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Journal articles on the topic 'Inhomogeneous matrices'

Author: Grafiati

Published: 26 October 2024

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1

Lu, Shih-Yau, and Russell A. Chipman. "Homogeneous and inhomogeneous Jones matrices." Journal of the Optical Society of America A 11, no. 2 (February 1, 1994): 766. http://dx.doi.org/10.1364/josaa.11.000766.

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2

Szwarc, Ryszard. "Inhomogeneous Jacobi Matrices on Trees." Constructive Approximation 48, no. 2 (May 7, 2018): 183–99. http://dx.doi.org/10.1007/s00365-018-9430-x.

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3

Alt, Johannes, and Torben Krüger. "Inhomogeneous circular law for correlated matrices." Journal of Functional Analysis 281, no. 7 (October 2021): 109120. http://dx.doi.org/10.1016/j.jfa.2021.109120.

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4

Yang, Z. L., J. W. Zhang, and Y. Wang. "Dynamic Inhomogeneous Isoparametric Element with Coordinate Transformation." Journal of Mechanics 32, no. 3 (December 11, 2015): 289–96. http://dx.doi.org/10.1017/jmech.2015.99.

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AbstractBased on the coordinate transformation method, the formula of the dynamic inhomogeneous isoparametric finite element method is presented for generating element stiffness, damping and mass matrices. First, the global coordinate form and simplified form of dynamic inhomogeneous finite element are given in this paper. Then, the discrete material parameter distributions under the isoparametric coordinate system are obtained by using the transformation relationship between the global coordinates and the isoparametric coordinates. The simplified form with the discrete material parameter distributions is obtained for generating the element stiffness and mass matrices of the dynamic inhomogeneous isoparametric element. The numerical examples show that the scheme proposed in present paper has high precision.

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5

S. Fox, Matthew. "Inhomogeneous Connotations across Square, Stoichiometrically-Based Matrices." American Journal of Applied Mathematics and Statistics 3, no. 4 (July 11, 2015): 142–45. http://dx.doi.org/10.12691/ajams-3-4-1.

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6

Chen, Bin, and Ke Wu. "R-Matrices for Some Inhomogeneous Quantum Groups." Communications in Theoretical Physics 21, no. 3 (April 30, 1994): 303–10. http://dx.doi.org/10.1088/0253-6102/21/3/303.

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7

Li, Wenxi, and Zhongzhi Wang. "A NOTE ON RÉNYI'S ENTROPY RATE FOR TIME-INHOMOGENEOUS MARKOV CHAINS." Probability in the Engineering and Informational Sciences 33, no. 4 (December 5, 2018): 579–90. http://dx.doi.org/10.1017/s026996481800044x.

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AbstractIn this note, we use the Perron–Frobenius theorem to obtain the Rényi's entropy rate for a time-inhomogeneous Markov chain whose transition matrices converge to a primitive matrix. As direct corollaries, we also obtain the Rényi's entropy rate for asymptotic circular Markov chain and the Rényi's divergence rate between two time-inhomogeneous Markov chains.

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8

Davidovich, M. V. "Scattering and transmission matrices of an inhomogeneous layer." Journal of Communications Technology and Electronics 55, no. 1 (January 2010): 20–27. http://dx.doi.org/10.1134/s1064226910010031.

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9

Lan, Nguyen Thanh, and Gregor Nickel. "Time-dependent operator matrices and inhomogeneous Cauchy problems." Rendiconti del Circolo Matematico di Palermo 47, no. 1 (January 1998): 5–24. http://dx.doi.org/10.1007/bf02844719.

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10

Loco, Daniele, Sandro Jurinovich, Lorenzo Cupellini, Maximilian F. S. J. Menger, and Benedetta Mennucci. "The modeling of the absorption lineshape for embedded molecules through a polarizable QM/MM approach." Photochemical & Photobiological Sciences 17, no. 5 (2018): 552–60. http://dx.doi.org/10.1039/c8pp00033f.

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11

Delgado, Jorge, Guillermo Peña, and Juan Manuel Peña. "Green Matrices, Minors and Hadamard Products." Axioms 12, no. 8 (August 10, 2023): 774. http://dx.doi.org/10.3390/axioms12080774.

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Green matrices are interpreted as discrete version of Green functions and are used when working with inhomogeneous linear system of differential equations. This paper discusses accurate algebraic computations using a recent procedure to achieve an important factorization of these matrices with high relative accuracy and using alternative accurate methods. An algorithm to compute any minor of a Green matrix with high relative accuracy is also presented. The bidiagonal decomposition of the Hadamard product of Green matrices is obtained. Illustrative numerical examples are included.

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12

Akram, Faiza. "The Non-homogeneous Groshev Convergence theorem for Diophantine Approximation on Manifolds." JOURNAL OF ADVANCES IN MATHEMATICS 13, no. 4 (October 26, 2017): 7354–69. http://dx.doi.org/10.24297/jam.v13i4.6352.

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This paper is based on Khintchine theorem, Groshev theorem and measure and dimension theorems for non-degenerate manifolds. The inhomogeneous Diophantine approximation of Groshev type on manifolds is studied. Major work is to discuss the inhomogeneous convergent theory of Diophantine approximation restricted to non-degenerate manifold in , based on the proof of Barker-Sprindzuk conjecture, the homogeneous theory of Diophantine approximation and inhomogeneous Groshev type theory for Diophantine approximation, by the decomposition of the set in manifold, with the aid of Borel Cantell lemma and transformation of lemma and its properties and the main inhomogeneous conversion principle, we know these two types of set in sense of Lebesgue measure is zero provided that the convergent sum condition is satisfied, from which several conclusions about the inhomogeneous convergent theory of Diophantine approximation is obtained. The main result is that Lebesgue measure is inhomogeneous strongly extremal. At last we use the fact that friendly measure is strongly contracting measure to develop an inhomogeneous strong extreme measure which is restricted to matrices with dependent quantities

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13

Dmitriev, K. V. "Object structure reconstruction using correlation processing of the acoustic field of active noise sources." Известия Российской академии наук. Серия физическая 87, no. 1 (January 1, 2023): 79–83. http://dx.doi.org/10.31857/s0367676522700144.

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The iterative algorithm is proposed for reconstructing the acoustic characteristics of an inhomogeneous medium based on the values of the coherence matrices obtained at several exposure angles using noise signals. Numerical simulations show good quality and fast convergence of the resulting estimates.

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14

Červený, Vlastislav, and Tijmen Jan Moser. "Ray propagator matrices in three-dimensional anisotropic inhomogeneous layered media." Geophysical Journal International 168, no. 2 (February 2007): 593–604. http://dx.doi.org/10.1111/j.1365-246x.2006.03141.x.

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15

Norris, A. N., and A. L. Shuvalov. "Wave Impedance Matrices for Cylindrically Anisotropic Radially Inhomogeneous Elastic Solids." Quarterly Journal of Mechanics and Applied Mathematics 63, no. 4 (July 22, 2010): 401–35. http://dx.doi.org/10.1093/qjmam/hbq010.

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16

Kazem, Saeed, Malihe Shaban, and Jamal Amani Rad. "Solution of the Coupled Burgers Equation Based on Operational Matrices of d-Dimensional Orthogonal Functions." Zeitschrift für Naturforschung A 67, no. 5 (May 1, 2012): 267–74. http://dx.doi.org/10.5560/zna.2012-0026.

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This paper aims to construct a general formulation for the d-dimensional orthogonal functions and their derivative and product matrices. These matrices together with the Tau method are utilized to reduce the solution of partial differential equations (PDEs) to the solution of a system of algebraic equations. The proposed method is applied to solve homogeneous and inhomogeneous two-dimensional parabolic equations. Also, the mentioned method is employed to find the solution of the coupled Burgers equation. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

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17

Lim, Su, and Kwang Shon. "Regular functions with values in a noncommutative algebra using Clifford analysis." Filomat 30, no. 7 (2016): 1747–55. http://dx.doi.org/10.2298/fil1607747l.

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We construct a noncommutative algebra C(2) that is a subalgebra of the Pauli matrices of M(2;C), and investigate the properties of solutions with values in C(2) of the inhomogeneous Cauchy-Riemann system of partial differential equations with coefficients in the associated Pauli matrices. In addition, we construct a commutative subalgebra C(4) of M(4;C), obtain some properties of biregular functions with values in C(2) on in C2 x C2, define a J-regular function of four complex variables with values in C(4), and examine some properties of J-regular functions of partial differential equations.

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18

Jain, Vishesh, and Sandeep Silwal. "A note on the universality of ESDs of inhomogeneous random matrices." Latin American Journal of Probability and Mathematical Statistics 18, no. 1 (2021): 1047. http://dx.doi.org/10.30757/alea.v18-39.

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19

Gutiérrez-Vega, Julio C. "Optical phase of inhomogeneous Jones matrices: retardance and ortho-transmission states." Optics Letters 45, no. 7 (March 17, 2020): 1639. http://dx.doi.org/10.1364/ol.387644.

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20

Orso, Joseph, and Anthony J. Vizzini. "Stress Effects of Inhomogeneous Expansion-Controlled Matrices in Continuous Fiber Composites." Journal of Composite Materials 29, no. 15 (October 1995): 2003–24. http://dx.doi.org/10.1177/002199839502901504.

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21

Gil, José J., and Ignacio San José. "Synthetic Mueller Imaging Polarimetry." Photonics 10, no. 9 (August 24, 2023): 969. http://dx.doi.org/10.3390/photonics10090969.

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The transformation of the state of polarization of a light beam via its linear interaction with a material medium can be modeled through the Stokes–Mueller formalism. The Mueller matrix associated with a given interaction depends on many aspects of the measurement configuration. In particular, different Mueller matrices can be measured for a fixed material sample depending on the spectral profile of the light probe. For a given light probe and a given sample with inhomogeneous spatial behavior, the polarimetric descriptors of the point-to-point Mueller matrices can be mapped, leading to respective polarimetric images. The procedure can be repeated sequentially using light probes with different central frequencies. In addition, the point-to-point Mueller matrices, consecutively measured, can be combined synthetically through convex sums leading to respective new Mueller matrices, in general with increased polarimetric randomness, thus exhibiting specific values for the associated polarimetric descriptors, including the indices of polarimetric purity, and generating new polarimetric images which are different from those obtained from the original Mueller matrices. In this work, the fundamentals for such synthetic generation of additional polarimetric images are described, providing a new tool that enhances the exploitation of Mueller polarimetry.

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22

Chakrabarty, Arijit, Rajat Subhra Hazra, Frank den Hollander, and Matteo Sfragara. "Spectra of adjacency and Laplacian matrices of inhomogeneous Erdős–Rényi random graphs." Random Matrices: Theory and Applications 10, no. 01 (December 4, 2019): 2150009. http://dx.doi.org/10.1142/s201032632150009x.

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This paper considers inhomogeneous Erdős–Rényi random graphs [Formula: see text] on [Formula: see text] vertices in the non-sparse non-dense regime. The edge between the pair of vertices [Formula: see text] is retained with probability [Formula: see text], [Formula: see text], independently of other edges, where [Formula: see text] is a continuous function such that [Formula: see text] for all [Formula: see text]. We study the empirical distribution of both the adjacency matrix [Formula: see text] and the Laplacian matrix [Formula: see text] associated with [Formula: see text], in the limit as [Formula: see text] when [Formula: see text] and [Formula: see text]. In particular, we show that the empirical spectral distributions of [Formula: see text] and [Formula: see text], after appropriate scaling and centering, converge to deterministic limits weakly in probability. For the special case where [Formula: see text] with [Formula: see text] a continuous function, we give an explicit characterization of the limiting distributions. Furthermore, we apply our results to constrained random graphs, Chung–Lu random graphs and social networks.

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23

Carron, Julien. "Real-world CMB lensing quadratic estimator power spectrum response." Journal of Cosmology and Astroparticle Physics 2023, no. 02 (February 1, 2023): 057. http://dx.doi.org/10.1088/1475-7516/2023/02/057.

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Abstract I describe a method to estimate response matrices of Cosmic Microwave Background (CMB) lensing power spectra estimators to the true sky power under realistic conditions. Applicable to all lensing reconstruction pipelines based on quadratic estimators (QE), it uses a small number of Gaussian CMB Monte-Carlos and specially designed QE's in order to obtain sufficiently accurate matrices with little computational effort. This method may be used to improve the modelling of CMB lensing band-powers by incorporating at least some of the non-idealities encountered in CMB lensing reconstruction. These non-idealities always include masking, and often inhomogeneous filtering, either in the harmonic domain or pixel space. I obtain these matrices for Planck latest lensing reconstructions, and then show that the residual couplings induced by masking explain very well the residual multiplicative bias seen on the Planck simulations, removing the need for an empirical correction.

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24

Wang, Xiao, Juan Wang, Xin Wang, and Chujun Yu. "A Pseudo-Spectral Fourier Collocation Method for Inhomogeneous Elliptical Inclusions with Partial Differential Equations." Mathematics 10, no. 3 (January 19, 2022): 296. http://dx.doi.org/10.3390/math10030296.

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Inhomogeneous elliptical inclusions with partial differential equations have aroused appreciable concern in many disciplines. In this paper, a pseudo-spectral collocation method, based on Fourier basis functions, is proposed for the numerical solutions of two- (2D) and three-dimensional (3D) inhomogeneous elliptic boundary value problems. We describe how one can improve the numerical accuracy by making some extra “reconstruction techniques” before applying the traditional Fourier series approximation. After the particular solutions have been obtained, the resulting homogeneous equation can then be calculated using various boundary-type methods, such as the method of fundamental solutions (MFS). Using Fourier basis functions, one does not need to use large matrices, making accrual computations relatively fast. Three benchmark numerical examples involving Poisson, Helmholtz, and modified-Helmholtz equations are presented to illustrate the applicability and accuracy of the proposed method.

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25

Eu, Byung Chan. "A novel method of inversion for a class of matrices: application to calculation of two-component plasma viscosities in a magnetic field." Canadian Journal of Chemistry 68, no. 7 (July 1, 1990): 1072–76. http://dx.doi.org/10.1139/v90-166.

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To calculate transport coefficients for a plasma in a magnetic field in a linear approximation it is necessary to invert matrices of fairly high dimensions. In this paper we present a novel method of inverting matrices involved in such problems. The method requires a solution of an inhomogeneous matrix integral equation in the Neumann series and a resummation of the series obtained. It involves inversions of lower order matrices, which can be achieved easily. We then apply the method to calculate viscosities of a two-component plasma subject to a homogeneous magnetic field. The structure of the viscosity matrix (tensor) calculated thereby is shown to be the same as that of a neutral system with an axial symmetry; namely, it can be decomposed into a scalar, a 2 × 2 matrix, and a 3 × 3 matrix. The method developed here can be applied to calculate other transport coefficients of the two-component plasma. Keywords: mathematical method, viscosity, plasmas, transport coefficients, kinetic theory.

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26

Amel’kin, V. V., M. N. Vasilevich, and L. A. Khvostchinskaya. "On one approach to the solution of miscellaneous problems of the theory of elasticity." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, no. 3 (October 7, 2021): 263–73. http://dx.doi.org/10.29235/1561-2430-2021-57-3-263-273.

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Herein, a miscellaneous contact problem of the theory of elasticity in the upper half-plane is considered. The boundary is a real semi-axis separated into four parts, on each of which the boundary conditions are set for the real or imaginary part of two desired analytical functions. Using new unknown functions, the problem is reduced to an inhomogeneous Riemann boundary value problem with a piecewise constant 2 × 2 matrix and four singular points. A diﬀerential equation of the Fuchs class with four singular points is constructed, the residue matrices of which are found by the logarithm method of the product of matrices. The single solution of the problem is represented in terms of Cauchy-type integrals when the solvability condition is met.

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27

FISHER, ALBERT M. "NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS." Stochastics and Dynamics 09, no. 03 (September 2009): 335–91. http://dx.doi.org/10.1142/s0219493709002701.

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We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

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28

Crépin, C., M. Broquier, H. Dubost, D. L'hermite, A. Tramer, J. P. Galaup, J. M. Berset, and J. M. Ortega. "Vibrational Dynamics in Molecular Condensed Phases With The Clio Free Electron Laser." Laser Chemistry 19, no. 1-4 (January 1, 1999): 65–69. http://dx.doi.org/10.1155/1999/95804.

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Single color pump-probe and photon-echo experiments have been performed on the CO stretching mode of W(CO)6 at about 1983 cm-1 in various liquids and solid environments. Combined with absorption data, the measured T1 and T2 times suggest the following conclusions: in all liquids studied, the IR absorption band is homogeneously broadened, whereas, inhomogeneous broadening is observed in solid matrices and in a xerogel. At low temperature, the echo decay is much faster in methane than in argon host.

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29

Parschau, Mirco. "Reconstruction of Λ hyperons in an inhomogeneous magnetic field with a Kalman Filter based tracking algorithm." EPJ Web of Conferences 295 (2024): 03033. http://dx.doi.org/10.1051/epjconf/202429503033.

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The high interaction rate, fixed target experiment HADES at GSI, located in Darmstadt, Germany, investigates collisions of heavy-ion, proton and secondary pion beams with a target material. Hyperons are one of the key observables for both heavy-ion and elementary collisions [1] [2]. The challenge is to detect displaced vertices with good accuracy without having a dedicated vertex detector, by employing state-of-the-art techniques. In this contribution we discuss a newly developed tracking algorithm that uses both a Kalman Filter (KF) and the high performance KF Particle package to further boost the reconstruction performance for hyperon decays with displaced vertices [3]. With the use of the covariance matrices, which take into account effects from multiple scattering and energy loss of the particles in the material, the reconstruction performance of the tracking algorithm can be significantly improved. The KF Particle utilises these covariance matrices together with its own internal KF to reconstruct primary and secondary decay vertices.

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30

Moradian, M., and M. Khalaj-Amirhosseini. "Numerical Analysis of Inhomogeneous Dielectric Waveguide Using Periodic Fourier Transform." International Journal of Microwave Science and Technology 2007 (March 11, 2007): 1–5. http://dx.doi.org/10.1155/2007/85181.

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A general method is introduced to obtain the propagation constants of the inhomogeneous dielectric waveguide. The periodic Fourier transform is applied to the normalized Maxwell's equations and makes the field components periodic. Then they are expanded in Fourier series. Finally, the trapezoidal rule is applied to approximate the convolution integral which leads to a set of coupled second-order differential equations that can be solved as an eigenvalue-eigenvector problem. The normalized propagation constant can be obtained as the square roots of the eigenvalues of the coefficient matrices. The proposed method is applied to the dielectric waveguide with a two-layered dielectric profile in the transverse direction, and the first four-confined TE modes are obtained. The propagation constants for the mentioned dielectric waveguide are also derived analytically and are then compared with those derived by the proposed method. Comparison of results shows the efficacy of the proposed method.

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31

Jankoski, Radoslav, Ulrich Römer, and Sebastian Schöps. "Modeling of spatial uncertainties in the magnetic reluctivity." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 4 (July 3, 2017): 1151–67. http://dx.doi.org/10.1108/compel-10-2016-0438.

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Purpose The purpose of this paper is to present a computationally efficient approach for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines such as a single-phase transformer (a benchmark example that is considered in this paper). The approach is based on the Karhunen–Loève expansion (KLE). The stochastic model is further used to study the statistics of the self-inductance of the primary coil as a quantity of interest (QoI). Design/methodology/approach The computation of the KLE requires solving a generalized eigenvalue problem with dense matrices. The eigenvalues and the eigenfunction are computed by using the Lanczos method that needs only matrix vector multiplications. The complexity of performing matrix vector multiplications with dense matrices is reduced by using hierarchical matrices. Findings The suggested approach is used to study the impact of the spatial variability in the magnetic reluctivity on the QoI. The statistics of this parameter are influenced by the correlation lengths of the random reluctivity. Both, the mean value and the standard deviation increase as the correlation length of the random reluctivity increases. Originality/value The KLE, computed by using hierarchical matrices, is used for uncertainty quantification of low frequency electrical machines as a computationally efficient approach in terms of memory requirement, as well as computation time.

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32

Yang, Chunmei, Wenyu Luo, Renhe Zhang, Liangang Lyu, and Fangli Qiao. "An Efficient Coupled-Mode Formulation for Acoustic Propagation in Inhomogeneous Waveguides." Journal of Computational Acoustics 24, no. 01 (March 2016): 1550019. http://dx.doi.org/10.1142/s0218396x15500198.

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The direct-global-matrix coupled-mode model (DGMCM) for sound propagation in range-dependent waveguides was recently developed by Luo et al. [A numerically stable coupled-mode formulation for acoustic propagation in range-dependent waveguides, Sci. China G: Phys. Mech. Astron. 55 (2012) 572–588]. A brief review of the formulation and characteristics of this model is given. This paper extends this model to deal with realistic problems involving an inhomogeneous water column and a penetrable sloping bottom. To this end, the normal mode model KRAKEN is adopted to provide local modal solutions and their associated coupling matrices. As a result, the extended DGMCM model is capable of providing full two-way solutions to two-dimensional (2D) realistic problems with a depth- and range-dependent sound speed profile as well as a penetrable sloping bottom. To validate this model, it is first applied to a benchmark problem of sound propagation in a plane-parallel waveguide with a depth- and range-dependent sound speed profile, and then it is applied to a problem involving both an inhomogeneous water column and a sloping bottom. Comparisons with the analytical solution proposed by DeSanto and with the numerical model COUPLE are also provided, which show that the extended DGMCM model is accurate and efficient and hence can serve as a benchmark for realistic problems of sound propagation in an inhomogeneous waveguide.

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33

Maisuradze, Gia G. "A Study of Raman Excitation Profiles for Soluble cis-Polyacetylene." Australian Journal of Chemistry 57, no. 3 (2004): 253. http://dx.doi.org/10.1071/ch03157.

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A quantitative analysis of the Raman excitation profiles (REPs) for soluble cis-polyacetylene, cis-(CH)x, in toluene observed by Sassi et al. was undertaken. This analysis took two approaches, namely improved vibronic interaction theory and resonance-Raman scattering theory for solute molecules coupled homogeneously and strongly to a continuum of environmental nuclear modes. For the former theory, a ‘static’ approach, the effect of inhomogeneous environmental broadening of REPs of a solute molecule due to the solvent–molecule interactions was investigated as well as the role of diagonal and non-diagonal terms of the scattering matrix. For the latter theory, a ‘dynamic’ approach which rests on vibrational density matrices including both molecular and solvent modes in the ground and excited electronic states, the solvent effects are regarded as dynamic and homogeneous. The values of the equilibrium coordinate shifts for the Raman-active mode and the homogeneous and inhomogeneous broadening parameters derived from the REPs by both approaches are compared with theoretical results of previous studies of soluble and of solid cis- and trans-(CH)x.

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34

Zahrani, Azam, Mashaallah Matinfar, and Mostafa Eslami. "Bivariate Chebyshev Polynomials to Solve Time-Fractional Linear and Nonlinear KdV Equations." Journal of Mathematics 2022 (September 19, 2022): 1–12. http://dx.doi.org/10.1155/2022/6554221.

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This work concerns the numerical solutions of a category of nonlinear and linear time-fractional partial differential equations (TFPDEs) that are called time-fractional inhomogeneous KdV and nonlinear time-fractional KdV equations, respectively. The fractional derivative operators are of the Caputo type. Two-variable second-kind Chebyshev wavelets (SKCWs) are constructed using one-variable ones; then, utilizing corresponding integral operational matrices leads to an approximate solution to the problem under study. Also, it is found that the perturbation term tends to zero even if a finite number of the basis functions is adopted. To exhibit the applicability and efficiency of the proposed scheme, two models of the KdV equations are given.

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35

Krovi, Hari. "Improved quantum algorithms for linear and nonlinear differential equations." Quantum 7 (February 2, 2023): 913. http://dx.doi.org/10.22331/q-2023-02-02-913.

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We present substantially generalized and improved quantum algorithms over prior work for inhomogeneous linear and nonlinear ordinary differential equations (ODE). Specifically, we show how the norm of the matrix exponential characterizes the run time of quantum algorithms for linear ODEs opening the door to an application to a wider class of linear and nonlinear ODEs. In Berry et al., (2017), a quantum algorithm for a certain class of linear ODEs is given, where the matrix involved needs to be diagonalizable. The quantum algorithm for linear ODEs presented here extends to many classes of non-diagonalizable matrices. The algorithm here is also exponentially faster than the bounds derived in Berry et al., (2017) for certain classes of diagonalizable matrices. Our linear ODE algorithm is then applied to nonlinear differential equations using Carleman linearization (an approach taken recently by us in Liu et al., (2021)). The improvement over that result is two-fold. First, we obtain an exponentially better dependence on error. This kind of logarithmic dependence on error has also been achieved by Xue et al., (2021), but only for homogeneous nonlinear equations. Second, the present algorithm can handle any sparse, invertible matrix (that models dissipation) if it has a negative log-norm (including non-diagonalizable matrices), whereas Liu et al., (2021) and Xue et al., (2021) additionally require normality.

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36

Jovanovic, Milos. "Vorticity evolution in perturbed Poiseuille flow." Theoretical and Applied Mechanics 40, no. 1 (2013): 71–86. http://dx.doi.org/10.2298/tam1301071j.

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We consider numerical simulation of temporal hydrodynamic instability with finite amplitude perturbations in plane incompressible Poiseuille flow. Two dimensional Navier Stokes equations have been used and reduced to vorticity-stream function form. Trigonometric polynomials have been used in homogeneous direction and Chebyshev polynomials in inhomogeneous direction. The problem of boundary conditions for vorticity has been solved by using the method of influence matrices. The Orr-Sommerfeld equation has been solved by Chebyshev polynomials, and linear combination of the obtained eigenfunctions has been optimized with regard to the corresponding eigenvalue. We present here the results of simulation for the perturbations optimized in regard to the least stable eigenvalue for the Reynolds number Re=1000.

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37

Khachatryan, Sh, and A. Sedrakyan. "Explicit R-matrices for inhomogeneous 3D chiral Potts models: Integrability and the action formulation for IM." Annals of Physics 437 (February 2022): 168735. http://dx.doi.org/10.1016/j.aop.2021.168735.

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38

Lomba, Enrique, Cecilia Bores, and Gerhard Kahl. "Explicit spatial description of fluid inclusions in porous matrices in terms of an inhomogeneous integral equation." Journal of Chemical Physics 141, no. 16 (October 28, 2014): 164704. http://dx.doi.org/10.1063/1.4898713.

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39

Khademi, J., H. Kunttu, and V. A. Apkarian. "Spectral hole burning in the inhomogeneous ν3 absorption profile in CH3F isolated in mixed Ar:Kr matrices." Chemical Physics Letters 149, no. 2 (August 1988): 145–49. http://dx.doi.org/10.1016/0009-2614(88)87211-7.

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Zidikheri, Meelis J., and Jorgen S. Frederiksen. "Stochastic Subgrid Parameterizations for Simulations of Atmospheric Baroclinic Flows." Journal of the Atmospheric Sciences 66, no. 9 (September 1, 2009): 2844–58. http://dx.doi.org/10.1175/2009jas3036.1.

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Abstract A stochastic subgrid modeling method is used to parameterize horizontal and vertical subgrid-scale transfers in large-eddy simulations (LESs) of baroclinic flows with large-scale jets and energy spectra typical of the atmosphere. The approach represents the subgrid-scale eddies for LES (at resolutions of T63 and T31) by a stochastic model that takes into account the memory effects of turbulent eddies. The statistics of the model are determined from a higher-resolution (T126) direct numerical simulation (DNS). The simulations use a quasigeostrophic two-level model and the subgrid terms are inhomogeneous in the vertical and anisotropic in the horizontal and are represented by 2 × 2 matrices at each wavenumber. The parameterizations have the largest magnitudes at a cusp near the largest total wavenumbers of the truncations. At T63 the off-diagonal elements of the matrices are negligible (corresponding to effectively decoupled levels) and the diagonal elements are almost isotropic. At the lower resolution of T31 the off-diagonal elements are more important and even the diagonal elements are more anisotropic. At both resolutions, and for anisotropic or isotropized subgrid terms, LESs are in excellent agreement with higher-resolution DNS.

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SALIMI, S., and R. YOSEFJANI. "ASYMPTOTIC ENTANGLEMENT IN 1D QUANTUM WALKS WITH A TIME-DEPENDENT COINED." International Journal of Modern Physics B 26, no. 20 (July 18, 2012): 1250112. http://dx.doi.org/10.1142/s0217979212501123.

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Discrete-time quantum walk evolve by a unitary operator which involves two operators a conditional shift in position space and a coin operator. This operator entangles the coin and position degrees of freedom of the walker. In this paper, we investigate the asymptotic behavior of the coin position entanglement (CPE) for an inhomogeneous quantum walk which determined by two orthogonal matrices in one-dimensional lattice. Free parameters of coin operator together provide many conditions under which a measurement perform on the coin state yield the value of entanglement on the resulting position quantum state. We study the problem analytically for all values that two free parameters of coin operator can take and the conditions under which entanglement becomes maximal are sought.

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Boichuk, A. A., and M. A. Elishevich. "Bounded Solutions of a System of Linear Inhomogeneous Differential Equations of the First Order with Rectangular Matrices." Ukrainian Mathematical Journal 72, no. 6 (November 2020): 880–99. http://dx.doi.org/10.1007/s11253-020-01830-w.

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Elishevich, M. A. "Cauchy Problem for a System of Linear Inhomogeneous Differential Equations of the First Order with Rectangular Matrices." Journal of Mathematical Sciences 198, no. 3 (March 25, 2014): 260–78. http://dx.doi.org/10.1007/s10958-014-1789-z.

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Dedushenko, Mykola, and Davide Gaiotto. "Correlators on the wall and sln spin chain." Journal of Mathematical Physics 63, no. 9 (September 1, 2022): 092301. http://dx.doi.org/10.1063/5.0073021.

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We study algebras and correlation functions of local operators at half-BPS interfaces engineered by the stacks of D5 or NS5 branes in the 4D [Formula: see text] super Yang–Mills. The operator algebra in this sector is isomorphic to a truncation of the Yangian [Formula: see text]. The correlators, encoded in a trace on the Yangian, are controlled by the inhomogeneous [Formula: see text] spin chain, where n is the number of fivebranes: they are given in terms of matrix elements of transfer matrices associated with Verma modules or, equivalently, of products of Baxter’s Q-operators. This can be viewed as a novel connection between the [Formula: see text] super Yang–Mills and integrable spin chains. We also remark on analogous constructions involving half-BPS Wilson lines.

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GOSSE, LAURENT. "A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS." Mathematical Models and Methods in Applied Sciences 11, no. 02 (March 2001): 339–65. http://dx.doi.org/10.1142/s021820250100088x.

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The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand side of the equations. In this context, we decided to use the results of Dal Maso, Le Floch and Murat about non-conservative products, and the generalized Roe matrices introduced by Toumi to derive a first-order linearized well-balanced scheme in the sense of Greenberg and Le Roux. As a main feature, this approach is able to preserve the right asymptotic behavior of the original inhomogeneous system, which is not an obvious property. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations.

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Khartovskii, V. E. "Designing asymptotic observers for linear completely regular differential algebraic systems with delay." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 61 (May 2023): 114–36. http://dx.doi.org/10.35634/2226-3594-2023-61-07.

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We study the problem of generating a solution estimate based on the observed output signal data for linear autonomous completely regular differential algebraic systems with commensurate delays. To obtain an estimate for the solution, two types of observers are proposed: an asymptotic observer and an asymptotic observer with bounded error. An asymptotic observer is characterized by the fact that its error asymptotically approaches zero. In this case, if the original system has the property of final observability, then the rate of convergence of the estimation error to zero can be set in advance by choosing the characteristic quasi-polynomial of the homogeneous system that describes the behavior of the error. Otherwise, the estimation error is described by an inhomogeneous system, and the rate of its convergence to zero depends not only on the choice of the characteristic quasi-polynomial of the homogeneous system, but also on the behavior of the inhomogeneous part, the dynamics of which depends on the matrices that determine the structure of the output signal. A distinctive feature of an asymptotic observer with bounded error is that its estimation error remains bounded by some constant depending on the observer's initial condition. In this case, the conditions for the existence of such an observer impose weaker requirements on the parameters of the original system in comparison with the conditions for the existence of an asymptotic observer.

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Cai, Yan, Guangwei Meng, and Liming Zhou. "An Inhomogeneous Cell-Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures." Shock and Vibration 2018 (2018): 1–17. http://dx.doi.org/10.1155/2018/5141060.

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To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

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Turovets, Sergei, Vasily Volkov, Aleksej Zherdetsky, Alena Prakonina, and Allen D. Malony. "A 3D Finite-Difference BiCG Iterative Solver with the Fourier-Jacobi Preconditioner for the Anisotropic EIT/EEG Forward Problem." Computational and Mathematical Methods in Medicine 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/426902.

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The Electrical Impedance Tomography (EIT) and electroencephalography (EEG) forward problems in anisotropic inhomogeneous media like the human head belongs to the class of the three-dimensional boundary value problems for elliptic equations with mixed derivatives. We introduce and explore the performance of several new promising numerical techniques, which seem to be more suitable for solving these problems. The proposed numerical schemes combine the fictitious domain approach together with the finite-difference method and the optimally preconditioned Conjugate Gradient- (CG-) type iterative method for treatment of the discrete model. The numerical scheme includes the standard operations of summation and multiplication of sparse matrices and vector, as well as FFT, making it easy to implement and eligible for the effective parallel implementation. Some typical use cases for the EIT/EEG problems are considered demonstrating high efficiency of the proposed numerical technique.

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CAUDRELIER, V. "ON A SYSTEMATIC APPROACH TO DEFECTS IN CLASSICAL INTEGRABLE FIELD THEORIES." International Journal of Geometric Methods in Modern Physics 05, no. 07 (November 2008): 1085–108. http://dx.doi.org/10.1142/s0219887808003223.

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We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Bäcklund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical r-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.

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Weber, Simon Oskar, Yuan Fang, Sumee Park, and Philip Leistner. "Sequentially coupling LBNL-method and Modelica to model and operate adaptive facades with inhomogeneous printing patterns." Journal of Physics: Conference Series 2600, no. 9 (November 1, 2023): 092017. http://dx.doi.org/10.1088/1742-6596/2600/9/092017.

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Abstract In this work, two U- and g-value Modelica models of a three-layer membrane construction with inhomogeneous stripe pattern were set up. Thus, a simple ISO 52022 model is compared with a detailed model with Modelica integration of Klems-Matrices by LBNL method calculation. For the U-value, both models equally predict the heat transmission. For the g-value, the detailed model shows an strong angular behavior depending on the stripe pattern, the layer distances. Compared to a reference glazing, the application of an adaptive operating strategy results in a reduction of the total energy consumption by up to 27%. Depending on the operation strategy the heating energy increases between 33-100% and cooling energy decreases by 50-80%. This is mainly due to the lower g-value with the detailed model. The actuation energy required for this can be neglected. The resulting reductions in heating and cooling energy exceed the actuation energy by several orders of magnitude.

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