Search results for "Matrix"
showing 10 items of 3205 documents
Speed-dependent broadening and line mixing in CH4 perturbed by Ar and N2 from multispectrum fits
2000
International audience; Speed-dependent broadenings and shifts have been determined for the P and R branches of the nu3 band of CH4 perturbed by Ar and N2 using a multispectrum fitting analysis of high-resolution tunable difference-frequency laser spectra recorded at pressures 3, the tetrahedral fine structure components in each J manifold are collisionally coupled and exhibit significant interference. The coupled lines are treated using a speed-dependent first-order line-mixing profile and are compared to a speed-independent full relaxation matrix inversion procedure with off-diagonal coupling elements calculated from an atom-atom Lennard-Jones potential model.
FDTD characterization of evanescent modes-multimode analysis of waveguide discontinuities
2000
In this paper, a finite-difference time-domain numerical dispersion relation for evanescent waves is derived, and its impact on the modeling accuracy is studied. The numerical evanescent constant is found to differ from the analytical one. As a result, a correction must be used to compute discontinuity parameters. This influences the reference plane chosen for the analysis of propagating modes. Moreover, on calculating multimode transmission and reflection coefficients, the dispersion for evanescent higher order modes is determinant. The dispersive relation is derived, discussed, and used to correct the evanescent constants for the multimode analysis of a waveguide discontinuity.
Analysis of inhomogeneously filled waveguides using a bi-orthonormal-basis method
2000
A general theoretical formulation to analyze inhomogeneously filled waveguides with lossy dielectrics is presented in this paper. The wave equations for the tranverse-field components are written in terms of a nonself-adjoint linear operator and its adjoint. The eigenvectors of this pair of linear operators define a biorthonormal-basis, allowing for a matrix representation of the wave equations in the basis of an auxiliary waveguide. Thus, the problem of solving a system of differential equations is transformed into a linear matrix eigenvalue problem. This formulation is applied to rectangular waveguides loaded with an arbitrary number of dielectric slabs centered at arbitrary points. The c…
Closed form for two-photon free–free transition matrix elements
2000
Abstract Two-photon free–free transitions happen in the multiphoton ionization with more than one excess photon and in bremsstralung. Up to now, the configuration space free–free transition amplitudes have not been written in closed form. We propose a modified Coulomb Green’s function (CGF) Sturmian expansion which allows one to obtain expressions for two-photon radial transition matrix elements in the closed form which are easy to continue analytically to calculate free–free transitions in H.
Control of matrix interferences by the multiple linear regression model in the determination of arsenic, antimony and tin in lead pellets by inductiv…
2002
A multiple linear regression technique was used to evaluate the matrix interferences in the determination of hydride-forming elements in lead shotgun pellets by inductively coupled plasma atomic emission spectrometry. The determination of arsenic, antimony, and tin in SRM C2416 (Bullet Lead) by ICP-AES failed to obtain the certified concentrations at the 95% level of confidence using the t-test. However, it proved possible, by using the multiple linear regression technique, to correct the concentrations of all three elements to a statistically acceptable level. This method of correction is based on the multiple regression line obtained from the analysis of 19 synthetic mixtures of matrix el…
Structure of eigenvectors of random regular digraphs
2018
Let $d$ and $n$ be integers satisfying $C\leq d\leq \exp(c\sqrt{\ln n})$ for some universal constants $c, C>0$, and let $z\in \mathbb{C}$. Denote by $M$ the adjacency matrix of a random $d$-regular directed graph on $n$ vertices. In this paper, we study the structure of the kernel of submatrices of $M-z\,{\rm Id}$, formed by removing a subset of rows. We show that with large probability the kernel consists of two non-intersecting types of vectors, which we call very steep and gradual with many levels. As a corollary, we show, in particular, that every eigenvector of $M$, except for constant multiples of $(1,1,\dots,1)$, possesses a weak delocalization property: its level sets have cardin…
Low-Rank Tucker-2 Model for Multi-Subject fMRI Data Decomposition with Spatial Sparsity Constraint
2022
Tucker decomposition can provide an intuitive summary to understand brain function by decomposing multi-subject fMRI data into a core tensor and multiple factor matrices, and was mostly used to extract functional connectivity patterns across time/subjects using orthogonality constraints. However, these algorithms are unsuitable for extracting common spatial and temporal patterns across subjects due to distinct characteristics such as high-level noise. Motivated by a successful application of Tucker decomposition to image denoising and the intrinsic sparsity of spatial activations in fMRI, we propose a low-rank Tucker-2 model with spatial sparsity constraint to analyze multi-subject fMRI dat…
EPR Studies of Atomic Impurities in Rare Gas Matrices
2003
In this article we give an overview of the matrix isolation technique combined with electron paramagnetic resonance (EPR) detection for embedded atomic impurities in solid rare gases. A special emphasis is put on impurity – matrix coupling effects combining both experimental and theoretical approaches.
Electronic Spectroscopy of C2 in Solid Rare Gas Matrixes
2006
Electronic spectroscopy of the C(2) molecule is investigated in Ar, Kr, and Xe matrixes in the 150-500 nm range. In the Ar matrix, the D ((1)Sigma(u)(+)) <-- ((1)Sigma(g)(+)) Mulliken band near 240 nm is the sole absorption in the UV range, whereas in the Kr matrix additional bands in the 188-209 nm range are assigned to the Kr(n)()(+)C(2)(-) <-- Kr(n)()C(2) charge-transfer absorptions. Because of the formation of a bound C(2)Xe species, the spectral observations in the Xe matrix differ dramatically from the lighter rare gases: the Mulliken band is absent and new bands appear near 300 and 423 nm. The latter is assigned to the forbidden B'((1)Sigma(g)(+)) <-- X ((1)Sigma(g)(+)) transition, b…
Study of periodic Dielectric Frequency-Selective Surfaces under 3D plane wave incidence
2016
A periodic Dielectric Frequency-Selective Surface (DFSS) is studied under 3D plane-wave incidence, whose unit cell in the periodic direction is composed of a dielectric grating and a homogeneous dielectric layer. The structure is excited by a linearly polarized plane-wave. The procedure for computing the Brillouin diagram of the structure under 2D plane-wave incidence with TE or TM polarization was already described by the authors, and the extension to the 3D incidence case has been performed in a similar way. Following the same formalism, it has been obtained the Generalized Scattering Matrix (GSM) of one period of the infinite periodic lattice. This requires the knowledge of the modal spe…