novel mechanism of superscattering from subwavelength resonators linked to the physics of bound states in the continuum (BICs). Enhanced scattering occurs due to constructive interference within the Friedrich-Wintgen mechanism of interfering resonances. Through this process, the scattering cross section of a single resonance can exceed the currently established limit. We develop a general non-Hermitian model to describe interfering resonances of quasi-normal modes, and study subwavelength dielectric nonspherical resonators exhibiting avoided crossing resonances and quasi-BIC states. Our results reveal novel physics of non-Hermitian systems suggesting important applications for metadevices.

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Beyeh, N. Kodiah, Mario Cetina e Kari Rissanen. "Binding Modes of Nonspherical Anions to N-Alkylammonium Resorcinarenes in the Solid State". Crystal Growth & Design 12, n. 10 (27 agosto 2012): 4919–26. http://dx.doi.org/10.1021/cg3008409.

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Harkin, Anthony A., Tasso J. Kaper e Ali Nadim. "Energy transfer between the shape and volume modes of a nonspherical gas bubble". Physics of Fluids 25, n. 6 (giugno 2013): 062101. http://dx.doi.org/10.1063/1.4807392.

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Guzik, Joyce A., T. H. Morgan, N. J. Nelson, C. Lovekin, K. Kosak, I. N. Kitiashvili, N. N. Mansour e A. Kosovichev. "2-D and 3-D models of convective turbulence and oscillations in intermediate-mass main-sequence stars". Proceedings of the International Astronomical Union 11, A29B (agosto 2015): 540–43. http://dx.doi.org/10.1017/s1743921316006086.

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AbstractWe present multidimensional modeling of convection and oscillations in main-sequence stars somewhat more massive than the Sun, using three separate approaches: 1) Using the 3-D planar StellarBox radiation hydrodynamics code to model the envelope convection zone and part of the radiative zone. Our goals are to examine the interaction of stellar pulsations with turbulent convection in the envelope, excitation of acoustic modes, and the role of convective overshooting; 2) Applying the spherical 3-D MHD ASH (Anelastic Spherical Harmonics) code to simulate the core convection and radiative zone. Our goal is to determine whether core convection can excite low-frequency gravity modes, and thereby explain the presence of low frequencies for some hybrid γ Dor/δ Sct variables for which the envelope convection zone is too shallow for the convective blocking mechanism to drive gravity modes; 3) Applying the ROTORC 2-D stellar evolution and dynamics code to calculate evolution with a variety of initial rotation rates and extents of core convective overshooting. The nonradial adiabatic pulsation frequencies of these nonspherical models are calculated using the 2-D pulsation code NRO. We present new insights into pulsations of 1-2 M⊙ stars gained by multidimensional modeling.

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Hartings, Justin M., Janice L. Cheung e Richard K. Chang. "Temporal beating of nondegenerate azimuthal modes in nonspherical microdroplets: technique for determining the distortion amplitude". Applied Optics 37, n. 15 (20 maggio 1998): 3306. http://dx.doi.org/10.1364/ao.37.003306.

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Cox, Arthur N. "The Periods of RR Lyrae". International Astronomical Union Colloquium 139 (1993): 409. http://dx.doi.org/10.1017/s0252921100118081.

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AbstractRR Lyrae (0.566 day period) exhibits the Blasko effect that suggests another natural mode with almost the same period as the accepted fundamental radial mode. This mode might be nonradial, but no one has done an extensive evaluation of this idea. An investigation requires a model that includes the deep composition structure where g-modes of low angular (observable) degree have weight and amplitude. An RR Lyrae model including the outer half of the mass and more than 99% of the radius, based on an asymptotic giant branch model from Hollowell (private communication), see below, was used for this study. It includes composition gradient ramps between the primordial surface hydrogen and helium and the almost pure helium shell and the one between this helium shell and the convective core that is burning helium.Nonradial mode periods almost resonant with the radial fundamental mode period seem to occur for all low ℓ values. In addition to significant pulsation amplitudes in the composition gradient regions where the Brunt Väisälä frequency is large, these low degree and low radial order modes have near-surface amplitudes very similar to the low order radial modes. These modes are evanescent in the convective core. Classical K and γ effects give enough driving in the very low mass surface layers, so that important deep radiative damping for these modes does not completely stabilize nonradial g-mode pulsations. The g4, ℓ=1 mode gives a. double-mode RR Lyrae with Blasko effect.A nonradial mode may not always be visible, depending on how rotation presents the nonspherical pulsations to the observer. Thus the Blasko effect might come and go, as observed for maybe 20% of all RR Lyrae variables. For many, the Blasko effect may not be observable, even when a nonradial mode is there.

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Michael Köhler, J., Danja Kuhfuß, Phillip Witthöft, Martina Hentschel e Andrea Knauer. "Single-Photon-Single-Electron Transition for Interpretation of Optical Spectra of Nonspherical Metal Nanoparticles in Aqueous Colloidal Solutions". Journal of Nanomaterials 2018 (30 agosto 2018): 1–8. http://dx.doi.org/10.1155/2018/1781389.

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Noble metal nanoparticles—especially shape anisotropic particles—have pronounced resonances in the optical spectrum. These sensitive absorption modes attract great interest in various fields of application. For nonspherical particles, no analytic description of the absorption spectra according to the commonly used Mie theory is possible. In this work, we present a semi-empirical approach for the explanation of the optical spectra of shape anisotropic particles such as silver nanoprisms and gold nanorods. We found an interpretation of the optical absorption spectra which is based on a single-photon-single-electron transition. This model is in a better agreement with the basic assumptions of quantum mechanics than the electrodynamic model of a localized surface plasmon excitation. Based on microfluidically obtained Ag nanoprisms and Au nanorods with very high ensemble homogeneities, dependencies between the geometrical properties of the shape anisotropic noble metal nanoparticles and the spectral position of the longitudinal absorption mode could be derived, which show that the assumption of a composed relative permittivity and the inclusion of the Rydberg constant is sufficient to describe the optical properties of the shape anisotropic particles. Within the scope of the measuring accuracy, the calculations furthermore lead to the value of the refractive index of the particle-surrounding medium.

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Shiryaeva, S. O., N. A. Petrushov e A. I. Grigor’ev. "Linear (in oscillation dimensionless amplitude) interaction between the modes of a nonspherical charged drop in an external electrostatic field". Technical Physics 61, n. 1 (gennaio 2016): 33–41. http://dx.doi.org/10.1134/s1063784216010187.

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Guzik, Joyce A., Arthur N. Cox, Kate M. Despain e Michael S. Soukup. "Pulsation Hydrodynamics of Luminous Blue Variables and Pulsation-Driven Winds". International Astronomical Union Colloquium 169 (1999): 337–44. http://dx.doi.org/10.1017/s0252921100072213.

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AbstractMany physical factors, including radial and nonradial pulsation, rotation, radiation pressure, convection, magnetic fields, or dynamical instabilities may play important roles in the hydrodynamics of Luminous Blue Variables. We review the current status of hydrodynamic modeling of LBV envelopes, and describe results of our models using the one-dimensional nonlinear hydrodynamics code of Ostlie and Cox. We find that the models pulsate in several simultaneous radial modes, driven by the helium and Fe ionization к effect. The pulsations have quasi-periods between 5 and 80 days, with radial velocity amplitudes of 50-200 km/sec, and may be identified with the LBV microvariations. In some cases, depending on luminosity-to-mass ratio and helium abundance, deep layers in the model can periodically exceed the Eddington luminosity limit. The key to exceeding LE is the inclusion of the time dependence of convection: Near the regions of opacity peaks produced by Fe and helium ionization, convection is turning on and off during each pulsation cycle. If convection cannot turn on rapidly enough to transport the required luminosity through the region, the Eddington limit is exceeded. If this region of the star is sufficiently adiabatic, an “outburst” may occur. In the hydrodynamic models, an outburst is indicated by the photospheric radial velocity suddenly becoming very large, and the photospheric radius increasing monotonically over several pulsation cycles. Such pulsation-triggered outbursts may be responsible for the driving of variable, nonspherical winds. If large and infrequent enough, these outbursts may be identified with the classic LBV eruptions accompanied by episodic mass loss.

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Gibson, Andrew J., Xin C. Yee e Michael L. Calvisi. "Application of Koopman operator theory to the control of nonlinear bubble dynamics". Journal of the Acoustical Society of America 151, n. 4 (aprile 2022): A110. http://dx.doi.org/10.1121/10.0010811.

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Microbubbles are widely used in biomedicine for ultrasound contrast imaging and are a promising vehicle for targeted drug and gene delivery. The ability to control the oscillations of bubbles through the applied ultrasound can improve the effectiveness of these treatments, for example, by enhancing the acoustic echo or inciting bubble rupture at precise locations. Koopman operator theory has gained interest in the past decade as a framework for rigorously transforming nonlinear dynamics on the state space into linear dynamics on abstract function spaces, which preserves the underlying nonlinear dynamics of the system. These spaces can be approximated purely through machine learning and data-driven methodologies, which then enables the application of classical linear control strategies to strongly nonlinear systems. Here, we use a Koopman linear quadratic regulator (LQR) to control the nonlinear dynamics of spherical bubbles, as described by the well-known Rayleigh-Plesset equation, with two novel objectives: (1) stabilization of the bubble at a nonequilibrium radius and (2) simple harmonic oscillation at amplitudes large enough to incite nonlinearities. Control is implemented through both broadband and single-frequency transducers that are modulated by the Koopman LQR controller. We repeat these results using Koopman model predictive control (MPC), which allows for the implementation of constraints. This work is a step towards controlling nonspherical shape modes of encapsulated microbubbles.

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Jiang, Tsung Leo, e Huei-Huang Chiu. "Combustion of a Fuel Droplet Surrounded by Oxidizer Droplets". Journal of Heat Transfer 113, n. 4 (1 novembre 1991): 959–65. http://dx.doi.org/10.1115/1.2911228.

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The interaction between a burning fuel droplet and satellite oxidizer droplets is studied analytically. The effects of droplet spacing and droplet size ratio on the flame configuration of a burning fuel droplet with a satellite oxidizer droplet are analyzed in a high-temperature oxidizing environment by using the bispherical coordinate system. Three combustion modes including normal combustion, conjugate combustion, and composite combustion are identified at appropriate droplet size ratio and droplet spacing. The burning rate of the fuel droplet is found to be greater than that of an isolated burning fuel droplet, and to increase with the decreasing distance between two droplets. This result has shown a positive effect on the interaction between fuel and oxidizer droplets, in contrast to that of two interacting fuel droplets where the burning rate decreases with decreasing droplet spacing. The combustion configuration of a fuel droplet surrounded by six satellite oxidizer droplets symmetrically is also examined by the method of images. The flame that encloses the fuel droplet is found to be “compressed” and distorted to a nonspherical shape due not only to the group effect among oxidizer droplets but also to the interaction of bipropellant droplets. The results indicate that the burning rate of a fuel droplet increases and the flame size decreases significantly as a result of an increased supply of oxidizer vapor provided by the surrounding oxidizer droplets. Therefore properly optimized bipropellant combustion is potentially able to achieve a desired combustion performance with a much smaller combustor than a conventional spray burner.

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Kuo, Kwo-Sen, William S. Olson, Benjamin T. Johnson, Mircea Grecu, Lin Tian, Thomas L. Clune, Bruce H. van Aartsen, Andrew J. Heymsfield, Liang Liao e Robert Meneghini. "The Microwave Radiative Properties of Falling Snow Derived from Nonspherical Ice Particle Models. Part I: An Extensive Database of Simulated Pristine Crystals and Aggregate Particles, and Their Scattering Properties". Journal of Applied Meteorology and Climatology 55, n. 3 (marzo 2016): 691–708. http://dx.doi.org/10.1175/jamc-d-15-0130.1.

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AbstractA 3D growth model is used to simulate pristine ice crystals, which are aggregated using a collection algorithm to create larger, multicrystal particles. The simulated crystals and aggregates have mass-versus-size and fractal properties that are consistent with field observations. The growth/collection model is used to generate a large database of snow particles, and the single-scattering properties of each particle are computed using the discrete dipole approximation to account for the nonspherical geometries of the particles. At 13.6 and 35.5 GHz, the bulk radar reflectivities of nonspherical snow particle polydispersions differ from those of more approximate spherical, homogeneous, ice–air particle polydispersions that have the same particle size distributions, although the reflectivities of the nonspherical particles are roughly approximated by polydispersions of spheres of 0.1–0.2 g cm−3 density. At higher microwave frequencies, such as 165.5 GHz, the bulk extinction (and scattering) coefficients of the nonspherical snow polydispersions are comparable to those of low-density spheres, but the asymmetry parameters of the nonspherical particles are substantially less than those of spheres for a broad range of assumed spherical particle densities. Because of differences in the asymmetry of scatter, simulated microwave-scattering depressions using nonspherical particles may well exceed those of spheres for snow layers with the same vertical water path. It may be concluded that, in precipitation remote sensing applications that draw upon input from radar and/or radiometer observations spanning a range of microwave frequencies, nonspherical snow particle models should be used to properly interpret the observations.

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Dang, Cheng, Qiang Fu e Stephen G. Warren. "Effect of Snow Grain Shape on Snow Albedo". Journal of the Atmospheric Sciences 73, n. 9 (18 agosto 2016): 3573–83. http://dx.doi.org/10.1175/jas-d-15-0276.1.

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Abstract Radiative transfer models of snow albedo have usually assumed a spherical shape for the snow grains, using Mie theory to compute single-scattering properties. The scattering by more realistic nonspherical snow grains is less in the forward direction and more to the sides, resulting in a smaller asymmetry factor g (the mean cosine of the scattering angle). Compared to a snowpack of spherical grains with the same area-to-mass ratio, a snowpack of nonspherical grains will have a higher albedo, thin snowpacks of nonspherical grains will more effectively hide the underlying surface, and light-absorbing particles in the snowpack will be exposed to less sunlight. These effects are examined here for nonspherical snow grains with aspect ratios from 0.1 to 10. The albedo of an opaque snowpack with equidimensional (i.e., aspect ratio 1) nonspherical snow grains is higher than that with spherical snow grains by 0.032 and 0.050, for effective grain radii of 100 and 1000 μm, respectively. For an effective radius of 100 μm, the albedo reduction caused by 100 ng g−1 of black carbon is 0.019 for spherical snow grains but only 0.012 for equidimensional nonspherical snow grains. The albedo of a snowpack consisting of nonspherical snow grains can be mimicked by using a smaller grain of spherical shape; this is why radiative transfer models using spherical grains were able to match measurements of spectral albedo. The scaling factor for snow grain radius is different for nonspherical grains with different aspect ratios and is about 2.4 for equidimensional snow grains.

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Sun, Ke, Lin Lu e Yu Jiang. "Analysis of orientation and tensor properties of airborne fibrous particle flow". International Journal of Numerical Methods for Heat & Fluid Flow 24, n. 8 (28 ottobre 2014): 1795–802. http://dx.doi.org/10.1108/hff-04-2013-0118.

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Purpose – The purpose of this paper is to study the effect of particle shapes (spherical particle and nonspherical fiber) on their orientation distributions in indoor environment. Design/methodology/approach – This paper adopted a particle model to predict the fibrous particle flow and distribution, and analyzed the orientation distributions of nonspherical fiber particles and spherical particles in airflows like indoor places. Fokker-Planck model was employed to solve the orientation behavior of nonspherical fiber particles. Findings – The simulation results discover that the nonspherical airborne fiber particles have very different characteristics and behaviors and their orientation distributions are totally different from the uniform distribution of spherical particles. The investigation of the particle orientation tensor and orientation strength indicates that the airflow field becomes more anisotropic due to the suspended fibers. The airborne fiber particles increase the viscosity of the room airflow due to the fiber induced additional viscosity. Originality/value – Orientation tensor, strength and additional viscosity in fibrous flow are seldom investigated indoor. This research reveals that the particle shape has to be considered in the analysis of particle transport and distribution in indoor places as most suspended indoor particles are nonspherical.

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Marohnic, Julian C., Joseph V. DeMartini, Derek C. Richardson, Yun Zhang e Kevin J. Walsh. "An Efficient Numerical Approach to Modeling the Effects of Particle Shape on Rubble-pile Dynamics". Planetary Science Journal 4, n. 12 (1 dicembre 2023): 245. http://dx.doi.org/10.3847/psj/ad0467.

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Abstract We present an approach for the inclusion of nonspherical constituents in high-resolution N-body discrete element method (DEM) simulations. We use aggregates composed of bonded spheres to model nonspherical components. Though the method may be applied more generally, we detail our implementation in the existing N-body code pkdgrav. It has long been acknowledged that nonspherical grains confer additional shear strength and resistance to flow when compared with spheres. As a result, we expect that rubble-pile asteroids will also exhibit these properties and may behave differently than comparable rubble piles composed of idealized spheres. Since spherical particles avoid some significant technical challenges, most DEM gravity codes have used only spherical particles or have been confined to relatively low resolutions. We also discuss the work that has gone into improving performance with nonspherical grains, building on pkdgrav's existing leading-edge computational efficiency among DEM gravity codes. This allows for the addition of nonspherical shapes while maintaining the efficiencies afforded by pkdgrav's tree implementation and parallelization. As a test, we simulated the gravitational collapse of 25,000 nonspherical bodies in parallel. In this case, the efficiency improvements allowed for an increase in speed by nearly a factor of 3 when compared with the naive implementation. Without these enhancements, large runs with nonspherical components would remain prohibitively expensive. Finally, we present the results of several small-scale tests: spin-up due to the YORP effect, tidal encounters, and the Brazil nut effect. In all cases, we find that the inclusion of nonspherical constituents has a measurable impact on simulation outcomes.

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Tsinganos, K. "Asymmetric MHD Stellar Winds and Related Flows". Highlights of Astronomy 9 (1992): 667–68. http://dx.doi.org/10.1017/s1539299600010017.

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Some well established observational facts about most wind-type astrophysical outflows are the following: (i) they are strongly nonspherically symmetric and at least two-dimensional; fast solar wind streams from polar coronal holes and jets from stars and galaxies are two representative and characteristic examples, (ii) some kind of nonthermal heating is required, at least during the initial acceleration stage of the outflow; therefore, the flow is far from beeing adiabatic and the assumption of polytropicity with an arbitrarily specified index γ, although useful from the mathematical point of view to solve the governing equations and provide some physical insight into the problem, is nevertheless artificial. (iii) the ubiquitous magnetic field seems to play a decisive direct, or at least, indirect role in heating stellar coronae and driving stellar winds. Nevertheless – perhaps for the sake of simplicity – most studies on astrophysical outflows and winds so far have neglected to incorporate the above three basic features of nonspherical expansion, nonpolytropic equation of state and magnetohydrodynamic description of the problem. We have recently embarked in an effort to model wind-type outflows by incorporating those basic physical constraints (Low and Tsinganos, 1986; Tsinganos and Low, 1989; Tsinganos and Trussoni, 1990, 1991; Tsinganos and Sauty, 1992a,b).

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Fu, Qiang. "A New Parameterization of an Asymmetry Factor of Cirrus Clouds for Climate Models". Journal of the Atmospheric Sciences 64, n. 11 (1 novembre 2007): 4140–50. http://dx.doi.org/10.1175/2007jas2289.1.

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Abstract The aspect ratio (AR) of a nonspherical ice particle is identified as the key microphysical parameter to determine its asymmetry factor for solar radiation. The mean effective AR is defined for cirrus clouds containing various nonspherical ice particles. A new parameterization of the asymmetry factor of cirrus clouds in terms of AR and mean effective size, Dge, is developed for solar radiation. It is based on geometric ray-tracing calculations for hexagonal ice crystals with a simple representation of particle surface roughness. The present parameterization well reproduces the asymmetry factors of complicated ice particles such as bullet rosettes, aggregates with rough surfaces, and fractal crystals and agrees well with observations. It thus can be properly applied to cirrus clouds containing various nonspherical ice particles. The asymmetry factor from this parameterization in the visible spectrum ranges from about 0.73 to more than 0.85. Radiative transfer calculations show that for a cirrus cloud with an optical depth of 4 and a solar zenith angle of 60°, changes in AR from 1.0 to 0.5 or from 1.0 to 0.1 result in differences in reflected solar fluxes of about −30 or −70 W m−2, respectively. For the same cloudy conditions, the effect of ice particle surface roughness on the reflected solar flux is found to be about 20 W m−2.

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Wei, Juan, Guo Tian He, Li Song, Ma Yan, Ming Li, Ze Yu Xu, Ying Chun Ran e De Sheng Zhang. "Study of Nonspherical Particle Magnetorheological Greases with Computer Simulation Technology". Applied Mechanics and Materials 246-247 (dicembre 2012): 1231–36. http://dx.doi.org/10.4028/www.scientific.net/amm.246-247.1231.

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Based on computer simulation technology, we put forward the shear stress model of nonspherical magnetic particle MRG, and take the hexagon form magnetic particle MRG as an example; this paper deduces hexagon magnetic particle MRG shear stress formula. The model simulate and calculate the relationship between shear yield stress and magnetic field intensity respectively when radius and side length is equal and when the volume is equal also shear yield stress in the zero field condition. The simulation results show that in the same volume condition the shear yield stress of nonspherical magnetic particle MRG is bigger than that of spherical magnetic particle MRG; the shear yield stress of nonspherical magnetic particle MRG cut down with contacting side length’s reducing but also greater than that of spherical magnetic particle MRG and this relationship is also the same in the zero field condition, so spherical magnetic particle MRG is not the best choice. Therefore, this research has an extremely vital significance for the development and application of high-performance MRG.

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Olson, William S., Lin Tian, Mircea Grecu, Kwo-Sen Kuo, Benjamin T. Johnson, Andrew J. Heymsfield, Aaron Bansemer, Gerald M. Heymsfield, James R. Wang e Robert Meneghini. "The Microwave Radiative Properties of Falling Snow Derived from Nonspherical Ice Particle Models. Part II: Initial Testing Using Radar, Radiometer and In Situ Observations". Journal of Applied Meteorology and Climatology 55, n. 3 (marzo 2016): 709–22. http://dx.doi.org/10.1175/jamc-d-15-0131.1.

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AbstractIn this study, two different particle models describing the structure and electromagnetic properties of snow are developed and evaluated for potential use in satellite combined radar–radiometer precipitation estimation algorithms. In the first model, snow particles are assumed to be homogeneous ice–air spheres with single-scattering properties derived from Mie theory. In the second model, snow particles are created by simulating the self-collection of pristine ice crystals into aggregate particles of different sizes, using different numbers and habits of the collected component crystals. Single-scattering properties of the resulting nonspherical snow particles are determined using the discrete dipole approximation. The size-distribution-integrated scattering properties of the spherical and nonspherical snow particles are incorporated into a dual-wavelength radar profiling algorithm that is applied to 14- and 34-GHz observations of stratiform precipitation from the ER-2 aircraftborne High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) radar. The retrieved ice precipitation profiles are then input to a forward radiative transfer calculation in an attempt to simulate coincident radiance observations from the Conical Scanning Millimeter-Wave Imaging Radiometer (CoSMIR). Much greater consistency between the simulated and observed CoSMIR radiances is obtained using estimated profiles that are based upon the nonspherical crystal/aggregate snow particle model. Despite this greater consistency, there remain some discrepancies between the higher moments of the HIWRAP-retrieved precipitation size distributions and in situ distributions derived from microphysics probe observations obtained from Citation aircraft underflights of the ER-2. These discrepancies can only be eliminated if a subset of lower-density crystal/aggregate snow particles is assumed in the radar algorithm and in the interpretation of the in situ data.

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Farafonov, V. G., V. B. Il’in, V. I. Ustimov e A. R. Tulegenov. "An ellipsoidal model for small nonspherical particles". Optics and Spectroscopy 122, n. 3 (marzo 2017): 489–98. http://dx.doi.org/10.1134/s0030400x17030079.

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Gusev, A. A., O. Chuluunbaatar, S. I. Vinitsky, K. G. Dvoyan, E. M. Kazaryan, H. A. Sarkisyan, V. L. Derbov, A. S. Klombotskaya e V. V. Serov. "Adiabatic description of nonspherical quantum dot models". Physics of Atomic Nuclei 75, n. 10 (ottobre 2012): 1210–26. http://dx.doi.org/10.1134/s1063778812100079.

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27

Runkel, Ingo. "String-net models for nonspherical pivotal fusion categories". Journal of Knot Theory and Its Ramifications 29, n. 06 (maggio 2020): 2050035. http://dx.doi.org/10.1142/s0218216520500352.

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Abstract (sommario):

A string-net model associates a vector space to a surface in terms of graphs decorated by objects and morphisms of a pivotal fusion category modulo local relations. String-net models are usually considered for spherical fusion categories, and in this case, the vector spaces agree with the state spaces of the corresponding Turaev–Viro topological quantum field theory. In the present work, some effects of dropping the sphericality condition are investigated. In one example of nonspherical pivotal fusion categories, the string-net space counts the number of [Formula: see text]-spin structures on a surface and carries an isomorphic representation of the mapping class group. Another example concerns the string-net space of a sphere with one marked point labeled by a simple object [Formula: see text] of the Drinfeld center. This space is found to be nonzero iff [Formula: see text] is isomorphic to a nonunit simple object determined by the nonspherical pivotal structure. The last example mirrors the effect of deforming the stress tensor of a two-dimensional conformal field theory, such as in the topological twist of a supersymmetric theory.

28

Tang, Hong, e Xian-Xia Li. "Research on the single scattering albedo of spheroids". International Journal of Numerical Methods for Heat & Fluid Flow 24, n. 8 (28 ottobre 2014): 1762–68. http://dx.doi.org/10.1108/hff-04-2013-0105.

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Purpose – The purpose of this paper is to discuss the light scattering of nonspherical particles that is very important for the research on the aerosol optical properties. Design/methodology/approach – In this paper, the authors use the spheroid model as the characteristic particle shape to study the single scattering albedo of real nonspherical particles. Meanwhile, the extinction and scattering cross section of spheroids are calculated with the T matrix method combined with the improved geometric optics approximation method (IGOM). Findings – Through this combination, the extinction and scattering cross section of spheroids can be obtained in the larger size range and aspect ratio range. Furthermore, the comparison of the single scattering albedo for the spheroids and their equivalent spheres is conducted in order to investigate the difference of the spherical and nonspherical particles. Originality/value – Simulation experiments indicate that the single scattering albedo of spheroids can be calculated well with this combination, and it has some obvious influence on the variation of the aspect ratio, incident wavelength, and complex refractive index of spheroid particles.

29

Ross, Oliver N., e Stuart G. Bradley. "Model for optical forward scattering by nonspherical raindrops". Applied Optics 41, n. 24 (20 agosto 2002): 5130. http://dx.doi.org/10.1364/ao.41.005130.

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30

Adams, A. J., D. E. Wennerstrom e M. K. Mazumder. "Use of bacteria as model nonspherical aerosol particles". Journal of Aerosol Science 16, n. 3 (gennaio 1985): 193–200. http://dx.doi.org/10.1016/0021-8502(85)90025-4.

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31

Davletshin, A. I., e T. F. Khalitova. "Numerical simulation of single vapor bubble dynamics in a liquid in an intense acoustic field". Multiphase Systems 13, n. 4 (24 dicembre 2018): 127–35. http://dx.doi.org/10.21662/mfs2018.4.018.

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Abstract (sommario):

The possibility of increasing the calculation efficiency by the joint use of two models of the dynamics of a single weakly-nonspherical vapor bubble under its strong collapse in liquid is studied. In both models the motion of liquid and vapor is split into a spherical component and its small nonspherical perturbation. The models differ in the description of the spherical component. In the first (simplified) model, it is described by a system of ODE together with partial differential equations in temperature, derived under the assumption of weak compressibility of liquid and bubble homobaricity. In the second model, one-dimensional gas dynamics equations are applied. The advantage of the simplified model consists in determining a numerical solution with much-less computer time costs in comparison with what is required for the numerical integration of gas dynamics equations. The assumptions used in the simplified model in the final stage of collapse become incorrect, and, as a result, the numerical solution errors increase. Therefore, the simplified model is applied at the beginning of bubble collapse, whereas the gas dynamics equations are used at its end. Within this approach, the numerical solution in the final stage of collapse is dependent on the moment of transition to the gas dynamics equations. It is shown that satisfactory description of evolution of bubble sphericity distortion is achieved when the transition is made under the condition that the Mach number M of vapor in the vicinity of the bubble surface is less than 0.4. Satisfactory resolution of the shock wave in the bubble is attained when the transition is performed at M<0.2.

32

Mai, Liting, Shuping Yang, Yu Wang e Rui Li. "Impacts of Shape Assumptions on Z–R Relationship and Satellite Remote Sensing Clouds Based on Model Simulations and GPM Observations". Remote Sensing 15, n. 6 (12 marzo 2023): 1556. http://dx.doi.org/10.3390/rs15061556.

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In this study, the spherical particle model and ten nonspherical particle models describing the scattering properties of snow are evaluated for potential use in precipitation estimation from spaceborne dual-frequency precipitation radar. The single scattering properties of nonspherical snow particles are computed using discrete dipole approximation (DDA), while those of spherical particles are determined using Mie theory. The precipitation profiles from WRF output are then input to a forward radiative transfer model to simulate the radar reflectivity at Ka-band and Ku-band. The results are validated with Global Precipitation Mission Dual-Frequency Precipitation Radar measurements. Greater consistency between the simulated and observed reflectivity is obtained when using the sector- and dendrite-shape assumptions. For the case in this study, when using the spherical-shape assumption, radar underestimates the error of the cloud’s top by about 300 m and underestimates the error of the cloud’s area by about 15%. As snowflake shapes change with temperature, we use the range between −40 °C and −5 °C to define three temperature layers. The relationships between reflectivity (Z) and precipitation rate (R) are fitted separately for the three layers, resulting in Z=134.59·R1.184 (sector) and Z=127.35·R1.221 (dendrite) below −40 °C.

33

Sturm, Robert. "A Computer Model for the Simulation of Nonspherical Particle Dynamics in the Human Respiratory Tract". Physics Research International 2012 (2 febbraio 2012): 1–11. http://dx.doi.org/10.1155/2012/142756.

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In the study presented here deposition of spheres and nonspherical particles with various aspect ratios (0.01–100) in the human respiratory tract was theoretically modeled. Shape of the nonspherical particles was considered by the application of the latest aerodynamic diameter concepts. Particle deposition was predicted by using a stochastic model of the lung geometry and simulating particle transport trajectories according to the random-walk algorithm. Concerning fibers total deposition is significantly enhanced with respect to that of spheres for μm-sized particles, whereby at normal breathing conditions peripheral lung compartments serve as primary deposition targets. In the case of oblate disks, total deposition becomes mostly remarkable for submicron particles, with the bronchioli and alveoli being targeted to a high extent. Enhancement of the aerodynamic diameter and/or flow rate generally causes a displacement of deposition maxima from peripheral to more proximal lung regions. From these findings, it can be concluded that these particle classes may represent tremendous occupational hazards, especially if they are attached with radioactive elements or heavy metals.

34

Chaturvedi, Anoop, Hikaru Hasegawa, Ajit Chaturvedi e Govind Shukla. "Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances". Econometric Theory 13, n. 3 (giugno 1997): 406–29. http://dx.doi.org/10.1017/s0266466600005879.

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In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

35

Farafonov, V. G., V. B. Il’in, M. S. Prokopjeva, A. R. Tulegenov e V. I. Ustimov. "A Spheroidal Model of Light Scattering by Nonspherical Particles". Optics and Spectroscopy 126, n. 4 (aprile 2019): 360–66. http://dx.doi.org/10.1134/s0030400x19040076.

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36

Janesko, Benjamin G., e Austin Aguero. "Nonspherical model density matrices for Rung 3.5 density functionals". Journal of Chemical Physics 136, n. 2 (14 gennaio 2012): 024111. http://dx.doi.org/10.1063/1.3675681.

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37

Sheu, H. R., M. S. El-Aasser e J. W. Vanderhoff. "Uniform nonspherical latex particles as model interpenetrating polymer networks". Journal of Polymer Science Part A: Polymer Chemistry 28, n. 3 (febbraio 1990): 653–67. http://dx.doi.org/10.1002/pola.1990.080280315.

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38

DEL POPOLO, A., F. PACE e J. A. S. LIMA. "EXTENDED SPHERICAL COLLAPSE AND THE ACCELERATING UNIVERSE". International Journal of Modern Physics D 22, n. 08 (21 giugno 2013): 1350038. http://dx.doi.org/10.1142/s0218271813500387.

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The influence of the shear stress and angular momentum on the nonlinear spherical collapse model is discussed in the framework of the Einstein–de Sitter and ΛCDM models. By assuming that the vacuum component is not clustering within the homogeneous nonspherical overdensities, we show how the local rotation and shear affect the linear density threshold for collapse of the nonrelativistic component (δc) and its virial overdensity (ΔV). It is also found that the net effect of shear and rotation in galactic scale is responsible for higher values of the linear overdensity parameter as compared with the standard spherical collapse model (no shear and rotation).

39

Diaz, Javier, Marco Pinna, Andrei V. Zvelindovsky e Ignacio Pagonabarraga. "Hybrid Time-Dependent Ginzburg–Landau Simulations of Block Copolymer Nanocomposites: Nanoparticle Anisotropy". Polymers 14, n. 9 (7 maggio 2022): 1910. http://dx.doi.org/10.3390/polym14091910.

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Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer–particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg–Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg–Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg–Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles.

40

ISRAEL, WERNER. "EFFECT OF RADIATIVE TAILS ON BLACK HOLE INTERIORS". International Journal of Modern Physics D 03, n. 01 (marzo 1994): 71–79. http://dx.doi.org/10.1142/s0218271894000083.

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Nonspherical collapse to a black hole leaves a wake of gravitational waves. Externally, this rapidly dies away. But it has a marked effect on the hole’s internal structure as it is blueshifted near the inner horizon. This article surveys recent attempts to understand the nature of these effects using idealized models.

41

Guo, Jing, He Zhang e Xiang-jin Zhang. "Analytical Model for Optical Scattering of Infrared Laser by Nonspherical Raindrops". International Journal of Optics 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/376898.

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Analytic model was developed to investigate the interaction of infrared laser with nonspherical raindrops. The method based on Fraunhofer diffraction and geometrical optics was presented to obtain the analytic solution for single-scattering properties by approximate ellipsoid raindrops. Light scattering patterns were obtained for different drop sizes and shapes. Computational results demonstrate that the scattering of raindrops was contributed by both Fraunhofer diffraction and geometric scattering, and the results obtained from analytic formulas were consistent with the conclusions of using Monte Carlo ray tracing approach.

42

Brito, Carolina, Harukuni Ikeda, Pierfrancesco Urbani, Matthieu Wyart e Francesco Zamponi. "Universality of jamming of nonspherical particles". Proceedings of the National Academy of Sciences 115, n. 46 (31 ottobre 2018): 11736–41. http://dx.doi.org/10.1073/pnas.1812457115.

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Amorphous packings of nonspherical particles such as ellipsoids and spherocylinders are known to be hypostatic: The number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell’s mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class. As an example, we explicitly map ellipsoids into a system of “breathing” particles. We show by using a marginal stability argument that in both cases jammed packings are hypostatic and that the critical exponents related to the contact number and the vibrational density of states are the same. Furthermore, we introduce a generalized perceptron model which can be solved analytically by the replica method. The analytical solution predicts critical exponents in the same hypostatic jamming universality class. Our analysis further reveals that the force and gap distributions of hypostatic jamming do not show power-law behavior, in marked contrast to the isostatic jamming of spherical particles. Finally, we confirm our theoretical predictions by numerical simulations.

43

Aganin, A. A., e D. Y. Toporkov. "Collapse of weakly nonspherical cavitation bubble". Proceedings of the Mavlyutov Institute of Mechanics 12, n. 1 (2017): 1–8. http://dx.doi.org/10.21662/uim2017.1.001.

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Possibility of realizing shock waves in a single cavitation bubble and the growth of bubble nonsphericity during its collapse in water, acetone, and tetradecane are studied. The radius of the bubble is 500 μm, the liquid pressure and temperature are in the ranges of 1–100 bar and 293–313 K, respectively. A relatively simple mathematical model is used in which the movement of the interphase boundary is governed by the Rayleigh-Plesset equation. The thermodynamic parameters of the vapor are assumed uniform, the state of the vapor being described by the modified Van der Waals equation. The calculations show that the shock waves inside a bubble in tetradecane are found to arise in all the conditions under consideration. Inside the bubble in acetone they do not appear at relatively low pressures while inside the bubble in water they never arise. Sphericity perturbations of the bubble grow to the highest degree in tetradecane (up to several thousand times) and to the smallest degree in acetone (up to several tens of times). In the case of water the perturbations increase up to a thousand times.

44

Baalss, Dieter. "The Viscosity Coefficients of Biaxial-Nematic Liquid Crystals. Phenomenology and Affine Transformation Model". Zeitschrift für Naturforschung A 45, n. 1 (1 gennaio 1990): 7–13. http://dx.doi.org/10.1515/zna-1990-0103.

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AbstractThe viscosity tensor of biaxial-nematic liquid crystals contains 16 independent elements. A complete set of these viscosity coefficients is introduced and related to experimentally accessible quantities. Furthermore, the flow alignment and its stability against an arbitrary infinitesimal disturbance are discussed. By the affine transformation model, formerly established for the uniaxial symmetric case, one can express the viscous anisotropy of perfectly ordered biaxial ellipsoids in terms of the two viscosities of an isotropic reference system and the axes ratios of the nonspherical particles.

45

He, Cenlin, Mark G. Flanner, Fei Chen, Michael Barlage, Kuo-Nan Liou, Shichang Kang, Jing Ming e Yun Qian. "Black carbon-induced snow albedo reduction over the Tibetan Plateau: uncertainties from snow grain shape and aerosol–snow mixing state based on an updated SNICAR model". Atmospheric Chemistry and Physics 18, n. 15 (15 agosto 2018): 11507–27. http://dx.doi.org/10.5194/acp-18-11507-2018.

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Abstract. We implement a set of new parameterizations into the widely used Snow, Ice, and Aerosol Radiative (SNICAR) model to account for effects of snow grain shape (spherical vs. nonspherical) and black carbon (BC)–snow mixing state (external vs. internal). We find that nonspherical snow grains lead to higher pure albedo but weaker BC-induced albedo reductions relative to spherical snow grains, while BC–snow internal mixing significantly enhances albedo reductions relative to external mixing. The combination of snow nonsphericity and internal mixing suggests an important interactive effect on BC-induced albedo reduction. Comparisons with observations of clean and BC-contaminated snow albedo show that model simulations accounting for both snow nonsphericity and BC–snow internal mixing perform better than those using the common assumption of spherical snow grains and external mixing. We further apply the updated SNICAR model with comprehensive in situ measurements of BC concentrations in the Tibetan Plateau snowpack to quantify the present-day (2000–2015) BC-induced snow albedo effects from a regional and seasonal perspective. The BC concentrations show distinct and substantial sub-regional and seasonal variations, with higher values in the non-monsoon season and low altitudes. As a result, the BC-induced regional mean snow albedo reductions and surface radiative effects vary by up to an order of magnitude across different sub-regions and seasons, with values of 0.7–30.7 and 1.4–58.4 W m−2 for BC externally mixed with fresh and aged snow spheres, respectively. The BC radiative effects are further complicated by uncertainty in snow grain shape and BC–snow mixing state. BC–snow internal mixing enhances the mean albedo effects over the plateau by 30–60 % relative to external mixing, while nonspherical snow grains decrease the mean albedo effects by up to 31 % relative to spherical grains. Based on this study, extensive measurements and improved model characterization of snow grain shape and aerosol–snow mixing state are urgently needed in order to precisely evaluate BC–snow albedo effects.

46

Hammouda, Boualem. "A new Guinier–Porod model". Journal of Applied Crystallography 43, n. 4 (22 maggio 2010): 716–19. http://dx.doi.org/10.1107/s0021889810015773.

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Small-angle scattering (SAS) curves are characterized by two main features: the Guinier region and the Porod region. Standard linear plots are available to fit SAS data and obtain a radius of gyration and a Porod exponent. A new Guinier–Porod empirical model is introduced to fit SAS data from spherical as well as nonspherical objects such as rods or platelets. It also applies to shapes intermediate between spheres and rods or between rods and platelets. The new model is used to fit SAS data from a Pluronic solution that sequentially forms unimers, then spherical micelles, then cylindrical micelles, then lamellar micelles upon heating. This single model can fit structures associated with all four phases as well as the intermediate structures.

47

de J. Guevara-Rodrı́guez, F., e M. Medina-Noyola. "A simple model of tracer-diffusion of nonspherical Brownian particles". Journal of Chemical Physics 111, n. 3 (15 luglio 1999): 1049–59. http://dx.doi.org/10.1063/1.479296.

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48

Bertin, G., e A. L. Varri. "The Construction of Nonspherical Models of Quasi‐Relaxed Stellar Systems". Astrophysical Journal 689, n. 2 (20 dicembre 2008): 1005–19. http://dx.doi.org/10.1086/592684.

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49

Richstone, Douglas O. "Spherical Galaxies: Methods and Models". Symposium - International Astronomical Union 127 (1987): 261–69. http://dx.doi.org/10.1017/s0074180900185237.

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Over the last 5 years, considerable progress has been made in our ability to construct self-gravitating stellar equilibria. One of these new methods is essentially a variant of Eddington's (1916) method. Two other key approaches are logical extensions of Schwarzschild's Linear Programming method, and can be applied to nonspherical models as well. These methods are reviewed below.The application of these methods to galaxies has yielded a few very interesting results within the last year or two. The methods described below unambiguously establish M/L's for M87 and M32 within about 30 arc seconds. They strongly support Tonry's contention that the nucleus of M32 contains a large invisible mass, possibly a 107M⊙ black hole. They also suggest that observational recovery of the projected velociy distribution might permit the observer to distinguish between a massive halo and an increasingly tangential velocity distribution function.

50

Hu, Weipeng, Tingting Yin, Wei Zheng e Zichen Deng. "Symplectic analysis on orbit-attitude coupling dynamic problem of spatial rigid rod". Journal of Vibration and Control 26, n. 17-18 (17 gennaio 2020): 1614–24. http://dx.doi.org/10.1177/1077546319901191.

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An orbit-attitude coupling dynamic model for the spatial rigid rod that is abstracted from the large-stiffness slender components widely used in spatial structures is established, and the symplectic method is used to estimate the validity of the dynamic model by analyzing the coupling dynamic behaviors of the rod in this work. Based on the Hamiltonian variational principle, the orbit-attitude dynamic model of the spatial rigid rod is proposed, and the canonical form of the model is presented first. Then, the symplectic Runge–Kutta method is developed, and the structure-preserving properties of the canonical form, including the conservation law of energy and conservative property in the phase space, are investigated to illustrate the validity of the numerical results obtained by the symplectic Runge–Kutta method subsequently. Finally, the effects of the nonspherical perturbations of the Earth on the coupling dynamic behaviors are investigated numerically. From the simulation results, it can be concluded that the main orbit-attitude coupling dynamic behaviors of the spatial large-stiffness slender component excited by the nonspherical perturbation can be described by the proposed dynamic model ignoring the deformation as well as the transverse vibration of the slender component, which provides an approach for simplifying rapid dynamic analysis on the spatial large-stiffness slender component. In addition, the validity and the structure-preserving properties of the symplectic Runge–Kutta method for the orbit-attitude coupling dynamic problem of the spatial rigid rod are also illustrated.

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