Relevant bibliographies by topics / Spheroidal geometry

Academic literature on the topic 'Spheroidal geometry'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Spheroidal geometry"

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Ivers, D. J. "Kinematic dynamos in spheroidal geometries." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2206 (October 2017): 20170432. http://dx.doi.org/10.1098/rspa.2017.0432.

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The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤ a / c ≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.
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Kiani, Mostafa, Nabi Chegini, Abdolreza Safari, and Borzoo Nazari. "SPHEROIDAL SPLINE INTERPOLATION AND ITS APPLICATION IN GEODESY." Geodesy and cartography 46, no. 3 (October 12, 2020): 123–35. http://dx.doi.org/10.3846/gac.2020.11316.

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The aim of this paper is to study the spline interpolation problem in spheroidal geometry. We follow the minimization of the norm of the iterated Beltrami-Laplace and consecutive iterated Helmholtz operators for all functions belonging to an appropriate Hilbert space defined on the spheroid. By exploiting surface Green’s functions, reproducing kernels for discrete Dirichlet and Neumann conditions are constructed in the spheroidal geometry. According to a complete system of surface spheroidal harmonics, generalized Green’s functions are also defined. Based on the minimization problem and corresponding reproducing kernel, spline interpolant which minimizes the desired norm and satisfies the given discrete conditions is defined on the spheroidal surface. The application of the results in Geodesy is explained in the gravity data interpolation over the globe.
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Momoh, O. D., M. N. O. Sadiku, and S. M. Musa. "Solution of Axisymmetric Potential Problem in Oblate Spheroid Using the Exodus Method." Journal of Computational Engineering 2014 (March 17, 2014): 1–6. http://dx.doi.org/10.1155/2014/126905.

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This paper presents the use of Exodus method for computing potential distribution within a conducting oblate spheroidal system. An explicit finite difference method for solving Laplace’s equation in oblate spheroidal coordinate systems for an axially symmetric geometry was developed. This was used to determine the transition probabilities for the Exodus method. A strategy was developed to overcome the singularity problems encountered in the oblate spheroid pole regions. The potential computation results obtained correlate with those obtained by exact solution and explicit finite difference methods.
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Xue, Changfeng, Robert Edmiston, and Shaozhong Deng. "Image Theory for Neumann Functions in the Prolate Spheroidal Geometry." Advances in Mathematical Physics 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/7683929.

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Interior and exterior Neumann functions for the Laplace operator are derived in terms of prolate spheroidal harmonics with the homogeneous, constant, and nonconstant inhomogeneous boundary conditions. For the interior Neumann functions, an image system is developed to consist of a point image, a line image extending from the point image to infinity along the radial coordinate curve, and a symmetric surface image on the confocal prolate spheroid that passes through the point image. On the other hand, for the exterior Neumann functions, an image system is developed to consist of a point image, a focal line image of uniform density, another line image extending from the point image to the focal line along the radial coordinate curve, and also a symmetric surface image on the confocal prolate spheroid that passes through the point image.
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Pincak, R. "Spheroidal geometry approach to fullerene molecules." Physics Letters A 340, no. 1-4 (June 2005): 267–74. http://dx.doi.org/10.1016/j.physleta.2005.04.023.

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Vafeas, Panayiotis, Eleftherios Protopapas, and Maria Hadjinicolaou. "On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation." Symmetry 14, no. 1 (January 15, 2022): 170. http://dx.doi.org/10.3390/sym14010170.

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Modern engineering technology often involves the physical application of heat and mass transfer. These processes are associated with the creeping motion of a relatively homogeneous swarm of small particles, where the spheroidal geometry represents the shape of the embedded particles within such aggregates. Here, the steady Stokes flow of an incompressible, viscous fluid through an assemblage of particles, at low Reynolds numbers, is studied by employing a particle-in-cell model. The mathematical formulation adopts the Kuwabara-type assumption, according to which each spheroidal particle is stationary and it is surrounded by a confocal spheroid that creates a fluid envelope, in which the Newtonian fluid moves with a constant velocity of arbitrary orientation. The boundary value problem in the fluid envelope is solved by imposing non-slip conditions on the surface of the spheroid, which is also considered as non-penetrable, while zero vorticity is assumed on the fictitious spheroidal boundary along with a uniform approaching velocity. The three-dimensional flow fields are calculated analytically for the first time, in the spheroidal geometry, by virtue of the Papkovich–Neuber representation. Through this, the velocity and the total pressure fields are provided in terms of a vector and the scalar spheroidal harmonic potentials, which enables the thorough study of the relevant physical characteristics of the flow fields. The newly obtained analytical expressions generalize to any direction with the existing results holding for the asymmetrical case, which were obtained with the aid of a stream function. These can be employed for the calculation of quantities of physical or engineering interest. Numerical implementation reveals the flow behavior within the fluid envelope for different geometrical cell characteristics and for the arbitrarily-assumed velocity field, thus reflecting the different flow/porous media situations. Sample calculations show the excellent agreement of the obtained results with those available for special geometrical cases. All of these findings demonstrate the usefulness of the proposed method and the powerfulness of the obtained analytical expansions.
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Öztürk, Yavuz, Ali Can Aktaş, and Bekir Aktaş. "A Z-gradient coil on spheroidal geometry." Journal of Magnetism and Magnetic Materials 552 (June 2022): 169169. http://dx.doi.org/10.1016/j.jmmm.2022.169169.

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Anastasiou, Eirini I., and Ioannis K. Chatjigeorgiou. "The Radiation Problem of a Submerged Oblate Spheroid in Finite Water Depth Using the Method of the Image Singularities System." Fluids 7, no. 4 (April 8, 2022): 133. http://dx.doi.org/10.3390/fluids7040133.

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This study examines the hydrodynamic parameters of a unique geometry that could be used effectively for wave energy extraction applications. In particular, we are concerned with the oblate spheroidal geometry that provides the advantage of a wider impact area on waves, closer to the free surface where the hydrodynamic pressure is higher. In addition, the problem is formulated and solved analytically via a method that is robust and most importantly very fast. In particular, we develop an analytical formulation for the radiation problem of a fully submerged oblate spheroid in a liquid field of finite water depth. The axisymmetric configuration of the spheroid is considered, i.e., the axis of symmetry is perpendicular to the undisturbed free surface. In order to solve the problem, the method of the image singularities system is employed. This method allows for the expansion of the velocity potential in a series of oblate spheroidal harmonics and the derivation of analytical expressions for the hydrodynamic coefficients for the translational degrees of freedom of the body. Numerical simulations and validations are presented taking into account the slenderness ratio of the spheroid, the immersion below the free surface and the water depth. The validations ensure the correctness and the accuracy of the proposed method. Utilizing the same approach, the whole process is implemented for a disc as well, given that a disc is the limiting case of an oblate spheroid since its semi-minor axis approaches zero.
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Sten, J. C. E., and E. A. Marengo. "Inverse Source Problem in an Oblate Spheroidal Geometry." IEEE Transactions on Antennas and Propagation 54, no. 11 (November 2006): 3418–28. http://dx.doi.org/10.1109/tap.2006.884292.

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Ghosh, Mithun. "Dark matter halo with charge in pseudo-spheroidal geometry." Modern Physics Letters A 36, no. 25 (August 20, 2021): 2150178. http://dx.doi.org/10.1142/s0217732321501789.

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The concept of dark matter (DM) hypothesis comes out as a result from the input of the observed flat rotational velocity. With the assumption that the galactic halo is pseudo-spheroidal and filled with charged perfect fluid, we have obtained a solution which has inkling to a (nearly) flat universe, compatible with the modern day cosmological observations. Various other important aspects of the solution such as attractive gravity in the halo region and the stability of the circular orbit are also explored. Also, the matter in the halo region satisfies the known equation of state which indicates its non-exotic nature.
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Dissertations / Theses on the topic "Spheroidal geometry"

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Tuncer, Necibe Meir Amnon J. "A novel finite element discretization of domains with spheroidal geometry." Auburn, Ala., 2007. http://repo.lib.auburn.edu/Send%2011-10-07/TUNCER_NECIBE_24.pdf.

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Kwok, T. T. "The influence of tumour geometry upon cellular response to cytotoxic agents : An in vitro study using multicellular spheroids." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372883.

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Bernard, Benjamin. "On the Quantization Problem in Curved Space." Wright State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=wright1344829165.

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Parry, Alan Reid. "Wave Dark Matter and Dwarf Spheroidal Galaxies." Diss., 2013. http://hdl.handle.net/10161/7125.

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We explore a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently been motivated by a new geometric perspective by Bray. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely on a fundamental constant Upsilon (also known as the ``mass term'' of the Klein-Gordon equation). Specifically, in this dissertation, we study spherically symmetric wave dark matter and compare these results with observations of dwarf spheroidal galaxies as a first attempt to compare the implications of the theory of wave dark matter with actual observations of dark matter. This includes finding a first estimate of the fundamental constant Upsilon.

In the introductory Chapter 1, we present some preliminary background material to define and motivate the study of wave dark matter and describe some of the properties of dwarf spheroidal galaxies.

In Chapter 2, we present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an especially useful form of the metric of a spherically symmetric spacetime in polar-areal coordinates and its properties. In particular, we show how the metric component functions chosen are extremely compatible with notions in Newtonian mechanics. We also show the monotonicity of the Hawking mass in these coordinates. Finally, we discuss how these coordinates and the metric can be used to solve the spherically symmetric Einstein-Klein-Gordon equations.

In Chapter 3, we explore spherically symmetric solutions to the Einstein-Klein-Gordon equations, the defining equations of wave dark matter, where the scalar field is of the form f(t,r) = exp(i omega t) F(r) for some constant omega in R and complex-valued function F(r). We show that the corresponding metric is static if and only if F(r) = h(r)exp(i a) for some constant a in R and real-valued function h(r). We describe the behavior of the resulting solutions, which are called spherically symmetric static states of wave dark matter. We also describe how, in the low field limit, the parameters defining these static states are related and show that these relationships imply important properties of the static states.

In Chapter 4, we compare the wave dark matter model to observations to obtain a working value of Upsilon. Specifically, we compare the mass profiles of spherically symmetric static states of wave dark matter to the Burkert mass profiles that have been shown by Salucci et al. to predict well the velocity dispersion profiles of the eight classical dwarf spheroidal galaxies. We show that a reasonable working value for the fundamental constant in the wave dark matter model is Upsilon = 50 yr^(-1). We also show that under precise assumptions the value of Upsilon can be bounded above by 1000 yr^(-1).

In order to study non-static solutions of the spherically symmetric Einstein-Klein-Gordon equations, we need to be able to evolve these equations through time numerically. Chapter 5 is concerned with presenting the numerical scheme we will use to solve the spherically symmetric Einstein-Klein-Gordon equations in our future work. We will discuss how to appropriately implement the boundary conditions into the scheme as well as some artificial dissipation. We will also discuss the accuracy and stability of the scheme. Finally, we will present some examples that show the scheme in action.

In Chapter 6, we summarize our results. Finally, Appendix A contains a derivation of the Einstein-Klein-Gordon equations from its corresponding action.


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Books on the topic "Spheroidal geometry"

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Jackson, J. E. Sphere, Spheroid and Projections for Surveyors. Sheridan House Inc, 1987.

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Book chapters on the topic "Spheroidal geometry"

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Coutelieris, F. A. "The effect of geometry and axial orientation of spheroidal particles on the adsorption rate in a granular porous medium." In Characterization of Porous Solids VI, Proceedings of the 6th International Symposium on the Characterization of Porous Solids (COPS-VI), 745–51. Elsevier, 2002. http://dx.doi.org/10.1016/s0167-2991(02)80205-1.

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MALING, D. H. "The geometry of the spheroid." In Coordinate Systems and Map Projections, 64–79. Elsevier, 1992. http://dx.doi.org/10.1016/b978-0-08-037233-4.50009-1.

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Tannous, Katia, and Fillipe de Souza Silva. "Particle Shape Analysis Using Digital Image Processing." In Encyclopedia of Information Science and Technology, Fourth Edition, 1331–43. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-2255-3.ch114.

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This chapter will discuss new software, Particles and Geometric Shapes Analyzer (APOGEO), aiming the determination of aspect ratio and sphericity of solid particles by image processing technique without any manual work. This software can quantify the major and minor axes correlating two or three dimensions of particles (e.g.: biomass, mineral, pharmaceutical and food products) to obtain their shape. The particles can be associated with different geometries such as, rectangular parallelepiped, cylinder, oblate and prolate spheroids, and irregular. The results are presented in histograms and tables, but also can be saved in a spreadsheet.
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Tannous, Katia, and Fillipe de Souza Silva. "Particle Shape Analysis Using Digital Image Processing." In Advanced Methodologies and Technologies in Artificial Intelligence, Computer Simulation, and Human-Computer Interaction, 377–91. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-7368-5.ch028.

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This chapter will discuss new software, Particles and Geometric Shapes Analyzer (APOGEO), aiming the determination of aspect ratio and sphericity of solid particles by image processing technique without any manual work. This software can quantify the major and minor axes correlating two or three dimensions of particles (e.g., biomass, mineral, pharmaceutical, and food products) to obtain their shape. The particles can be associated with different geometries, such as rectangular parallelepiped, cylinder, oblate and prolate spheroids, and irregular. The results are presented in histograms and tables, but also can be saved in a spreadsheet.
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Sohor, Andrii. "A PRIORI RESEARCH RELATED TO THE CALCULATION OF THE REGIONAL ELLIPSOID FOR UKRAINE AND ITS EFFECTIVENESS." In Theoretical and practical aspects of the development of modern scientific research. Publishing House “Baltija Publishing”, 2022. http://dx.doi.org/10.30525/978-9934-26-195-4-13.

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Despite the high accuracy of global geodetic reference systems and their widespread use in GPS measurements, regional (local) geodetic systems are becoming more widely used. For example, the World Geodetic System 1984 (WGS84) has 83 such local systems. The emergence of the latter is caused by the emergence of new problems of physical geodesy. These are the so-called regional problems, which make it possible to study in more detail both the geometric and gravimetric (physical) properties of the studied region (territory). For example, the tasks of constructing a high-precision regional geoid (quasi-geoid), regional ellipsoid, determining the regional normal formula of gravity, and others are becoming increasingly important. That is why at present both national and regional reference ellipsoids are accepted for processing geodetic data on a regional scale (for example, for a specific country), and for global research – a general terrestrial reference ellipsoid GRS80 or, when processing GPS data – a general terrestrial reference ellipsoid WGS84.In principle, any reference ellipsoid that represents a generalized figure of the Earth with appropriate accuracy can be used to process geodetic information. The deviations of the geoid from such an ellipsoid can determine the corrections that must be made in the results of geodetic measurements to bring the latter to the surface of this ellipsoid. However, with large deviations of the geoid from the reference ellipsoid, there are large corresponding reductions of geodetic measurements, which are burdened with significant errors due to the linearization of the main problem of geodesy and, consequently, the problem of bringing geodetic measurements to the ellipsoid. Therefore, from a practical point of view, to reduce the impact of these linearization errors and obtain methodologically optimal results of geodetic data processing, it is expedient and even necessary to use a reference ellipsoid that best describes the generalized geoid surface in the region of specific geodetic works.Given the above, the question arose about the national reference coordinate system, as such a system has some advantages over the national system in the process of practical processing of mass geodetic measurements, especially linear. In this regard, the issues of building a national reference system, namely, the definition of a regional ellipsoid, are very important and relevant. Therefore, the scope of our research is the construction of a national reference system based on data on the regional gravitational field of Ukraine. The methodology of such research is that the task of determining the regional ellipsoid is practically reduced to finding some corrections to the known, accepted by us, the general terrestrial ellipsoid GRS80. The regional ellipsoid for the territory of Ukraine should be the one that would best represent the geoid (quasi-geoid) of the region. That is, the heights of the geoid relative to the regional ellipsoid within the territory of Ukraine should be as small as possible. These questions are reflected in this monograph, the purpose of which is to investigate a priori calculations to determine the parameters of the internal orientation of the regional ellipsoid according to its gravitational field in Ukraine. Thus, based on the results of the above a priori studies, the following can be noted. Determining all five parameters of a regional ellipsoid leads to a strong functional dependence of the parameters. This dependence (correlation) is quite well demonstrated on the values of root mean square errors, which are proportional to the obtained parameters and even exceed the latter. Taking into account these remarks, we can conclude that the joint calculation of all five parameters by the method of least squares on the territory of Ukraine does not give us the expected good results. This is well seen from a priori calculations based on the heights of the geoid, presented in the form of a spheroidal trapezoid, which describes the territory of Ukraine. In contrast to this solution, studies to determine only the parameters of the internal orientation of the ellipsoid at a given major half-axis and compression of this ellipsoid, make it possible to choose a terrestrial regional ellipsoid that would best represent a geoid (quasi-geoid) built in Ukraine.
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Conference papers on the topic "Spheroidal geometry"

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Petkov, T., K. F. Ren, J. C. Loudet, and B. Pouligny. "Nonlinear Oscillatory States of Spheroidal Particles in a Two-Beam Trap Geometry." In Optical Trapping Applications. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/ota.2017.ots1d.2.

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Borrelli, Francesca, Amedeo Capozzoli, Claudio Curcio, and Angelo Liseno. "A NFFF approach using spheroidal wave functions in a cylindrical scanning geometry." In 2021 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (APS/URSI). IEEE, 2021. http://dx.doi.org/10.1109/aps/ursi47566.2021.9703838.

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Borrelli, Francesca, Amedeo Capozzoli, Claudio Curcio, and Angelo Liseno. "Numerical results for antenna characterization in a cylindrical scanning geometry using a spheroidal modelling." In 2021 IEEE International Conference on Microwaves, Antennas, Communications and Electronic Systems (COMCAS). IEEE, 2021. http://dx.doi.org/10.1109/comcas52219.2021.9629098.

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Wei, Guowu, and Jian S. Dai. "Linkages That Transfer Rotations to Radially Reciprocating Motion." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28678.

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Stemming from study of polyhedral and spheroidal linkages and investigation of reciprocating motion of the PRRP chain, this paper presents four overconstrained linkages that are capable of transferring rotations to radially reciprocating motion. The linkages connected by revolute joints are of symmetrical arrangement and mobility one and are analysed by using the screw-loop equation method. The paper further investigates geometry and kinematics of the linkages and reveals their kinematic characteristics, leading to the constraint equation.
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GERGIDIS, L. N., D. KOUROUNIS, S. MAVRATZAS, and A. CHARALAMBOPOULOS. "ON THE SENSITIVITY OF THE ACOUSTIC SCATTERING PROBLEM IN PROLATE SPHEROIDAL GEOMETRY WITH RESPECT TO WAVENUMBER AND SHAPE VIA VEKUA TRANFORMATION - THEORY AND NUMERICAL RESULTS." In Proceedings of the 8th International Workshop on Mathematical Methods in Scattering Theory and Biomedical Engineering. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812814852_0004.

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Chen, Howard, and Ibrahim T. Ozbolat. "Development of a Multi-Arm Bioprinter for Hybrid Tissue Engineering." In ASME 2013 International Manufacturing Science and Engineering Conference collocated with the 41st North American Manufacturing Research Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/msec2013-1025.

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This paper highlights the development of a multi-arm bioprinter (MABP) capable of concurrent deposition of multiple materials with independent dispensing parameters including deposition speed, material dispensing rate and frequency for functional zonal-stratified articular cartilage tissue fabrication. The MABP consists of two Cartesian robots mounted in parallel on the same mechanical frame. This platform is used for concurrent filament fabrication and cell spheroid deposition. A single-layer structure is fabricated and concurrently deposited with spheroids to validate this system. Preliminary results showed that the MABP was able to produce filaments and spheroids with well-defined geometry and high cell viability. The resulting filament width has a variation of +/-170 μm and the center-to-center filament distance was within 100 μm of the specified distance. This fabrication system is aimed to be further refined for printing structures with varying porosities to mimic the natural cartilage structure in order to produce functional tissue-engineered articular cartilage using cell spheroids containing cartilage progenitor cells (CPCs).
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Farafonov, V. G., V. I. Ustimov, and A. E. Farafonova. "OPTICAL RESONANCES OF A PLASMA NATURE IN TWO-LAYER NANOSPHEROIDS." In MODELING AND SITUATIONAL MANAGEMENT THE QUALITY OF COMPLEX SYSTEMS. Saint Petersburg State University of Aerospace Instrumentation, 2021. http://dx.doi.org/10.31799/978-5-8088-1558-2-2021-2-47-50.

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The process of light scattering by two-layer spheroids consisting of a dielectric core and a silver shell, which depends on the length of an incident wave and particle geometry, is considered. One optical resonance is observed when the foci of the nuclear surfaces and the shell coincide, while when this condition is violated, additional resonances appear. Namely, in the absorption and scattering bands, resonances were found, including previously unknown ones, the position and intensity of which depended on the shell thickness, the shape of the spheroid and its core. To substantiate the reliability of the results obtained, the convergence of the calculations was analyzed depending on the number of harmonics which were taken into consideration in the calculations.
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Lugovtsov, Andrei E., Alexander V. Priezzhev, and Sergei Y. Nikitin. "Light scattering by biological spheroidal particles in geometric optics approximation." In SPIE Proceedings, edited by Qingming Luo, Lihong V. Wang, Valery V. Tuchin, and Min Gu. SPIE, 2007. http://dx.doi.org/10.1117/12.741344.

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Deng, Tao, James R. Cournoyer, James H. Schermerhorn, Joleyn Balch, and Margaret L. Blohm. "Manipulating Shape and Size of Nanoparticles With Plasma Field." In ASME 2008 International Manufacturing Science and Engineering Conference collocated with the 3rd JSME/ASME International Conference on Materials and Processing. ASMEDC, 2008. http://dx.doi.org/10.1115/msec_icmp2008-72293.

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Tuning the plasma field in reactive ion etching generates different etching profile of nanoparticles. For nanoparticles in an isotropic plasma field, there will be uniform shrinkage of the particle sizes due to the isotropic etching, with the curvature of the particles unchanged after the etching. An anisotropic etching, on the other hand, provides rich opportunities to modify the shape of the particles with reduced dimensions. For a monolayer of silica nanoparticles on a flat substrate in a unidirectional plasma field, the reactive ion etching changed the shape of silica nanoparticles from spherical to spheroid-like geometry. The mathematical description of the final spheroid-like geometry was discussed and matched well with the experimental results. The surface curvature of the particles after etching remained the same for both the top and the bottom surfaces, while the overall shape transformed to spheroid-like geometry. Varying the etching time resulted in particles with different height to width ratios. The unique geometry of these non-spherical particles will impact fundament properties of such particles, such as packing and assembly. In the case of spheroid-like particles, packing of such particles into ordered structures will involve an orientational order, which is different from spherical nanoparticles that have no orientational order.
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Pfister, Felix M. J., and Sunil K. Agrawal. "Analytical Dynamics of Unrooted Multibody-Systems With Symmetries." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5869.

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Abstract The objectives of this paper are to (i) exploit the structure of Euler-Liouville equations for multibody systems and separate the external and internal aspects of motion, (ii) specialize these equations to systems with special mass and geometric properties such as holonomoids and orthotropoids, (iii) apply the results to special orthotropoids, the spheroidal linkages of Wohlhart, and write their equations of motion in a simple and elegant manner.
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