180 research outputs found
Polarization Elements-A Group Theoretical Study
The Classification of Polarization elements, the polarization affecting
optical devices which have a Jones matrix representation, according to the
types of eigenvectors they possess, is given a new visit through the
Group-theoretical connection of polarization elements. The diattenuators and
retarders are recognized as the elements corresponding to boosts and rotations
respectively. The structure of homogeneous elements other than diattenuators
and retarders are identified by giving the quaternion corresponding to these
elements. The set of degenerate polarization elements is identified with the so
called `null' elements of the Lorentz Group. Singular polarization elements are
examined in their more illustrative Mueller matrix representation and finally
the eigenstructure of a special class of singular Mueller matrices is studied.Comment: 7 pages, 2 tables, submitted to `Optics Communications
Fatigue Strength Improvement of Welded Structures Using New Low Transformation Temperature Filler Materials
AbstractThe results reported in this research study are part of a larger EU RFCS (Research Fund for Coal and Steel) project where the aim is to study the fatigue behavior of improved welds in high strength steels by utilizing different improvement techniques. In this particular study LTT (Low Transformation Temperature) weld filler material have been investigated and their possibility to improve the fatigue strength. The characteristic of these filler material is that they undergo phase transformation at temperature close to room temperature which will reduce the tensile residual stress in the weld and in some cases result in compressive residual stresses. Two different LTT alloy compositions have been developed, with different Ms (Martensite Start) temperatures in order to study the amount of tensile/compressive residual stresses produced by these wires. Welding residual stress measurements were carried out by X-ray diffraction technique. Plates with welded longitudinal attachments were fabricated in 700MPa and 960MPa steel grades using different LTT filler materials. These specimens were fatigue tested in constant and variable amplitude loading and the fatigue test results were compared with results from specimen welded with conventional weld filler material
Exact Solutions to the Sine-Gordon Equation
A systematic method is presented to provide various equivalent solution
formulas for exact solutions to the sine-Gordon equation. Such solutions are
analytic in the spatial variable and the temporal variable and they
are exponentially asymptotic to integer multiples of as
The solution formulas are expressed explicitly in terms of a real triplet of
constant matrices. The method presented is generalizable to other integrable
evolution equations where the inverse scattering transform is applied via the
use of a Marchenko integral equation. By expressing the kernel of that
Marchenko equation as a matrix exponential in terms of the matrix triplet and
by exploiting the separability of that kernel, an exact solution formula to the
Marchenko equation is derived, yielding various equivalent exact solution
formulas for the sine-Gordon equation.Comment: 43 page
Stability of polar decompositions
Certain continuity properties of the factors in generalized polar decompositions of real and complex matrices are studied. A complete characterization is given of those generalized polar decompositions that persist under small perturbations in the matrix and in the scalar product. Connections are made with quadratic matrix equations, and with stability properties of certain invariant subspaces
Explicit solutions to the Korteweg-de Vries equation on the half line
Certain explicit solutions to the Korteweg-de Vries equation in the first
quadrant of the -plane are presented. Such solutions involve algebraic
combinations of truly elementary functions, and their initial values correspond
to rational reflection coefficients in the associated Schr\"odinger equation.
In the reflectionless case such solutions reduce to pure -soliton solutions.
An illustrative example is provided.Comment: 17 pages, no figure
A unified approach to Darboux transformations
We analyze a certain class of integral equations related to Marchenko
equations and Gel'fand-Levitan equations associated with various systems of
ordinary differential operators. When the integral operator is perturbed by a
finite-rank perturbation, we explicitly evaluate the change in the solution. We
show how this result provides a unified approach to Darboux transformations
associated with various systems of ordinary differential operators. We
illustrate our theory by deriving the Darboux transformation for the
Zakharov-Shabat system and show how the potential and wave function change when
a discrete eigenvalue is added to the spectrum.Comment: final version that will appear in Inverse Problem
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