Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

Shaping Solid-State Supramolecular Cavities: Chemically Induced Accordionlike Movement of gamma-Zirconium Phosphate Containing Polyethylenoxide Pillars

The hydrophilic oxygen atoms of polyethylenoxide chains inserted as pillars in gamma-zirconium phosphate form hydrogen bonds with the acid groups of the host. As a result the pillars are almost perpendicular to the gamma layers. Upon changing the pH level of the supernatant solution the hydrogen bonds are broken and the pillars become almost perpendicular to the layers (shown schematically). Thus there is a reversible enlargement-shortening of the interlayer space.     

On a Fermat principle in general relativity. A Morse theory for light rays

In this paper an infinite dimensional Morse theory for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds is developed under intrinsic assumptions. It yields applications to the gravitational lens effect. In particular we show that the number of images in the gravitational lens effect is infinite or odd.     

Variational derivation of nuclear hydrodynamics

Equations of nuclear motion are derived from a time-dependent variational principle. They have the same form as the equations of classical hydrodynamics for irrotational flow, and can described motions with arbitrary amplitudes. The theory also gives an equation of state for the nuclear medium.     

On the Finiteness of Light Rays Between a Source and an Observer on Conformally Stationary Space-Times

We use a convexity condition to prove the finiteness of the number of light rays joining a pointlike source with a pointlike observer in a stationary relativistic spacetime. The result is extended to the case of conformally stationary metrics under suitable boundedness assumptions on the conformal factor. We discuss our hypotheses in some explicit examples of standard static and stationary Lorentzian manifolds.     

On a Fermat principle in general relativity. A Ljusternik-Schnirelmann theory for light rays

Summary In this paper existence and multiplicity results for lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds are proved under intrinsic assumptions. Such results are obtained using an extension to Lorentzian Geometry of the classical Fermat principle in optics. The results are proved using critical point theory on infinite dimensional manifolds. An application to the gravitational lens effect is presented.     

A timelike extension of Fermat's principle in general relativity and applications

We define a variational problem based on the arrival time functional for timelike curves on a Lorentzian manifold parameterized by a fixed constant multiple of their proper time. Under a causality assumption for the manifold , we prove that the stationary points of our problem are geodesics, obtaining an extension of the Fermat's Principle for light rays proven in [14] (see also [2]). Moreover, we study the compactness pr operties of the arrival time functional by global variational techniques. Under intrinsic assumptions on the metric of we get results of existence and multiplicity for geodesics with a given energy between an event and an observer of .