We show that the volume of any Riemannian metric on a three sphere is bounded below by the length of the shortest closed curve that links its antipodal image.

For the complex Ginzburg-Landau equation on a large periodic interval, we show that the transition from defectto phase-turbulence is more accurately described as a smooth crossover rather than as a sharp continuous transition. We obtain this conclusion by using a powerful parallel computer to calculate various order parameters, especially the density of space-time defects, the Lyapunov dimensio...

We derive a scaling relationship for the mean square rotation rate of rods with lengths in the inertial range in turbulence: ∝ l(-4/3). We present experimental measurements of the rotational statistics of neutrally buoyant rods with lengths 2.8<l/η<72.9, and find that the measurements approach the predicted scaling. The approach to inertial range scaling is shown to be more complex t...

We set up recursion relations for calculating all even moments of the end-to-end distance of Porod-Kratky wormlike chains in D dimensions. From these moments we derive a simple analytic expression for the end-to-end distribution in three dimensions valid for all peristence lengths. It is in excellent agreement with Monte Carlo data for stiff chains and approaches the Gaussian random-walk distri...

When we describe time, we often use the language of space (The movie was long; The deadline is approaching). Experiments 1-3 asked whether-as patterns in language suggest-a structural similarity between representations of spatial length and temporal duration is easier to access than one between length and other dimensions of experience, such as loudness. Adult participants were shown pairings o...

a non-abelian finite group is called sequenceable if for some positive integer , is -generated ( ) and there exist integers such that every element of is a term of the -step generalized fibonacci sequence , , , . a remarkable application of this definition may be find on the study of random covers in the cryptography. the 2-step generalized sequences for the dihedral groups studied for their pe...