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The Tipler cylinder, on the other hand, does not involve any negative energy. Tipler's original solution involved a cylinder of infinite length, which is easier to analyze mathematically, and although Tipler suggested that a finite cylinder might produce closed timelike curves if the rotation rate were fast enough, [6] he did not prove this ...
3D illustration of Gabriel's horn Torricelli's truncated acute hyperbolic solid with the added cylinder (in red) used by his proof. A Gabriel's horn (also called Torricelli's trumpet) is a type of geometric figure that has infinite surface area but finite volume.
A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that ...
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. [1] [2] A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies' surfaces (known as normal stress) and frictional stresses acting tangentially between the surfaces (shear stress).
Thus we find the maximum speed in the flow, V = 2U, in the low pressure on the sides of the cylinder. A value of V > U is consistent with conservation of the volume of fluid. With the cylinder blocking some of the flow, V must be greater than U somewhere in the plane through the center of the cylinder and transverse to the flow.
A crucial step towards a unified theory of both finite and infinite (lattice and non-lattice) sphere packings was the introduction of parametric densities by Jörg Wills in 1992. The parametric density takes into account the influence of the edges of the packing. [7]
The strictly jammed (mechanically stable even as a finite system) regular sphere packing with the lowest known density is a diluted ("tunneled") fcc crystal with a density of only π √ 2 /9 ≈ 0.49365. [6] The loosest known regular jammed packing has a density of approximately 0.0555. [7]
In the same manner, in case of measurable spaces, the cylinder σ-algebra is the one which is generated by cylinder sets corresponding to the components' measurable sets. The restriction that the cylinder set be the intersection of a finite number of open cylinders is important; allowing infinite intersections generally results in a finer topology.