Lower Limit to the Scale of an Effective Quantum Theory of Gravitation

An effective quantum theory of gravitation in which gravity weakens at energies higher than ~10^-3 eV is one way to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from the Newtonian inverse-square force law on distances below ~0.05 mm. However, it is shown that this modification also leads to changes in the long-range behavior of gravity and is inconsistent with observed gravitational lenses

Structural evaluation of candidate designs for the large space telescope primary mirror

Structural performance analyses were conducted on two candidate designs (Itek and Perkin-Elmer designs) for the large space telescope three-meter mirror. The mirror designs and the finite-element models used in the analyses evaluation are described. The results of the structural analyses for several different types of loading are presented in tabular and graphic forms. Several additional analyses are also reported: the evaluation of a mirror design concept proposed by the Boeing Co., a study of the global effects of local cell plate deflections, and an investigation of the fracture mechanics problems likely to occur with Cervit and ULE. Flexibility matrices were obtained for the Itek and Perkin-Elmer mirrors to be used in active figure control studies. Summary, conclusions, and recommendations are included

Lower Limit to The Scale of an Effective Theory of Gravitation

We consider a linearized, effective quantum theory of gravitation in which gravity weakens at energies higher than ~10^-3 eV in order to accommodate the apparent smallness of the cosmological constant. Such a theory predicts departures from the static Newtonian inverse-square force law on distances below ~0.05 mm. However, we show that such a modification also leads to changes in the long-range behavior of gravity and is inconsistent with observed gravitational lenses.Comment: 4 pages, 1 figures. V3: matches published versio

Unconventional magnetism in multivalent charge-ordered YbPtGe2_2 probed by 195^{195}Pt- and 171^{171}Yb-NMR

Detailed $^{195}$Pt- and $^{171}$Yb nuclear magnetic resonance (NMR) studies on the heterogeneous mixed valence system YbPtGe$_2$ are reported. The temperature dependence of the $^{195}$Pt-NMR shift $^{195}K(T)$ indicates the opening of an unusual magnetic gap below 200\,K. $^{195}K(T)$ was analyzed by a thermal activation model which yields an isotropic gap $\Delta/k_B \approx 200$\,K. In contrast, the spin-lattice relaxation rate $^{195}$($1/T_1$) does not provide evidence for the gap. Therefore, an intermediate-valence picture is proposed while a Kondo-insulator scenario can be excluded. Moreover, $^{195}$($1/T_1$) follows a simple metallic behavior, similar to the reference compound YPtGe$_2$. A well resolved NMR line with small shift is assigned to divalent $^{171}$Yb. This finding supports the proposed model with two sub-sets of Yb species (di- and trivalent) located on the Yb2 and Yb1 site of the YbPtGe$_2$ lattice.Comment: Submitted in Physical Review B (Rapid Communication

Lower and upper bounds for the number of limit cycles on a cylinder

We consider autonomous systems with cylindrical phase space. Lower and upper bounds for the number of limit cycles surrounding the cylinder can be obtained by means of an appropriate Dulac-Cherkas function. We present different possibilities to improve these bounds including the case that the exact number of limit cycles can be determined. These approaches are based on the use of several Dulac-Cherkas functions or on applying some factorized Dulac function

Study of the bifurcation of a multiple limit cycle of the second kind by means of a Dulac--Cherkas function: A case study

We consider a generalized pendulum equation depending on the scalar parameter $\mu$ having for $\mu=0$ a limit cycle $\Gamma$ of the second kind and of multiplicity three. We study the bifurcation behavior of $\Gamma$ for $-1 \le \mu \le (\sqrt{5}+3)/2$ by means of a Dulac-Cherkas function

Global bifurcation analysis of limit cycles for a generalized van der Pol system

We present a new approach for the global bifurcation analysis of limit cycles for a generalized van der Pol system. It is based on the existence of a Dulac-Cherkas function and on applying two topologically equivalent systems: one of them is a rotated vector field, the other one is a singularly perturbed system

Global algebraic Poincaré-Bendixson annulus for the Rayleigh equation

We consider the Rayleigh equation x¨ + λ(x˙ 2/3 − 1)x˙ + x = 0 depending on the real parameter λ and construct a Poincaré–Bendixson annulus Aλ in the phase plane containing the unique limit cycle Γλ of the Rayleigh equation for all λ > 0. The novelty of this annulus consists in the fact that its boundaries are algebraic curves depending on λ. The polynomial defining the interior boundary represents a special Dulac–Cherkas function for the Rayleigh equation which immediately implies that the Rayleigh equation has at most one limit cycle. The outer boundary is the diffeomorphic image of the corresponding boundary for the van der Pol equation. Additionally we present some equations which are linearly topologically equivalent to the Rayleigh equation and provide also for these equations global algebraic Poincaré–Bendixson annuli

Construction of generalized pendulum equations with prescribed maximum number of limit cycles of the second kind

Consider a class of planar autonomous differential systems with cylindric phase space which represent generalized pendulum equations. We describe a method to construct such systems with prescribed maximum number of limit cycles which are not contractible to a point (limit cycles of the second kind). The underlying idea consists in employing Dulac-Cherkas functions. We also show how this approach can be used to control the bifurcation of multiple limit cycles