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Journal articles on the topic 'Density eigenvalue'

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Author: Grafiati

Published: 14 March 2023

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1

Fyodorov, Yan V., Boris A. Khoruzhenko, and Mihail Poplavskyi. "Extreme Eigenvalues and the Emerging Outlier in Rank-One Non-Hermitian Deformations of the Gaussian Unitary Ensemble." Entropy 25, no. 1 (December 30, 2022): 74. http://dx.doi.org/10.3390/e25010074.

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Complex eigenvalues of random matrices J=GUE+iγdiag(1,0,…,0) provide the simplest model for studying resonances in wave scattering from a quantum chaotic system via a single open channel. It is known that in the limit of large matrix dimensions N≫1 the eigenvalue density of J undergoes an abrupt restructuring at γ=1, the critical threshold beyond which a single eigenvalue outlier (“broad resonance”) appears. We provide a detailed description of this restructuring transition, including the scaling with N of the width of the critical region about the outlier threshold γ=1 and the associated scaling for the real parts (“resonance positions”) and imaginary parts (“resonance widths”) of the eigenvalues which are farthest away from the real axis. In the critical regime we determine the density of such extreme eigenvalues, and show how the outlier gradually separates itself from the rest of the extreme eigenvalues. Finally, we describe the fluctuations in the height of the eigenvalue outlier for large but finite N in terms of the associated large deviation function.

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2

Chen, Lung-Hui. "On Certain Translation Invariant Properties of Interior Transmission Spectra and Their Doppler’s Effect." Advances in Mathematical Physics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/3838507.

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We study the translation invariant properties of the eigenvalues of scattering transmission problem. We examine the functional derivative of the eigenvalue density function Δ(x^) to the defining index of refraction n(x). By the limit behaviors in frequency sphere, we prove some results on the inverse uniqueness of index of refraction. In physics, Doppler’s effect connects the variation of the frequency/eigenvalue and the motion velocity/variation of position variable. In this paper, we proved the functional derivative ∂rΔx^=(1+nrx^)/π.

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3

Christandl, Matthias, Brent Doran, Stavros Kousidis, and Michael Walter. "Eigenvalue Distributions of Reduced Density Matrices." Communications in Mathematical Physics 332, no. 1 (August 19, 2014): 1–52. http://dx.doi.org/10.1007/s00220-014-2144-4.

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4

Wu, Na, Ke Wang, Liangtian Wan, and Ning Liu. "A Source Number Estimation Algorithm Based on Data Local Density and Fuzzy C-Means Clustering." Wireless Communications and Mobile Computing 2021 (February 20, 2021): 1–7. http://dx.doi.org/10.1155/2021/6658785.

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An advanced source number estimation (SNE) algorithm based on both fuzzy C-means clustering (FCM) and data local density (DLD) is proposed in this paper. The DLD of an eigenvalue refers to the number of eigenvalues within a specific neighborhood of this eigenvalue belonging to the data covariance matrix. This local density essentially as the one-dimensional sample feature of the FCM is extracted into the SNE algorithm based on FCM and can enable to improve the probability of correct detection (PCD) of the SNE algorithm based on the FCM especially for low signal-to-noise ratio (SNR) environment. Comparison experiment results demonstrate that compared to the SNE algorithm based on the FCM and other similar algorithms, our proposed algorithm can achieve highest PCD of the incident source number in both cases of spatial white noise and spatial correlation noise.

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5

CASTRO, C., and E. ZUAZUA. "High frequency asymptotic analysis of a string with rapidly oscillating density." European Journal of Applied Mathematics 11, no. 6 (December 2000): 595–622. http://dx.doi.org/10.1017/s0956792500004307.

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We consider the eigenvalue problem associated with the vibrations of a string with rapidly oscillating periodic density. In a previous paper we stated asymptotic formulae for the eigenvalues and eigenfunctions when the size of the microstructure ε is shorter than the wavelength of the eigenfunctions 1/√λε. On the other hand, it has been observed that when the size of the microstructure is of the order of the wavelength of the eigenfunctions (ε ∼ 1/√λε) singular phenomena may occur. In this paper we study the behaviour of the eigenvalues and eigenfunctions when 1/√λε is larger than the critical size ε. We use the WKB approximation which allows us to find an explicit formula for eigenvalues and eigenfunctions with respect to ε. Our analysis provides all order correction formulae for the limit eigenvalues and eigenfunctions above the critical size. Each term of the asymptotic expansion requires one more derivative of the density. Thus, a full description requires the density to be C∞ smooth.

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6

SaiToh, Akira, Roabeh Rahimi, and Mikio Nakahara. "Limitation for linear maps in a class for detection and quantification of bipartite nonclassical correlation." Quantum Information and Computation 12, no. 11&12 (November 2012): 944–52. http://dx.doi.org/10.26421/qic12.11-12-3.

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Eigenvalue-preserving-but-not-completely-eigenvalue-preserving (EnCE) maps were previously introduced for the purpose of detection and quantification of nonclassical correlation, employing the paradigm where nonvanishing quantum discord implies the existence of nonclassical correlation. It is known that only the matrix transposition is nontrivial among Hermiticity-preserving (HP) linear EnCE maps when we use the changes in the eigenvalues of a density matrix due to a partial map for the purpose. In this paper, we prove that this is true even among not-necessarily HP (nnHP) linear EnCE maps. The proof utilizes a conventional theorem on linear preservers. This result imposes a strong limitation on the linear maps and promotes the importance of nonlinear maps.

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7

Frank, Olaf, and Bruno Eckhardt. "Eigenvalue density oscillations in separable microwave resonators." Physical Review E 53, no. 4 (April 1, 1996): 4166–75. http://dx.doi.org/10.1103/physreve.53.4166.

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8

Menon, Ravishankar, Peter Gerstoft, and William S. Hodgkiss. "Asymptotic Eigenvalue Density of Noise Covariance Matrices." IEEE Transactions on Signal Processing 60, no. 7 (July 2012): 3415–24. http://dx.doi.org/10.1109/tsp.2012.2193573.

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9

He, Yukun, and Antti Knowles. "Mesoscopic eigenvalue density correlations of Wigner matrices." Probability Theory and Related Fields 177, no. 1-2 (October 4, 2019): 147–216. http://dx.doi.org/10.1007/s00440-019-00946-w.

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10

Erdős, László, and Brendan Farrell. "Local Eigenvalue Density for General MANOVA Matrices." Journal of Statistical Physics 152, no. 6 (July 18, 2013): 1003–32. http://dx.doi.org/10.1007/s10955-013-0807-8.

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11

Zhang, Qian, Xinyu Wang, Jianguo Cai, Jingyao Zhang, and Jian Feng. "Closed-Form Solutions for the Form-Finding of Regular Tensegrity Structures by Group Elements." Symmetry 12, no. 3 (March 2, 2020): 374. http://dx.doi.org/10.3390/sym12030374.

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An analytical form-finding method for regular tensegrity structures based on the concept of force density is presented. The self-equilibrated state can be deduced linearly in terms of force densities, and then we apply eigenvalue decomposition to the force density matrix to calculate its eigenvalues. The eigenvalues are enforced to satisfy the non-degeneracy condition to fulfill the self-equilibrium condition. So the relationship between force densities can also be obtained, which is followed by the super-stability examination. The method has been developed to deal with planar tensegrity structure, prismatic tensegrity structure (triangular prism, quadrangular prism, and pentagonal prism) and star-shaped tensegrity structure by group elements to get closed-form solutions in terms of force densities, which satisfies the super stable conditions.

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12

Ubaru, Shashanka, Yousef Saad, and Abd-Krim Seghouane. "Fast Estimation of Approximate Matrix Ranks Using Spectral Densities." Neural Computation 29, no. 5 (May 2017): 1317–51. http://dx.doi.org/10.1162/neco_a_00951.

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Many machine learning and data-related applications require the knowledge of approximate ranks of large data matrices at hand. This letter presents two computationally inexpensive techniques to estimate the approximate ranks of such matrices. These techniques exploit approximate spectral densities, popular in physics, which are probability density distributions that measure the likelihood of finding eigenvalues of the matrix at a given point on the real line. Integrating the spectral density over an interval gives the eigenvalue count of the matrix in that interval. Therefore, the rank can be approximated by integrating the spectral density over a carefully selected interval. Two different approaches are discussed to estimate the approximate rank, one based on Chebyshev polynomials and the other based on the Lanczos algorithm. In order to obtain the appropriate interval, it is necessary to locate a gap between the eigenvalues that correspond to noise and the relevant eigenvalues that contribute to the matrix rank. A method for locating this gap and selecting the interval of integration is proposed based on the plot of the spectral density. Numerical experiments illustrate the performance of these techniques on matrices from typical applications.

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13

Maeda, Yasuyuki, Yasunori Futamura, and Tetsuya Sakurai. "Stochastic estimation method of eigenvalue density for nonlinear eigenvalue problem on the complex plane." JSIAM Letters 3 (2011): 61–64. http://dx.doi.org/10.14495/jsiaml.3.61.

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14

He, Yang-Hui, Vishnu Jejjala, and Djordje Minic. "Eigenvalue Density, Li's Positivity, and the Critical Strip." inSTEMM Journal 1, S1 (July 15, 2022): 1–14. http://dx.doi.org/10.56725/instemm.v1is1.23.

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We rewrite the zero-counting formula within the critical strip of the Riemann zeta function as a cumulative density distribution;this subsequently allows us to formally derive an integral expression for the Li coefficients associated with the Riemann Xi-function which, in particular, indicate that their positivity criterion is obeyed, whereby entailing the criticality of the non-trivial zeros. We conjecture the validity of this and related expressions without the need for the Riemann Hypothesis and also offer a physical interpretation of the result and discuss the Hilbert-Polya approach.

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15

Sobolev, Alexander. "Eigenvalue estimates for the one-particle density matrix." Journal of Spectral Theory 12, no. 2 (September 21, 2022): 857–75. http://dx.doi.org/10.4171/jst/407.

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16

Bohigas, O., and M. P. Pato. "Decomposition of spectral density in individual eigenvalue contributions." Journal of Physics A: Mathematical and Theoretical 43, no. 36 (July 22, 2010): 365001. http://dx.doi.org/10.1088/1751-8113/43/36/365001.

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17

Miyoshi, T., H. Ichihashi, and K. Nagasaka. "Fuzzy projection pursuit density estimation by eigenvalue method." International Journal of Approximate Reasoning 20, no. 3 (March 1999): 237–48. http://dx.doi.org/10.1016/s0888-613x(99)00004-3.

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18

Sen, Kali D., and Sai Nath. "A simple eigenvalue sum-density relationship for atoms." Theoretica Chimica Acta 68, no. 2 (August 1985): 139–42. http://dx.doi.org/10.1007/bf00527529.

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19

Girouard, Alexandre. "Fundamental Tone, Concentration of Density, and Conformal Degeneration on Surfaces." Canadian Journal of Mathematics 61, no. 3 (June 1, 2009): 548–65. http://dx.doi.org/10.4153/cjm-2009-029-1.

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Abstract.We study the effect of two types of degeneration of a Riemannian metric on the first eigenvalue of the Laplace operator on surfaces. In both cases we prove that the first eigenvalue of the round sphere is an optimal asymptotic upper bound. The first type of degeneration is concentration of the density to a point within a conformal class. The second is degeneration of the conformal class to the boundary of the moduli space on the torus and on the Klein bottle. In the latter, we follow the outline proposed by N. Nadirashvili in 1996.

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20

Shahverdi, H., Cristinel Mares, W. Wang, C. H. Greaves, and John E. Mottershead. "Finite Element Model Updating of Large Structures by the Clustering of Parameter Sensitivities." Applied Mechanics and Materials 5-6 (October 2006): 85–92. http://dx.doi.org/10.4028/www.scientific.net/amm.5-6.85.

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Finite element model updating of a Westland Lynx XZ649 helicopter tail is presented. Eigenvalue sensitivities with respect to Young’s modulus and mass density are used. Large groups based on material input data were divided to form smaller subgroups so that those parts of the model responsible for errors in the predicted eigenvalues were located. A particular new development was the use of parameter clustering based on the similarity of different columns of the sensitivity matrix. Finally the finite element model was updated successfully with regard to the lower frequency tail-bending modes.

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21

MIGDAL, A. A. "PHASE TRANSITIONS IN INDUCED QCD." Modern Physics Letters A 08, no. 02 (January 20, 1993): 153–66. http://dx.doi.org/10.1142/s0217732393000167.

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The variety of the phase transitions in induced QCD are studied. Depending on the parameters in the scalar field potential, there could be infinite number of fixed points, with different critical behavior. The integral equation for the density of the eigenvalues of the scalar field are generalized to the weak coupling phases, with the gap at the origin. We find a wide class of the massive solutions of these integral equations in the strong coupling phases, and derive an explicit eigenvalue equation for the scalar branch of the mass spectrum.

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22

Peligrad, Costel, and Magda Peligrad. "The limiting spectral distribution in terms of spectral density." Random Matrices: Theory and Applications 05, no. 01 (January 2016): 1650003. http://dx.doi.org/10.1142/s2010326316500039.

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For a large class of symmetric random matrices with correlated entries, selected from stationary random fields of centered and square integrable variables, we show that the limiting distribution of eigenvalue counting measure always exists and we describe it via an equation satisfied by its Stieltjes transform. No rate of convergence to zero of correlations is imposed, therefore the process is allowed to have long memory. In particular, if the symmetrized matrices are constructed from stationary Gaussian random fields which have spectral density, the result of this paper gives a complete solution to the limiting eigenvalue distribution. More generally, for matrices whose entries are functions of independent and identically distributed random variables the result also holds.

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23

Ullah, N. "Analytic continuation of the single-eigenvalue probability density function." Journal of Physics A: Mathematical and General 21, no. 4 (February 21, 1988): 903–8. http://dx.doi.org/10.1088/0305-4470/21/4/019.

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24

Girolami, Mark. "Orthogonal Series Density Estimation and the Kernel Eigenvalue Problem." Neural Computation 14, no. 3 (March 1, 2002): 669–88. http://dx.doi.org/10.1162/089976602317250942.

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Kernel principal component analysis has been introduced as a method of extracting a set of orthonormal nonlinear features from multivariate data, and many impressive applications are being reported within the literature. This article presents the view that the eigenvalue decomposition of a kernel matrix can also provide the discrete expansion coefficients required for a nonparametric orthogonal series density estimator. In addition to providing novel insights into nonparametric density estimation, this article provides an intuitively appealing interpretation for the nonlinear features extracted from data using kernel principal component analysis.

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25

Lohmayer, Robert, Herbert Neuberger, and Tilo Wettig. "Eigenvalue density of Wilson loops in 2DSU(N) YM." Journal of High Energy Physics 2009, no. 05 (May 26, 2009): 107. http://dx.doi.org/10.1088/1126-6708/2009/05/107.

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26

Hiai, Fumio, and Dénes Petz. "Eigenvalue Density of the Wishart Matrix and Large Deviations." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 04 (October 1998): 633–46. http://dx.doi.org/10.1142/s021902579800034x.

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A large deviation theorem is obtained for a certain sequence of random measures which includes the empirical eigenvalue distribution of Wishart matrices, as the matrix size tends to infinity. The rate function is convex and one of its ingredients is the logarithmic energy. In the case of the singular Wishart matrix, the limit distribution has an atom.

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27

Kiessling, Michael K. H., and Herbert Spohn. "A Note on the Eigenvalue Density of Random Matrices." Communications in Mathematical Physics 199, no. 3 (January 1, 1999): 683–95. http://dx.doi.org/10.1007/s002200050516.

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28

Mays, Anthony, and Anita Ponsaing. "An induced real quaternion spherical ensemble of random matrices." Random Matrices: Theory and Applications 06, no. 01 (January 2017): 1750001. http://dx.doi.org/10.1142/s2010326317500010.

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We study the induced spherical ensemble of non-Hermitian matrices with real quaternion entries (considering each quaternion as a [Formula: see text] complex matrix). We define the ensemble by the matrix probability distribution function that is proportional to [Formula: see text] These matrices can also be constructed via a procedure called ‘inducing’, using a product of a Wishart matrix (with parameters [Formula: see text]) and a rectangular Ginibre matrix of size [Formula: see text]. The inducing procedure imposes a repulsion of eigenvalues from [Formula: see text] and [Formula: see text] in the complex plane with the effect that in the limit of large matrix dimension, they lie in an annulus whose inner and outer radii depend on the relative size of [Formula: see text], [Formula: see text] and [Formula: see text]. By using functional differentiation of a generalized partition function, we make use of skew-orthogonal polynomials to find expressions for the eigenvalue [Formula: see text]-point correlation functions, and in particular the eigenvalue density (given by [Formula: see text]). We find the scaled limits of the density in the bulk (away from the real line) as well as near the inner and outer annular radii, in the four regimes corresponding to large or small values of [Formula: see text] and [Formula: see text]. After a stereographic projection, the density is uniform on a spherical annulus, except for a depletion of eigenvalues on a great circle corresponding to the real axis (as expected for a real quaternion ensemble). We also form a conjecture for the behavior of the density near the real line based on analogous results in the [Formula: see text] and [Formula: see text] ensembles; we support our conjecture with data from Monte Carlo simulations of a large number of matrices drawn from the [Formula: see text] induced spherical ensemble. This ensemble is a quaternionic analog of a model of a one-component charged plasma on a sphere, with soft wall boundary conditions.

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29

LECHTENFELD, OLAF. "SEMICLASSICAL APPROACH TO FINITE-N MATRIX MODELS." International Journal of Modern Physics A 07, no. 28 (November 10, 1992): 7097–118. http://dx.doi.org/10.1142/s0217751x92003264.

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We reformulate the zero-dimensional Hermitian one-matrix model as a (nonlocal) collective field theory, for finite N. The Jacobian arising as a result of changing variables from matrix eigenvalues to their density distribution is treated exactly. The semiclassical loop expansion turns out not to coincide with the (topological) [Formula: see text] expansion, because the classical background has a nontrivial N dependence. We derive a simple integral equation for the classical eigenvalue density, which displays strong nonperturbative behavior around N=∞. This leads to IR singularities in the large-N expansion, but UV divergencies appear as well, despite remarkable cancelations among the Feynman diagrams. We evaluate the free energy at the two-loop level and discuss its regularization. A simple example serves to illustrate the problems and admits explicit comparison with orthogonal-polynomial results.

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30

Manoli, Soheil D., and Michael A. Whitehead. "Generalized exchange local-spin-density-functional theory: One-electron energies and eigenvalues." Collection of Czechoslovak Chemical Communications 53, no. 10 (1988): 2279–307. http://dx.doi.org/10.1135/cccc19882279.

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Within the Generalized Exchange (GX) LSD scheme, a method to calculate the ionization potential (IP) of an atom has been developed involving correction terms to the negative of the eigenvalue of the highest occupied atomic orbital (HOAO). These correction terms are evaluated non-iteratively using the fully occupied orbitals of the ground state of the neutral atom. Within the unrelaxed orbital approximation, this corrected eigenvalue IP, IPcorr, is completely equivalent to the Transition State IP, calculated from an SCF calculation at half-occupancy of the HOAO, when used with density-functional (DF) schemes that do not include self-interaction. The present scheme can also be used with self-interaction corrected DF schemes. In both cases, the corrected eigenvalue method of calculating IP's gives good results. The techniques used to derive IPcorr are applied to derive an expression for the electronegativity of the free atom which can be used with both self-interaction and non-self-interaction corrected DF schemes. The results of IP and electronegativity calculations for the helium to krypton atoms are reported using a variety of DF schemes. These are compared to each other and to the experimental values whenever possible.

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31

Linetsky, Vadim. "The spectral representation of Bessel processes with constant drift: applications in queueing and finance." Journal of Applied Probability 41, no. 2 (June 2004): 327–44. http://dx.doi.org/10.1239/jap/1082999069.

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Bessel processes with constant negative drift have recently appeared as heavy-traffic limits in queueing theory. We derive a closed-form expression for the spectral representation of the transition density of the Bessel process of order ν > −1 with constant drift μ ≠ 0. When ν > -½ and μ < 0, the first term of the spectral expansion is the steady-state gamma density corresponding to the zero principal eigenvalue λ0 = 0, followed by an infinite series of terms corresponding to the higher eigenvalues λn, n = 1,2,…, as well as an integral over the continuous spectrum above μ2/2. When −1 < ν < -½ and μ < 0, there is only one eigenvalue λ0 = 0 in addition to the continuous spectrum. As well as applications in queueing, Bessel processes with constant negative drift naturally lead to two new nonaffine analytically tractable specifications for short-term interest rates, credit spreads, and stochastic volatility in finance. The two processes serve as alternatives to the CIR process for modelling mean-reverting positive economic variables and have nonlinear infinitesimal drift and variance. On a historical note, the Sturm–Liouville equation associated with Bessel processes with constant negative drift is closely related to the celebrated Schrödinger equation with Coulomb potential used to describe the hydrogen atom in quantum mechanics. Another connection is with D. G. Kendall's pole-seeking Brownian motion.

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32

Zhou, Da-Sheng, Dang-Zheng Liu, and Tao Qian. "Fixed trace β-Hermite ensembles: Asymptotic eigenvalue density and the edge of the density." Journal of Mathematical Physics 51, no. 3 (2010): 033301. http://dx.doi.org/10.1063/1.3321578.

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33

Sagdinc, Seda Gunesdogdu, Banu Kevser Akcay, Salih Zeki Yildiz, and Ilknur Baldan Isik. "Single-crystal X-ray structural characterization, Hirshfeld surface analysis, electronic properties, NBO, and NLO calculations and vibrational analysis of the monomeric and dimeric forms of 5-nitro-2-oxindole." New Journal of Chemistry 45, no. 22 (2021): 10070–88. http://dx.doi.org/10.1039/d1nj00264c.

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The information of interactions is given by RDG versus sign(λ₂)ρ product of the sign of the second largest eigenvalue of electron density Hessian matrix and electron density) investigated by RDG surface analysis.

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34

Feinberg, Joshua, and Roman Riser. "Pseudo-hermitian random matrix theory: a review." Journal of Physics: Conference Series 2038, no. 1 (October 1, 2021): 012009. http://dx.doi.org/10.1088/1742-6596/2038/1/012009.

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Abstract We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of this new type of random matrices, we focus on two specific models of matrices which are pseudo-hermitian with respect to a given indefinite metric B. Eigenvalues of pseudo-hermitian matrices are either real, or come in complex-conjugate pairs. The diagrammatic method is applied to deriving explicit analytical expressions for the density of eigenvalues in the complex plane and on the real axis, in the large-N, planar limit. In one of the models we discuss, the metric B depends on a certain real parameter t. As t varies, the model exhibits various ‘phase transitions’ associated with eigenvalues flowing from the complex plane onto the real axis, causing disjoint eigenvalue support intervals to merge. Our analytical results agree well with presented numerical simulations.

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35

Kumar, Santosh, Gabriel F. Pivaro, Yogeesh R. Yerrababu, Gustavo Fraidenraich, Dayan A. Guimaraes, and Rausley A. A. de Souza. "Asymptotic Eigenvalue Density for the Quotient Ensemble of Wishart Matrices." IEEE Communications Letters 22, no. 12 (December 2018): 2575–78. http://dx.doi.org/10.1109/lcomm.2018.2877327.

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36

BOUTET de MONVEL, A., and A. KHORUNZHY. "Asymptotic distribution of smoothed eigenvalue density. I. Gaussian random matrices." Random Operators and Stochastic Equations 7, no. 1 (1999): 1–22. http://dx.doi.org/10.1515/rose.1999.7.1.1.

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37

Wei, Yi, Boris A. Khoruzhenko, and Yan V. Fyodorov. "Integral formulae for the eigenvalue density of complex random matrices." Journal of Physics A: Mathematical and Theoretical 42, no. 46 (October 22, 2009): 462002. http://dx.doi.org/10.1088/1751-8113/42/46/462002.

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38

Broderick, S. R., and K. Rajan. "Eigenvalue decomposition of spectral features in density of states curves." EPL (Europhysics Letters) 95, no. 5 (August 18, 2011): 57005. http://dx.doi.org/10.1209/0295-5075/95/57005.

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39

Fyodorov, Yan V., Boris A. Khoruzhenko, and Hans-Jürgen Sommers. "Almost-Hermitian random matrices: eigenvalue density in the complex plane." Physics Letters A 226, no. 1-2 (February 1997): 46–52. http://dx.doi.org/10.1016/s0375-9601(96)00904-8.

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40

Nilantha, K. G. D. R., Ranasinghe, and P. K. C. Malmini. "Eigenvalue density of cross-correlations in Sri Lankan financial market." Physica A: Statistical Mechanics and its Applications 378, no. 2 (May 2007): 345–56. http://dx.doi.org/10.1016/j.physa.2006.10.101.

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41

Liné, A. "Eigenvalue spectrum versus energy density spectrum in a mixing tank." Chemical Engineering Research and Design 108 (April 2016): 13–22. http://dx.doi.org/10.1016/j.cherd.2015.10.023.

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42

Pushnitski, Alexander, Georgi Raikov, and Carlos Villegas-Blas. "Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian." Communications in Mathematical Physics 320, no. 2 (December 25, 2012): 425–53. http://dx.doi.org/10.1007/s00220-012-1643-4.

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43

Waltner, Daniel, Tim Wirtz, and Thomas Guhr. "Eigenvalue density of the doubly correlated Wishart model: exact results." Journal of Physics A: Mathematical and Theoretical 48, no. 17 (April 8, 2015): 175204. http://dx.doi.org/10.1088/1751-8113/48/17/175204.

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44

Salomonson, Sten, Fredrik Moller, and Ingvar Lindgren. "Accurate Kohn-Sham potential for the 1s2s 3S state of the helium atom: Tests of the locality and the ionization-potential theorems." Canadian Journal of Physics 83, no. 1 (January 1, 2005): 85–90. http://dx.doi.org/10.1139/p05-001.

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The local KohnSham potential is constructed for the 1s2s 3S state of the helium atom, using the procedure proposed by van Leeuwen and Baerends (Phys. Rev. A, 49, 2138 (1994)) and the many-body electron density, obtained from the pair-correlation program of Salomonson and Öster (Phys. Rev. A, 40, 5559 (1989)). The KohnSham orbitals reproduce the many-body density very accurately, demonstrating the validity of the KohnSham model and the locality theorem in this case. The ionization-potential theorem, stating that the KohnSham energy eigenvalue of the outermost electron orbital agrees with the negative of the corresponding many-body ionization energy (including electronic relaxation), is verified in this case to nine digits. A KohnSham potential is also constructed to reproduce the HartreeFock density of the same state, and the KohnSham 2s eigenvalue is then found to agree with the same accuracy with the corresponding HartreeFock eigenvalue. This is consistent with the fact that in this model the energy eigenvalue equals the negative of the ionization energy without relaxation due to Koopmans' theorem. Related calculations have been performed previously, particularly for atomic and molecular ground states, but none of matching accuracy. In the computations presented here there is no conflict between the locality of the KohnSham potential and the exclusion principle, as claimed by Nesbet (Phys. Rev. A, 58, R12 (1998)). PACS Nos.: 31.15.Ew, 31.15.Pf, 02.30.Sa

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Ortakaya, S., M. Kirak, and A. Guldeste. "Size-dependent electronic and optical properties in zinc-blende InGaN/GaN multilayer spherical quantum dot." Journal of Nonlinear Optical Physics & Materials 26, no. 03 (September 2017): 1750035. http://dx.doi.org/10.1142/s0218863517500357.

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A theoretical investigation of the binding energy, the radial probability distribution and optical properties (absorption coefficient (AC) and refractive index change (RIC)) of InGaN/GaN multilayer quantum dot (QD) is presented. The calculations are performed within the effective-mass approximation. A shooting method is presented to obtain numerical values for the eigenvalues and eigenfunctions of the structure. The energy eigenvalue, density of probability and optical absorption are compared for cases without and with impurity. It is also found that the ACs and RICs exhibit blue or redshift with different structure of potential profile. The results indicate that the optical properties can be sensitively adjusted by geometry of structure and the presence of impurity.

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Lal, Roshan, and Renu Saini. "Mode shapes and frequencies of thin rectangular plates with arbitrarily varying non-homogeneity along two concurrent edges." Journal of Vibration and Control 23, no. 17 (January 22, 2016): 2841–65. http://dx.doi.org/10.1177/1077546315623710.

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Analysis and numerical results are presented for free transverse vibrations of isotropic rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges on the basis of Kirchhoff plate theory. For the non-homogeneity, a general type of variation for Young’s modulus and density of the plate material has been assumed. Generalized differential quadrature method has been used to obtain the eigenvalue problem for such model of plates for four different combinations of boundary conditions at the edges namely, (i) fully clamped, (ii) two opposite edges are clamped and other two are simply supported, (iii) two opposite edges are clamped and other two are free, and (iv) two opposite edges are simply supported and other two are free. By solving these eigenvalue problems using software MATLAB, the lowest three eigenvalues have been reported as the first three natural frequencies for the first three modes of vibration. The effect of various plate parameters on the vibration characteristics has been analysed. Three dimensional mode shapes have been plotted. A comparison of results with those available in literature has been presented.

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XIANG, LINYING, ZENGQIANG CHEN, ZHONGXIN LIU, FEI CHEN, and ZHUZHI YUAN. "STABILITY AND CONTROLLABILITY OF ASYMMETRIC COMPLEX DYNAMICAL NETWORKS: EIGENVALUE ANALYSIS." International Journal of Modern Physics C 20, no. 02 (February 2009): 237–52. http://dx.doi.org/10.1142/s0129183109013571.

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The stability and controllability of asymmetric complex dynamical networks are investigated in detail based on eigenvalue analysis. Pinning control is suggested to stabilize the homogenous stationary state of the whole coupled network. The complicated coupled problem is reduced to two independent problems: clarifying the stable regions of the coupled network and specifying the eigenvalue distribution of the asymmetric coupling and control matrices. The dependence of the controllability on both pinning density and pinning strength is studied.

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Chen, Kevin K., and Geoffrey R. Spedding. "Boussinesq global modes and stability sensitivity, with applications to stratified wakes." Journal of Fluid Mechanics 812 (January 12, 2017): 1146–88. http://dx.doi.org/10.1017/jfm.2016.847.

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For the Boussinesq equations, we present a theory of linear stability sensitivity to base flow density and velocity modifications. Given a steady-state flow with small density variations, the sensitivity of the stability eigenvalues is computed from the direct and adjoint global modes of the linearised Boussinesq equations, similarly to Marquetet al.(J. Fluid Mech., vol. 615, 2008, pp. 221–252). Combinations of the density and velocity components of these modes reveal multiple production and transport mechanisms that contribute to the eigenvalue sensitivity. We present an application of the sensitivity theory to a stably linearly density-stratified flow around a thin plate at a$90^{\circ }$angle of attack, a Reynolds number of 30 and Froude numbers of 1, 8 and$\infty$. The global mode analysis reveals lightly damped undulations pervading through the entire domain, which are predicted by both inviscid uniform base flow theory and Orr–Sommerfeld theory. The sensitivity to base flow velocity modifications is primarily concentrated just downstream of the bluff body. On the other hand, the sensitivity to base flow density modifications is concentrated in regions both immediately upstream and immediately downstream of the plate. Both sensitivities have a greater upstream presence for lower Froude numbers.

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Monvel, A. Boutet de, and A. Khorunzhy. "On universality of the smoothed eigenvalue density of large random matrices." Journal of Physics A: Mathematical and General 32, no. 38 (September 7, 1999): L413—L417. http://dx.doi.org/10.1088/0305-4470/32/38/101.

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Akuzawa, Toshinao, and Miki Wadati. "Diffusion onGL(N,C)/U(N)and Eigenvalue Density forN→∞Limit." Journal of the Physical Society of Japan 67, no. 2 (February 15, 1998): 421–25. http://dx.doi.org/10.1143/jpsj.67.421.

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