Artykuły w czasopismach: „Arbitrary bodies”

1

Cetto, A. M., i L. de la Peña. "Casimir effect for bodies of arbitrary size". Il Nuovo Cimento B 108, nr 4 (kwiecień 1993): 447–58. http://dx.doi.org/10.1007/bf02828725.

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Lachand-Robert†, Thomas, i Édouard Oudet. "Bodies of constant width in arbitrary dimension". Mathematische Nachrichten 280, nr 7 (maj 2007): 740–50. http://dx.doi.org/10.1002/mana.200510512.

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3

Davidovich, M. V. "Dispersion Interaction between Bodies of an Arbitrary Shape". Journal of Communications Technology and Electronics 67, nr 10 (październik 2022): 1207–15. http://dx.doi.org/10.1134/s1064226922100011.

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4

Tricarico, Pasquale. "Global gravity inversion of bodies with arbitrary shape". Geophysical Journal International 195, nr 1 (3.08.2013): 260–75. http://dx.doi.org/10.1093/gji/ggt268.

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5

Sun, Xiuquan, Teng Lin i J. Daniel Gezelter. "Langevin dynamics for rigid bodies of arbitrary shape". Journal of Chemical Physics 128, nr 23 (21.06.2008): 234107. http://dx.doi.org/10.1063/1.2936991.

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6

Tran Van Nhieu, Michel, i Frédérique Ywanne. "Sound scattering by slender bodies of arbitrary shape". Journal of the Acoustical Society of America 95, nr 4 (kwiecień 1994): 1726–33. http://dx.doi.org/10.1121/1.408691.

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7

Radha, R., i B. Sri Padmavati. "Stokes Flow Past Porous Bodies of Arbitrary Shape". Indian Journal of Pure and Applied Mathematics 51, nr 3 (wrzesień 2020): 1247–63. http://dx.doi.org/10.1007/s13226-020-0462-0.

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8

Schnell, Uwe. "Lattice inequalities for convex bodies and arbitrary lattices". Monatshefte f�r Mathematik 116, nr 3-4 (wrzesień 1993): 331–37. http://dx.doi.org/10.1007/bf01301537.

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9

Ivanov, Ts, i R. Savova. "Stability of elastic bodies under an arbitrary load". International Applied Mechanics 29, nr 8 (sierpień 1993): 610–13. http://dx.doi.org/10.1007/bf00847010.

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10

Ma, Chien-Ching, i I.-Kuang Shen. "Boundary Weight Functions for Cracks in Three-Dimensional Finite Bodies". Journal of Mechanics 15, nr 1 (marzec 1999): 17–26. http://dx.doi.org/10.1017/s1727719100000289.

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ABSTRACTAn efficient boundary weight function method for the determination of mode I stress intensity factors in a three-dimensional cracked body with arbitrary shape and subjected to arbitrary loading is presented in this study. The functional form of the boundary weight functions are successfully demonstrated by using the least squares fitting procedure. Explicit boundary weight functions are presented for through cracks in rectangular finite bodies. If the stress distribution of a cut out rectangular cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple integration. Comparison of the calculated results with some solutions by other workers from the literature confirms the efficiency and accuracy of the proposed boundary weight function method.

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11

Buhmann, Stefan Yoshi, Hassan Safari, Dirk-Gunnar Welsch i Ho Trung Dung. "Microscopic Origin of Casimir-Polder Forces". Open Systems & Information Dynamics 13, nr 04 (grudzień 2006): 427–36. http://dx.doi.org/10.1007/s11080-006-9024-0.

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We establish a general relation between dispersion forces. First, based on QED in causal media, leading-order perturbation theory is used to express both the single-atom Casimir-Polder and the two-atom van der Waals potentials in terms of the atomic polarizabilities and the Green tensor for the body-assisted electromagnetic field. Endowed with this geometry-independent framework, we then employ the Born expansion of the Green tensor together with the Clausius-Mosotti relation to prove that the macroscopic Casimir-Polder potential of an atom in the presence of dielectric bodies is due to an infinite sum of its microscopic many-atom van der Waals interactions with the atoms comprising the bodies. This theorem holds for inhomogeneous, dispersing, and absorbing bodies of arbitrary shapes and arbitrary atomic composition on an arbitrary background of additional magnetodielectric bodies.

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12

Rao, S. M., C. C. Cha, R. L. Cravey i D. L. Wilkes. "Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness". IEEE Transactions on Antennas and Propagation 39, nr 5 (maj 1991): 627–31. http://dx.doi.org/10.1109/8.81490.

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13

Zschocke, Sven. "Light propagation in the Solar System for astrometry on sub-micro-arcsecond level". Proceedings of the International Astronomical Union 12, S330 (kwiecień 2017): 106–7. http://dx.doi.org/10.1017/s1743921317005245.

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AbstractWe report on recent advancement in the theory of light propagation in the Solar System aiming at sub-micro-arcsecond level of accuracy: (1)A solution for the light ray in 1.5PN approximation has been obtained in the field of N arbitrarily moving bodies of arbitrary shape, inner structure, oscillations, and rotational motion.(2)A solution for the light ray in 2PN approximation has been obtained in the field of one arbitrarily moving pointlike body.

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14

Brunel, Victor-Emmanuel. "Deviation inequalities for random polytopes in arbitrary convex bodies". Bernoulli 26, nr 4 (listopad 2020): 2488–502. http://dx.doi.org/10.3150/19-bej1164.

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15

Cranganu-Cretu, B., R. Hiptmair i Z. Andjelic. "Transmission through arbitrary apertures in metal-coated dielectric bodies". IEEE Transactions on Magnetics 41, nr 5 (maj 2005): 1492–95. http://dx.doi.org/10.1109/tmag.2005.844568.

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16

Xiao Hua Huang i M. Pardavi-Horvath. "Local demagnetizing tensor calculation for arbitrary non-ellipsoidal bodies". IEEE Transactions on Magnetics 32, nr 5 (1996): 4180–82. http://dx.doi.org/10.1109/20.539330.

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17

Sham, T. L., i Y. Zhou. "Weight functions in two-dimensional bodies with arbitrary anisotropy". International Journal of Fracture 40, nr 1 (maj 1989): 13–41. http://dx.doi.org/10.1007/bf01150864.

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18

Moheb, H., i L. Shafai. "A numerical solution for conducting bodies of arbitrary shape". Canadian Journal of Physics 68, nr 6 (1.06.1990): 459–68. http://dx.doi.org/10.1139/p90-073.

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An efficient numerical technique based on a Fourier expansion of the surface current is developed to study the electromagnetic scattering from three-dimensional geometries of arbitrary shape. In this method, the discrete domain representing the structure surface is geometrically represented by two orthogonal contours. One is selected along the intersection of the x–z plane with the object's surface, and the other along the corresponding one in the x–y plane. Entire domain basis functions are selected for the current component in the x–y plane, and subdomain linear basis functions are used to represent the other current component. The method of moments is used to solve the problem numerically. The technique is then applied to study the scattering from discrete surfaces such as squares and rectangles, to compare them with those of the coordinate-transformation technique developed earlier. The behavior of the solutions with the number of modes is investigated to determine their coupling.

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19

Wang, X., i R. O. Hansen. "Inversion for magnetic anomalies of arbitrary three‐dimensional bodies". GEOPHYSICS 55, nr 10 (październik 1990): 1321–26. http://dx.doi.org/10.1190/1.1442779.

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Two‐dimensional (profile) inversion techniques for magnetic anomalies are widely used in exploration geophysics: but, until now, the three‐dimensional (3-D) methods available have been restricted in their geologic applicability, dependent upon good initial values or limited by the capabilities of existing computers. We have developed a fully 3-D inversion algorithm intended for routine application to large data sets. The algorithm based on a Fourier transform expression for the magnetic field of homogeneous polyhedral bodies (Hansen and Wang, 1998), is a 3-D generalization of CompuDepth (O’Brien, 1972). Like CompuDepth, the new inversion algorithm employs thespatial equivalent of frequency‐domain autoregression to determine a series of coefficients from which the depths and locations of polyhedral vertices are calculated by solving complex polynomials. These vertices are used to build a 3-D geologic model. Application to the Medicine Lake Volcano aeromagnetic anomaly resulted in a geologically reasonable model of the source.

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20

Mariano, John, i William J. Hinze. "Modeling complexly magnetized two‐dimensional bodies of arbitrary shape". GEOPHYSICS 58, nr 5 (maj 1993): 637–44. http://dx.doi.org/10.1190/1.1443447.

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A method has been devised for the forward computation of magnetic anomalies due to two‐dimensional (2-D) polygonal bodies with heterogeneously directed magnetization. The calculations are based on the equivalent line source approach wherein the source is subdivided into discrete elements that vary spatially in their magnetic properties. This equivalent dipole line method provides a fast and convenient means of representing and computing magnetic anomalies for bodies possessing complexly varying magnitude and direction of magnetization. The algorithm has been tested and applied to several generalized cases to verify the accuracy of the computation. The technique has also been used to model observed aeromagnetic anomalies associated with the structurally deformed, remanently magnetized Keweenawan volcanic rocks in eastern Lake Superior. This method is also easily adapted to the calculation of anomalies due to two and one‐half‐dimensional (2.5-D) and three‐dimensional (3-D) heterogeneously magnetized sources.

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21

Choi, Sung Rak, Seung-Jo Jung, Jinhyung Park i Joonyeong Won. "A Product Formula for Volumes of Divisors Via Okounkov Bodies". International Mathematics Research Notices 2019, nr 22 (8.10.2018): 7118–37. http://dx.doi.org/10.1093/imrn/rnz199.

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22

Ma, C. C., i I.-K. Shen. "Calculation of Stress Intensity Factors for Elliptical Cracks in Finite Bodies by Using the Boundary Weight Function Method". Journal of Pressure Vessel Technology 121, nr 2 (1.05.1999): 181–87. http://dx.doi.org/10.1115/1.2883684.

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In this study, mode I stress intensity factors for a three-dimensional finite cracked body with arbitrary shape and subjected to arbitrary loading is presented by using the boundary weight function method. The weight function is a universal function for a given cracked body and can be obtained from any arbitrary loading system. A numerical finite element method for the determination of weight function relevant to cracked bodies with finite dimensions is used. Explicit boundary weight functions are successfully demonstrated by using the least-squares fitting procedure for elliptical quarter-corner crack and embedded elliptical crack in parallelepipedic finite bodies. If the stress distribution of a cut-out parallelepipedic cracked body from any arbitrary shape of cracked body subjected to arbitrary loading is determined, the mode I stress intensity factors for the cracked body can be obtained from the predetermined boundary weight functions by a simple surface integration. Comparison of the calculated results with some available solutions in the published literature confirms the efficiency and accuracy of the proposed boundary weight function method.

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23

Purss, Matthew B. J., i James P. Cull. "A new iterative method for computing the magnetic field at high magnetic susceptibilities". GEOPHYSICS 70, nr 5 (wrzesień 2005): L53—L62. http://dx.doi.org/10.1190/1.2052469.

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Failure to adequately correct for the effects of self-demagnetization can lead to misinterpretation of magnetic survey data, thereby reducing the success of mineral exploration programs. Numeric methods commonly used to correct for self-demagnetization of finite three-dimensional bodies are restricted to moderate magnetic susceptibilities (χ < 1 SI) because at higher values (χ ≥ 1 SI), the approximation errors for nonellipsoidal bodies become excessive. This paper reports a new method that allows for calculation of the magnetic field from arbitrary finite bodies with high magnetic susceptibility while minimizing approximation errors caused by the use of self-demagnetization corrections for nonellipsoidal bodies. This technique uses a segmented model defined by spherical elements (or voxels) of arbitrary diameter and an iterative computation of the magnetic field at the center of each voxel in free space and then with respect to the surrounding voxels.

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24

Zhao, R., i O. Faltinsen. "Water entry of two-dimensional bodies". Journal of Fluid Mechanics 246 (styczeń 1993): 593–612. http://dx.doi.org/10.1017/s002211209300028x.

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A numerical method for studying water entry of a two-dimensional body of arbitrary cross-section is presented. It is a nonlinear boundary element method with a jet flow approximation. The method has been verified by comparisons with new similarity solution results for wedges with deadrise angles varying from 4° to 81°. A simple asymptotic solution for small deadrise angles α based on Wagner (1932) agrees with the similarity solution for small α.

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25

Karavaev, A. S., S. P. Kopysov i A. S. Sarmakeeva. "A discrete element method for dynamic simulation of arbitrary bodies". Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki 25, nr 4 (grudzień 2015): 473–82. http://dx.doi.org/10.20537/vm150404.

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26

Ahuja, Vivek, i R. J. Hartfield. "Aerodynamic Loads over Arbitrary Bodies by Method of Integrated Circulation". Journal of Aircraft 53, nr 6 (listopad 2016): 1719–30. http://dx.doi.org/10.2514/1.c033619.

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27

Creticos, J. P., i D. H. Schaubert. "Electromagnetic Scattering by Mixed Conductor-Dielectric Bodies of Arbitrary Shape". IEEE Transactions on Antennas and Propagation 54, nr 8 (sierpień 2006): 2402–7. http://dx.doi.org/10.1109/tap.2006.879200.

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28

Boyev, N. V., i M. A. Sumbatyan. "Short-wave diffraction on bodies with an arbitrary smooth surface". Doklady Physics 48, nr 10 (październik 2003): 540–44. http://dx.doi.org/10.1134/1.1623532.

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29

Ghosh, S., i A. Chakrabarty. "Capacitance Evaluation of Arbitrary-shaped Multiconducting Bodies Using Rectangular Subareas". Journal of Electromagnetic Waves and Applications 20, nr 14 (styczeń 2006): 2091–102. http://dx.doi.org/10.1163/156939306779322666.

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30

Arvas, E., A. Rahhal Arabi, A. Sadigh i S. M. Rao. "Scattering from multiple conducting and dielectric bodies of arbitrary shape". IEEE Antennas and Propagation Magazine 33, nr 2 (kwiecień 1991): 29–36. http://dx.doi.org/10.1109/74.88184.

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31

PETER, MALTE A., MICHAEL H. MEYLAN i C. M. LINTON. "Water-wave scattering by a periodic array of arbitrary bodies". Journal of Fluid Mechanics 548, nr -1 (1.02.2006): 237. http://dx.doi.org/10.1017/s0022112005006981.

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32

Yovanovich, M. M., P. Teertstra i J. R. Culham. "Modeling transient conduction from isothermal convex bodies of arbitrary shape". Journal of Thermophysics and Heat Transfer 9, nr 3 (lipiec 1995): 385–90. http://dx.doi.org/10.2514/3.678.

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33

Subramanian, S. "Dynamics of rigid bodies rotating about an arbitrary fixed axis". European Journal of Physics 12, nr 4 (1.07.1991): 156–59. http://dx.doi.org/10.1088/0143-0807/12/4/002.

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34

Tsoulis, Dimitrios, i Sveto Petrović. "On the singularities of the gravity field of a homogeneous polyhedral body". GEOPHYSICS 66, nr 2 (marzec 2001): 535–39. http://dx.doi.org/10.1190/1.1444944.

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The study of the gravity field of arbitrary polyhedral bodies of homogeneous density has provoked a series of publications over the last decades. Some of the researchers represented an arbitrary three dimensional body in terms of contours obtained by the intersection of horizontal planes with the body.

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35

Popov, Igor. "MODELING OF THE PRIVILEGED REFERENCE SYSTEMS". Applied Mathematics and Control Sciences, nr 1 (30.03.2019): 63–69. http://dx.doi.org/10.15593/2499-9873/2019.1.04.

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It is shown that for uniform and rectilinear motion of two, three or several free inert bodies in one-dimensional or three-dimensional space, arbitrary inertial frames of reference, including those associated with each of the moving inert bodies, are not substantially equivalent in the part of the total kinetic energy. In this case, none of these frames of reference is not unique or distinguished. If it is necessary to select a unique or selected inertial reference frame, one can start from the condition of a minimum of the total kinetic energy of the moving inert bodies in this system. In this case, a unique or distinguished inertial reference system is a relict reference frame connected with the center of masses of the moving inert bodies and with the epicenter of their initial hypothetical interaction. Relict systems of reference are calculated. The bodies do not necessarily interact with them in the first place. The use of relict reference systems allows you to maintain a balance between kinetic energy and the work done. The number of inert bodies in calculating the relict frame of reference can be arbitrarily large.

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36

Boutaghou, Z. E., i A. G. Erdman. "A Unified Approach for the Dynamics of Beams Undergoing Arbitrary Spatial Motion". Journal of Vibration and Acoustics 113, nr 4 (1.10.1991): 494–502. http://dx.doi.org/10.1115/1.2930213.

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A unified approach to systematically derive the dynamic equations for flexible bodies is proposed. This approach is not limited to a particular definition of the field of kinematic representation of deformation. Dynamics of flexible bodies in arbitrary spatial motion experiencing small and large elastic deflections are considered. Two test cases are analyzed via the unified approach. For the first case, linear partial differential equations based on the Euler-Bernoulli beam theory with the von Ka´rma´n geometric constraint for flexible bodies in planar motion are derived. These equations capture the centrifugal stiffening effects arising in fast rotating structures. For the second case, analytical and numerical evidence of out-of-plane vibrations of an in-plane rotating three-dimensional Timoshenko beam with cross sectional area of arbitrary shape is reported.

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37

Morino, L., G. Bernardini i M. Gennaretti. "A Boundary Element Method for Aerodynamics and Aeroacoustics of Bodies in Arbitrary Motions". International Journal of Aeroacoustics 2, nr 2 (kwiecień 2003): 129–56. http://dx.doi.org/10.1260/147547203322775506.

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The validation for a boundary element formulation for the combined potential–flow aerodynamic and aeroacoustic analysis of bodies in arbitrary motion (applicable for instance to a tiltrotor during the conversion phase) is presented. The formulation, introduced in the past by the authors, is based on the velocity potential for compressible flows. The distinguishing feature being validated is the fact that the boundary integral representation is written for a surface that moves in arbitrary motion with respect to a frame of reference that in turn moves in arbitrary motion with respect to the undisturbed air. Thus, the integrals are evaluated on the emission surface, which is the locus of the emitting points at the moving–frame locations that they had when the signal influencing a given point at a given time was emitted. Numerical validation results are presented for helicopter rotors in hover and forward flight.

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38

Му, Цюань, Борис Александрович Каргин i Евгения Геннадьевна Каблукова. "Computer-aided construction of three-dimensional convex bodies of arbitrary shapes". Вычислительные технологии, nr 2 (11.05.2022): 54–61. http://dx.doi.org/10.25743/ict.2022.27.2.005.

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Представлена компьютерная реализация алгоритмов, предназначенных для численного моделирования трехмерных выпуклых тел со случайным числом вершин. Построение выпуклых многогранников является классической проблемой вычислительной геометрии. Интерес к таким моделям возникает в целом ряде задач физики, биологии, медицины. В данной работе модели построения выпуклых тел ориентированы на приложения, связанные с решением задач расчета характеристик рассеяния оптического излучения ледяными кристаллами перистых облаков. Алгоритмы построения выпуклых многогранников были положены в основу программы ConvexHull, предназначенной для моделирования кристаллов произвольных выпуклых форм в трехмерном пространстве. В работе описаны алгоритмы построения и результаты визуализации с помощью библиотеки OpenGL. Cirrus clouds consist of ice crystals of various shapes, sizes, and orientations. In the numerical study of the radiation characteristics of cirrus clouds, simplified crystal forms likes regular polyhedra (for example, prisms with hexagonal bases) are often used. To study the optical properties of irregularly shaped ice crystals, a number of authors of the previously constructed models in which, for example, a part of the crystal is cut off by a random plane, or the angle between some crystal faces changes randomly. In this paper, it is proposed to use the convex hull of randomly generated or user-specified points in three-dimensional space as a model for irregularly shaped ice crystals. A method for modeling three-dimensional convex polyhedra with a random arrangement of vertices is presented, which is based on the incremental and the directed edges algorithms. Each face of the modeled convex polyhedron is triangular. By stretching and squeezing, as well as an appropriate choice of the distribution function of random points in space, the resulting polyhedra can simulate the irregular shapes of ice cloud crystals. As a result of the algorithm execution, the number of vertices, their coordinates are saved, and for each face of the polyhedron, the sequence of vertices is ordered to make their vector product corresponds to the right-hand rule and determines the direction of the outer normal. These models of three-dimensional convex bodies of various sizes and irregular shapes are designed to calculate the attenuation coefficients and the scattering phase functions of optical radiation by cloud crystals using the ray tracing method. The paper presents a visualization of crystals modeled according to the given algorithm, and the dependence of the number of vertices and faces of the polyhedron on the number of generated random points. The program code is written in C++ using the OpenGL library.

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39

Okan, M. B., i S. M. Umpleby. "Free surface flow around arbitrary two-dimensional bodies by B-splines". International Shipbuilding Progress 32, nr 372 (1.08.1985): 182–87. http://dx.doi.org/10.3233/isp-1985-3237201.

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40

Chen, P. C., i D. D. Liu. "Unified Hypersonic/Supersonic Panel Method for Aeroelastic Applications to Arbitrary Bodies". Journal of Aircraft 39, nr 3 (maj 2002): 499–506. http://dx.doi.org/10.2514/2.2956.

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41

Arvas, E., R. Harrington i J. Mautz. "Radiation and scattering from electrically small conducting bodies of arbitrary shape". IEEE Transactions on Antennas and Propagation 34, nr 1 (styczeń 1986): 66–77. http://dx.doi.org/10.1109/tap.1986.1143716.

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42

Wang, T., R. F. Harrington i J. R. Mautz. "Electromagnetic scattering from and transmission through arbitrary apertures in conducting bodies". IEEE Transactions on Antennas and Propagation 38, nr 11 (1990): 1805–14. http://dx.doi.org/10.1109/8.102743.

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43

Wong, Seung Kai, i William B. Bush. "Low‐frequency acoustic scattering by slender bodies of arbitrary cross sections". Journal of the Acoustical Society of America 92, nr 1 (lipiec 1992): 487–91. http://dx.doi.org/10.1121/1.404259.

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44

Zhdan, I. A., V. P. Stulov, P. V. Stulov i L. I. Turchak. "Motion of meteor form bodies at an arbitrary angle of attack". Solar System Research 43, nr 5 (październik 2009): 434–37. http://dx.doi.org/10.1134/s0038094609050050.

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45

Seybert, A. F., i T. K. Rengarajan. "The High-Frequency Radiation of Sound from Bodies of Arbitrary Shape". Journal of Vibration and Acoustics 109, nr 4 (1.10.1987): 381–87. http://dx.doi.org/10.1115/1.3269457.

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In this paper the problem of calculating the sound field in a three-dimensional fluid of infinite extent due to a body of arbitrary shape which is vibrating harmonically is considered. Interest is focused on the case in which the parameter a/λ is large, where a is some characteristic dimension of the radiator. The approach here is to replace the familiar Helmholtz integral formula with an algebraic relationship which is approximately valid on the surface S of the body and to use this relationship to determine the acoustic potential at each point on S, given the normal gradient of the acoustic potential at that point. The acoustic potential exterior to the body is then calculated by numerical evaluation of the Helmholtz formula. By replacing the Helmholtz integral formula on the surface with the algebraic relationship, two troublesome problems associated with integral equation methods are avoided: the need to evaluate singular integrands and the problem of nonuniqueness of the solution at certain frequencies. The approach is evaluated by considering the high-frequency radiation from a finite cylinder up to a value of ka = 15. Comparison data are provided by solving the Helmholtz integral equation using an overdeter-mination method to circumvent nonuniqueness.

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46

Chandrasekhar, B., i Sadasiva M. Rao. "Acoustic scattering from rigid bodies of arbitrary shape—Double layer formulation". Journal of the Acoustical Society of America 115, nr 5 (maj 2004): 1926–33. http://dx.doi.org/10.1121/1.1703536.

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47

Wittich, C. E., i T. C. Hutchinson. "Rocking bodies with arbitrary interface defects: Analytical development and experimental verification". Earthquake Engineering & Structural Dynamics 47, nr 1 (27.07.2017): 69–85. http://dx.doi.org/10.1002/eqe.2937.

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48

Gennaretti, M., i L. Morino. "A boundary element method for the potential, compressible aerodynamics of bodies in arbitrary motion". Aeronautical Journal 96, nr 951 (styczeń 1992): 15–19. http://dx.doi.org/10.1017/s0001924000024428.

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A new integral equation, and the corresponding boundary-element method, is presented for the aerodynamic analysis of compressible, subsonic, potential flows around bodies in arbitrary motion, with applications to helicopter rotors in hover. The formulation is closely related to that introduced by Morino for the aerodynamic analysis of aircraft: in that paper, the surface of the aircraft is assumed to be in arbitrary motion with respect to a frame of reference that moves in uniform translation. Such a formulation is very useful for the analysis of aircraft undergoing small oscillations with respect to a reference configuration. However, for the analysis of more complex motions (e.g. helicopter rotors in forward flight), it is more convenient to use a frame of reference that moves in arbitrary motion (in particular, for the case of a body moving in rigid-body motion, a frame of reference rigidly connected with the body).

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Dinnebier, Robert E. "Rigid bodies in powder diffraction. A practical guide". Powder Diffraction 14, nr 2 (czerwiec 1999): 84–92. http://dx.doi.org/10.1017/s0885715600010356.

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Recipes are given to assist in setting up rigid bodies for common molecules and coordination polyhedra, to define satellite groups, to perform rotations around arbitrary axes through the origin of the rigid body, and to refine intramolecular degrees of freedom under consideration of the special needs of powder diffraction. To the greatest possible extent, the notation follows that of the well known Rietveld refinement program GSAS (Larson and Von Dreele, 1994).

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Beck, Robert F., i Stergios Liapis. "Transient Motions of Floating Bodies at Zero Forward Speed". Journal of Ship Research 31, nr 03 (1.09.1987): 164–76. http://dx.doi.org/10.5957/jsr.1987.31.3.164.

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Linear, time-domain analysis is used to solve the radiation problem for the forced motion of a floating body at zero forward speed. The velocity potential due to an impulsive velocity (a step change in displacement) is obtained by the solution of a pair of integral equations. The integral equations are solved numerically for bodies of arbitrary shape using discrete segments on the body surface. One of the equations must be solved by time stepping, but the kernel matrix is identical at each step and need only be inverted once. The Fourier transform of the impulse-response function gives the more conventional added-mass and damping in the frequency domain. The results for arbitrary motions may be found as a convolution of the impulse response function and the time derivatives of the motion. Comparisons are shown between the time-domain computations and published results for a sphere in heave, a sphere in sway, and a right circular cylinder in heave. Theoretical predictions and experimental results for the heave motion of a sphere released from an initial displacement are also given. In all cases the comparisons are excellent.

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