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