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Journal articles on the topic 'Inverse geometry problem'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Karpov, Petr I., and Tatyana Zakharova. "Magnetoencephalography inverse problem in the spheroid geometry." Journal of Inverse and Ill-posed Problems 27, no. 2 (2019): 159–69. http://dx.doi.org/10.1515/jiip-2017-0101.

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AbstractThe inverse problem of magnetoencephalography is ill-posed and difficult for both analytical and numerical solutions. Additional complications arise from the volume (passive) currents and the associated magnetic fields, which strongly depend on the brain geometry. In this paper, we find approximate analytical solutions for the forward and the inverse problems in the spheroid geometry. We compare the obtained results with the exact solution of the forward problem and deduce that for a wide range of parameters our approximation is valid. The analysis sheds new light on the role of the vo

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2

Ivey, Thomas A. "An Inverse Problem from sub-Riemannian geometry." Pacific Journal of Mathematics 208, no. 1 (2003): 111–24. http://dx.doi.org/10.2140/pjm.2003.208.111.

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Solovjeva, Inna A., Denis S. Solovjev, and Yuri V. Litovka. "Solving the Inverse Problem of Recovering the 3D Surface of a Detail According to its 2D Projections in the Modelling of Electroplating Processes." Materials Science Forum 1037 (July 6, 2021): 581–88. http://dx.doi.org/10.4028/www.scientific.net/msf.1037.581.

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The article considers the influence of the surface geometry of a detail on the deposition of coating thickness in the simulation of electroplating processes. The methods for obtaining sets of points describing the surface of a detail are analyzed. Solving the inverse problem (recovering the 3D surface of a detail according to its 2D drawings) is the most promising method. The inverse problem solution is decomposed into simpler geometric problems: input data processing; obtaining primitives; obtaining the desired surface of a detail by applying logical operations to primitives. Mathematical sta

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4

Andrieux, S., and H. D. Bui. "On some nonlinear inverse problems in elasticity." Theoretical and Applied Mechanics 38, no. 2 (2011): 125–54. http://dx.doi.org/10.2298/tam1102125a.

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In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack pl

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Nicolet, Baptiste, Alec Jacobson, and Wenzel Jakob. "Large steps in inverse rendering of geometry." ACM Transactions on Graphics 40, no. 6 (2021): 1–13. http://dx.doi.org/10.1145/3478513.3480501.

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Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to millions of parameters to solve such problems via gradient-based optimization. At the same time, the availability of cheap derivatives does not necessarily make an inverse problem easy to solve. Mesh-based representations remain a particular source of irritation: an adverse gradient step involving vertex positions could turn parts of the mesh i

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Padmanabhan, B., V. Arun, and C. F. Reinholtz. "Closed-Form Inverse Kinematic Analysis of Variable-Geometry Truss Manipulators." Journal of Mechanical Design 114, no. 3 (1992): 438–43. http://dx.doi.org/10.1115/1.2926571.

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A variety of applications for variable-geometry truss manipulators (VGTMs) have been demonstrated or proposed in the literature. Most of these applications require solution to the inverse kinematic problem, yet only a few isolated examples of closed-form solution methods have been presented to date. This paper provides an overview to the general problem of inverse kinematic analysis of variable-geometry truss manipulators and presents new closed-form solution techniques for problems of practical importance.

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BEALS, RICHARD, and PETER C. GREINER. "STRINGS, WAVES, DRUMS: SPECTRA AND INVERSE PROBLEMS." Analysis and Applications 07, no. 02 (2009): 131–83. http://dx.doi.org/10.1142/s0219530509001335.

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This survey treats a number of interconnected topics related in one way or another to the famous paper of Mark Kac, "Can one hear the shape of a drum?": wave motion, classical and quantum inverse problems, integrable systems, and the relations between spectra and geometry. We sketch the history and some of the principal developments from the vibrating string to quantum inverse problems, the KdV equation and integrable systems, spectral geometry and the index problem.

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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 (2006): 3418–28. http://dx.doi.org/10.1109/tap.2006.884292.

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9

Li, Ying, Xiaohuan Mo, and Yaoyong Yu. "Inverse problem of sprays with scalar curvature." International Journal of Mathematics 30, no. 09 (2019): 1950041. http://dx.doi.org/10.1142/s0129167x19500411.

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Every Finsler metric on a differential manifold induces a spray. The converse is not true. Therefore, it is one of the most fundamental problems in spray geometry to determine whether a spray is induced by a Finsler metric which is regular, but not necessary positive definite. This problem is called inverse problem. This paper discuss inverse problem of sprays with scalar curvature. In particular, we show that if such a spray [Formula: see text] on a manifold is of vanishing [Formula: see text]-curvature, but [Formula: see text] has not isotropic curvature, then [Formula: see text] is not indu

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10

Michel, Vincent. "The Two-Dimensional Inverse Conductivity Problem." Journal of Geometric Analysis 30, no. 3 (2019): 2776–842. http://dx.doi.org/10.1007/s12220-018-00139-2.

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11

Henkin, Gennadi, and Vincent Michel. "Inverse Conductivity Problem on Riemann Surfaces." Journal of Geometric Analysis 18, no. 4 (2008): 1033–52. http://dx.doi.org/10.1007/s12220-008-9035-x.

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12

ERCOLESSI, ELISA, and GIUSEPPE MORANDI. "ON THE GEOMETRY OF QUANTUM MECHANICS." International Journal of Geometric Methods in Modern Physics 09, no. 02 (2012): 1260025. http://dx.doi.org/10.1142/s0219887812600250.

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We will present a short review of some work we have done in the last ten years with Giuseppe Marmo, on the attempt to formulate some interesting physical problems — such as the Quantum Inverse Problem, Alternative Structures and Berry Phase — in a geometrical setting.

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13

Szyszkiewicz, K., P. Dziembaj, and R. Filipek. "Heat Transfer And Inverse Problems; Selected Cases In 1D And 3D Geometries / Transport Ciepła I Zagadnienia Odwrotne; Wybrane Przykłady W Geometrii Jedno- I Trójwymiarowej." Archives of Metallurgy and Materials 58, no. 1 (2013): 9–18. http://dx.doi.org/10.2478/v10172-012-0143-z.

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Heat transport phenomena in the framework of continuum media mechanics is presented. Equations for conservation laws and finite volume numerical method based on these equations are discussed. This method is the foundation of the FLUENT computational fluid dynamics (CFD) package which was used for calculations of the temperature distribution in several examples: steady and evolutional states for single and multiphase systems. Comparison with analytical solutions was carried out. This allows verification of the FLUENT results for various boundary conditions. Independent procedure based on the me

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14

Huang, Cheng-Hung, Cheng-Chia Chiang, and Shean-Kwang Chou. "An Inverse Geometry Design Problem in Optimizing Hull Surfaces." Journal of Ship Research 42, no. 02 (1998): 79–85. http://dx.doi.org/10.5957/jsr.1998.42.2.79.

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The technique of the inverse design problem for optimizing the shape of a bow from a specified pressure distribution is presented. This desired pressure distribution can be obtained by modifying the existing pressure distribution of the parent ship. The surface geometry of the ship is generated using the B-spine surface method which enables the shape of the hull to be completely specified using only a small number of parameters (i.e. control points). The technique of parameter estimation for the inverse problem is thus chosen. Results show that the accuracy of the final desired ship form depen

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15

Sten, Johan C. E., and Edwin A. Marengo. "Inverse Source Problem in the Spheroidal Geometry: Vector Formulation." IEEE Transactions on Antennas and Propagation 56, no. 4 (2008): 961–69. http://dx.doi.org/10.1109/tap.2008.919176.

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16

Huang, Cheng-Hung, and Bor-Herng Chao. "An inverse geometry problem in identifying irregular boundary configurations." International Journal of Heat and Mass Transfer 40, no. 9 (1997): 2045–53. http://dx.doi.org/10.1016/s0017-9310(96)00280-3.

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17

Gonzalez, Marcial, and Marcela B. Goldschmit. "Inverse geometry heat transfer problem based on a radial basis functions geometry representation." International Journal for Numerical Methods in Engineering 65, no. 8 (2006): 1243–68. http://dx.doi.org/10.1002/nme.1487.

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18

Romanov, Vladimir. "AN INVERSE PROBLEM FOR A NONLINEAR WAVE EQUATION WITH DAMPING." Eurasian Journal of Mathematical and Computer Applications 11, no. 2 (2023): 99–115. http://dx.doi.org/10.32523/2306-6172-2023-11-2-99-115.

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We consider an inverse problem of recovering two coefficients in a semi-linear wave equation. This equation contains a damping term and a term with a quadratic nonlinearity. The inverse problem consists in recovering coefficients under these terms as function of the space variable x ∈ R 3 . A forward problem for the equation with a point source is studied. As a result, the inverse problem reduce to two problems, one of them is the well known problem of X-ray tomography, the other one is the problem of the integral geometry with a with a special weight function. The latter problem is studied an

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19

Ciaglia, F. M., G. Marmo, and J. M. Pérez-Pardo. "Generalized potential functions in differential geometry and information geometry." International Journal of Geometric Methods in Modern Physics 16, supp01 (2019): 1940002. http://dx.doi.org/10.1142/s0219887819400024.

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Potential functions can be used for generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study whether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.

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20

Hatamleh, R., and V. A. Zolotarev. "On the Abstract Inverse Scattering Problem for Trace Class Perturbations." Zurnal matematiceskoj fiziki, analiza, geometrii 13, no. 1 (2017): 3–34. http://dx.doi.org/10.15407/mag13.01.003.

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21

Kang, Jeong Gi. "In Newton’s proof of the inverse square law, geometric limit analysis and Educational discussion." Korean School Mathematics Society 24, no. 2 (2021): 173–90. http://dx.doi.org/10.30807/ksms.2021.24.2.001.

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This study analyzed the proof of the inverse square law, which is said to be the core of Newton's <Principia>, in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximatio

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22

Nelson, Garcia Roman, Costas dos Santos Pedro, and Henrique de Almeida Konzen Pedro. "ANN-MoC Method for Inverse Transient Transport Problems in One-Dimensional Geometry." Latin-American Journal of Computing 11, no. 2 (2024): 41–50. https://doi.org/10.5281/zenodo.12191947.

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Transport problems of neutral particles have important applications in engineering and medical fields, from safety and quality protocols to optical medical procedures. In this paper, the ANN-MoC approach is proposed to solve the inverse transient transport problem of estimating the absorption coefficient from scalar flux measurements at the boundaries of the model domain. The central idea is to fit an Artificial Neural Network (ANN) using samples generated by direct solutions computed by a Method of Characteristics (MoC) solver. The direct solver validation is performed on a manufactured solut

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23

Huiskamp, G., and A. van Oosterom. "Tailored versus realistic geometry in the inverse problem of electrocardiography." IEEE Transactions on Biomedical Engineering 36, no. 8 (1989): 827–35. http://dx.doi.org/10.1109/10.30808.

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24

Dalalyan, Arnak, and Renaud Keriven. "Robust Estimation for an Inverse Problem Arising in Multiview Geometry." Journal of Mathematical Imaging and Vision 43, no. 1 (2011): 10–23. http://dx.doi.org/10.1007/s10851-011-0281-3.

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25

Tenzer, Robert. "Gravimetric recovery of the Moho geometry based on a generalized compensation model." Contributions to Geophysics and Geodesy 43, no. 4 (2013): 253–69. http://dx.doi.org/10.2478/congeo-2013-0016.

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Abstract Gravity data used for a recovery of the Moho depths should (optimally) comprise only the gravitational signal of the Moho geometry. This theoretical assumption is typically not required in classical isostatic models, which are applied in gravimetric inverse methods for a recovery of the Moho interface. To overcome this theoretical deficiency, we formulate the gravimetric inverse problem for the consolidated crust-stripped gravity disturbances, which have (theoretically) a maximum correlation with the Moho geometry, while the gravitational contributions of anomalous density structures

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26

HOJMAN, SERGIO A., J. GAMBOA, and F. MÉNDEZ. "DYNAMICS DETERMINES GEOMETRY." Modern Physics Letters A 27, no. 33 (2012): 1250186. http://dx.doi.org/10.1142/s0217732312501866.

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The inverse problem of calculus of variations and s-equivalence are re-examined by using results obtained from non-commutative geometry ideas. The role played by the structure of the modified Poisson brackets is discussed in a general context and it is argued that classical s-equivalent systems may be non-equivalent at the quantum mechanical level. This last fact is explicitly discussed comparing different approaches to deal with the Nair–Polychronakos oscillator.

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27

Son, Tran Dinh. "Pentagoning the Circle with Straightedge & Compass." Scholars Journal of Physics, Mathematics and Statistics 11, no. 09 (2024): 101–7. http://dx.doi.org/10.36347/sjpms.2024.v11i09.001.

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This study idea came from the exact solution “Circling the Regular Pentagon with Straightedge & compass in Euclidean Geometry”, published by the Scholars Journal of Physics, Mathematics and Statistics on 22/08/2024 [1]. In this research, the ANALYSIS method is adopted to prove the process of solving this new challenge problem, which has not existed in the Mathematics field till today. The process is an inverse/converse solution solving the inverse problem “Circling the Regular Pentagon with Straightedge & compass in Euclidean Geometry” problem, using a straightedge & a compass. I h

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28

Curtis, Andrew, and Roel Snieder. "Reconditioning inverse problems using the genetic algorithm and revised parameterization." GEOPHYSICS 62, no. 5 (1997): 1524–32. http://dx.doi.org/10.1190/1.1444255.

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The better conditioned an inverse problem is, the more independent pieces of information may be transferred from the data to the model solution, and the less independent prior information must be added to resolve trade offs. We present a practical measure of conditioning that may be calculated swiftly even for large inverse problems. By minimizing this measure, a genetic algorithm can be used to find a model parameterization that gives the best conditioned inverse problem. We illustrate the method by finding an optimal, irregular cell parameterization for a cross‐borehole tomographic example w

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Wang, Shoubin, Yunlong Li, Guili Peng, Wenbin Xu, Xuejun Zhou, and Yongqiang ju. "Research on geometric inverse problem based on the firefly conjugate gradient method." Thermal Science, no. 00 (2023): 57. http://dx.doi.org/10.2298/tsci221230057w.

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In this paper the two-dimensional steady-state heat transfer geometric inverse problem is solved using the Finite Element Method (FEM), Conjugate Gradient Method (CGM), and Firefly Algorithm (FA). Based on the finite element method for solving the forward heat transfer model, and based on continuous iterative optimisation of the conjugate gradient method, the accuracy of the error function of the measured and estimated values is kept within a certain range, so that the geometry of the object under test can be calculated in an inverse way. In the study of the forward problem, the temperature fi

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30

Burnett, Christopher L., Darryl D. Holm, and David M. Meier. "Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2160 (2013): 20130249. http://dx.doi.org/10.1098/rspa.2013.0249.

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We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler–Lagrange equations is obtained from a higher-order Hamilton–Pontryagin variational formulation. In this context, the previou

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Hart, John C., Wayne O. Cochran, and Patrick J. Flynn. "Similarity Hashing: A Computer Vision Solution to the Inverse Problem of Linear Fractals." Fractals 05, supp01 (1997): 39–50. http://dx.doi.org/10.1142/s0218348x97000620.

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The difficult task of finding a fractal representation of an input shape is called the inverse, problem of fractal geometry. Previous attempts at solving this problem have applied techniques from numerical minimization, heuristic search and image compression. The most appropriate domain from which to attack this problem is not numerical analysis nor signal processing, but model-based computer vision. Self-similar objects cause an existing computer vision algorithm called geometric hashing to malfunction. Similarity hashing capitalizes on this observation to not only detect a shape's morphologi

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32

Escudero González, Ruben, Zulima Fernández Muñiz, Antonio Bernardo Sánchez, and Juan Luis Fernández Martínez. "Inverse Gravimetric Problem Solving via Prolate Ellipsoidal Parameterization and Particle Swarm Optimization." Mathematics 13, no. 12 (2025): 2017. https://doi.org/10.3390/math13122017.

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We present a method for 3D gravity inversion using ellipsoidal parametrization and Particle Swarm Optimization (PSO), aimed at estimating the geometry, density contrast, and orientation of subsurface bodies from gravity anomaly data. The subsurface is modeled as a set of prolate ellipsoids whose parameters are optimized to minimize the misfit between observed and predicted anomalies. This approach enables efficient forward modeling with closed-form solutions and allows the incorporation of geometric and physical constraints. The algorithm is first validated on synthetic models with Gaussian no

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33

Ljujić, Željka, and Camilo Sanabria. "A note on an inverse problem for lattice points." Topology and its Applications 158, no. 8 (2011): 1012–18. http://dx.doi.org/10.1016/j.topol.2011.02.005.

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34

Romanov, V. G. "AN INVERSE PROBLEM FOR THE WAVE EQUATION WITH TWO NONLINEAR TERMS." Дифференциальные уравнения 60, no. 4 (2024): 508–20. http://dx.doi.org/10.31857/s0374064124040061.

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An inverse problem for a hyperbolic equation of the second order containing two nonlinear terms is studied. It consists in recovering coefficients under nonlinearities. The Cauchy problem with a point source located at point y is considered. This point is a parameter of the problem and runs an spherical surface ???? successively. It is supposed that unknown coefficients are differed from zero in domain be situated inside of ???? only. The trace of a solution of the Cauchy problem is given on ???? for all values of y and for all times closed to moments of arriving of the wave from y to points o

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35

Mavroidis, C., F. B. Ouezdou, and P. Bidaud. "Inverse kinematics of six-degree of freedom “general” and “special” manipulators using symbolic computation." Robotica 12, no. 5 (1994): 421–30. http://dx.doi.org/10.1017/s0263574700017975.

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SUMMARYThis paper presents an algorithm that solves the inverse kinematics problem of all six degrees of freedom manipulators, “general” or “special”. A manipulator is represented by a chain of characters that symbolizes the position of prismatic and revolute joints in the manipulator and the special geometry that may exist between its joint axes. One form of the loop closure equation is chosen and the Raghavan and Roth method is used to obtain symbolically a square matrix. The determinant of this matrix yields the characteristic polynomial of the manipulator in one of the kinematic variables.

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36

Amirov, Arif, Fikret Gölgeleyen, and Masahiro Yamamoto. "Uniqueness in an integral geometry problem and an inverse problem for the kinetic equation." Applicable Analysis 96, no. 13 (2016): 2236–49. http://dx.doi.org/10.1080/00036811.2016.1213387.

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37

Lee, Hong-You, and Charles F. Reinholtz. "Inverse Kinematics of Serial-Chain Manipulators." Journal of Mechanical Design 118, no. 3 (1996): 396–404. http://dx.doi.org/10.1115/1.2826899.

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This paper proposes a unified method for the complete solution of the inverse kinematics problem of serial-chain manipulators. This method reduces the inverse kinematics problem for any 6 degree-of-freedom serial-chain manipulator to a single univariate polynomial of minimum degree from the fewest possible closure equations. It is shown that the univariate polynomials of 16th degree for the 6R, 5R-P and 4R-C manipulators with general geometry can be derived from 14, 10 and 6 closure equations, respectively, while the 8th and 4th degree polynomials for all the 4R-2P, 3R-P-C, 2R-2C, 3R-E and 3R-

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Jolly, Jean-Claude, Laetitia Perez, and Laurent Autrique. "Inverse geometry problem for a 1D heat equation: a globality criterion." IFAC Proceedings Volumes 46, no. 12 (2013): 41–46. http://dx.doi.org/10.3182/20130703-3-fr-4039.00021.

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Huiskamp, G., M. Vroeijenstijn, R. van Dijk, G. Wieneke, and A. C. van Huffelen. "The need for correct realistic geometry in the inverse EEG problem." IEEE Transactions on Biomedical Engineering 46, no. 11 (1999): 1281–87. http://dx.doi.org/10.1109/10.797987.

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40

Vásárhelyi, Gábor, Balázs Fodor, and Tamás Roska. "Tactile sensing-processing: Interface-cover geometry and the inverse-elastic problem." Sensors and Actuators A: Physical 140, no. 1 (2007): 8–18. http://dx.doi.org/10.1016/j.sna.2007.05.028.

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41

Duda, Piotr. "Solution of an inverse axisymmetric heat conduction problem in complicated geometry." International Journal of Heat and Mass Transfer 82 (March 2015): 419–28. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.11.002.

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42

Huang, Cheng-Hung, and Meng-Ting Chaing. "A three-dimensional inverse geometry problem in identifying irregular boundary configurations." International Journal of Thermal Sciences 48, no. 3 (2009): 502–13. http://dx.doi.org/10.1016/j.ijthermalsci.2008.05.007.

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43

Vagin, Denis. "The structure and features of the software for geophysical geometrical 3D inversions." Analysis and data processing systems, no. 2 (June 18, 2021): 35–46. http://dx.doi.org/10.17212/2782-2001-2021-2-35-46.

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The structure and features of a software package for 3D inversion of geophysical data are considered. The presented software package is focused on solving direct and inverse problems of electrical exploration and engineering geophysics. In addition to the parameters that determine physical properties of the medium, the software package allows you to restore the geometry parameters of the geophysical model, namely layer reliefs and boundaries of three-dimensional inclusions. The inclusions can be in the form of arbitrary hexagons or prisms with a polygonal base. The software package consists of

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44

Son, Tran Dinh. "Circling the Square with Straightedge & Compass in Euclidean Geometry." Scholars Journal of Physics, Mathematics and Statistics 11, no. 05 (2024): 54–64. http://dx.doi.org/10.36347/sjpms.2024.v11i05.001.

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There are three classical problems remaining from ancient Greek mathematics which are extremely influential in the development of Geometry. They are Trisecting an Angle, Squaring the Circle, and Doubling the Cube problems. I solve the Squaring the Circle problem, of which paper is published in the International Journal of Mathematics Trends and Technology (Volume 69, June 2023). Upstream from this method of exact “Squaring the Circle”, we can deduce, conversely/inversely, to get a new Mathematical challenge "CIRCLING THE SQUARE" with a straightedge & a compass in Euclidean Geometry. This s

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45

Marin, Rodrigo A., and Placid M. Ferreira. "Analysis of the Influence of Fixture Locator Errors on the Compliance of Work Part Features to Geometric Tolerance Specifications." Journal of Manufacturing Science and Engineering 125, no. 3 (2003): 609–16. http://dx.doi.org/10.1115/1.1578669.

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A machining fixture controls position and orientation of datum references (used to define important functional features of the geometry of a mechanical part) relative the reference frame for an NC program. Inaccuracies in fixture’s location scheme result in a deviation of the work part from its nominal specified geometry. For a part to be acceptable this deviation must be within the limits allowed by the geometric tolerances specified. This paper addresses the problem of characterizing the acceptable level of inaccuracy in the location scheme so that the features machined on the part comply wi

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46

Baddoo, P. J., and L. J. Ayton. "Potential flow through a cascade of aerofoils: direct and inverse problems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2217 (2018): 20180065. http://dx.doi.org/10.1098/rspa.2018.0065.

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The potential flow through an infinite cascade of aerofoils is considered as both a direct and inverse problem. In each case, a perturbation expansion about a background uniform flow is assumed where the size of the perturbation is comparable to the aspect ratio of the aerofoils. This perturbation must decay far upstream and also satisfy particular edge conditions, including the Kutta condition at each trailing edge. In the direct problem, the flow field through a cascade of aerofoils of known geometry is calculated. This is solved analytically by recasting the situation as a Riemann–Hilbert p

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Krishna, Arvind, Steven R. Craig, Chengzhi Shi, and V. Roshan Joseph. "Inverse design of acoustic metasurfaces using space-filling points." Applied Physics Letters 121, no. 7 (2022): 071701. http://dx.doi.org/10.1063/5.0096869.

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Acoustic metasurfaces are two-dimensional materials that impart non-trivial amplitude and phase shifts on incident acoustic waves at a predetermined frequency. While acoustic metasurfaces enable extraordinary wavefront engineering capabilities, they are not developed well enough to independently control the amplitude and phase of reflected and transmitted acoustic waves simultaneously, which are governed by their geometry. We aim to solve the inverse design problem of finding a geometry to achieve a specified set of acoustic properties. The geometry is modeled by discretizing the continuous sp

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Drexler, Dániel András. "Regularization of the Spatial Inverse Positioning Problem of Revolute Joint Manipulators." Periodica Polytechnica Electrical Engineering and Computer Science 61, no. 3 (2017): 279. http://dx.doi.org/10.3311/ppee.8607.

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Inverse kinematics is a central problem in robotics, and its solution is burdened with kinematic singularities, i.e. the task Jacobian of the problem is singular. A subproblem of the general inverse kinematics problem, the inverse positioning problem is considered for spatial manipulators consisting of revolute joints, and a regularization method is proposed that results in a regular task Jacobian in singular configurations as well, provided that the manipulator’s geometry makes movement in singular directions possible. The conditions of regularizability are investigated, and bounds on the sin

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de León, Manuel, Jordi Gaset, and Manuel Lainz. "Inverse problem and equivalent contact systems." Journal of Geometry and Physics 176 (June 2022): 104500. http://dx.doi.org/10.1016/j.geomphys.2022.104500.

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Fikal, Najib, Rajae Aboulaich, El Mahdi El Guarmah, and Nejib Zemzemi. "Propagation of two independent sources of uncertainty in the electrocardiography imaging inverse solution." Mathematical Modelling of Natural Phenomena 14, no. 2 (2019): 206. http://dx.doi.org/10.1051/mmnp/2018065.

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This study investigates the effects of the input parameter uncertainties (organ conductivities, boundary data, etc.) on the electrocardiography (ECG) imaging problem. These inputs are very important for the construction of the torso potential for the forward problem and for the non-invasive electrical potential on the heart surface in the case of the inverse problem. We propose a new stochastic formulation that allows us to combine both sources of errors. We formulate the forward and inverse stochastic problems by considering the input parameters as random fields and a stochastic optimal contr

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