Sidles and Sigg have shown that advanced LIGO interferometers will encounter a serious tilt instability, in which symmetric tilts of the mirrors of an arm cavity cause the cavity’s light beam to slide sideways, so its radiation pressure exerts a torque that increases the tilt. Sidles and Sigg showed that the strength T of this torque is 26.2 times greater for advanced LIGO’s baseline cavities—n...

In a gedankenexperiment N particles in a generalised GHZ-type beam entangled state (each particle can be in one of M beams) are fed into N symmetric 2M-port beam splitters (spatially separated). Correlation functions for such a process (using the Bell numbers value assignment approach) reveal a remarkable symmetry. For N = M + 1 ≥ 4 a series of GHZ paradoxes are shown.

We consider an infinite square-cell lattice of elastic beams with a semi-infinite crack. Symmetric and antisymmetric bending modes of fracture under remote loads are examined. The related long-wave asymptotes corresponding to a continuous anisotropic bending plate are also considered. In the latter model, the symmetric mode is characterized by the square-root type singularity, whereas the antis...

Let f be an isometry of the sphere which is an involution (that is, f−1 = f). For any n ≥ 1 we prove that there is an n-curve Venn diagram on the sphere whose isometry group is generated by f and which has the property that f(Θ) = Θ, where Θ is a curve of the diagram. One of the constructions uses a new chain decomposition of the Boolean lattice, a decomposition which is based on the well-known...

This paper presents a new theory for the lateral buckling of web-tapered I-beams. Linear analysis is first conducted by taking account into the tapering effects of web-tapered I-beams, where the deformation compatibilities of the two flanges and web are considered in terms of the basic assumptions of thin-walled members. Subsequently, the total potential for the lateral buckling analysis of web...

Abstract Local stiffeners affect the behaviour of thin-walled beams (TWBs). An in-house code based on a one-dimensional model proved effective in several instances compressive buckling TWBs but gave counterintuitive results for locally stiffened TWBs. To clarify matter, we investigated with multi-symmetric double I cross-section, widely used practical applications where high bending stiffness i...

We predict the self-collimation phenomena (or equivalently, dynamical localization) in two-dimensional PT symmetric complex potentials, where the complex modulation is considered in the transverse, longitudinal, or simultaneously in both directions. Nondiffractive propagation is analytically predicted and further confirmed by numerical integration of a paraxial model. The parameter space is exp...