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Journal articles on the topic 'Geodesic structure'

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Published: 4 June 2021

Last updated: 31 January 2023

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1

Jones, Kerry N., and Alan W. Reid. "Non-simple geodesics in hyperbolic 3-manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 116, no. 2 (September 1994): 339–51. http://dx.doi.org/10.1017/s0305004100072625.

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AbstractChinburg and Reid have recently constructed examples of hyperbolic 3-manifolds in which every closed geodesic is simple. These examples are constructed in a highly non-generic way and it is of interest to understand in the general case the geometry of and structure of the set of closed geodesics in hyperbolic 3-manifolds. For hyperbolic 3-manifolds which contain immersed totally geodesic surfaces there are always non-simple closed geodesics. Here we construct examples of manifolds with non-simple closed geodesics and no totally geodesic surfaces.

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2

Azam, Muhammad, Ghulam Abbas, Syeda Sumera, and Abdul Rauf Nizami. "Geodesic structure of magnetically charged regular black hole." International Journal of Geometric Methods in Modern Physics 14, no. 09 (August 2, 2017): 1750120. http://dx.doi.org/10.1142/s0219887817501201.

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The purpose of this paper is to study the geodesic structure of magnetically charged regular black hole (MCRBH). The behavior of timelike and null geodesics of MCRBH is investigated. The graphs have been plotted to show the relation between distance versus time and proper time for photon-like and massive particle. For radial and circular motion, the effective potential has been plotted with different parameters of BH. We conclude that massive particles move around the BH in timelike geodesic path.

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3

LEIVA, CARLOS, JOEL SAAVEDRA, and JOSÉ VILLANUEVA. "GEODESIC STRUCTURE OF THE SCHWARZSCHILD BLACK HOLE IN RAINBOW GRAVITY." Modern Physics Letters A 24, no. 18 (June 14, 2009): 1443–51. http://dx.doi.org/10.1142/s0217732309029983.

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In this paper we study the geodesic structure of the Schwarzschild black hole in rainbow gravity analyzing the behavior of null and time-like geodesic. We find that the structure of the geodesics essentially does not change when the semiclassical effects are included. However, we can distinguish different scenarios if we take into account the effects of rainbow gravity. Depending on the type of rainbow functions under consideration, inertial and external observers see very different situations in radial and non-radial motion of a test particle.

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HERZLICH, MARC. "PARABOLIC GEODESICS AS PARALLEL CURVES IN PARABOLIC GEOMETRIES." International Journal of Mathematics 24, no. 09 (August 2013): 1350067. http://dx.doi.org/10.1142/s0129167x13500675.

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We give a simple characterization of the parabolic geodesics introduced by Čap, Slovák and Žádník for all parabolic geometries. This goes through the definition of a natural connection on the space of Weyl structures. We then show that parabolic geodesics can be characterized as the following data: a curve on the manifold and a Weyl structure along the curve, so that the curve is a geodesic for its companion Weyl structure and the Weyl structure is parallel along the curve and in the direction of the tangent vector of the curve.

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RUGGIERO, RAFAEL O. "Expansive geodesic flows in manifolds with no conjugate points." Ergodic Theory and Dynamical Systems 17, no. 1 (February 1997): 211–25. http://dx.doi.org/10.1017/s0143385797060963.

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Let $M$ be a compact Riemannian manifold with no conjugate points such that its geodesic flow is expansive. We show that there exists a local product structure in the unit tangent bundle of the manifold which is invariant under the geodesic flow. In particular, we have that the set of closed geodesics is dense and that the flow is topologically transitive.

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6

Rodrigues, Hugo Murilo, and Ryuichi Fukuoka. "Geodesic fields for Pontryagin type C⁰-Finsler manifolds." ESAIM: Control, Optimisation and Calculus of Variations 28 (2022): 19. http://dx.doi.org/10.1051/cocv/2022013.

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Let M be a differentiable manifold, TxM be its tangent space at x ∈ M and TM = {(x, y);x ∈ M;y ∈ TxM} be its tangent bundle. A C0-Finsler structure is a continuous function F : TM → [0, ∞) such that F(x, ⋅) : TxM → [0, ∞) is an asymmetric norm. In this work we introduce the Pontryagin type C0-Finsler structures, which are structures that satisfy the minimum requirements of Pontryagin’s maximum principle for the problem of minimizing paths. We define the extended geodesic field ℰ on the slit cotangent bundle T*M\0 of (M, F), which is a generalization of the geodesic spray of Finsler geometry. We study the case where ℰ is a locally Lipschitz vector field. We show some examples where the geodesics are more naturally represented by ℰ than by a similar structure on TM. Finally we show that the maximum of independent Finsler structures is a Pontryagin type C0-Finsler structure where ℰ is a locally Lipschitz vector field.

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7

ELDER, MURRAY J. "PATTERNS THEORY AND GEODESIC AUTOMATIC STRUCTURE FOR A CLASS OF GROUPS." International Journal of Algebra and Computation 13, no. 02 (April 2003): 203–30. http://dx.doi.org/10.1142/s0218196703001274.

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We introduce a theory of patterns in order to study geodesics in a certain class of group presentations. Using patterns we show that there does not exist a geodesic automatic structure for certain group presentations, and that certain group presentations are almost convex.

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8

Mrówczyńska, Maria, and Jacek Sztubecki. "The use of evolutionary algorithms for designing an optimum structure of a geodesic measurement and control network." MATEC Web of Conferences 262 (2019): 07008. http://dx.doi.org/10.1051/matecconf/201926207008.

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The paper presents an attempt to determine an optimum structure of a geodesic measurement and control network used for geodesic monitoring to determine horizontal displacements of buildings. In geodesy, horizontal networks can be used to determine terrain deformations as well as displacements of engineering structures (dams, water reservoirs, open-cast mines). The network subjected to analysis is a directional network. In order to find a correct solution, its structure should include so-called supernumerary observations. An adequate number of observations should be carried out in the network to obtain a solution with reliable values of horizontal displacements. Moreover, the way in which the observations are carried out and their number should make it possible to show changes taking place in the object and meet the economic criteria of geodesic measurements. In order to optimize the structure of a geodesic measurement and control network, information entropy and evolutionary algorithms are used in the paper. Information entropy is a logarithmic measure of probability, and an optimum number of observations carried out in the network depends on the increment of the content of information in the observation system. Evolutionary algorithms were developed in the 1980s, and they are currently very popular and widely used. Their main principle is based on the evolution or behaviour of the best adapted individuals in subsequent computational cycles.

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9

Lenells, Jonatan. "Spheres, Kähler geometry and the Hunter–Saxton system." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2154 (June 8, 2013): 20120726. http://dx.doi.org/10.1098/rspa.2012.0726.

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Many important equations of mathematical physics arise geometrically as geodesic equations on Lie groups. In this paper, we study an example of a geodesic equation, the two-component Hunter–Saxton (2HS) system, which displays a number of unique geometric features. We show that 2HS describes the geodesic flow on a manifold, which is isometric to a subset of a sphere. Since the geodesics on a sphere are simply the great circles, this immediately yields explicit formulae for the solutions of 2HS. We also show that when restricted to functions of zero mean, 2HS reduces to the geodesic equation on an infinite-dimensional manifold, which admits a Kähler structure. We demonstrate that this manifold is in fact isometric to a subset of complex projective space, and that the above constructions provide an example of an infinite-dimensional Hopf fibration.

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10

Goluk, Victor P., and Denis G. Nazarov. "FEATURES OF GEODECTIC NETWORKS DENSIFICATION ON THE EXAMPLE OF A RAILWAY BRIDGE CROSSING CONSTRUCTION ACROSS THE KERCHEN STRAIT." Interexpo GEO-Siberia 1, no. 1 (July 8, 2020): 93–105. http://dx.doi.org/10.33764/2618-981x-2020-1-1-93-105.

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The geodetic center base for the construction of bridge structures is the basis of all measurement work. Often it is necessary to carry out the densification of the geodetic center base in compliance with the necessary accuracy of recoverable structures. In the process of geodesic control of the construction of a railway bridge on Section No. 3 of the channel between Tuzlinsky Spit and Tuzla Island, difficulties arose in bringing the project to life at all stages of the construction of a structure associated with the low density of geodetic center base points located in the aquatic area. Based on the above the geodesic service of the LLC “Bridge Bureau” carried out work on the concentration of the geodetic center at the construction site of the bridge crossing (the working bridge RM-1 - site No. 3), as well as taking into account: Section 4 of the joint venture 126.13330.2017 "Geodetic works in construction", GOST 21780-2006 "System for ensuring the accuracy of geometrical parameters in construction. Calculation of accuracy ", as well as SP 46.13330.2012" Bridges and pipes." An a priori assessment of the accuracy of the measurement results for each of the methods for monitoring the planning and altitude position of the condensation points was made. A combined approach to densification of the geodetic center base is suggested.

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11

GU, JIANGWEN, QIANQIAN YE, and LIFENG XI. "GEODESICS OF HIGHER-DIMENSIONAL SIERPINSKI GASKET." Fractals 27, no. 04 (June 2019): 1950049. http://dx.doi.org/10.1142/s0218348x1950049x.

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It is of great interest to analyze geodesics in fractals. We investigate the structure of geodesics in [Formula: see text]-dimensional Sierpinski gasket [Formula: see text] for [Formula: see text], and prove that there are at most eight geodesics between any pair of points in [Formula: see text]. Moreover, we obtain that there exists a unique geodesic for almost every pair of points in [Formula: see text].

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12

Peng, Linyu, Huafei Sun, and Xiao Sun. "Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–26. http://dx.doi.org/10.1155/2011/710274.

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We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, anNdegrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads.

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13

Uniyal, Rashmi, Hemwati Nandan, and K. D. Purohit. "Geodesic motion in a charged 2D stringy black hole spacetime." Modern Physics Letters A 29, no. 29 (September 21, 2014): 1450157. http://dx.doi.org/10.1142/s0217732314501570.

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We study the time-like geodesics and geodesic deviation for a two-dimensional (2D) stringy black hole (BH) spacetime in Schwarzschild gauge. We have analyzed the properties of effective potential along with the structure of the possible orbits for test particles with different settings of BH parameters. The exactly solvable geodesic deviation equation is used to obtain corresponding deviation vector. The nature of deviation and tidal force is also examined in view of the behavior of corresponding deviation vector. The results are also compared with an another 2D stringy BH spacetime.

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14

JOHNSGARD, KARIN. "TWO AUTOMATIC SPANNING TREES IN SMALL CANCELLATION GROUP PRESENTATIONS." International Journal of Algebra and Computation 06, no. 04 (August 1996): 429–40. http://dx.doi.org/10.1142/s0218196796000258.

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Gersten and Short showed that group presentations satisfying certain minimal small cancellation conditions are automatic. The automatic structure they described does not have unique group element representatives. It is easy, however, to modify their language to produce an automatic spanning tree of geodesics: that is, an automatic structure of geodesics which is both prefix-closed and has unique representatives. When combined with a construction showing that all geodesic representatives of a group element are encoded in a tiling of a particular geometric form, this shows that in fact the language of lexicographically least geodesics is also automatic (it is clearly a spanning tree).

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15

MONDAINI, RUBEM P. "GEODESIC CURVES FOR BIOMOLECULAR STRUCTURE MODELLING." Biophysical Reviews and Letters 03, no. 01n02 (April 2008): 303–12. http://dx.doi.org/10.1142/s1793048008000769.

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The present literature has several contributions to the understanding of biomolecular structure by adopting helix curves through the atom sites as a paradigm. In the present contribution we introduce the weaker paradigm of geodesic curves of the manifold along ordered sets of points. This alternative allows us to use many interesting curves with some basic properties of helices in the modelling of protein and DNA structures.

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16

Stuchlík, Zdeněk, and Jaroslav Vrba. "Geodesic Model of HF QPOs Tested for Black Holes in Spacetimes Reflecting the Effect of Surrounding Dark Matter." Astrophysical Journal 935, no. 2 (August 1, 2022): 91. http://dx.doi.org/10.3847/1538-4357/ac7f27.

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Abstract Using the simple but robust model of a shell of dark matter (DM) around a Schwarzschild black hole (BH), represented by the mass ratio of the shell and BH ΔM/M, the shell extension Δr s and its inner radius r s, we study the influence of DM on the spacetime structure and geodesic motion, and provide a classification of the BH+DM shell spacetimes according to the properties of the stable circular geodesics governing Keplerian disks. We focus our attention on the epicyclic motion around circular geodesics that can be related to observational phenomena in X-ray radiation from Keplerian accretion disks, assumed to be influenced by the DM shell only gravitationally. We give the frequencies of the orbital and epicyclic motions and discuss their properties in terms of the parameters governing the DM shell. Using the frequencies in relevant variants of the standard geodesic model of high-frequency quasiperiodic oscillations (HF QPOs), we test the role of DM by fitting the HF QPO data from some microquasars and active galactic nuclei with supermassive BHs where no variant of the geodesic model applied in the standard vacuum BH background is able to explain the data. We thus provide a robust review of the applicability of the geodesic model of HF QPOs, and also provide limits on the amount of DM around a BH. We demonstrate that the geodesic model could be well applied to most observations of active galactic nuclei, with strong restrictions on the amount of invisible matter around BHs.

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17

Duan, Yu Zhu, Fei Hu, Lei Zhang, Yi Chen Li, Yue Chao Guan, and Jia Long Zhu. "The Application of Geodesic in Deployable Antenna Mesh Dividing." Journal of Physics: Conference Series 2239, no. 1 (April 1, 2022): 012010. http://dx.doi.org/10.1088/1742-6596/2239/1/012010.

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Abstract Space deployable antennna has the characteristics of Lightweight, large diameter, high precision etc, which can meet the requirements of the launch vehicle carrying and payload’s Electromagnetic performance. Antenna’s mesh dividing have the direct bearing on payload’s Electromagnetic performance, geodesic mesh dividing has the advantage of shortest length of mseh line. but the equation solving of geodesic is complicated,which Impeding the geodesic’s application In academic and engineering fields. in this paper, a method has be proposed to solve the difficulty of geodesic equation solving. the solving result can be used in antenna’s mesh dividing, meanwhile the solving result can be used in Robot trajectory planning, Air route planning,Navigation route planning,Architectural structure design,etc. great care should be taken in constructing both.

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18

Meilvin, Rivven, and Leo S. Tedianto. "ANALISIS PENGARUH PEMODELAN SAMBUNGAN TITIK BUHUL PADA STRUKTUR KUBAH GEODESIK." JMTS: Jurnal Mitra Teknik Sipil 4, no. 2 (May 31, 2021): 503. http://dx.doi.org/10.24912/jmts.v0i0.10725.

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The geodesic dome consists of steel rod elements joined together to form a single structure. Generally, these geodesic domes are analyzed by assuming the joints of the gusset points are joints and only receive axial forces on the rods. However, in reality, it is not easy to apply gusset joints as pure joints in construction. This research will analyze the geodesic dome by modeling the joints of the gusset points as joints where there is only axial force arising on the rods and modeling the rigid gusset points where there will also be moments and shear on the rods. The analysis will only be carried out by comparing the value of the displacement at each gusset joint modeling and checking the cross-sectional dimensions of the internal forces that arise with the help of the MIDAS GEN program in modeling the geodesic dome structure which has a diameter of 20000 mm and a height of 10000 mm with the type of steel profile. used is a pipe profile using two types of geodesic dome, namely type 2V and 3V. For loads that are calculated, namely dead load, live load, and wind load. The results showed a relatively small difference in translational displacement and the axial force was relatively the same in the internal force analysis, so it is better if the analysis by modeling the gusset connection as rigid.ABSTRAKKubah geodesik terdiri dari elemen batang baja yang disambung menjadi satu kesatuan struktur. Umumnya kubah geodesik ini dianalisis dengan menganggap sambungan titik buhulnya berupa sendi dan hanya menerima gaya aksial saja pada batang - batangnya. Namun pada kenyataannya untuk mengaplikasikan sambungan titik buhul sebagai sendi murni pada konstruksi tidaklah mudah. Penelitian ini akan menganalisis kubah geodesik dengan memodelkan sambungan titik buhulnya sebagai sendi dimana hanya ada gaya aksial saja yang timbul pada batang - batangnya dan memodelkan titik buhulnya rigid dimana akan terjadi juga momen dan geser pada batang tersebut. Analisis hanya akan dilakukan dengan membandingkan nilai dari perpindahan pada setiap pemodelan sambungan titik buhul dan pengecekan dimensi penampang terhadap gaya – gaya dalam yang timbul dengan bantuan program MIDAS GEN dalam memodelkan struktur kubah geodesik yang mempunyai diameter 20000 mm dan tinggi 10000 mm dengan jenis profil baja yang digunakan adalah profil pipa dengan menggunakan dua tipe kubah geodesik yaitu tipe 2V dan 3V. Untuk beban yang diperhitungkan yaitu beban mati, beban hidup, dan beban angin. Hasil penelitian menunjukkan nilai perbedaan yang relatif kecil pada perpindahan translasi dan diperoleh gaya aksial yang relatif sama pada analisis gaya dalam yang timbul, sehingga sebaiknya analisis dengan pemodelan sambungan titik buhul sebagai rigid.

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19

Atkin, C. J. "The Finsler geometry of groups of isometries of Hilbert Space." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 2 (April 1987): 196–222. http://dx.doi.org/10.1017/s1446788700028202.

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AbstractThe paper deals with six groups: the unitary, orthogonal, symplectic, Fredholm unitary, special Fredholm orthogonal, and Fredholm symplectic groups of an infinite-dimensional Hilbert space. When each is furnished with the invariant Finsler structure induced by the operator-norm on the Lie algebra, it is shown that, between any two points of the group, there exists a geodesic realising this distance (often, indeed, a unique geodesic), except in the full orthogonal group, in which there are pairs of points that cannot be joined by minimising geodesics, and also pairs that cannot even be joined by minimising paths. A full description is given of each of these possibilities.

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20

Roopa, M., H. Venugopal, Jayachandra Jayachandra, and Madeva Nagaral. "Soil Structure Interaction Analysis of a Single Layer Latticed Geodesic Dome." Indian Journal of Science and Technology 15, no. 7 (February 21, 2021): 292–99. http://dx.doi.org/10.17485/ijst/v15i7.35.

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21

Strigin, Boris, and Roman Korol. "TECHNOLOGY OF INSTALLATION OF A SOFT ENCLOSING STRUCTURE OF THE GEODESIC DOME." Construction and Architecture 10, no. 2 (June 27, 2022): 21–25. http://dx.doi.org/10.29039/2308-0191-2022-10-2-21-25.

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This article deals with the issues of transformable coatings. Modern trends in construction and architecture pose the problem of using prefabricated and transformable enclosing structures of buildings and structures for various functional purposes. Awning materials from polymer films, fabrics, and other elastic types of coverings, on load-bearing frames, in the form of rod and other support systems are used as such enclosing structures. The most resistant to force effects are spatially-rod structures in the form of spheres, hemispheres, or part of a hemisphere, called «geodetic structural systems», geodesic domes.

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22

Chen, Da, Jean-Marie Mirebeau, and Laurent D. Cohen. "Vessel tree extraction using radius-lifted keypoints searching scheme and anisotropic fast marching method." Journal of Algorithms & Computational Technology 10, no. 4 (July 7, 2016): 224–34. http://dx.doi.org/10.1177/1748301816656289.

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Geodesic methods have been widely applied to image analysis. They are particularly efficient to extract a tubular structure, such as a blood vessel, given its two endpoints in a 2D or 3D medical image. We address here a more difficult problem: the extraction of a full vessel tree structure given a single initial root point, by growing a collection of keypoints or new initial source points, connected by minimal geodesic paths. In this article, those keypoints are iteratively added, using a new detection criteria, which utilize the weighted geodesic distances with respect to a radius-lifted Riemannian metric, the standard Euclidean curve length and a path score. Two main weaknesses of classical keypoints searching approach are that the weighted geodesic distance and the Euclidean path length do not take into account the orientation of the tubular structure or object boundaries, due to the use of an isotropic geodesic Riemannian metric, and suffer from a leakage problem. In contrast, we use an anisotropic geodesic Riemannian metric, and develop new criteria for selecting keypoints based on the path score and automatically stopping the tree growth. Experimental results demonstrate that our method can obtain the expected results, which can extract vessel structures at a finer scale, with increased accuracy.

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23

Yashnikov, V. P., and H. J. Bunge. "Geometrical Foundations of Texture Analysis. Geodesic Curves and Motions in the group Space of Three-Dimensional Rotations." Textures and Microstructures 30, no. 1-2 (January 1, 1997): 1–42. http://dx.doi.org/10.1155/tsm.30.1.

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Principal concepts and selected results relating to the inner geometry of the three-dimensional rotation group SO(3) are presented in a form which is appropriate for further applications to various problems of texture analysis. Starting from the basic concepts of regular and piecewise regular curves in the group space SO(3) we consider the functional of the angular length and introduce further geodesic curves. It is shown that the geodesics can be fully characterized, in the group-theoretical terms, as cosets of all possible one-parametric subgroups in the space SO(3). Two kinds of parallelism between geodesics in the group space are discussed as well as related congruences. Geodesic curves are characterized also in terms of their constitutive vectors. The related transformational rules under motions are obtained. The geometrical structure of general motions and non-euclidean rotations of the space SO(3) is described on the base.

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MUSTAFA, M. T. "THE STRUCTURE OF HARMONIC MORPHISMS WITH TOTALLY GEODESIC FIBRES." Communications in Contemporary Mathematics 06, no. 03 (June 2004): 419–30. http://dx.doi.org/10.1142/s0219199704001409.

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The structure of local and global harmonic morphisms between Riemannian manifolds, with totally fibres, is investigated. It is shown that non-positive curvature of the domain obstructs the existence of global harmonic morphisms with totally geodesic fibres and the only such maps from compact Riemannian manifolds of non-positive curvature are, up to a homothety, totally geodesic Riemannian submersions. Similar results are obtained for local harmonic morphisms with totally geodesic fibres from open subsets of non-negatively curved compact and non-compact manifolds. During the course, we prove non-existence of submersive harmonic morphisms with totally geodesic fibres from some important domains, for instance from compact locally symmetric spaces of non-compact type and open subsets of symmetric spaces of compact type.

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Wang, Peng, Gang Zeng, Rui Gan, Jingdong Wang, and Hongbin Zha. "Structure-Sensitive Superpixels via Geodesic Distance." International Journal of Computer Vision 103, no. 1 (November 9, 2012): 1–21. http://dx.doi.org/10.1007/s11263-012-0588-6.

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Sudira, I. Gusti Ngurah, Bambang K. Hadi, Mochammad Agoes Moelyadi, and Djarot Widagdo. "Application of Genetic Algorithm for the Design Optimization of Geodesic Beam Structure." Applied Mechanics and Materials 842 (June 2016): 266–72. http://dx.doi.org/10.4028/www.scientific.net/amm.842.266.

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Application of optimization method for structure design and analysis is a technology trend to provide optimum products. This paper describe optimization process using genetic algorithm that was applied on non traditional structure, geodesic beam element. Finite element method program was developed as a main computer code for supporting optimization process. Pre-and post processor program was created to support GA. Based on minimum structure weight as the target of design optimization, the number of beam, beam element angle, and its size are to be the output of optimization process. The geodesic structure weight of plane model have been compared with traditional structure, and the results show that geodesic structure provide better performance of responding load direction than traditional structure. The influence of swept angle to the weight structure show that the higher the swept angle of geodesic beam structure, the higher values of weight structure are resulted.

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Blaga, Adara-Monica. "CONFORMAL AND PARACONTACTLY GEODESIC TRANSFORMATIONS OF ALMOST PARACONTACT METRIC STRUCTURES." Facta Universitatis, Series: Mathematics and Informatics 35, no. 1 (April 6, 2020): 121. http://dx.doi.org/10.22190/fumi2001121b.

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We give the expressions of the virtual and the structure tensor fields of an almost paracontact metric structure. We also introducethe notion of paracontactly geodesic transformation and prove thatthe structure tensor field is invariant under conformal andparacontactly geodesic transformations. For the particular case of para-Kenmotsu structure, we give a necessary and sufficient condition for a conformal transformation to map it to an $\alpha$-para-Kenmotsu structure and show that a para-Kenmotsu manifold admits no nontrivial paracontactly geodesic transformation of the metric. In the conformal case, the virtual tensor field is invariant.

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Al-Badawi, A., M. Q. Owaidat, and S. Tarawneh. "The geodesics structure of Schwarzschild black hole immersed in an electromagnetic universe." International Journal of Modern Physics D 26, no. 14 (December 2017): 1750169. http://dx.doi.org/10.1142/s0218271817501693.

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The geodesic equations are considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic (em) field. Due to the em field horizon shrinks and geodesics are modified. By analyzing the behavior of the effective potentials for the massless and massive particle we study the radial and circular trajectories. Radial geodesics for both photons and particles are solved exactly. It is shown that a particle that falls toward the horizon in a finite proper time slows down so that the particle reaches the singularity slower than Schwarzschild case. Timelike and null circular geodesics are investigated. We have shown that, there are no stable circular orbits for photons, however stable and unstable second-kind orbits exist for the massive particle. An exact analytical solution for the innermost stable circular orbits (ISCO) has been obtained. It has been shown that the radius of the ISCO shrinks due to the presence of the em field.

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Boucetta, Mohamed, Aissa Meliani, and Abdelghani Zeghib. "Kundt three-dimensional left invariant spacetimes." Journal of Mathematical Physics 63, no. 11 (November 1, 2022): 112501. http://dx.doi.org/10.1063/5.0091202.

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Kundt spacetimes are of great importance to general relativity. We show that a Kundt spacetime is a Lorentz manifold with a non-singular isotropic geodesic vector field having its orthogonal distribution integrable and determining a totally geodesic foliation. We give the local structure of Kundt spacetimes and some properties of left invariant Kundt structures on Lie groups. Finally, we classify all left invariant Kundt structures on three-dimensional simply connected unimodular Lie groups.

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Heck, T., and M. Sorg. "Geodesic Motion in Trivializable Gauge Fields." Zeitschrift für Naturforschung A 46, no. 8 (August 1, 1991): 655–68. http://dx.doi.org/10.1515/zna-1991-0802.

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AbstractThe geodesic problem is studied for a Riemannian structure, which is generated by an SO(4) trivializable gauge field. The topological and elliptic geometric defects of such a structure act as attractors for the geodesic curves

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Bormotova, Irina, Elena Kopteva, and Zdeněk Stuchlík. "Geodesic Structure of the Accelerated Stephani Universe." Symmetry 13, no. 6 (June 3, 2021): 1001. http://dx.doi.org/10.3390/sym13061001.

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For the spherically symmetric Stephani cosmological model with an accelerated expansion, we investigate the main scenarios of the test particle and photon motion. We show that a comoving observer sees an appropriate picture. In the case of purely radial motion, the radial velocity decreases slightly with time due to the universe expansion. Both particles and photons spiral out of the center when the radial coordinate is constant. In the case of the motion with arbitrary initial velocity, the observable radial distance to the test particle can increase under negative observable radial velocity.

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32

Allison, Dean E., and Bülent Ünal. "Geodesic structure of standard static space–times." Journal of Geometry and Physics 46, no. 2 (May 2003): 193–200. http://dx.doi.org/10.1016/s0393-0440(02)00154-7.

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Ossola, Enrico, Eugenio Brusa, and Raffaella Sesana. "Geodesic domes for planetary exploration." Curved and Layered Structures 7, no. 1 (December 17, 2020): 215–25. http://dx.doi.org/10.1515/cls-2020-0018.

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AbstractVenus and the Ocean Worlds are emerging areas of interest for space exploration, as they can potentially host, or have hosted, conditions compatible with life. Landers and probes for in-situ exploration, however, must deal with very high external pressure, due to the environmental conditions, often resulting in thick and heavy structures. Robust, reinforced shell structures can provide a lightweight solution for the primary structure. In this frame, the isogrid layout is already a standard in aerospace, especially for flat panels or cylindrical shells. In this paper, isogrid-stiffened hemispherical shells, or “geodesic domes”, are described, focusing on the case of a concept of a Venus lander. Early design methods for both plain and geodesic domes subjected to external pressure are presented, providing design equations. Additive Manufacturing is identified as the key technology for fabricating metallic geodesic domes, due to the complexity of the internal features. Moreover, it allows to fabricate ports and integrated thermostructural systems in the same process, potentially resulting in improved performance or cost and schedule savings.

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Kolpakov, Andrey, Oleg Dolgov, Vladislav Korolskiy, Semen Popov, Vyacheslav Anchutin, and Vadim Zykov. "Analysis of Structural Layouts of Geodesic Dome Structures with Bar Filler Considering Air Transportation." Buildings 12, no. 2 (February 19, 2022): 242. http://dx.doi.org/10.3390/buildings12020242.

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The results are presented from a study of three-layer geodesic dome structures with bar fillers under their own weight. An algorithm was developed for selecting the type of structural layout used and the reference parameters chosen in terms of the technological, strength, and weight characteristics. The results of this analysis aim to make it easier for designers to determine the optimal reference parameters in the initial stage of the designing of geodetic hemispherical dome structures, the construction of which is planned to be carried out in remote areas with harsh climatic conditions. Due to the lack of sufficient ground transport infrastructure, cargo delivery to these regions is currently possible only with the help of air transport. The importance of this study rests on the lack of adequate methods for the determination of the reference parameters for geodesic hemispherical dome structures at an early stage of design. In particular, it is common for the issues regarding the transportation of structural elements as well as those that involve ensuring the strength and the technological characteristics of the structure to not be considered simultaneously. This study owes its relevance to the rapid development of the uninhabited territories of the Russian Federation in the context of the global ecological crisis caused by anthropogenic impact on the environment.

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Lee, K. S., and S. E. Han. "Geodesic shape finding of membrane structure with geodesic string by the dynamic relaxation method." Structural Engineering and Mechanics 39, no. 1 (July 10, 2011): 93–113. http://dx.doi.org/10.12989/sem.2011.39.1.093.

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Tomasowa, Riva. "Kajian Sketsa Digital dalam Proses Reka-Struktur Bentuk-Bentuk Surface." ComTech: Computer, Mathematics and Engineering Applications 4, no. 2 (December 1, 2013): 1087. http://dx.doi.org/10.21512/comtech.v4i2.2551.

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Free form surface has a multiple complexity curve intrinsically, so that special approach is needed to form the structure. Geodesic shell is well-known as the shortest path between two points on a curved surface. This method is used to generate the structure of form, which can be easily determined by its basic shape or the complex form. This paper explains how Geodesic theory can assist to generate structures in the early stage of digital sketching. A workshop that has initially started becomes a topic to this discussion. The digital sketching process to apply the theory is the aim of this paper.

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Georgiou, Nikos. "On area stationary surfaces in the space of oriented geodesics of hyperbolic 3-space." MATHEMATICA SCANDINAVICA 111, no. 2 (December 1, 2012): 187. http://dx.doi.org/10.7146/math.scand.a-15224.

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We study area-stationary surfaces in the space $\mathbf{L}(\mathbf{H}^3)$ of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. We prove that every holomorphic curve in $\mathbf{L}(\mathbf{H}^3)$ is an area-stationary surface. We then classify Lagrangian area-stationary surfaces $\Sigma$ in $\mathbf{L}(\mathbf{H}^3)$ and prove that the family of parallel surfaces in $\mathbf{H}^3$ orthogonal to the geodesics $\gamma\in \Sigma$ form a family of equidistant tubes around a geodesic. Finally we find an example of a two parameter family of rotationally symmetric area-stationary surfaces that are neither Lagrangian nor holomorphic.

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Medvedskyi, Yurii, Andriy Annenkov, Oleksandr Isayev, and Roman Demianenko. "AUTOMATION OF GEODESIC MONITORING HIGH-RISE STRUCTURES." Urban development and spatial planning, no. 81 (August 31, 2022): 244–53. http://dx.doi.org/10.32347/2076-815x.2022.81.244-253.

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The article considers the existing methods used in the problem of geodetic monitoring of structures, analyzes the possibilities and gives a preliminary assessment of the accuracy of their use in monitoring high-rise structures. Methods have been identified that allow obtaining measurement results with a high sampling rate and have the potential for automation. Methods have been identified that allow solving the problem of calculating the daily fluctuations of a structure from the effects of solar radiation and wind load separately from the values of heel and draft.

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Bretón, Nora. "Geodesic structure of the Born–Infeld black hole." Classical and Quantum Gravity 19, no. 4 (January 30, 2002): 601–12. http://dx.doi.org/10.1088/0264-9381/19/4/301.

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ZHOU, SHENG, JUHUA CHEN, and YONGJIU WANG. "GEODESIC STRUCTURE OF TEST PARTICLE IN BARDEEN SPACETIME." International Journal of Modern Physics D 21, no. 09 (September 2012): 1250077. http://dx.doi.org/10.1142/s0218271812500770.

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The Bardeen model describes a regular spacetime, i.e. a singularity-free black hole spacetime. In this paper, by analyzing the behavior of the effective potential for the particles and photons, we investigate the timelike and null geodesic structures in the Bardeen spacetime. At the same time, all kinds of orbits, which are allowed according to the energy level corresponding to the effective potentials, are numerically simulated in detail. We find many-world bound orbits, two-world escape orbits and escape orbits in this spacetime. We also find that bound orbits precession directions are opposite and their precession velocities are different, the inner bound orbits shift along counter-clockwise with high velocity while the exterior bound orbits shift along clockwise with low velocity.

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Zhou, Sheng, Ruanjing Zhang, Juhua Chen, and Yongjiu Wang. "Geodesic Structure of Janis-Newman-Winicour Space-time." International Journal of Theoretical Physics 54, no. 8 (January 27, 2015): 2905–20. http://dx.doi.org/10.1007/s10773-015-2526-1.

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Nikonorov, Yuriĭ Gennadievich. "On the structure of geodesic orbit Riemannian spaces." Annals of Global Analysis and Geometry 52, no. 3 (May 6, 2017): 289–311. http://dx.doi.org/10.1007/s10455-017-9558-0.

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CORACH, GUSTAVO, HORACIO PORTA, and LÁZARO RECHT. "GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS." International Journal of Mathematics 04, no. 02 (April 1993): 193–202. http://dx.doi.org/10.1142/s0129167x9300011x.

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The set A+ of positive invertible elements of a C*-algebra has a natural structure of reductive homogeneous manifold with a Finsler metric. Because pairs of points can be joined by uniquely determined geodesics and geodesics are "short" curves, there is a natural notion of convexity: C ⊂ A+ is convex if the geodesic segment joining a, b ∈ C is contained in C. We show that this notion is related to the classical convexity of real and operator valued functions. Several results about convexity are proved in this paper. The expressions of these results are closely related to the operator means of Kubo and Ando, in particular to the geometric mean of Pusz and Woronowicz, and they produce several norm estimations and operator inequalities.

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CAMCI, UGUR. "DIRAC ANALYSIS AND INTEGRABILITY OF GEODESIC EQUATIONS FOR CYLINDRICALLY SYMMETRIC SPACETIMES." International Journal of Modern Physics D 12, no. 08 (September 2003): 1431–44. http://dx.doi.org/10.1142/s0218271803003621.

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Dirac's constraint analysis and the symplectic structure of geodesic equations are obtained for the general cylindrically symmetric stationary spacetime. For this metric, using the obtained first order Lagrangian, the geodesic equations of motion are integrated, and found some solutions for Lewis, Levi-Civita, and Van Stockum spacetimes.

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CREACO, ANTHONY J., and NIKOS KALOGEROPOULOS. "THE GEODESIC RULE FOR HIGHER CODIMENSIONAL GLOBAL DEFECTS." Modern Physics Letters A 23, no. 25 (August 20, 2008): 2053–66. http://dx.doi.org/10.1142/s0217732308027242.

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We generalize the geodesic rule to the case of formation of higher codimensional global defects. Relying on energetic arguments, we argue that, for such defects, the geometric structures of interest are the totally geodesic submanifolds. On the other hand, stochastic arguments lead to a diffusion equation approach, from which the geodesic rule is deduced. It turns out that the most appropriate geometric structure that one should consider is the convex hull of the values of the order parameter on the causal volumes whose collision gives rise to the defect. We explain why these two approaches lead to similar results when calculating the density of global defects by using a theorem of Cheeger and Gromoll. We present a computation of the probability of formation of strings/vortices in the case of a system, such as nematic liquid crystals, whose vacuum is ℝP2.

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46

Gilodo, A. Y., V. P. Kovtun, A. N. Arsirii, and A. A. Angel. "EFFECTIVE STRUCTURE OF A WOODEN RESIDENTIAL BUILDING IN THE FORM OF A GEODESIC DOME WITH A UNIVERSAL CONNECTOR." Bulletin of Odessa State Academy of Civil Engineering and Architecture, no. 82 (March 4, 2021): 19–26. http://dx.doi.org/10.31650/2415-377x-2021-82-19-26.

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Abstract. Since the middle of the twentieth century, a new architectural solution has been spherical shells broken down into elements by geodesic lines – circles with radii equal to the radius of the sphere. A geodesic dome is a dome made of a spherical polyhedron with an optimally distributed arrangement of vertices and edges tending to a perfect sphere. Using the technical capabilities of computer design, digital models of the layout and calculation of geodesic domes became available. It is possible not only to calculate multi-mesh network layouts with high accuracy, but also to automate the design. At the same time, it cannot be said that the optimal system has already been obtained and studied. The issues of optimal shaping, taking into account a simple universal connector and confirmation of theoretical results by field tests, remain not fully studied. Development of the design of a mesh wooden house in the form of a geo dome with optimal parameters of the geodetic network and nodal connections of the frame elements using a universal connector is the theme of this publication. The proposed form of division is a fullerene polyhedron describing a sphere and consisting of five and hexagonal faces. The dome polyhedron is built on the basis of the icosahedron. The number of partitions of vertices and edges that make up the split edge ‒ the frequency, is chosen equal to 3. The first class of partitioning by the "equal chords" method is adopted. The proposed universal connector for connecting parts of building structures at any angle and a method of mounting building structures using a universal connector. As a result of introduction of new technical decisions we receive essential simplification of a design, reduction of quantity of its components, at the same time increase of its manufacturability and providing an opportunity to connect details of building designs in an end face at any angle.

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Pilarska, Dominika, and Tomasz Maleska. "Numerical Analysis of Steel Geodesic Dome under Seismic Excitations." Materials 14, no. 16 (August 10, 2021): 4493. http://dx.doi.org/10.3390/ma14164493.

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The paper presents the response of two geodesic domes under seismic excitations. The structures subjected to seismic analysis were created by two different methods of subdividing spherical triangles (the original octahedron face), as proposed by Fuliński. These structures are characterised by the similar number of elements. The structures are made of steel, which is a material that undoubtedly gives lightness to structures and allows large spans. Designing steel domes is currently a challenge for constructors, as well as architects, who take into account their aesthetic considerations. The analysis was carried out using the finite element method of the numerical program. The two designed domes were analysed using four different seismic excitations. The analysis shows what influence particular earthquakes have on the geodesic dome structures by two different methods. The study analysed the maximum displacements, axial forces, velocities, and accelerations of the designed domes. In addition, the Time History method was used for the analysis, which enabled the analysis of the structure in the time domain. The study will be helpful in designing new structures in seismic areas and in assessing the strength of various geodesic dome structures under seismic excitation.

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Rebelo, Hugo Bento, Filipe Amarante dos Santos, Corneliu Cismaşiu, and Duarte Santos. "Exploratory study on geodesic domes under blast loads." International Journal of Protective Structures 10, no. 4 (March 13, 2019): 439–56. http://dx.doi.org/10.1177/2041419618820540.

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This article studies the feasibility of using geodesic domes as expeditionary protective structures, since they are fast-assembly lightweight structures and are able to withstand very heavy loads due to their specific geometry. A 6-m standard International Orginization for Standardization container is used as a benchmark structure for the study, which is developed using the nonlinear explicit code LS-DYNA. The blast simulations were performed with the Load Blast Enhanced option, using the phenomenological Johnson–Cook constitutive model to reproduce the behaviour of steel subjected to a large range of strain rates. The performance assessment of the protective structures under blast loading was based on the evaluation of the associated safety zones inside the protective shelter as well as on the characterization of the potential structural damage. With the additional insights provided by this article, it is possible to identify some of the competitive advantages shown by this type of structures which will hopefully foster new advances in the field.

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Iftikhar, Sehrish, and Fizza Saeed. "Geodesic study of spherically symmetric black holes in Palatini-type gravity." International Journal of Modern Physics D 30, no. 07 (April 29, 2021): 2150052. http://dx.doi.org/10.1142/s0218271821500528.

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This paper probes the geodesic structure of spherically symmetric charged black holes using modified theory of gravity. We explore the geodesic structures of different black holes in the background of Palatini [Formula: see text] theory as well as Eddington-inspired Born–Infeld gravity. We have examined the stability of orbits with the analysis of effective potential. The impacts of modified gravity on particle dynamics specially the circular orbits, the deflection angle and trajectory followed by lightlike as well as for timelike particles are scrutinized. We find that the orbits are more stable for the large values of charge and Born–Infeld parameter.

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AICHHOLZER, OSWIN, THOMAS HACKL, MATIAS KORMAN, ALEXANDER PILZ, and BIRGIT VOGTENHUBER. "GEODESIC-PRESERVING POLYGON SIMPLIFICATION." International Journal of Computational Geometry & Applications 24, no. 04 (December 2014): 307–23. http://dx.doi.org/10.1142/s0218195914600097.

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Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-to-describe linear-time method to replace an input polygon [Formula: see text] by a polygon [Formula: see text] such that (1) [Formula: see text] contains [Formula: see text], (2) [Formula: see text] has its reflex vertices at the same positions as [Formula: see text], and (3) the number of vertices of [Formula: see text] is linear in the number of reflex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both [Formula: see text] and [Formula: see text], our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reflex vertices rather than on the size of [Formula: see text]. We describe several of these applications (including linear-time post-processing steps that might be necessary).

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