We have generalized the ABCD propagation law, Q(2) = (AQ(1) + B)/(CQ(1) + D), for an optical system by introducing a generalized complex radius of curvature Q for a general optical beam. The real part of 1/Q is related to the mean radius of curvature of the wave front, while the imaginary part is related to the second moment of the amplitude of the beam.

The geometrical structure of the magnetic field is a critical character in the magnetospheric dynamics. Using the magnetic field data measured by the Cluster constellation satellites, the geometrical structure including the curvature radius, directions of curvature and normal of the osculating planes of the magnetic field lines within the current sheet/neutral sheet have been investigated. The ...

Free energy as a function of temperature and the bubble radius is determined for spherical bubbles created in cosmological first order phase transitions. The phase transition is assumed to be driven by an order parameter (e.g. a Higgs field) with quartic potential. The definition of the bubble radius and the corresponding generalized, curvature-dependent surface tensions are discussed. In the f...

An inwardly directed curvature of the distal segment of both forelegs of the rabbit has been described. The condition was detected at 2 to 3 weeks of age, developed rapidly, and reached its final and permanent stage at 2 to 3 months of age. Only the distal epiphysis of the ulna was primarily affected and this in the form of a massive chondrodystrophic lesion accompanied by a progressive curvatu...

This paper proposes techniques of interpolation of intrinsically defined planar curves to Hermite data. In particular, a family of planar curves corresponding to which the curvature radius functions are polynomials in terms of the tangent angle are used for the purpose. The Cartesian coordinates, the arc lengths and the offsets of this type of curves can be explicitly obtained provided that the...

Precise control of micromirror curvature is critical in many optical microsystems. Micromirrors with current-controlled curvature are demonstrated. The working principle is that resistive heating changes the temperature of the micromirrors and thermal expansion induces a controlled curvature whose magnitude is determined by coating design. For example, for wide focal-length tuning, the radius o...

This article presents investigations of self-positioning microstructures and nanostructures by analytical techniques, finite element analysis and atomic-scale modeling. Closed-form solutions for curvature radius of self-positioning hinge structures are obtained for plane strain and generalized plane strain deformation. The finite element method is used for predicting hinge curvature radius for ...

INTRODUCTION This study investigated the fatigue and fracture modes of RaCe and ProTaper rotary instruments. MATERIALS AND METHODS Fatigue resistance was evaluated by rotating the files 30° or 60° and with 2 or 5mm radius of curvature. RaCe taper 06 size 25 and ProTaper F1 files (n=40) were used. The number of rotations to failure was analyzed by two-way ANOVA and independent sample t-test. F...

In recent papers (Lowe, I968, I969a) it was shown that in normal eyes, lens position and thickness were coordinated with axial length and radius of corneal curvature, whereas in eyes with primary angle-closure glaucoma these correlations were lacking. Throughout adult life, lenses increase in thickness at the same rate in normal eyes and those with angle-closure glaucoma, but no change could be...

It is known that the topological entropy for the geodesic flow on a Riemannian manifoldM is bounded if the absolute value of sectional curvature |KM | is bounded. We replace this condition by the condition of Ricci curvature and injectivity radius.