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...

This paper characterizes when a Delone setX in Rn is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the hetereogeneity of their distribution. For a Delone set X, let NX(T ) count the number of translation-inequivalent patches of radius T in X and let MX(T ) be the minimum radius such that every closed ball of radius MX(T ) contains the center ...

The standard radius of curvature at a point q(s) on a smooth curve can be defined as the limiting radius of circles through three points that all coalesce to q(s). In the study of ideal knot shapes it has recently proven useful to consider a global radius of curvature of the curve at q(s) defined as the smallest possible radius amongst all circles passing through this point and any two other po...

In this paper, uniform and variable edge microgeometry design inserts are utilised and tested for 3D turning process. In 3D tool engagement with workpiece, thickness of the chip varies from a maximum equal to the feed rate (at primary cutting edge) to a minimum on the tool’s corner radius (at trailing cutting edge). The ideal tool edge preparation should posses a variable configuration which ha...

PURPOSE Recent literature comparing the effectiveness of above-elbow and below-elbow plaster casts appears to suggest that either cast type offers adequate immobilization for distal radius and ulna fractures. The idea that an appropriate mold placed on the cast is the most significant determinant of successful immobilization and, thereby, patient outcome has also been elucidated. The purpose of...

The -core in Euclidean spatial voting is the set of points that cannot be dislodged by a point more than closer to a simple majority of voter ideal points. If is greater than the yolk radius of the set, then the -core is nonempty. If exceeds twice the yolk radius, then there are no global intransitivities and any sequence of proposals starting from x will reach the -core from x in at most ||x||...

The radius of gyration of a polymer chain immersed in a low molecular weight solvent is known to vary monotonically with the solvent quality. Here, we consider the behavior of a chain immersed in a high molecular weight solvent (polymer melt). Unsurprisingly, we find that, as the incompatibility between the chain and the polymer melt is increased, the two limiting conformations of the chain are...

Abstract: Let n points be given in the plane. For each point a weight and a radius is given. The radius of each point is our expected ideal distance from the point to a new facility. In this paper we consider the location problem with minimum absolute errors. In this problem we want to find the location of the new facility such that the sum of weighted absolute errors between points and this ne...

We computed the phase-separation behavior and effective interactions of colloid-polymer mixtures in the "protein limit," where the polymer radius of gyration is much larger than the colloid radius. For ideal polymers, the critical colloidal packing fraction tends to zero, whereas for interacting polymers in a good solvent the behavior is governed by a universal binodal, implying a constant crit...