Search results for "Matrix"
showing 10 items of 3205 documents
Spectroscopy of Hexafluorides with an Odd Number of Electrons: The Vibronic Bands of IrF6
1996
Abstract The low resolution absorption spectroscopy of the first five excited electronic states of IrF 6 has made possible some new assignments for the vibronic transitions of this molecule, and the determination of new vibronic parameter values. They are more accurate than those found in the literature. In this aim, we introduce a simplified tensorial formulation for the linear Jahn–Teller terms in a fourfold degenerate electronic state of an XY 6 -type molecule, which allows easier computation of matrix elements and avoids the use of perturbation theory. Methods for IrF 6 synthesis (using a dynamical flow system) and purification are also presented.
Effect of Topological Structure and Coupling Strength in Weighted Multiplex Networks
2018
Algebraic connectivity (second smallest eigenvalue of the supra-Laplacian matrix of the underlying multilayer network) and inter-layer coupling strength play an important role in the diffusion processes on the multiplex networks. In this work, we study the effect of inter-layer coupling strength, topological structure on algebraic connectivity in weighted multiplex networks. The results show a remarkable transition in the value of algebraic connectivity from classical cases where the inter-layer coupling strength is homogeneous. We investigate various topological structures in multiplex networks using configuration model, the Barabasi-Albert model (BA) and empirical data-set of multiplex ne…
Anisotropy in strain gradient elasticity: Simplified models with different forms of internal length and moduli tensors
2018
Abstract Anisotropy of centro-symmetric (first) strain gradient elastic materials is addressed and the role there played by the dual gradient directions (i.e. directions of strain gradient and of double stress lever arm) is investigated. Anisotropy manifests itself not only through the classical fourth-rank elasticity tensor C (21 independent constants) in the form of moduli anisotropy, but also through a sixth-rank elasticity tensor B (171 independent constants) in a unified non-separable form as compound internal length/moduli anisotropy. Depending on the microstructure properties, compound anisotropy may also manifest itself in a twofold separable form through a decoupled tensor B = L C …
Stability analysis of an electromagnetically levitated sphere
2006
We present a combined numerical and analytical approach to analyze the static and dynamic stabilities of an electromagnetically levitated spherical body depending on the ac frequency and the configuration of a three-dimensional (3D) coil made of thin winding which is modeled by linear current filaments. First, we calculate numerically the magnetic vector potential in grid points on the surface of the sphere and then use Legendre and fast Fourier transforms to find the expansion of the magnetic field in terms of spherical harmonics. Second, we employ a previously developed gauge transformation to solve analytically the 3D electromagnetic problem in terms of the numerically obtained expansion…
S-matrix formulation of mesoscopic systems and evanescent modes.
2009
The Landauer-Butikker formalism is an important formalism to study mesoscopic systems. Its validity for linear transport is well established theoretically as well as experimentally. Akkermans et al [Phys. Rev. Lett. {\bf 66}, 76 (1991)] had shown that the formalism can be extended to study thermodynamic properties like persistent currents. It was earlier verified for simple one dimensional systems. We study this formula very carefully and conclude that it requires reinterpretation in quasi one dimension. This is essentially because of the presence of evanescent modes in quasi one dimension.
Lifetime of the 4D 3/2 and 4D 5/2 metastable states in Sr II
1987
Sr+ ions were confined in a r.f. quadrupole trap for times of the order of 30 min. The metastable 4D states were populated via laser excitation of the 5P states. The weak quadrupole transition rate into the 5S 1/2 ground state at 674 and 687 nm was deduced from observation of the exponential decay. At background pressures above 10−7 mbar the radiative decay is dominated by collisional quenching. Extrapolation of the observed decay rate to zero background pressure yields the radiative lifetimes. At pressures around 10−6 mbar fine structure mixing collisions between the 4D states have been observed, which lead to corrections of the extrapolated lifetimes. As the final result we obtain 395±38 …
A finite difference time domain model for the Titan ionosphere Schumann resonances
2007
[1] This paper presents a numerical approach to model the electrical properties of Titan's atmosphere. The finite difference time domain technique is applied to model the atmosphere of Saturn's satellite in order to determine Schumann resonant frequencies and electromagnetic field distributions at the extremely low frequency range. Spherical coordinates are employed, and periodic boundary conditions are implemented in order to exploit the symmetry in rotation of the celestial body. Results are compared with a previous model using the transmission line matrix method up to 180 km altitude. For the first time a numerical FDTD model up to 800 km altitude is carried out, and we report lower freq…
Reduced scaling in electronic structure calculations using Cholesky decompositions
2003
The small numerical rank of the two-electron integral matrix for large molecular systems and large basis sets was demonstrated. Though, the current implementation still requires some improvements on the calculations done in the inner most loop of the decomposition do not exploit the parsity in the Cholesky vectors. With respect to the practical applicability of the presented method an efficient approach to geometrical derivatives was imperative. Such an approach was obtained including certain derivative product functions and decomposing an expanded integral matrix.
Multichannel0→2and1→2transition amplitudes for arbitrary spin particles in a finite volume
2015
We present a model-independent, nonperturbative relation between finite-volume matrix elements and infinite-volume $\mathbf{0}\ensuremath{\rightarrow}\mathbf{2}$ and $\mathbf{1}\ensuremath{\rightarrow}\mathbf{2}$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utilit…
Ordinary muon capture studies for the matrix elements in ββ decay
2018
Precise measurement of $\gamma$-rays following ordinary (non-radiative) capture of negative muons by natural Se, Kr, Cd and Sm, as well as isotopically enriched $^{48}$Ti, $^{76}$Se, $^{82}$Kr, $^{106}$Cd and $^{150}$Sm targets was performed by means of HPGe detectors. Energy and time distributions were investigated and total life time of negative muon in different isotopes was deduced. Detailed analysis of $\gamma$-lines intensity allows to extract relative yield of several daughter nuclei and partial rates of ($\mu$,$\nu$) capture to numerous excited levels of the $^{48}$Sc, $^{76}$As, $^{82}$Br, $^{106}$Ag and $^{150}$Tc isotopes which are considered to be virtual states of an intermedia…