The global radius of curvature of a space curve is introduced. This function is related to, but distinct from, the standard local radius of curvature and is connected to various physically appealing properties of a curve. In particular, the global radius of curvature function provides a concise characterization of the thickness of a curve, and of certain ideal shapes of knots as have been inves...

We consider packings of radius r collars about hyperplanes in H. For such packings, we prove that the Delaunay cells are truncated ultra-ideal simplices which tile H. If we place n+1 hyperplanes in H each at a distance of exactly 2r to the others, we could place radius r collars about these hyperplanes. The density of these collars within the corresponding Delaunay cell is an upper bound on den...

Changes in volume play a significant but often under-emphasized role in governing the stability of proteins in the cell.1!6 When proteins fold from extended unfolded state to a compact or folded native state, there is a concomitant decrease in the characteristic volume occupied by the protein as probed by osmolyte particles, and thus an increase in the volume available to osmolytes or crowding ...

One of the main sources of efficiency loss in heat engines is the inability of a sinusoidally displaced piston engines to approximate the ideal heat volumetric cycles the engines require. While attempts have been made to address this issue in the past, recent developments in Stirling engine technology utilizing rolling diaphragm seals on the cylinders has offered an opportunity to greatly incre...

This short article is not meant to be understood as a paper on the foundations of physics, but purely concerned with the application of Newtonian mechanics to the dynamics of skiing. We neglect relativistic corrections, as well as quantum mechanical effects. In addition, we should mention that the paper contains a lengthy didactic presentation of a specific example of vector calculus. Neverthel...

This short article is not meant to be understood as a paper on the foundations of physics, but purely concerned with the application of Newtonian mechanics to the dynamics of skiing. We neglect relativistic corrections, as well as quantum mechanical effects. In addition, we should mention that the paper contains a lengthy didactic presentation of a specific example of vector calculus. Neverthel...

Mixtures of ideal polymers with hard spheres whose diameters are smaller than the radius of gyration of the polymer, exhibit extensive immiscibility. The interfacial tension between demixed phases of these mixtures is estimated, as is the barrier to nucleation. The barrier is found to scale linearly with the radius of the polymer, causing it to become large for large polymers. Thus for large po...

Abstract We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit...

We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increase...