Relevant bibliographies by topics / Inhomogeneous matrices

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Inhomogeneous matrices'

Author: Grafiati
Published: 26 October 2024

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Journal articles on the topic "Inhomogeneous matrices"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Inhomogeneous matrices"

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Oliveira, Santos Patrick. "On the moment method for inhomogeneous matrices : From regular graphs to quantum channels." Electronic Thesis or Diss., Université Gustave Eiffel, 2024. http://www.theses.fr/2024UEFL2025.

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Cette thèse étudie les statistiques spectrales de matrices aléatoires inhomogènes, telles que les graphes aléatoires pondérés, les matrices de covariance et les canaux quantiques. L'une des principales techniques de preuve est l'adaptation de la méthode des moments à ces modèles. Nos objectifs sont doubles. Premièrement, nous étudions la distribution spectrale limite des graphes dirigés réguliers, des canaux quantiques et des produits tensoriels de variables aléatoires non commutatives. Deuxièmement, nous établissons des limites asymptotiques et non asymptotiques précises sur la norme de ces matrices et de leurs formes quadratiques. Pour atteindre nos objectifs, dans la première partie, nous montrons la convergence des grands graphes aléatoires dirigés d-réguliers G_n en n sommets, analysons la combinatoire de leurs moments, et explorons la connexion entre les digraphes réguliers aléatoires uniformément choisis, l'arbre régulier dirigé infini, et la conjecture orientée de Kesten-McKay. Nous travaillons également sur sa contrepartie quantique, connue sous le nom de canaux quantiques. Nous déduisons un théorème central limite libre avec la loi du demi-cercle comme la limite. En outre, nous étendons la notion de canaux quantiques aux espaces et algèbres de probabilité non commutatifs et prouvons un théorème de limite centrale pour ces variables. Nous montrons que la limite est la loi du demi-cercle si et seulement si les variables sont centrées ; sinon, la limite peut être écrite comme une convolution libre de la loi du demi-cercle et des lois gaussiennes.Dans la deuxième partie, nous examinons les graphes réguliers pondérés dont les matrices d'adjacence X_n sont formées en prenant le produit d'Hadamard de la matrice d'adjacence du graphe et d'une matrice pondérée. Nous prouvons que lorsque les poids sont des variables aléatoires sousgaussiennes, la norme de la matrice aléatoire inhomogène X_n présente une transition abrupte autour de dsim log n, indiquant la présence de valeurs aberrantes. En outre, nous étudions la forme quadratique centrée X_nX^t_n - mathbb{E} [X_nX^t_n] et fournissons des estimations précises de sa norme, ce qui est connu comme le problème d'estimation de la covariance. Nous présentons des exemples qui améliorent les travaux précédents ainsi que des limites inférieures
This thesis studies the spectral statistics of inhomogeneous random matrices, such as weighted random graphs, covariance matrices, and quantum channels. One of the main proof techniques is adapting the moment method to these models. Our objectives are twofold. First, we investigate the limiting spectral distribution of regular directed graphs, quantum channels, and tensor products of non-commutative random variables. Second, we establish precise asymptotic and non-asymptotic bounds on the norm of such matrices and their quadratic forms.To achieve our objectives, in the first part, we show the convergence of large directed d-regular graphs G_n in n vertices, analyze the combinatorics of its moments, and explore the connection between random uniformly chosen regular digraphs, the infinite regular directed tree, and the oriented Kesten-McKay conjecture. We also work on its quantum counterpart, which is known as quantum channels. We will derive a free central limit theorem with the semi-circle law as the limit. Additionally, we extend the notion of quantum channels to non-commutative probability spaces and algebras and prove a central limit theorem for these variables. We show that the limit is the semi-circle law if and only if the variables are centered; otherwise, the limit can be written as a free convolution of the semi-circle law and an explicit probability measure.In the second part, we examine regular weighted graphs whose adjacency matrices X_n are formed by taking the Hadamard product of the adjacency matrix of the graph and a weighted matrix. We prove that when the weights are subgaussian random variables, the norm of the inhomogeneous random matrix X_n shows a sharp transition around dsim log n, indicating the presence of outliers. Additionally, we investigate the centered quadratic form X_nX^t_n - mathbb{E} [X_nX^t_n] and provide precise upper bounds on its norm, which is known as the covariance estimation problem. We present examples that improve upon previous works and also lower bounds
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Sacristán, López-Mingo Carlos Javier. "Etude des propriétés acoustiques et comportement à l'impact de matériaux poreux de type mousses métalliques homogènes et inhomogènes." Thesis, Dijon, 2015. http://www.theses.fr/2015DIJOS035/document.

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Ce travail concerne l’étude acoustique théorique et expérimentale des matériaux poreux à squelette métallique, macroscopiquement homogènes et inhomogènes ainsi que l’étude de leurs propriétés mécaniques de comportement au choc pour comparaison. Le modèle acoustique de Johnson -Champoux - Allard s’est montré adapté pour la modélisation acoustique. Ce modèle associé à une approche proposée récemment et utilisant le concept de matrices de transfert en parallèle a permis, dans une nouvelle approche basée sur les “mélanges de matériaux”, d’étudier les matériaux poreux macroscopiquement inhomogènes. Par ailleurs, une étude paramétrique du coefficient d’absorption en fonction de la porosité et de la fréquence a été proposée. Les maxima d’absorption ainsi que l’enveloppe des courbes d’absorption en fonction de la porosité ont été étudiés. En premier lieu, un matériau théorique à propriétés indépendantes a été étudié. Les matériaux réels à propriétés interdépendantes ont ensuite été abordés à l’aide d’un modèle reliant leurs propriétés à la porosité. Enfin, une comparaison entre les propriétés acoustiques et les propriétés mécaniques de comportement à l’impact a été initiée en vue de déterminer un critère objectif permettant de proposer un compromis entre les deux domaines
This work is concerned with the theoretical and experimental study of the acoustical properties of macroscopically homogenous and inhomogeneous porous media as well as their mechanical response to impacts. The model of Johnson - Champoux - Allard appeared adapted for the acoustical modeling. This model, associated with a recently developed approach involving the concept of parallel transfer matrices has lead to a new approach of macroscopically inhomogeneous porous materials based on “mixtures of materials”. Furthermore, a parametric study of the absorption coefficient as a function of porosity and frequency has been proposed. The maximums of absorption as well as the envelop of the absorption curves have been studied as functions of porosity. First, a theoretical material with independent parameters has been studied. Real materials with nonindependent parameters were then investigated with the help of a model relating their properties to the porosity. Finally, a comparison between the acoustical and mechanical properties has been initiated in view of determining an objective criterion that will allow to propose a trade off between the two fields
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Ducatez, Raphaël. "Analyse mathématique de divers systèmes de particules en milieu désordonné." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED013/document.

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Cette thèse est consacrée à l’étude mathématique de divers systèmes de particules classiques et quantiques, en milieu désordonné. Elle comprend quatre travaux publiés ou soumis. Dans le premier nous fournissons une nouvelle formule permettant de prouver la localisation d’Anderson en une dimension d’espace et de caractériser la décroissance des fonctions propres à l’infini. Le second contient l’une des premières preuves de la localisation pour une infinité de particules en intéraction, dans l’approximation d’Hartree-Fock. Le troisième est dédié au modèle d’Anderson soumis à une perturbation périodique en temps. Sous certaines conditions sur la fréquence d’oscillation nous prouvons l’absence de diffusion. Dans le dernier travail nous montrons la décroissancedes corrélations pour le modèle du Jellium en une dimension dans un fond inhomogène, en utilisant la distance de Hilbert sur les cônes et le théorème de Birkhoff-Hopf
This thesis is devoted to the mathematical study of some systems of classical and quantum particles, in a disordered medium. It comprises four published or submitted works. In the first one we provide a new formula allowing to prove Anderson localisation in one space dimension and to characterise the decay at infinity of the eigenfunctions. The second contains one of the first proofs of localisation for infinitely many particles in interaction, in the Hartree-Fock approximation. The third work is dedicated to the Anderson model in a time-periodic perturbation. Under certain conditions on the oscillation frequency we prove the absence of diffusion. In the last work we show the decay of correlations for the one-dimensional Jellium model in an inhomogeneous background, using the Hilbert distance on cones and the Birkhoff-Hopf theorem
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Benkemoun, Nathan. "Contribution aux approches multi-échelles séquencées pour la modélisation numérique des matériaux à matrice cimentaire." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2010. http://tel.archives-ouvertes.fr/tel-00657311.

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L'objectif principal de cette thèse est de développer un modèle numérique capable de proposer une représentation fine des phénomènes de fissuration pour les matériaux quasi-fragiles à matrice cimentaire. Dans ce sens, l'échelle pertinente retenue est l'échelle mesoscopique. L'échelle mesoscopique est ici de l'ordre du centimètre et le matériau peut être considéré comme bi-phasique (agrégats inclus dans un mortier, contenant lui même des inclusions de taille inférieure). Par ailleurs, de part la diversité des phénomènes de fissuration pour les matériaux quasi-fragiles comme le béton, il est nécessaire de mettre en place un modèle capable de représenter explicitement les fissures à l'interface agrégats/mortier et/ou dans n'importe quelles des deux phases (agrégats et mortier). La modélisation numérique des phénomènes de fissuration proposée s'inscrit, ici, dans le cadre de la méthode des éléments finis à discontinuité forte. Plus précisément, la fissure est ici définie comme l'apparition d'une discontinuité de déplacements ou encore d'une zone d'épaisseur nulle dans laquelle toutes les déformations sont localisées. Elle correspond au cas extrême des bandes de localisation observées dans les sols ou les roches avec une largeur des bandes tendant vers zéro. Par ailleurs, le modèle proposé intégre aussi une discontinuité faible (discontinuité de déformations) afin de capturer les hétérogénéités sans que le maillage soit contraint. Finalement le but est d'intégrer ce meso-modèle dans le cadre d'une approche multi-échelle séquencée permettant le transfert des informations du niveau mesoscopique vers le niveau macroscopique ou au moins sa borne inférieure, le Volume élémentaire Représentatif. Cette approche séquencée permet, par exemple, de déterminer une surface de rupture macroscopique (dans l'esprit d'une fonction seuil) intégrant les principales caractéristiques des matériaux cimentaires.
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Francescato, Pascal. "Prévision du comportement plastique des matériaux hétérogènes à constituants métalliques : application aux composites à matrice métallique à fibres continues et aux plaques perforées." Université Joseph Fourier (Grenoble), 1994. http://www.theses.fr/1994GRE10110.

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Ce travail de these porte sur la mise en uvre numerique de la methode d'homogeneisation periodique en calcul a la rupture ou analyse limite et son application a la prevision des proprietes de resistance macroscopiques de materiaux composites a fibres longues ou de plaques metalliques perforees. La methode numerique adoptee consiste a ramener la mise en uvre des approches statique par l'interieur et cinematique par l'exterieur a la resolution d'un probleme d'optimisation lineaire pose sur le volume elementaire representatif (v. E. R. ). Les programmes numeriques font appel a une utilisation originale de la methode des elements finis avec une discretisation discontinue des differents v. E. R. Etudies ainsi qu'a une technique nouvelle de linearisation des criteres de tresca et von mises. Une premiere validation de ces methodes est faite a partir de resultats theoriques et experimentaux obtenus par ailleurs, de meme qu'une campagne experimentale est menee sur des plaques minces perforees par des trous circulaires. Ces methodes donnent une evaluation tres precise de l'anisotropie de resistance de ce type de materiau. Dans la suite, une extension de ces methodes au cas de la deformation plane generalisee et au cas general tridimensionnel est proposee afin d'etudier le comportement plastique de composites a matrice metallique (c. M. M. ). Les maillages elements finis restant plans du fait du cas des fibres continues unidirectionnelles considere ici, l'objectif est de determiner le convexe de resistance de c. M. M. Unidirectionnels sous un chargement hors axes quelconque. Dans le cas d'une interface fibre/matrice a adherence maximale, les calculs mettent clairement en evidence l'anisotropie transverse de ce type de composite, y compris dans le cas d'un v. E. R. Hexagonal. Enfin l'etude se termine par une serie de calculs prenant en compte un critere de decohesion a l'interface fibre/matrice alors que la fibre et la matrice obeissent au critere de tresca tridimensionnel isotrope. Les parametres caracteristiques du critere a l'interface sont identifies a partir d'un essai de traction simple transversalement aux fibres
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Books on the topic "Inhomogeneous matrices"

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Zabrodin, Anton. Quantum spin chains and classical integrable systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0013.

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This chapter is a review of the recently established quantum-classical correspondence for integrable systems based on the construction of the master T-operator. For integrable inhomogeneous quantum spin chains with gl(N)-invariant R-matrices in finite-dimensional representations, the master T-operator is a sort of generating function for the family of commuting quantum transfer matrices depending on an infinite number of parameters. Any eigenvalue of the master T-operator is the tau-function of the classical modified KP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0th time of the hierarchy. This implies a remarkable relation between the quantum spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, a system of algebraic equations can be obtained for the spectrum of the spin chain Hamiltonians.
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Book chapters on the topic "Inhomogeneous matrices"

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Byun, Sung-Soo, and Peter J. Forrester. "Further Extensions to GinSE." In KIAS Springer Series in Mathematics, 185–200. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-5173-0_11.

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AbstractThe elliptic extension of GinSE considered in the previous chapter gives rise to a potential which is not spherically symmetric. In contrast, the extensions of GinSE to be considered in this chapter—specifically the induced GinSE relating to a polar decomposition involving a rectangular generalisation of GinSE and a random Haar symplectic unitary matrix, the quaternion spherical ensemble of matrices $$G_1^{-1}G_2$$ G 1 - 1 G 2 with $$G_1,G_2$$ G 1 , G 2 both GinSE matrices, a sub-block of a Haar symplectic unitary matrix, and products of GinSE matrices—all have the common feature that the corresponding potential is spherically symmetric. This allows for a unified treatment in relation to the corresponding skew-orthogonal polynomials. Furthermore, in each case the pre-kernel can be shown to satisfy an inhomogeneous partial differential equation, from which scaled limits can be computed.
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Byun, Sung-Soo, and Peter J. Forrester. "Statistical Properties of GinSE and Elliptic GinSE." In KIAS Springer Series in Mathematics, 163–83. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-5173-0_10.

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AbstractEigenvalues of GinSE matrices occur in complex conjugate pairs as for complex GinOE eigenvalues, but now with zero probability of an eigenvalue being real. Also in common with complex GinOE eigenvalues is that the GinSE eigenvalues form a Pfaffian point process, and that their PDF admits a Coulomb gas interpretation with image terms. While the determination of the required skew-orthogonal polynomials is straightforward, the particular form gives a new challenge in relation to analysing the various scaling limits. This is overcome by making use of a certain inhomogeneous partial differential equation satisfied by the pre-kernel. Such an approach carries over to the analysis of a weakly non-Hermitian regime. Also contained in this chapter is the large N analysis of the partition function and gap probability associated with GinSE eigenvalues, and results relating to the singular values and eigenvectors. Furthermore, a study is undertaken of an elliptic generalisation, which interpolates between GinSE and Hermitian GSE matrices.
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Ram-Mohan, L. Ramdas. "The boundary element method." In Finite Element and Boundary Element Applications in Quantum Mechanics, 399–434. Oxford University PressOxford, 2002. http://dx.doi.org/10.1093/oso/9780198525219.003.0016.

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Abstract The boundary element method (BEM) is based on an integral equation formulation for the solution of differential equations. As we have seen in the context of the finite element method (FEM), analytical methods become cumbersome when the geometrical shape of the physical domain is complex or when the boundary conditions (BCs) for the physical property being calculated are complicated. If there are inhomogeneous terms in the differential equation, they lead to a "particular integral" which is difficult to evaluate in a direct analytical manner. In general, inhomogeneous terms in the differential equation are treated by the method of Green’s function. A somewhat lengthy, but self-contained, exposition in Appendix C introduces the essential ideas of the Green’s function technique. We show below that by using Green’s theorem of vector calculus we can convert the differential equation under consideration into an integral equation on the boundary of the physical region. The discretization of the boundary integral leads to self-consistency conditions for the solution at the boundary. Once the solution at the boundary is obtained, the construction of the solution in the interior region proceeds in a straightforward manner. Thus the BEM employs the discretization of only the boundary, and not the interior of the physical region. This is a distinct advantage over the FEM, in which the entire physical region is discretized, which in turn leads to fairly large global matrices. The "reduction in dimensionality" associated with the BEM gives rise to global matrices of much fewer dimensions.
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Conference papers on the topic "Inhomogeneous matrices"

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Lueneburg, Ernst, and Wolfgang-Martin Boerner. "Homogeneous and inhomogeneous Sinclair and Jones matrices." In Optical Science, Engineering and Instrumentation '97, edited by Harold Mott and Wolfgang-Martin Boerner. SPIE, 1997. http://dx.doi.org/10.1117/12.283851.

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Bovard, Bertrand G. "Derivation of a new matrix for an inhomogeneous dielectric thin film." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/oam.1986.mc4.

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Varying the refractive index of a thin film from one boundary to the other is a very appealing design approach for new types of coating with higher performance. An exact expression for the amplitude reflection coefficient of a single inhomogeneous layer has been given by Sossi in the particular case where there is no refractive-index discontinuity at the layer boundaries.1 Nevertheless, the most efficient way to calculate the optical properties of a coating remains the matrix method where each layer is characterized by a 2 × 2 matrix. Although matrices have been listed in the literature for particular refractive-index profiles,2 no general expression has ever been given. Until now, the only general way to deal with inhomogeneous layers has been to consider each layer as a stack of numerous homogeneous sublayers and to multiply all the corresponding matrices. We introduce a new matrix characterizing any type of inhomogeneous layer, which can easily be included in the traditional programs and allows the calculation of the optical properties of any stack of inhomogeneous and homogeneous layers.
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Painchaud-April, Guillaume, Joey Dumont, Denis Gagnon, and Louis J. Dube. "S and Q matrices reloaded: Applications to open, inhomogeneous, and complex cavities." In 2013 15th International Conference on Transparent Optical Networks (ICTON). IEEE, 2013. http://dx.doi.org/10.1109/icton.2013.6602811.

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Dubolazov, A. V., O. Yu Telenga, and A. O. Karachevtcev. "Polarization metrology of Mueller matrices images of biological tissues phase-inhomogeneous layers." In Correlation Optics 2009. SPIE, 2009. http://dx.doi.org/10.1117/12.853295.

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Güttler, Frank, Marco Pirotta, Alois Renn, and Urs P. Wild. "Single molecule spectroscopy: Stark effect of pentacene in p-terphenyl." In Spectral Hole-Burning and Luminescence Line Narrowing: Science and Applications. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/shbl.1992.mb1.

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Based on the occurrence of extremely narrow zero phonon lines and their inhomogeneous distribution spectroscopic isolation of single absorbers in solid matrices can be achieved. Pentacene molecules in a p-terphenyl host crystal have been studied at cryogenic temperatures using absorption [1] and fluorescence excitation [2,3] techniques. Such investigations provide information on a variety of guest host properties such as homogeneous dephasing, spectral diffusion [3] and inhomogeneous broadening. Single molecule detection also is a key to the investigations of fundamental spectroscopic properties of individual molecules.
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Dian, J., F. Adamec, M. Ambroz, J. Psencik, M. Vacha, and J. Hala. "Fluorescence Line Narrowing and Hole Burning of Uroporphyrin." In Spectral Hole-Burning and Luminescence Line Narrowing: Science and Applications. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/shbl.1992.tub6.

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Uroporhyrin, like other natural porphyrins such as coproporphyrin or protoporphyrin, is an important intermediate occurring in the metabolic pathway to protoheme. These porphyrins are important indicators of pathogenic states in an organism. Luminescence spectra of these molecules consist of (≈ 100 cm–1) broad bands due to an inhomogeneous broadening. Fluorescence line narrowing and hole burning spectroscopies enable to remove an inhomogeneous broadening and high resolution spectra can be obtained (≈ 5 cm–1 and ≈ 0.01 cm–1, respectively). Low temperature optical spectra of coproporphyrin and protoporphyrin in various matrices have been measured [1-4]. The aim of this contribution is to present hole burning and fluorescence line narrowing spectra of uroporphyrin.
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Geissinger, P., L. Kador, Th Giering, and D. Haarer. "Analysis of the Importance of Matrix Correlations through Hole-Burning Experiments in Dye-Doped Rare Gas Matrices." In Spectral Hole-Burning and Related Spectroscopies: Science and Applications. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/shbs.1994.wd48.

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Stochastic models to describe the inhomogeneous broadening of electronic transitions of dye molecules in amorphous hosts [1] and to account for the effects of external hydrostatic pressure on spectral holes [2] have been applied to analyze experimental results obtained in a variety of samples, with hosts ranging from polymers to aerogels. With these models it was possible to determine the compressibilities of various polymers by purely optical experiments. It is interesting that these results are in agreement with mechanically obtained data within approx. 15%. Furthermore, the depth ϵ of the assumed Lennard-Jones dye-matrix interaction potential could be calculated.
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Jones, Simon. "Predicting Wave Propagation Through Inhomogeneous Soils Using a Finite-Element Model Incorporating Perfectly-Matched Layers." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-50136.

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A 2D, plane-strain, finite element model, with perfectly-matched layer elements acting as absorbing boundaries, is used to investigate the effect of soil inhomogeneity on resultant surface vibration. The stiffness and mass matrices for the perfectly-matched layer element is derived and included for reference. Stochastic variability of the soil’s shear wave velocity is introduced using a K-L expansion; the shear wave velocity is assumed to have a log-normal distribution and a modified exponential co-variance kernel. Results suggest that local soil inhomogeneity can significantly affect surface velocity predictions; 90% confidence intervals showing 7dB averages and peak values up to 11dB are computed. This is a significant source of uncertainty and should be considered when using predictions from models assuming homogeneous soil properties.
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Kador, L. "Electric-Field Effects on Hole Spectra in Doped Polymers: A Step towards Two-Dimensional Optical Spectroscopy." In Persistent Spectral Hole Burning: Science and Applications. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/pshb.1991.thd4.

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Abstract:
Optical absorption bands of organic dye molecules or inorganic ions in condensed matter are affected by inhomogeneous broadening [1] and are thus usually much broader than the corresponding homogeneous lines. In disordered systems, the difference can amount to several orders of magnitude at low temperatures. In order to detect the effects of external perturbations such as hydrostatic pressure or electric fields on an inhomogeneous band, the perturbations must therefore have very large magnitudes. The sensitivity can be greatly enhanced by investigating the changes of hole-burning spectra caused by the external fields. In amorphous matrices, an external electric field gives rise to a symmetrical broadening of spectral holes due to the linear Stark effect. This was shown to be true even in the case of centrosymmetric dopant molecules where the first-order Stark effect is ascribed to matrix-induced dipole moments [2] (see Fig. 1). The magnitude of the broadening yields thus information on the electrostatic dye-matrix interaction.
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10

Luo, B., and J. P. Galaup. "Photon-Gated Spectral Hole-Burning in a Polymer Doped with a Mixture of Several Zn-Benzoporphyrin Derivatives." In Spectral Hole-Burning and Related Spectroscopies: Science and Applications. Washington, D.C.: Optica Publishing Group, 1994. http://dx.doi.org/10.1364/shbs.1994.wd28.

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Photochemical spectral hole-burning (PSHB) has attracted particular attention in the past decade because of its potential for frequency domain optical storage. In order to apply PSHB to a practical optical memory, the material should have high burning temperature, high thermal stability, erasability and high frequency multiplexing. Two ways are possible to increase the storage density: one is to narrow the homogeneous line width, the other is to broaden the inhomogeneous line width. In previous works, the larger inhomogeneous line width (greater than 1,000 cm–1) has been reached in polymethylmethacrylate (PMMA) doped with two kinds of Zn-benzoporphyrin derivatives with roughly the same hole-burning efficiencies [1]. In this paper, the authors investigate systematically the optical properties of Zn-benzoporphyrin derivatives, their hole-burning mechanisms, thermal stability and electron-phonon coupling in cellulose acetate (CA) and in PMMA matrices. The choice of CA was motivated mainly by the fact this polymer allows to prepare samples with excellent optical quality.
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