Modern Logic and Judicial Decision Making: A Sketch of One View

Two hundred years elapsed before the nineteenth century logicians Boole, De Morgan, and others, finally succeeded in formally developing the calculus of reason-ing first suggested by the German mathematician, Leibniz. It is, perhaps, to the credit of the legal profession that less than one century has subsequently elapsed, and already some lawyers and legal writers, along with other scholars, are beginning to explore the relationship between modern logic and law. What is attempted here is to outline the bare bones of one tentative way of looking at the relationship between modern logic and the judicial decision process. From the useful vantage point of a Lasswellian social process framework of analysis, logic and judicial decision making are considered contextually within that total mani-fold of events that we call the world. Thus viewed, the judicial decision making process is just one constituent of the complex unfolding of events through time. We attempt to represent some of the complexities involved in each of these processes and the relationships between them by means of a series of diagrams. By suggesting that we begin with the world as our context, we make no claim to describing it in complete detail. To the contrary, the sketch presented here-we would emphasize the word sketch and the word tentative -is rough, incomplete, and subject to considerable improvement. But one of our purposes will be served if the outline points the way toward cumulative efforts to achieve a comprehensive description of the judicial decision process. In addition to this broad look at logic, judicial decision making, and the world, a more modest aim is to describe, in some detail and with reasonable clarity, one aspect of the relation between logic and judicial decision making

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Cosmic Microwave Background Radiation Anisotropy Induced by Cosmic Strings

We report on a current investigation of the anisotropy pattern induced by cosmic strings on the cosmic microwave background radiation (MBR). We have numerically evolved a network of cosmic strings from a redshift of $Z = 100$ to the present and calculated the anisotropies which they induce. Based on a limited number of realizations, we have compared the results of our simulations with the observations of the COBE-DMR experiment. We have obtained a preliminary estimate of the string mass-per-unit-length $\mu$ in the cosmic string scenario.Comment: 8 pages of TeX - [Color] Postscript available by anonymous ftp at ftp://fnas08.fnal.gov:/pub/Publications/Conf-94-197-A, FERMILAB-Conf-94/197-

Measurements of the methane relaxation times for application to the infrared emission models of the upper atmospheres of outer planets and Titan

The 7.8 micrometer emission from the nu(sub 4) band of methane (CH4) is a regularly observed feature in the stratosphere of all the giant planets and Titan. On Jupiter, enhancements in this emission are associated with the infrared hot spots in the auroral zone. Attempts to model this phenomenon in particular, and to understand the role of methane in general, have been hampered in part by a lack of adequate laboratory measurements of the collisional relaxation times for the nu(sub 3) and nu(sub 4) levels over the appropriate temperature range. To provide this needed data, a series of laboratory experiments were initiated. In the experimental arrangement the nu(sub3) band of methane is pumped at 3.3 micrometers using a pulsed infrared source (Nd:YAG/dye laser system equipped with a wave-length extender). The radiative lifetime of the nu(sub 3) level (approximately 37 ms) is much shorter than the nu(sub 4) lifetime (approximately 390 ms); however, a rapid V-V energy transfer rate ensures that the nu(sub 4) level is substantially populated. The photoacoustic technique is used to acquire relaxation rate information. The experiments are performed using a low-temperature, low-pressure cell. Experimental apparatus and technique are described. In addition some of the experimental difficulties associated with making these measurements are discussed and some preliminary results are presented

Large Angular Scale CMB Anisotropy Induced by Cosmic Strings

We simulate the anisotropy in the cosmic microwave background (CMB) induced by cosmic strings. By numerically evolving a network of cosmic strings we generate full-sky CMB temperature anisotropy maps. Based on $192$ maps, we compute the anisotropy power spectrum for multipole moments $\ell \le 20$. By comparing with the observed temperature anisotropy, we set the normalization for the cosmic string mass-per-unit-length $\mu$, obtaining $G\mu/c^2=1.05 {}^{+0.35}_{-0.20} \times10^{-6}$, which is consistent with all other observational constraints on cosmic strings. We demonstrate that the anisotropy pattern is consistent with a Gaussian random field on large angular scales.Comment: 4 pages, RevTeX, two postscript files, also available at http://www.damtp.cam.ac.uk/user/defects/ to appear in Physical Review Letters, 23 September 199

Analytic Results for the Gravitational Radiation from a Class of Cosmic String Loops

Cosmic string loops are defined by a pair of periodic functions ${\bf a}$ and ${\bf b}$, which trace out unit-length closed curves in three-dimensional space. We consider a particular class of loops, for which ${\bf a}$ lies along a line and ${\bf b}$ lies in the plane orthogonal to that line. For this class of cosmic string loops one may give a simple analytic expression for the power $\gamma$ radiated in gravitational waves. We evaluate $\gamma$ exactly in closed form for several special cases: (1) ${\bf b}$ a circle traversed $M$ times; (2) ${\bf b}$ a regular polygon with $N$ sides and interior vertex angle $\pi-2\pi M/N$; (3) ${\bf b}$ an isosceles triangle with semi-angle $\theta$. We prove that case (1) with $M=1$ is the absolute minimum of $\gamma$ within our special class of loops, and identify all the stationary points of $\gamma$ in this class.Comment: 15 pages, RevTex 3.0, 7 figures available via anonymous ftp from directory pub/pcasper at alpha1.csd.uwm.edu, WISC-MILW-94-TH-1

Constraints on Cosmic Strings due to Black Holes Formed from Collapsed Cosmic String Loops

The cosmological features of primordial black holes formed from collapsed cosmic string loops are studied. Observational restrictions on a population of primordial black holes are used to restrict $f$, the fraction of cosmic string loops which collapse to form black holes, and $\mu$, the cosmic string mass-per-unit-length. Using a realistic model of cosmic strings, we find the strongest restriction on the parameters $f$ and $\mu$ is due to the energy density in $100 MeV$ photons radiated by the black holes. We also find that inert black hole remnants cannot serve as the dark matter. If earlier, crude estimates of $f$ are reliable, our results severely restrict $\mu$, and therefore limit the viability of the cosmic string large-scale structure scenario.Comment: (Plain Tex, uses tables.tex -- wrapped lines corrected), 11 pages, FERMILAB-Pub-93/137-

CMB Anisotropy Induced by Cosmic Strings on Angular Scales > 15′>~ 15'

We have computed an estimate of the angular power spectrum of the Cosmic Microwave Background (CMB) induced by cosmic strings on angular scales $>~ 15'$, using a numerical simulation of a cosmic string network; and decomposed this pattern into scalar, vector, and tensor parts. We find no evidence for strong acoustic oscillations in the scalar anisotropy but rather a broad peak. The anisotropies from vector modes dominate except on very small angular scales while the tensor anisotropies are sub-dominant on all angular scales. The anisotropies generated after recombination are even more important than in adiabatic models. We expect that these qualitative features are robust to the varying of cosmological parameters, a study which has not yet been done.Comment: 4 pages, 2 figure

CBR Temperature Fluctuations Induced by Gravitational Waves in a Spatially-Closed Inflationary Universe

Primordial gravitational waves are created during the de Sitter phase of an exponentially-expanding (inflationary) universe, due to quantum zero-point vacuum fluctuations. These waves produce fluctuations in the temperature of the Cosmic Background Radiation (CBR). We calculate the multipole moments of the correlation function for these temperature fluctuations in a spatially-closed Friedman-Robertson-Walker (FRW) cosmological model. The results are compared to the corresponding multipoles in the spatially-flat case. The differences are small unless the density parameter today, $\Omega_0$, is greater than 2. (Submitted to Physical Review D).Comment: 18 pages of RevTex + 3 uuencoded postscript figure