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黃義珏,Gustafson, Robert L. 圓光大學校 1972 論文集 Vol.6 No.-
The task assigned was to estimate a function describing the demand for nonfood by nonfarmers(the total pupolation excluding the pupolation on farms). It was then decided to estimate also a demand functions for food and for nonfood by farmers and by the total population, the reason being partly that these functions would be of some interest and usefulness in themselves and partly that the consistency or inconsistency of the different functions with each other would provide a partial check on the validity of each of them. Thus, the objective was to obtain estimates of the following six demand relations.
MHz gravitational wave constraints with decameter Michelson interferometers
Chou, Aaron S.,Gustafson, Richard,Hogan, Craig,Kamai, Brittany,Kwon, Ohkyung,Lanza, Robert,Larson, Shane L.,McCuller, Lee,Meyer, Stephan S.,Richardson, Jonathan,Stoughton, Chris,Tomlin, Raymond,Weiss, American Physical Society 2017 Physical Review D Vol.95 No.6
<P>A new detector, the Fermilab Holometer, consists of separate yet identical 39-meter Michelson interferometers. Strain sensitivity achieved is better than 10(-21) / root Hz between 1 to 13 MHz from a 130-h data set. This measurement exceeds the sensitivity and frequency range made from previous high frequency gravitational wave experiments by many orders of magnitude. Constraints are placed on a stochastic background at 382 Hz resolution. The 3 sigma upper limit on Omega(GW), the gravitational wave energy density normalized to the closure density, ranges from 5.6 x 10(12) at 1 MHz to 8.4 x 10(15) at 13 MHz. Another result from the same data set is a search for nearby primordial black hole binaries (PBHB). There are no detectable monochromatic PBHBs in the mass range 0.83-3.5 x 10(21) g between the Earth and the Moon. Projections for a chirp search with the same data set increase the mass range to 0.59 - 2.5 x 10(25) g and distances out to Jupiter. This result presents a new method for placing limits on a poorly constrained mass range of primordial black holes. Additionally, solar system searches for PBHBs place limits on their contribution to the total dark matter fraction.</P>
The Holometer: an instrument to probe Planckian quantum geometry
Chou, Aaron,Glass, Henry,Gustafson, H Richard,Hogan, Craig,Kamai, Brittany L,Kwon, Ohkyung,Lanza, Robert,McCuller, Lee,Meyer, Stephan S,Richardson, Jonathan,Stoughton, Chris,Tomlin, Ray,Weiss, Rainer Institute of Physics 2017 Classical and quantum gravity Vol.34 No.6
<P>This paper describes the Fermilab Holometer, an instrument for measuring correlations of position variations over a four-dimensional volume of space-time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. A noise model constrained by diagnostic and environmental data distinguishes among physical origins of measured correlations, and is used to verify shot-noise-limited performance. These features allow searches for exotic quantum correlations that depart from classical trajectories at spacelike separations, with a strain noise power spectral density sensitivity smaller than the Planck time. The Holometer in current and future configurations is projected to provide precision tests of a wide class of models of quantum geometry at the Planck scale, beyond those already constrained by currently operating gravitational wave observatories.</P>
Interferometric constraints on quantum geometrical shear noise correlations
Chou, Aaron,Glass, Henry,Richard Gustafson, H,Hogan, Craig J,Kamai, Brittany L,Kwon, Ohkyung,Lanza, Robert,McCuller, Lee,Meyer, Stephan S,Richardson, Jonathan W,Stoughton, Chris,Tomlin, Ray,Weiss, Rai IOP 2017 Classical and quantum gravity Vol.34 No.16
<P>Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry—those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.</P>