Order Transfer Matrices Research Articles

A spectral global matrix method for modelling the response of a fluid-loaded multilayered cylindrical shell excited by an acoustic plane wave

This paper proposes a numerically stable method for modelling a fluid-loaded multilayered cylindrical shell excited by a plane wave, which solves the fd instability problem that is usually observed when using the well-known transfer matrix method (TMM). In the considered modelling, each layer can be either a viscoelastic coating described by a general three-dimensional (3D) elasticity model or an intermediate perfect fluid layer. The transfer matrix of each layer relating the state vector at the layer's two interfaces is estimated with an appropriate standard method. Instead of multiplying together the layer transfer matrices in order to deduce the transfer matrix of the multilayer cylinder, we propose an alternative approach. This one consists in writing the continuity relations at each interface of the considered systems and in building a global matrix that can be solved to obtain the system response. As shown by numerical applications on typical naval test cases, the proposed global matrix assembly procedure as opposed to the classical TMM provides numerical stability over both a wide range of axial wavenumbers and circumferential orders, but also the ability to consider intermediate fluid layers. Besides, this model is well-suited to describe elastic solid layers of any anisotropy as illustrated by an additional case considering a transverse isotropic layer.

Third order transfer matrices for real Wien filters with homogeneous main fields

The determination of the ion optical aberrations of the Wien filters operated independently or in more complex mass analyzing or charged particle transport systems needs the calculation of the trajectories in a third order approximation. The trajectory calculations for crossed electric and magnetic fields generate unmanageably long formulas for the matrix elements. The reduction of the extent of the matrix elements to usable size can be reached by restricting calculations to less complex configurations as the homogeneous main fields Wien filters, which are probably the most often used crossed field velocity filters. Analytic expressions for transfer matrix elements for homogeneous main fields Wien filters were determined up to third order accuracy level. The elements of three pairs of matrices, those of entry fringing fields, those of the main fields and those of the exit fringing fields were derived for the plane of mass dispersion (radial) and for a direction normal to it (axial). The third order accuracy was kept over all the calculated contributions to the ion trajectory. The first order elements, to be multiplied by first order small quantities were calculated in a second order approximation, those of second order with a first order accuracy, while those of third order were not allowed to contain small quantities in their expressions. The matrix elements describing the ion position, trajectory slope, ion energy and mass were accounted for. In the fringing field matrix elements the effect of the electric and magnetic field boundary curvature radii were included. In a brief application, on one spectrometer geometry, the calculated matrices were used to determine the effect of third order angular aberration generated by the Wien filter alone on the resolution when the second order aberration has been cancelled.

Uniform Spectral Properties of One-Dimensional Quasicrystals, II. The Lyapunov Exponent

In this Letter we introduce a method that allows one to prove uniform local results for one-dimensional discrete Schrodinger operators with Sturmian potentials. We apply this method to the transfer matrices in order to study the Lyapunov exponent and the growth rate of eigenfunctions. This gives uniform vanishing of the Lyapunov exponent on the spectrum for all irrational rotation numbers. For irrational rotation numbers with bounded continued fraction expansion, it gives uniform existence of the Lyapunov exponent on the whole complex plane. Moreover, it yields uniform polynomial upper bounds on the growth rate of transfer matrices for irrational rotation numbers with bounded density. In particular, all our results apply to the Fibonacci case.

Semiconductivity of Protein: The Saxon–Hutner–Luttinger Theorem in Biopolymers

We study semiconductivity of protein with a primary structure, where we use the transfer matrix method of the tight-binding model for electrons in a protein. We first introduce the model and the scheme for obtaining the spectrum. Second, we set up the transfer matrices in order to apply for a protein with an amino acid sequence. Third, we prove the Saxon–Hutner conjecture for the one-dimensional disordered polyatomic chains, and apply it to the protein system. We show that this theorem provides a good foundation for understanding the intriguing semiconductive character of the protein, which was first suggested by Szent–Györgyi a long time ago.

Transfer Matrices From the AES‐LRT Model

Abstract The Canadian Atmospheric Environment Service (A ES) Long‐ Range Transport (LRT) model has been used in the Canada‐United States Memorandum of Intent programme to compute transfer matrices in order to quantify the source‐receptor relationships between emission regions and selected receptor sites. Four‐day backward trajectories were computed from the selected sites for the year 1978 and were started from the 925‐mb level(∼600 m). The Lagrangian concentration / deposition model computed sulphur concentrations and depositions for 9 receptor sites using an emissions inventory divided into 15 Canadian and25 United States emission regions. The 40×9 source‐receptor matrices show that the greatest impact on a receptor site usually results from an emission region close to the site although the regions giving the greatest impact for air concentration and wet deposition are not necessarily identical. In addition, the matrices show the impacts of all the emission regions on all of the receptor sites ranked by...

An Exact Benchmark Calculation for l′th Mode Multigroup Transfer Matrix Analysis

There are few exact numerical solutions to which results from multigroup transfer matrix algorithms can be compared. Therefore, for isotropic elastic scattering in the center-of-mass system, exact numerical values have been calculated for , the average Legendre coefficient of the scattered particle in the laboratory system. Both projectile and target masses are allowed to vary between 1 and 238 amu. It can be concluded that significant numerical uncertainties are possible in the calculation of the higher order transfer matrices.

First order transfer matrices for relativistically fast particles in magnetic and electric sector fields and quadrupoles

The lateral motions and flight time deviations of relativistically fast particles in magnetic or electrostatic sector fields or quadrupoles are described. All effects are presented in the form of transfer matrices.

Design of a High Resolution Ultrahigh Vacuum Electron Spectrometer

With the help of second order transfer matrices the focusing properties and second order image aberrations of a spherical electrostatic analyser have been calculated including all effects of the fringing fields. Using these results a new ultrahigh vacuum electron spectrometer has been constructed. Theoretical data for the image aberrations and the window function of the spectrometer are presented and compared with experimental results. A brief description of the apparatus is given.

Third order transfer matrices for the fringing field of magnetic and electrostatic quadrupole lenses

Third order transfer matrices are derived for the fringing field of magnetic and electrostatic quadrupole lenses. All ion optical effects of the fringing field are reduced to a simple transformation at the ideal field boundary. The dominant third order elements are independent of the distribution of the fringing field. The other third order and the first order elements can be evaluated using the distribution function of the field gradient. The calculations are done in an effective fourth order approximation under the assumption that the extension of the fringing field is of about the same size as the beam diameter.

Stability conditions for the spatial focusing in a racetrack microtron

The free parameters available to obtain a beam of limited extension in a racetrack microtron are investigated and discussed. The obtained result may be thought as a generalization of the analogous synchrotron problem. First order transfer matrices will be used to approach the problem. The influence of possible approximations will also be discussed.

Third order transfer matrices of the fringing field of an inhomogeneous magnet

All ion optical fringing field effects of an inhomogeneous magnet are described in the transfer matrix representation. The resulting 49 × 49 matrices include all radial effects due to oblique and curved field boundaries in a third order approximation. The elements of the 10 × 10 axial transfer matrices necessary to describe all corresponding axial effects in a second order approximation are also derived. The necessary radial shifts of the optic axes are determined in a third order approximation.

Second order transfer matrices of real magnetic and electrostatic sector fields

With the help of second order transfer matrices 1 ) it is easily possible to calculate focusing and dispersion properties as well as second order image aberrations of any ion optical apparatus consisting of one or of several sector fields. Taking into account, in addition to the defrections in the main fields, all effects of the fringing fields 2,3 ), such transfer matrices are presented here for magnetic and electrostatic sector fields which have circular main paths in the main deflecting fields.