HZE ion fragmentation cross-section sensitivity and propagated errors in HZE exposure estimates

It has long been recognized that galactic cosmic rays are of such high energy that they tend to pass through available shielding materials resulting in exposure of astronauts and equipment within space vehicles and habitats. Any protection provided by shielding materials result not so much from stopping such particles but by changing their physical character in interaction with shielding material nuclei forming, hopefully, less dangerous species. Clearly, the fidelity of the nuclear cross-sections is essential to correct specification of shield design and sensitivity to cross-section error is important in guiding experimental validation of cross-section models and database. We examine the Boltzmann transport equation which is used to calculate dose equivalent during solar minimum, with units (cSv/yr), associated with various depths of shielding materials. The dose equivalent is a weighted sum of contributions from neutrons, protons, light ions, medium ions and heavy ions using the ICRP-60 LET dependent quality factors. We investigate the sensitivity of dose equivalent calculations due to errors in nuclear fragmentation cross-sections. We do this error analysis for all possible projectile-fragment combinations (14,365 such combinations) to estimate the sensitivity of the shielding calculations to errors in the nuclear fragmentation cross-sections. Numerical differentiation with respect to the cross-sections will be evaluated in a broad class of materials including polyethylene, aluminum and copper. We will identify the most important cross-sections to ensure adequate experimental study and evaluate their impact on propagated errors in shielding estimates.     

Patterns of quadratic residues and nonresidues for infinitely many primes

If S is a nonempty, finite subset of the positive integers, we address the question of when the elements of S consist of various mixtures of quadratic residues and nonresidues for infinitely many primes. We are concerned in particular with the problem of characterizing those subsets of integers that consist entirely of either (1) quadratic residues or (2) quadratic nonresidues for such a set of primes. We solve problem (1) and we show that problem (2) is equivalent to a purely combinatorial problem concerning families of subsets of a finite set. For sets S of (essentially) small cardinality, we solve problem (2). Related results and some associated enumerative combinatorics are also discussed.     

Semiconductor lasers and fiber lasers for fiber-optic telecommunications

Be performance characteristics of semiconductor lasers for fiber telecommunication systems will be reviewed. Modulation speed, intensity noise, singlefrequency line width, and tunability are addressed. In addition, recent results concerning the same characteristics in single-frequency, tunable, fiber lasers are reviewed and compared with the semiconductor laser.     

PMMA adsorption over previously adsorbed PS studied by polarized FTIR-ATR

Polarized infrared spectroscopy in attenuated total reflection was used to investigate the adsorption of PMMA (polymethylmethacrylate) onto PS (polystyrene) that was previously adsorbed onto oxidized silicon from dilute solution in carbon tetrachloride at 30°C. The carbonyl group of PMMA forms hydrogen bonds with surface silanol groups, giving segment-surface interaction energy of 4 kT as against 1 kT for PS (k is the Boltzmann constant, T the absolute temperature). The formation of hydrogen-bonding by PMMA was unaffected, in rate or amount, by preadsorbed PS, but a lesser total amount of PMMA adsorbed onto PS, resulting in a higher average bound fraction. The histogram of the mass adsorbed, attributable to subpopulations of chains with different bound fractions, was inferred by subtracting infrared spectra acquired at successive times. Whereas this histogram was broad and bimodal for adsorption onto bare surface, it was narrower and unimodal for adsorption onto preadsorbed PS. © 1995 John Wiley & Sons, Inc.     

Lorentz Invariance and the retarded Bohm Model

We show how a recently introduced retarded version of the Bohm Model evades the Hardy proof that hidden-variable models must violate Lorentz Invariance. We also discuss a possible test of such models.We are happy to have this article included in a volume honoring Jean-Pierre Vigier, who has long recognized the significance of the hidden-variable model following from the work of L. de Broglie and D. Bohm.S.W.M. would like to thank S.E.R.C. for financial support.     

Synthesis and crystal structure of barium thioborate Ba7(BS3)4S

The thioborate phase Ba7(BS3)4S was synthesized from solid state reaction and its crystal structure determined by single crystal X-ray diffraction analysis. It crystallizes in the monoclinic space group C2/c (No. 15) with a = 10.1750(15) A, b = 23.970(4) A, c = 10.1692(15) A, beta = 90.095(2) degrees, and Z = 4. The structure consists of isolated trigonal planar (BS3)3- anions, and isolated S2- anions and Ba2+ cations. The additional sulfur anions have five-fold barium coordination, while the barium cations are coordinated by eight or nine sulfur atoms. Powder X-ray diffraction patterns from a bulk sample are compared to the calculated diffraction pattern from the single crystal structural analysis, and there is excellent agreement in general. The vibrational modes of the isolated (BS3)3- units were measured from Raman scattering and IR absorption spectra, and the frequencies agree very well with those found for similar orthothioborate phases.     

From Stochastics to Complexity in Models of Economic Instability

Sixty years ago, the leading lights of the economics profession chose to model economic fluctuations as if they were caused by stochastic disturbances to an underlying stable, heavily damped system, in the mistaken belief that a mathematically unstable system does not fluctuate; it just breaks down. A perceptive minority instead concluded that the fundamental relations in economics must be nonlinear. It is shown that a single sector model with nonlinear behavior by workers, capitalists and the government generates a chaotic explanation for the most extreme of economic fluctuations, a Great Depression. A multi-sectoral model of a stylized economy confirms the judgment that economics is fundamentally a nonlinear discipline, by establishing that the input-output nature of production generates substantive nonlinearities, even when linear behavioral functions are assumed.     

Methyl side-chain dynamics in proteins using selective enrichment with a single isotopomer

13C relaxation studies on side-chain methyl groups in proteins typically involve measurements on (13)CHD(2) isotopomers, where the (13)C relaxation mechanism is particularly straightforward in the presence of a single proton. While such isotopomers can be obtained in proteins overexpressed in bacteria by use of (13)C enriched and fractionally deuterated media, invariably all possible (2)H isotopomers are obtained. This results in a loss of both resolution and sensitivity, which becomes particularly severe for larger proteins. We describe an approach that overcomes this problem by chemical synthesis of amino acids containing a pure (13)CHD(2) isotopomer. We illustrate the benefits of this approach in (13)C side-chain relaxation measurements on the mouse major urinary protein selectively enriched with [gamma(1),gamma(2)-(13)C(2),alpha,beta,gamma(1),gamma(1),gamma(2),gamma(2)-(2)H(6)] valine. Relaxation measurements in the absence and presence of pyrazine-derived ligands suggest that valine side-chain dynamics do not contribute significantly to binding entropy.