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Journal articles on the topic 'Model matriciel'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

POPESCU, Ionel, Lică FLORE, and Albert ARNAU CUBILLO. "DERIVATION OF MASS, STIFFNESS AND DAMPING MATRICES OF A MODEL WING FROM EXPERIMENTAL MODAL DATA." SCIENTIFIC RESEARCH AND EDUCATION IN THE AIR FORCE 19, no. 1 (July 31, 2017): 323–30. http://dx.doi.org/10.19062/2247-3173.2017.19.1.39.

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Lenczewski, Romuald. "Matricial circular systems and random matrices." Random Matrices: Theory and Applications 05, no. 04 (October 2016): 1650012. http://dx.doi.org/10.1142/s201032631650012x.

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We introduce and study matricial circular systems of operators which play the role of matricial counterparts of circular operators. They describe the asymptotic joint *-distributions of blocks of independent block-identically distributed Gaussian random matrices with respect to partial traces. Using these operators, we introduce circular free Meixner distributions as the non-Hermitian counterparts of free Meixner distributions and construct for them a random matrix model. Our approach is based on the concept of matricial freeness applied to operators on Hilbert spaces. It is closely related to freeness with amalgamation over the algebra [Formula: see text] of [Formula: see text] diagonal matrices applied to operators on Hilbert [Formula: see text]-bimodules.

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3

Minas, C., and D. J. Inman. "Matching Finite Element Models to Modal Data." Journal of Vibration and Acoustics 112, no. 1 (January 1, 1990): 84–92. http://dx.doi.org/10.1115/1.2930103.

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A technique is proposed which systematically adjusts a finite element model of a structure to produce an updated model in agreement with measured modal results. The approach suggested here is to consider the desired perturbations in stiffness and damping matrices as gain matrices in a feedback control algorithm designed to perform eigenstructure assignment. The improved stiffness and damping matrices combined with the analytical mass matrix, more closely predict the modal test results. The technique is applicable to undamped, proportionally damped, as well as non-proportionally damped models. The proposed method assumes that the analytical mass, damping and stiffness matrices are known and that vibration test data is available in the form of natural frequencies, damping ratios, and mode shapes.

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Fendley, Paul, and Nicholas Read. "ExactS-matrices for supersymmetric sigma models and the Potts model." Journal of Physics A: Mathematical and General 35, no. 50 (December 2, 2002): 10675–704. http://dx.doi.org/10.1088/0305-4470/35/50/301.

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5

Barauskas, R. "Optimum Mass Matrices for Short Wave Pulse Propagation Finite Element Models." Nonlinear Analysis: Modelling and Control 8, no. 2 (July 25, 2003): 3–25. http://dx.doi.org/10.15388/na.2003.8.2.15180.

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The matrices of a substructure ensuring minimum modal errors of the whole structure are obtained by using optimization approach. The mass and stiffness matrices of a small component domain of selected dimension are obtained by applying the modal synthesis of a limited number of closeto-exact modes such that after assembling a larger joined domain model the modal convergence rate of the latter should be as high as possible. The goal is achieved by formulating the minimization problem for the penaltytype target function representing the cumulative relative modal error of the joined domain and by applying the gradient descent minimization method. After the optimum matrices of a component domain are obtained, they can be used in any structure as higher-order elements or super-elements. The “combined” mass matrices can be treated as a special case of the presented approach. The performance of the obtained dynamic models is demonstrated by solving short wave pulse propagation problems by using a only few nodal points per pulse length.

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Yuan, Yongxin. "Structural Dynamics Model Updating with Positive Definiteness and No Spillover." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/896261.

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Model updating is a common method to improve the correlation between structural dynamics models and measured data. In conducting the updating, it is desirable to match only the measured spectral data without tampering with the other unmeasured and unknown eigeninformation in the original model (if so, the model is said to be updated with no spillover) and to maintain the positive definiteness of the coefficient matrices. In this paper, an efficient numerical method for updating mass and stiffness matrices simultaneously is presented. The method first updates the modal frequencies. Then, a method is presented to construct a transformation matrix and this matrix is used to correct the analytical eigenvectors so that the updated model is compatible with the measurement of the eigenvectors. The method can preserve both no spillover and the symmetric positive definiteness of the mass and stiffness matrices. The method is computationally efficient as neither iteration nor numerical optimization is required. The numerical example shows that the presented method is quite accurate and efficient.

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Lee, Eun-Taik, and Hee-Chang Eun. "Update of parameter matrices of the dynamic system using the least-squares approach." Advances in Mechanical Engineering 11, no. 11 (November 2019): 168781401989080. http://dx.doi.org/10.1177/1687814019890806.

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Model-based responses rarely coincide with the actual responses owing to modeling and measurement errors, deterioration of structural performance, and presence of damages in the structure. The parameter matrices should be updated for successful subsequent analysis and design efforts. This study derives the mathematical forms of variations in the parameter matrices between the actual system and the analytical model. A method using the least-squares principle constrained by the measured modal data is presented. The method is directly derived by minimizing the performance indices expressed by the norm of the variation in the parameter matrices between the actual system and the analytical model. The proposed update methods predict the updated parameter matrices depending on the prescribed weighting matrices and detect damages from the predicted parameter matrix variations. Examples compare the methods depending on the established weighting matrices, the number of measurement data sets of the first modal data only and the lowest two modal data. This study also investigates the effect of external noise contained in the measured data.

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Vanrolleghem, Peter A., and Karel J. Keesman. "Identification of Biodegradation models under model and data uncertainty." Water Science and Technology 33, no. 2 (January 1, 1996): 91–105. http://dx.doi.org/10.2166/wst.1996.0040.

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In this paper a number of nonlinear parameter estimation methods are evaluated with respect to their ability to identify biodegradation models from “real-world” data. Important aspects are then the sensitivity to local minima, rate of convergence, required prior knowledge and direct or indirect availability of parameter estimates uncertainty. Furthermore, it is important whether a method is robust against invalid assumptions. In addition to the final parameter values, covariance and correlation matrices, confidence intervals and residual sequences are presented to obtain information about the validity of the models and noise assumptions. Finally, recommendations on the method's applicability range are provided.

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9

Hwang, Jae-Seung, Hongjin Kim, and Bong-Ho Cho. "Modal Parameters Estimation of Building Structures from Vibration Test Data Using Observability Measurement." Shock and Vibration 2015 (2015): 1–13. http://dx.doi.org/10.1155/2015/627852.

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The load distribution to each mode of a structure under seismic loading depends on the modal participation factors and mode shapes and thus the exact estimation of modal participation factors and mode shapes is essential to analyze the seismic response of a structure. In this study, an identification procedure for modal participation factors and mode shapes from a vibration test is proposed. The modal participation factors and mode shapes are obtained from the relationship between observability matrices realized from the system identification. Using the observability matrices, it is possible to transform an arbitrarily identified state space model obtained from the experimental data into a state space model which is defined in a domain with physical meaning. Then, the modal participation factor can be estimated based on the transformation matrix between two state space models. The numerical simulation is performed to evaluate the proposed procedure, and the results show that the modal participation factor and mode shapes are estimated from the structural responses accurately. The procedure is also applied to the experimental data obtained from the shaking table test of a three-story shear building model.

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10

Nadi, Azin, and Mehdi Raghebi. "Finite element model of circularly curved Timoshenko beam for in-plane vibration analysis." FME Transactions 49, no. 3 (2021): 615–26. http://dx.doi.org/10.5937/fme2103615n.

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Curved beams are used so much in the arches and railway bridges and equipments for amusement parks. There are few reports about the curved beam with the effects of both the shear deformation and rotary inertias. In this paper, a new finite element model investigates to analyze In-Plane vibration of a curved Timoshenko beam. The Stiffness and mass matrices of the curved beam element was obtained from the force-displacement relations and the kinetic energy equations, respectively. Assembly of the elemental property matrices is simple and without need to transformation matrix because of using the local polar coordinate system. The natural frequencies of curved Euler-Bernoulli beam with large thickness are not sufficiently accurate. In this case, using the curved Timoshenko beam element is necessary. Moreover, the influence of vibration absorber is discussed on the natural frequencies of the curved beam.

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Guillet, Jérôme, Benjamin Mourllion, Abderazik Birouche, and Michel Basset. "Extracting second-order structures from single-input state-space models: Application to model order reduction." International Journal of Applied Mathematics and Computer Science 21, no. 3 (September 1, 2011): 509–19. http://dx.doi.org/10.2478/v10006-011-0039-5.

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Extracting second-order structures from single-input state-space models: Application to model order reductionThis paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations with real matrices and has been applied to reduce a single-input second-order form model by balanced truncation and modal truncation.

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McFarland, Dennis. "The Effects of Using Partial or Uncorrected Correlation Matrices When Comparing Network and Latent Variable Models." Journal of Intelligence 8, no. 1 (February 15, 2020): 7. http://dx.doi.org/10.3390/jintelligence8010007.

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Network models of the WAIS-IV based on regularized partial correlation matrices have been reported to outperform latent variable models based on uncorrected correlation matrices. The present study sought to compare network and latent variable models using both partial and uncorrected correlation matrices with both types of models. The results show that a network model provided better fit to matrices of partial correlations but latent variable models provided better fit to matrices of full correlations. This result is due to the fact that the use of partial correlations removes most of the covariance common to WAIS-IV tests. Modeling should be based on uncorrected correlations since these represent the majority of shared variance between WAIS-IV test scores.

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13

Delgado, O. "Modelos geométricos para el aprendizaje de movimientos en el plano." Modelling in Science Education and Learning 3 (June 19, 2010): 39. http://dx.doi.org/10.4995/msel.2010.3110.

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<p>En geometría moderna, la relación entre la estructura algebraica de los elementos geométricos y la descripción física de estos mismos es a menudo demasiado abstracta para que se pueda explicar usando sólo su representación matricial. En este artículo presentamos algunas herramientas para la enseñanza de los movimientos en el plano. Junto con los elementos matemáticos abstractos (vectores, matrices,...), el archivo pdf que facilitamos proporciona modelos sencillos para la explicación y autoaprendizaje de esta materia mediante los efectos de movimiento que se añaden a los dibujos que aparecen en el modelo.</p>

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14

Cébron, Guillaume. "Matricial model for the free multiplicative convolution." Annals of Probability 44, no. 4 (July 2016): 2427–78. http://dx.doi.org/10.1214/15-aop1024.

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15

Cudeck, Robert. "Msultiplicative Models and MTMM Matrices." Journal of Educational Statistics 13, no. 2 (June 1988): 131–47. http://dx.doi.org/10.3102/10769986013002131.

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The rationale for multiplicative models in the context of MTMM covariance matrices, as developed by Swain and Browne, is described and illustrated with several sets of empirical data. Comparisons with restricted factor analysis models are made, and certain criticisms of this approach are noted. An extension of the multiplicative model to three-facet data that includes occasions, methods, and traits is also presented.

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16

Liu, Gang. "Study on Torsion Vibration of Ship’s Complex Shaf." Applied Mechanics and Materials 397-400 (September 2013): 365–68. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.365.

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The method of transfer matrices used for torsion vibration of ships complex shafts was analyzed, and various simplified models of transfer matrices were obtained by building a hybrid model for lumped parameter elements and distributed parameter elements. Based on the above, verified by an example of a complex shaft with one propeller driven by two turbines, the method of simplifying model was provided by analyzing the calculation results on the different simplified models.

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17

Batchelor, Murray T. "Sparse matrix factorizations of transfer matrices." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 28, no. 4 (April 1987): 462–75. http://dx.doi.org/10.1017/s0334270000005531.

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AbstractSparse matrix factorizations of transfer matrices for the interactions round a face model are reviewed. The sparse factors of a more general Ising model containing first, second and third nearest neighbour interactions are also presented. For both models the factorizations are achieved by considering the required auxiliary spin sets as a hierarchy of interacting spins.

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18

LAVOURA, LUÍS, and ERNEST MA. "TWO PREDICTIVE SUPERSYMMETRIC S3×Z2 MODELS FOR THE QUARK MASS MATRICES." Modern Physics Letters A 20, no. 16 (May 30, 2005): 1217–25. http://dx.doi.org/10.1142/s0217732305017561.

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We propose two simple models for the quark mass matrices which may be implemented through an S3×Z2 symmetry in a supersymmetric context. Each model has eight parameters and, therefore, makes two independent predictions for the quark mixing matrix. The first model predicts [Formula: see text] and [Formula: see text]. The second model, in which the forms of the up-type-quark and down-type-quark mass matrices are interchanged relative to the first one, predicts |Vub/Vcb|~0.11 and |Vtd/Vts|~0.33. Both models have sin 2β~0.5.

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19

Li, Shi Qi, Zhe Zhang, Shi Ping Liu, and Heng Zhang. "Mass and Stiffness Matrices Updating Using the First Modal Data." Applied Mechanics and Materials 851 (August 2016): 834–39. http://dx.doi.org/10.4028/www.scientific.net/amm.851.834.

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This paper presents a new direct approach to simultaneously update the analytical mass and stiffness matrices in an undamped model .First, we assume that the difference between the finite element model and the real model is little. Second, only by utilizing the first order modal data orthogonal normalization conditions and eigen equations , we derive the updated matrices. Third, the method can maintain matrices symmetry and sparsity and preserve system connectivity. The merit of the proposed method is simple and accurate in a practical engineering computation. Finally,a numerical example is given to demonstrate the accuracy and effectiveness of the presented updating method.

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20

O’Connell, Ross, and Daniel J. Eisenstein. "Large covariance matrices: accurate models without mocks." Monthly Notices of the Royal Astronomical Society 487, no. 2 (May 21, 2019): 2701–17. http://dx.doi.org/10.1093/mnras/stz1359.

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Abstract Covariance matrix estimation is a persistent challenge for cosmology. We focus on a class of model covariance matrices that can be generated with high accuracy and precision, using a tiny fraction of the computational resources that would be required to achieve comparably precise covariance matrices using mock catalogues. In previous work, the free parameters in these models were determined using sample covariance matrices computed using a large number of mocks, but we demonstrate that those parameters can be estimated consistently and with good precision by applying jackknife methods to a single survey volume. This enables model covariance matrices that are calibrated from data alone, with no reference to mocks.

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21

Kojaku, Sadamori, and Naoki Masuda. "Constructing networks by filtering correlation matrices: a null model approach." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2231 (November 2019): 20190578. http://dx.doi.org/10.1098/rspa.2019.0578.

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Network analysis has been applied to various correlation matrix data. Thresholding on the value of the pairwise correlation is probably the most straightforward and common method to create a network from a correlation matrix. However, there have been criticisms on this thresholding approach such as an inability to filter out spurious correlations, which have led to proposals of alternative methods to overcome some of the problems. We propose a method to create networks from correlation matrices based on optimization with regularization, where we lay an edge between each pair of nodes if and only if the edge is unexpected from a null model. The proposed algorithm is advantageous in that it can be combined with different types of null models. Moreover, the algorithm can select the most plausible null model from a set of candidate null models using a model selection criterion. For three economic datasets, we find that the configuration model for correlation matrices is often preferred to standard null models. For country-level product export data, the present method better predicts main products exported from countries than sample correlation matrices do.

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Kim, Jaewoong. "A note on Putinar's matricial models." Filomat 27, no. 5 (2013): 739–46. http://dx.doi.org/10.2298/fil1305739k.

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In this note we consider the conjecture that every hyponormal Putinar's matricial model of rank two is subnormal. Related to this conjecture, we show that there exists a non rationally cyclic subnormal Putinar's matricial model of rank two and then give a sufficient condition for it to be a subnormal operator.

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23

Ciche, Todd A., Kwi-suk Kim, Bettina Kaufmann-Daszczuk, Ken C. Q. Nguyen, and David H. Hall. "Cell Invasion and Matricide during Photorhabdus luminescens Transmission by Heterorhabditis bacteriophora Nematodes." Applied and Environmental Microbiology 74, no. 8 (February 15, 2008): 2275–87. http://dx.doi.org/10.1128/aem.02646-07.

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ABSTRACT Many animals and plants have symbiotic relationships with beneficial bacteria. Experimentally tractable models are necessary to understand the processes involved in the selective transmission of symbiotic bacteria. One such model is the transmission of the insect-pathogenic bacterial symbionts Photorhabdus spp. by Heterorhabditis bacteriophora infective juvenile (IJ)-stage nematodes. By observing egg-laying behavior and IJ development, it was determined that IJs develop exclusively via intrauterine hatching and matricide (i.e., endotokia matricida). By transiently exposing nematodes to fluorescently labeled symbionts, it was determined that symbionts infect the maternal intestine as a biofilm and then invade and breach the rectal gland epithelium, becoming available to the IJ offspring developing in the pseudocoelom. Cell- and stage-specific infection occurs again in the pre-IJ pharyngeal intestinal valve cells, which helps symbionts to persist as IJs develop and move to a new host. Synchronous with nematode development are changes in symbiont and host behavior (e.g., adherence versus invasion). Thus, Photorhabdus symbionts are maternally transmitted by an elaborate infectious process involving multiple selective steps in order to achieve symbiont-specific transmission.

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24

Simmons, N. A., B. S. A. Schuberth, S. C. Myers, and D. R. Knapp. "Resolution and Covariance of the LLNL-G3D-JPS Global Seismic Tomography Model: Applications to Travel time Uncertainty and Tomographic Filtering of Geodynamic Models." Geophysical Journal International 217, no. 3 (February 26, 2019): 1543–57. http://dx.doi.org/10.1093/gji/ggz102.

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SUMMARY Resolution and covariance of global seismic tomography models are most often unknown quantities. However, there are many potential applications of these matrices in the broad solid Earth research community as well as more focused scientific groups including the nuclear explosion monitoring research community. In this study, we construct both the resolution and covariance matrices for the recent LLNL-G3D-JPS global joint model of P- and S-wave velocity. The global model consists of >1 million free parameters, creating matrices with >1 trillion elements. Given the scale of the problem and computational limitations, we used a custom method to calculated impulse responses at every node in the earth model and produced sparse, yet representative, resolution and covariance matrices that can be practically used for several real applications. We apply the matrices to real problems as example use cases. Utilizing the covariance matrix, we computed traveltime uncertainties for thousands of P waves emanating from (or coming to) specified points around the globe and constructed maps of the traveltime error to illustrate the variability of path-specific traveltime uncertainty. Utilizing the resolution matrix as a tomographic filter, we converted geodynamically derived renditions of Earth structure to images that may be visible through the often-distorted lens of seismic tomography.

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25

Toivonen, Jarkko, Pratyush K. Das, Jussi Taipale, and Esko Ukkonen. "MODER2: first-order Markov modeling and discovery of monomeric and dimeric binding motifs." Bioinformatics 36, no. 9 (January 30, 2020): 2690–96. http://dx.doi.org/10.1093/bioinformatics/btaa045.

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Abstract Motivation Position-specific probability matrices (PPMs, also called position-specific weight matrices) have been the dominating model for transcription factor (TF)-binding motifs in DNA. There is, however, increasing recent evidence of better performance of higher order models such as Markov models of order one, also called adjacent dinucleotide matrices (ADMs). ADMs can model dependencies between adjacent nucleotides, unlike PPMs. A modeling technique and software tool that would estimate such models simultaneously both for monomers and their dimers have been missing. Results We present an ADM-based mixture model for monomeric and dimeric TF-binding motifs and an expectation maximization algorithm MODER2 for learning such models from training data and seeds. The model is a mixture that includes monomers and dimers, built from the monomers, with a description of the dimeric structure (spacing, orientation). The technique is modular, meaning that the co-operative effect of dimerization is made explicit by evaluating the difference between expected and observed models. The model is validated using HT-SELEX and generated datasets, and by comparing to some earlier PPM and ADM techniques. The ADM models explain data slightly better than PPM models for 314 tested TFs (or their DNA-binding domains) from four families (bHLH, bZIP, ETS and Homeodomain), the ADM mixture models by MODER2 being the best on average. Availability and implementation Software implementation is available from https://github.com/jttoivon/moder2. Supplementary information Supplementary data are available at Bioinformatics online.

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Amburg, Natalia, Aleksander Orlov, and Dmitry Vasiliev. "On Products of Random Matrices." Entropy 22, no. 9 (August 31, 2020): 972. http://dx.doi.org/10.3390/e22090972.

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We introduce a family of models, which we name matrix models associated with children’s drawings—the so-called dessin d’enfant. Dessins d’enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of such a graph are small disks that we call stars. We attach random matrices to the edges of the graph and get multimatrix models. Additionally, to the stars we attach source matrices. They play the role of free parameters or model coupling constants. The answers for our integrals are expressed through quantities that we call the “spectrum of stars”. The answers may also include some combinatorial numbers, such as Hurwitz numbers or characters from group representation theory.

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BATCHELOR, M. T., J. de GIER, and B. NIENHUIS. "THE ROTOR MODEL AND COMBINATORICS." International Journal of Modern Physics B 16, no. 14n15 (June 20, 2002): 1883–89. http://dx.doi.org/10.1142/s0217979202011597.

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We examine the groundstate wavefunction of the rotor model for different boundary conditions. Three conjectures are made on the appearance of numbers enumerating alternating sign matrices. In addition to those occurring in the O (n = 1) model we find the number A V (2m + 1;3), which 3-enumerates vertically symmetric alternating sign matrices.

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28

Bourdon, A., J. F. Rigal, and D. Play. "Static Rolling Bearing Models in a C.A.D. Environment for the Study of Complex Mechanisms: Part I—Rolling Bearing Model." Journal of Tribology 121, no. 2 (April 1, 1999): 205–14. http://dx.doi.org/10.1115/1.2833923.

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This paper, the first of two companion papers, proposes a general methodology for accurate modeling of the nonlinear behavior of ball and roller bearings. The models give stiffness matrices which can be introduced into standard finite element models of complex mechanical systems, with the aim of predicting mechanical behavior and load and strain distributions. In the case of an “isolated” ball bearing, the results obtained with the proposed approach are compared to results from the literature. Applications are implemented to evaluate the influence of external loadings on the stiffness matrices of tapered roller bearings mounted in a rigid mechanical environment.

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Lee, Jun Ik. "ON PUTINAR'S MATRICIAL MODEL OPERATOR OF RANK 2." Journal of the Chungcheong Mathematical Society 26, no. 1 (February 15, 2013): 181–90. http://dx.doi.org/10.14403/jcms.2013.26.1.181.

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Le, Si Quang, Nicolas Lartillot, and Olivier Gascuel. "Phylogenetic mixture models for proteins." Philosophical Transactions of the Royal Society B: Biological Sciences 363, no. 1512 (October 7, 2008): 3965–76. http://dx.doi.org/10.1098/rstb.2008.0180.

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Standard protein substitution models use a single amino acid replacement rate matrix that summarizes the biological, chemical and physical properties of amino acids. However, site evolution is highly heterogeneous and depends on many factors: genetic code; solvent exposure; secondary and tertiary structure; protein function; etc. These impact the substitution pattern and, in most cases, a single replacement matrix is not enough to represent all the complexity of the evolutionary processes. This paper explores in maximum-likelihood framework phylogenetic mixture models that combine several amino acid replacement matrices to better fit protein evolution. We learn these mixture models from a large alignment database extracted from HSSP, and test the performance using independent alignments from TreeBase . We compare unsupervised learning approaches, where the site categories are unknown, to supervised ones, where in estimations we use the known category of each site, based on its exposure or its secondary structure. All our models are combined with gamma-distributed rates across sites. Results show that highly significant likelihood gains are obtained when using mixture models compared with the best available single replacement matrices. Mixtures of matrices also improve over mixtures of profiles in the manner of the CAT model. The unsupervised approach tends to be better than the supervised one, but it appears difficult to implement and highly sensitive to the starting values of the parameters, meaning that the supervised approach is still of interest for initialization and model comparison. Using an unsupervised model involving three matrices, the average AIC gain per site with TreeBase test alignments is 0.31, 0.49 and 0.61 compared with LG (named after Le & Gascuel 2008 Mol. Biol. Evol. 25 , 1307–1320), WAG and JTT, respectively. This three-matrix model is significantly better than LG for 34 alignments (among 57), and significantly worse for 1 alignment only. Moreover, tree topologies inferred with our mixture models frequently differ from those obtained with single matrices, indicating that using these mixtures impacts not only the likelihood value but also the output tree. All our models and a PhyML implementation are available from http://atgc.lirmm.fr/mixtures .

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Gunda, R., S. Gau, and C. Dohrmann. "Analytical Model of Tire Cavity Resonance and Coupled Tire/Cavity Modal Model." Tire Science and Technology 28, no. 1 (January 1, 2000): 33–49. http://dx.doi.org/10.2346/1.2135990.

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Abstract The acoustic resonance of the air cavity in the tire/wheel assembly may be a contributor to vehicle interior noise through the structure-borne noise transmission path. This problem has been examined in the past using approximate closed form solutions (based on plane wave theory for a two-tube model) and numerically, using FEA. The coupling between the cavity resonance and structural resonance of the wheel may result in higher levels of interior noise as noted previously. The two primary goals of this paper are (1) to develop simple analytical models to gain fundamental understanding of some observed phenomena and for a quick estimation of cavity resonance frequency to assist in the design process, and (2) to develop tire modal models incorporating the acoustic cavity to predict coupled system natural frequencies and response. An improved analytical model for accurate calculation of acoustic cavity resonance frequencies of a static, unloaded tire is developed using variational principles. The sensitivities of the cavity resonance frequencies to tire width and aspect ratio are examined. For the case of a loaded tire, an improved analytical formulation based on plane wave propagation (for linearly varying cross-sectional area) is developed. Deformed structure geometry from FEA is used as input to the analytical model. The FEA-based methodology used in the tire/cavity coupling analysis is as follows: The tire structural modes are calculated, ignoring the effect of the acoustic cavity. The tire cavity modes are calculated using deformed cavity geometry only. Next, the structural/acoustic coupling matrix is calculated. Finally, a coupled cavity-structure modal model is generated from modal mass and stiffness of the tire/wheel assembly, the cavity modal matrices, and the coupling matrix. This process is an improvement over conventional tire modal models, which only include structural modes.

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Yang, W. C., and W. E. Tobler. "Dissipative Modal Approximation of Fluid Transmission Lines Using Linear Friction Model." Journal of Dynamic Systems, Measurement, and Control 113, no. 1 (March 1, 1991): 152–62. http://dx.doi.org/10.1115/1.2896342.

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For both hydraulic and pneumatic transmission lines, analytical dissipative modal approximation techniques, which take into account the frequency dependent viscosity and heat transfer effects, are developed by introducing frequency dependent damping and natural frequency modification factors to the quadratic modes obtained analytically from linear friction model. The main advantage over the existing dissipative modal approximations is that the modal parameters of the resulting modal transfer function matrices and modal state space equations can be determined analytically rather than determined by table and/or numerical computer calculations. This introduces modeling flexibilities and greatly alleviates the difficulties of modeling complex fluid networks but still maintaining the modal accuracy and complexities. Unit step response comparisons are made with quasi-method of characteristics showing good agreements for both hydraulic and pneumatic lines.

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33

KUROKI, TSUNEHIDE, and FUMIHIKO SUGINO. "SPONTANEOUS SUPERSYMMETRY BREAKING BY LARGE-N MATRICES." International Journal of Modern Physics A 23, no. 14n15 (June 20, 2008): 2192–94. http://dx.doi.org/10.1142/s0217751x08040809.

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Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity.

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34

Kane, K., and B. J. Torby. "The Extended Modal Reduction Method Applied to Rotor Dynamic Problems." Journal of Vibration and Acoustics 113, no. 1 (January 1, 1991): 79–84. http://dx.doi.org/10.1115/1.2930159.

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In this paper, the existing Modal Reduction Method, which was developed to handle symmetric mass and stiffness matrices, is extended utilizing state-space formulation to handle nonsymmetric mass, damping, and stiffness matrices. These type of matrices typically accompany rotor dynamic problems since journal bearings supporting the rotor have nonsymmetric stiffness and damping characteristics. The purpose of modal reduction is to eliminate unimportant modes and degrees of freedom from the analytical model after they are found, so that further numerical analysis can be accelerated. The reduction described here leaves the retained eigenvalues and mode shapes unaltered from their original values. This method is demonstrated for a simple rotor problem having nonsymmetric system matrices including gyroscopic effects.

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35

Jiang, Jiashang, and Yongxin Yuan. "Updating Stiffness and Hysteretic Damping Matrices Using Measured Modal Data." Shock and Vibration 2018 (2018): 1–7. http://dx.doi.org/10.1155/2018/3727021.

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A new direct method for the finite element (FE) matrix updating problem in a hysteretic (or material) damping model based on measured incomplete vibration modal data is presented. With this method, the optimally approximated stiffness and hysteretic damping matrices can be easily constructed. The physical connectivity of the original model is preserved and the measured modal data are embedded in the updated model. The numerical results show that the proposed method works well.

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36

Li, Yao Xiang, and Li Chun Jiang. "Fitting Growth Model Using Nonlinear Regression with Random Parameters." Key Engineering Materials 480-481 (June 2011): 1308–12. http://dx.doi.org/10.4028/www.scientific.net/kem.480-481.1308.

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Mixed Effect models are flexible models to analyze grouped data including longitudinal data, repeated measures data, and multivariate multilevel data. One of the most common applications is nonlinear growth data. The Chapman-Richards model was fitted using nonlinear mixed-effects modeling approach. Nonlinear mixed-effects models involve both fixed effects and random effects. The process of model building for nonlinear mixed-effects models is to determine which parameters should be random effects and which should be purely fixed effects, as well as procedures for determining random effects variance-covariance matrices (e.g. diagonal matrices) to reduce the number of the parameters in the model. Information criterion statistics (AIC, BIC and Likelihood ratio test) are used for comparing different structures of the random effects components. These methods are illustrated using the nonlinear mixed-effects methods in S-Plus software.

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37

Adachi, Kohei. "An unfolding model for confusion matrices." Japanese journal of psychology 66, no. 1 (1995): 58–62. http://dx.doi.org/10.4992/jjpsy.66.58.

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38

Cottereau, Régis, Didier Clouteau, Christian Soize, and Simon Cambier. "Probabilistic nonparametric model of impedance matrices." European Journal of Computational Mechanics 15, no. 1-3 (January 2006): 131–42. http://dx.doi.org/10.3166/remn.15.131-142.

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39

Comper, W. D., L. Pratt, C. J. Handley, and G. S. Harper. "Cell transport in model extracellular matrices." Archives of Biochemistry and Biophysics 252, no. 1 (January 1987): 60–70. http://dx.doi.org/10.1016/0003-9861(87)90008-7.

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40

DEGUCHI, TETSUO. "BRAIDS, LINK POLYNOMIALS AND TRANSFORMATIONS OF SOLVABLE MODELS." International Journal of Modern Physics A 05, no. 11 (June 10, 1990): 2195–239. http://dx.doi.org/10.1142/s0217751x9000101x.

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It is shown that braid matrices and link polynomials can be systematically constructed from exactly solvable models in statistical mechanics. Through symmetry breaking transformations, different braid matrices are derived from a solvable model. By associating the Markov traces with multi-variable representations, multi-variable link polynomials are obtained. Infinitesimal operators for braid matrices are constructed. Connection of our approach to the conformal field theories and the topological quantum field theory is discussed.

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41

Vázquez da Silva, M., and João M. P. Q. Delgado. "Extraction of Useful Food and Cosmetic Ingredients of Vegetable Origin." Defect and Diffusion Forum 312-315 (April 2011): 1161–66. http://dx.doi.org/10.4028/www.scientific.net/ddf.312-315.1161.

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In the present work, three different mathematical models that can be applied to simulate the supercritical fluid extraction from herbaceous matrices were studied: Single-Sphere Model I (SS I), Single-Sphere Model II (SS II) and Characteristic Time Model (CTM). It was tested and compared the agreement between models results and available experimental data reported in literature.

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42

Dyda, Alexander Aleksandrovich, Kseniya Chumakova, and Van Thanh Nguyen. "DESIGNING SHIP COURSE MOVEMENT USING PSEUDOINVERSE MATRICES FOR MEASURING STATE VECTOR OF CONTROLLED OBJECT." Vestnik of Astrakhan State Technical University. Series: Management, computer science and informatics 2021, no. 1 (January 25, 2021): 61–69. http://dx.doi.org/10.24143/2072-9502-2021-1-61-69.

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To configure the control systems of the ship movement along the trajectory, it is necessary to be concerned with the parameters of its controllability. There has been proposed building a matrix model based on measurements of the state vector of a controlled object. The construction of the model is considered on the example of the problem of ship course control. An algorithm for determining the matrix coefficients of the selected model is proposed. The operation of the considered algorithm has been checked for square matrices by finding their inverse matrices, as well as for rectangular matrices for which the pseudo inverse matrix was found. The illustration of the proposed approach is carried out using the example of a simple 1-order linear Nomoto model. The considered approach is quite universal and can be applied to higher order models, including nonlinear ones.

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43

KAVALOV, AL R., R. L. MKRTCHYAN, and L. A. ZURABYAN. "RANDOM MATRICES WITH DISCRETE SPECTRUM AND FINITE TODA CHAINS." Modern Physics Letters A 06, no. 39 (December 21, 1991): 3627–33. http://dx.doi.org/10.1142/s0217732391004188.

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Restricting the eigenvalues of matrices in random matrix models produces different models (Hermitian, unitary, (anti)symmetric, Penner's, etc.). We consider the model in which the eigenvalues receive values from some discrete finite set of points, establish the connection of such a model with a finite Toda chain and study the details of this connection. We derive also the string equation, which in the limit, when eigenvalues become dense on a real axis, tends to the usual string equation.

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Li, Cai Zhen, Fei Liu, Cong Bo Li, and Qiu Lian Wang. "Analysis Model for Energy Consumption in Manufacturing Enterprises Based on Input-Output Theory and its Applications." Applied Mechanics and Materials 16-19 (October 2009): 1058–63. http://dx.doi.org/10.4028/www.scientific.net/amm.16-19.1058.

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Analysis of energy consumption which could explore energy saving potential is of important significance for energy saving in manufacturing enterprises. An analysis model including physical and monetary input-output models for energy consumption in manufacturing enterprises based on input-output theory is constructed. Physical and monetary energy consumption coefficient matrices are obtained from the analysis model. Then, some application ideas are proposed, including vertical and horizontal comparison of coefficient matrices elements of a manufacturing enterprise in per unit time, comparison of coefficient matrices elements of a manufacturing enterprise in different unit times, comparison of coefficient matrices elements of manufacturing enterprises within the same industry in per unit time, effect analysis of energy price change to energy consumption of a manufacturing enterprise. Finally, a case study of a heavy-machinery manufacturing enterprises validates its practicability.

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45

PATGIRI, MAHADEV, and N. NIMAI SINGH. "RIGHT-HANDED MAJORANA NEUTRINO MASS MATRICES FOR GENERATING BIMAXIMAL MIXINGS IN DEGENERATE AND INVERTED MODELS OF NEUTRINOS." International Journal of Modern Physics A 18, no. 05 (February 20, 2003): 743–53. http://dx.doi.org/10.1142/s0217751x03014022.

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An attempt is made to generate the bimaximal mixings of the three species of neutrinos from the textures of the right-handed Majorana neutrino mass matrices. We extend our earlier work in this paper for the generation of the nearly degenerate as well as the inverted hierarchical models of the left-handed Majorana neutrino mass matrices using the non-diagonal textures of the right-handed Majorana neutrino mass matrices and the diagonal form of Dirac neutrino mass matrices, within the framework of the see-saw mechanism in a model independent way. Such Majorana neutrino mass models are important in explaining the recently reported result on the neutrinoless double beta decay (0νββ) experiment, together with the earlier established data on LMA MSW solar and atmospheric neutrino oscillations.

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Vaca Oyola, Luis S., Mónica R. Jaime Fonseca, and Ramsés Rodríguez Rocha. "Damaged Flexibility Matrix Method for Damage Detection of Frame Buildings." Advances in Civil Engineering 2020 (February 10, 2020): 1–14. http://dx.doi.org/10.1155/2020/3534957.

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This study presents the damaged flexibility matrix method (DFM) to identify and determine the magnitude of damage in structural elements of plane frame buildings. Damage is expressed as the increment in flexibility along the damaged structural element. This method uses a new approach to assemble the flexibility matrix of the structure through an iterative process, and it adjusts the eigenvalues of the damaged flexibility matrices of each system element. The DFM was calibrated using numerical models of plane frames of buildings studied by other authors. The advantage of the DFM, with respect to other flexibility-based methods, is that DFM minimizes the adverse effect of modal truncation. The DFM demonstrated excellent accuracy with complete modal information, even when it was applied to a more realistic scenario, considering frequencies and modal shapes measured from the recorded accelerations of buildings stories. The DFM also presents a new approach to simulate the effects of noise by perturbing matrices of flexibilities. This approach can be useful for research on realistic damage detection. The combined effects of incomplete modal information and noise were studied in a ten-story four-bay building model taken from the literature. The ability of the DFM to assess structural damage was corroborated. Application of the proposed method to a ten-story four-bay building model demonstrates its efficiency to identify the flexibility increment in damaged structural elements.

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47

Carvalho, Carolina Goulart de, Eduardo C. Marques Costa, Sérgio Kurokawa, and José Pissolato. "Alternative Phase-domain Model for Multi-conductor Transmission Lines Using Two Modal Transformation Matrices." Electric Power Components and Systems 44, no. 3 (December 29, 2015): 291–301. http://dx.doi.org/10.1080/15325008.2015.1110733.

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Logofet, D. O., and I. N. Belova. "Nonnegative matrices as a tool to model population dynamics: Classical models and contemporary expansions." Journal of Mathematical Sciences 155, no. 6 (November 22, 2008): 894–907. http://dx.doi.org/10.1007/s10958-008-9249-2.

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49

Campbell, Christopher S., and Dominic W. Massaro. "Perception of Visible Speech: Influence of Spatial Quantization." Perception 26, no. 5 (May 1997): 627–44. http://dx.doi.org/10.1068/p260627.

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Visible speech reading was studied to determine which features are functional and to test several models of pattern recognition. Nine test syllables differing in their initial consonant were presented in intact form or under various levels of spatial quantization. Performance decreased in increasing quantization but remained relatively good at moderate levels of degradation. Different models were tested against the confusion matrices. Six features were identified as functional in distinguishing among the nine consonant – vowel syllables. These features were used as sources of information in a fuzzy-logical model of perception and an additive model. The fuzzy-logical model provided a significantly better description of the confusion matrices, showing that speech reading is analogous to other domains of pattern recognition such as face recognition and facial-affect perception.

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50

Giorgio, Giorgi, and Cesare Zuccotti. "Metzlerian and Generalized Metzlerian Matrices: Some Properties and Economic Applications." Journal of Mathematics Research 7, no. 2 (March 26, 2015): 42. http://dx.doi.org/10.5539/jmr.v7n2p42.

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In the first part of the paper we consider the main properties, with respectto stability and existence of solutions of multi-sectoral economic models,of Metzlerian and Morishima matrices. In the second part we introducevarious generalized Metzlerian matrices, in order to enlarge the results ofOhyama (1972) in the study of stability and comparative statics for aWalrasian-type equlibrium model.

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