Preparation of ethylene glycol oligomers

Procedures are described for the preparation of pure nonaethylene glycol and practically pure pentadecaethylene glycol from the monosodium salt and the ditosylate of triethylene glycol, using both toluene and tetrahydrofuran as diluents. The much faster reaction in the latter makes this the preferred reaction medium.     

Positivstellens?tze for real function algebras

We look for algebraic certificates of positivity for functions which are not necessarily polynomial functions. Similar questions were examined earlier by Lasserre and Putinar [Positivity and optimization for semi-algebraic functions (to appear), Proposition 1] and by Putinar [A Striktpositivestellensatz for measurable functions (corrected version) (to appear), Theorem 2.1]. We explain how these results can be understood as results on hidden positivity: The required positivity of the functions implies their positivity when considered as polynomials on the real variety of the respective algebra of functions. This variety is however not directly visible in general. We show how algebras and quadratic modules with this hidden positivity property can be constructed. We can then use known results, for example Jacobi’s representation theorem (Jacobi in Math Z 237:259–273, 2001, Theorem 4), or the Krivine-Stengle Positivstellensatz (Marshall in Positive polynomials and sums of squares. Mathematical Surveys and Monographs 146, 2008, page 25), to obtain certificates of positivity relative to a quadratic module of an algebra of real-valued functions. Our results go beyond the results of Lasserre and Putinar, for example when dealing with non-continuous functions. The conditions are also easier to check. We explain the application of our result to various sorts of real finitely generated algebras of semialgebraic functions. The emphasis is on the case where the quadratic module is also finitely generated. Our results also have application to optimization of real-valued functions, using the semidefinite programming relaxation methods pioneered by Lasserre [SIAM J Optim 11(3): 796–817, 2001; Lasserre in Moments, positive polynomials and their applications. Imperial College Press, London, 2009; Lasserre and Putinar in Positivity and optimization for semi-algebraic functions (to appear); Marshall in Positive polynomials and sums of squares. Mathematical Surveys and Monographs 146, 2008, page 25].     

Investigation,design and analysis of a fast neutron facility on beam port 4 at the University of Texas MARK II TRIGA Reactor

Graduate students in the Mechanical Engineering department at the University of Texas at Austin have designed and modeled a fast neutron prompt-gamma activation analysis facility as part of a new course introduced in the graduate program titled “The Design of Nuclear Systems.” The students were responsible for creating a design concept as well as implementing and modeling the concept to ensure its safety and functionality. The purpose of the class was to give graduate students the independence to create a project of their own vision, but to do so in a collaborative and formal manner as will be necessary in their future work. The fast neutron PGAA facility was successfully designed and computational models have been analyzed to display benefits of the fast neutron facility compared to the thermal neutron PGAA facility that also exists at The University of Texas at Austin.     

A global approach to automatic solution of jigsaw puzzles

We present a new algorithm for automatically solving jigsaw puzzles by shape alone. The algorithm can solve more difficult puzzles than could be solved before, without the use of backtracking or branch-and-bound. The algorithm can handle puzzles in which pieces border more than four neighbors, and puzzles with as many as 200 pieces. Our overall strategy follows that of previous algorithms but applies a number of new ideas, such as robust fiducial points, “highest-confidence-first” search, and frequent global reoptimization of partial solutions.     

Spectroscopic diagnosis of the temperature profile of an Al:MgZ-pinch

We consider the question of how the temperature profile of a Z-pinch plasma can be determined and/or constrained by the requirement that its observed K-shell spectrum be replicated. As a case study we employ spatially integrated, time-resolved K-shell data obtained from the implosion of 30-wire Al:Mg alloy arrays on the Saturn driver at Sandia National Laboratories. Given the measured pinch size, its K-shell power and line intensities are compared with the predictions of a collisional-radiative-equilibrium plasma model whose temperature profile is varied in seeking agreement with the data. The Al data rules out a large range of possible temperature profiles, but two quite different temperature distributions can both match the measurements. These are: a uniform temperature, or, one with a sharply dropping temperature near the pinch outer edge. However, the measured ratio of the Mg α resonance lines to those of Al, even though time-integrated, excludes the possibility of a uniform temperature distribution     

A comparison of computational and experimental lift-off heights of coflow laminar diffusion flames

As a sensitive marker of changes in flame structure, the number densities of excited-state CH (denoted CH^*), and excited-state OH (denoted OH^*) are imaged in coflow laminar diffusion flames. Measurements are made both in normal gravity and on the NASA KC-135 reduced-gravity aircraft. The spatial distribution of these radicals provides information about flame structure and lift-off heights that can be directly compared with computational predictions. Measurements and computations are compared over a range of buoyancy and fuel dilution levels. Results indicate that the lift-off heights and flame shapes predicted by the computations are in excellent agreement with measurement for both normal gravity (1g) and reduced gravity flames at low dilution levels. As the fuel mixture is increasingly diluted, however, the 1g lift-off heights become underpredicted. This trend continues until the computations predict stable flames at highly dilute fuel mixtures beyond the 1g experimental blow-off limit. To better understand this behavior, an analysis was performed, which indicates that the lift-off height is sensitive to the laminar flame speed of the corresponding premixed mixture at the flame edge. By varying the rates of two key “flame speed” controlling reactions, we were able to modify the predicted lift-off heights so as to be in closer agreement with the experiments. The results indicate that reaction sets that work well in low dilution systems may need to be modified to accommodate high dilution flames.     

Synthesis and characterization of ether derivatives of brominated poly(isobutylene‐co‐isoprene)

Variations of the Williamson ether synthesis were employed to prepare a range of new derivatives of brominated poly(isobutylene‐co‐isoprene) (BIIR). Unambiguous characterization of the polymeric products was accomplished by spectroscopic comparisons to low‐molecular‐weight analogues derived from brominated 2,2,4,8,8‐pentamethyl‐4‐nonene, which served as a model for the reactive functionality found within BIIR. The substitution of bromide from BIIR occurred at moderate temperatures with stoichiometric amounts of quaternary ammonium phenoxide to yield O‐alkylation products in high yields. Simple mixtures of BIIR, KOH, and aliphatic alcohols generated the desired allylic ethers when heated above 110 °C in the absence of quaternary ammonium salts. Knowledge gained from these small‐molecule alkylations was used to prepare graft copolymers from BIIR and poly(ethylene oxide) through the exploitation of the apparent ability of polyethers to activate potassium alkoxides in nucleophilic substitutions. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 983–992, 2006