304 research outputs found
Almost rolling motion: An investigation of rolling grooved cylinders
We examine the dynamics of cylinders that are grooved to form N teeth for
rolling motion down an inclined plane. The grooved cylinders are experimentally
found to reach a terminal velocity. This result can be explained by the
inclusion of inelastic processes which occur whenever a tooth hits the surface.
The fraction of the angular velocity that is lost during an inelastic collision
is phenomenologically found to be proportional to
(2*sin^2*pi/N)-(alpha*sin^3*pi/N), and the method of least squares is used to
find the constant alpha=0.98. The adjusted theoretical results for the time of
rolling as well as for terminal velocity are found to be in good agreement with
the experimental results.Comment: 8 pages, 6 figures http://link.aip.org/link/?AJPIAS/66/202/
Induced matter: Curved N-manifolds encapsulated in Riemann-flat N+1 dimensional space
Liko and Wesson have recently introduced a new 5-dimensional induced matter
solution of the Einstein equations, a negative curvature Robertson-Walker space
embedded in a Riemann flat 5-dimensional manifold. We show that this solution
is a special case of a more general theorem prescribing the structure of
certain N+1-dimensional Riemann flat spaces which are all solutions of the
Einstein equations. These solutions encapsulate N-dimensional curved manifolds.
Such spaces are said to "induce matter" in the sub-manifolds by virtue of their
geometric structure alone. We prove that the N-manifold can be any maximally
symmetric space.Comment: 3 page
A Selection Rule for Transitions in PT-Symmetric Quantum Theory
Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian. To implement this theory, the inner product was redefined to guarantee positive norms of eigenstates of the Hamiltonian. In the general case, which includes arbitrary time-dependence in the Hamiltonian, a modification of the Schrödinger equation is necessary as shown by Gong and Wang to conserve probability. In this paper, we derive the following selection rule: transitions induced by time dependence in a PT-symmetric Hamiltonian cannot occur between normalized states of differing PT-norm. We show three examples of this selection rule in action: two matrix models and one in the continuum
A Selection Rule for Transitions in PT-Symmetric Quantum Theory
Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian. To implement this theory, the inner product was redefined to guarantee positive norms of eigenstates of the Hamiltonian. In the general case, which includes arbitrary time-dependence in the Hamiltonian, a modification of the Schrödinger equation is necessary as shown by Gong and Wang to conserve probability. In this paper, we derive the following selection rule: transitions induced by time dependence in a PT-symmetric Hamiltonian cannot occur between normalized states of differing PT-norm. We show three examples of this selection rule in action: two matrix models and one in the continuum
A New Formula Describing the Scaffold Structure of Spiral Galaxies
We describe a new formula capable of quantitatively characterizing the Hubble sequence of spiral galaxies including grand design and barred spirals. Special shapes such as ring galaxies with inward and outward arms are also described by the analytic continuation of the same formula. The formula is r() = A/log [B tan (/2N)]. This function intrinsically generates a bar in a continuous, fixed relationship relative to an arm of arbitrary winding sweep. A is simply a scale parameter while B, together with N, determines the spiral pitch. Roughly, greater N results in tighter winding. Greater B results in greater arm sweep and smaller bar/bulge, while smaller B fits larger bar/bulge with a sharper bar/arm junction. Thus B controls the \u27bar/bulge-to-arm\u27 size, while N controls the tightness much like the Hubble scheme. The formula can be recast in a form dependent only on a unique point of turnover angle of pitch - essentially a one-parameter fit, aside from a scalefactor. The recast formula is remarkable and unique in that a single parameter can define a spiral shape with either constant or variable pitch capable of tightly fitting Hubble types from grand design spirals to late-type large barred galaxies. We compare the correlation of our pitch parameter to Hubble type with that of the traditional logarithmic spiral for 21 well-shaped galaxies. The pitch parameter of our formula produces a very tight correlation with ideal Hubble type suggesting it is a good discriminator compared to logarithmic pitch, which shows poor correlation here similar to previous works. Representative examples of fitted galaxies are shown
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