Phenomena Affecting the Equilibrium of Al(III) and Zn(II) Extraction with Winsor II Microemulsions

The extraction of Al(III) and Zn(II) from an aqueous solution with two water-in-oil microemulsions, one containing di(2-ethylhexyl)phosphoric acid (DEHPA), was investigated to aid the understanding of the role of the extractant and the metal specific characteristics in the mechanism of microemulsion extraction. The extraction of Al with the DEHPA microemulsion increased by a factor of about 10 with respect to that in the conventional DEHPA system, whereas the extraction of Zn was lower than that in the single DEHPA system. Extraction with the DEHPA-free microemulsion was very low, showing that metal ion solubilization was not important in the mechanism of microemulsion extraction. It is proposed that the effect of the mixed microemulsion on the metal distribution coefficient is the result of the balance between a decrease in the complexation reaction yield due to the interaction between butanol and DEHPA, and the adsorption of the metal complex at the macro- and microinterfaces. The former leads to a decrease in Zn(II) extraction and the latter to Al(III) extraction synergism. Copyright 2000 Academic Press.     

Wind-generated ambient noise in a topographically isolated basin: a pre-industrial era proxy

During the mid-1980s, calibrated measurements of ambient noise and wind speed were made in the Tongue of the Ocean in the Bahamas to quantify the spectra and statistics of wind-generated noise. This deep basin is topographically isolated from the Atlantic Ocean and, therefore, largely acoustically decoupled from the Atlantic Ocean deep sound channel. The quantitative effects of contaminating (non-surface wind-generated) noise sources within the basin were eliminated by careful measurement and robust statistical analysis methodologies. Above 500 Hz, the spectral slopes are approximately -5 dB per octave and independent of wind speed. Below 500 Hz, the ambient noise is no longer a linear function of wind speed. Below 100 Hz and for wind speeds greater than 18.5 knots (kt), the ambient noise is independent of frequency. The minimum observed ambient noise level falls 13 dB below Urick's "light shipping" level at 30 Hz and 2-5 dB below Wenz's sea state zero level through the wind-dominated portion of the spectrum. The basin's geographical isolation and the rigorous measurement and analysis methodologies employed make this two-decade-old data set a reasonable and justified proxy for pre-industrial era ocean noise levels in the 20 Hz to 20 kHz frequency band.     

Experimental study of the shock response of an HMX-based explosive

Experiments have been fired in which the HMX-based explosive EDC37 was subjected to one-dimensional shocks generated by plate impact. The response of the explosive to sustained shocks, double shocks and a short-pulse shock was monitored using embedded particle velocity gauges and shock tracker gauges. The final stages of the growth to detonation process were similar for all of the different input profiles. A strong reactive wave grows and accelerates to overtake and dominate the initial shock. It is shown that the curves showing the growth of the shock and the reactive wave in the sustained shock experiments can be normalised to give universal curves. These curves provides a reference against which to compare the explosive's response, not only to single sustained shocks, but also to double shock and short-pulse inputs. The treatment provides an empirical route for predicting the effects of sustained and more complex shocks on EDC37. PACS 47.40.-x; 82.33.Vx     

Flow over a Wing with an Attached Free Vortex

Exact solutions are constructed for two-dimensional inviscid potential flow over a wing with a free line vortex standing over the wing. The loci of positions of the free vortex are found, and the lift is calculated. It is found that the lift on the wing can be significantly increased by the free vortex.     

Mass spectroscopic observation of shock-induced chemistry in liquid CS2

We have observed, via time-of-flight mass spectrometry, 13 chemical species more massive than CS2 produced by shocking liquid CS2 to very high pressure/temperature. The stoichiometry of three of these species is uniquely determined from the 12CS2 experiments; these species are C2S2, C3S2, and C4S2. The stoichiometry of the other 10 structures cannot be uniquely determined from 12CS2 experiments. However, by redoing the experiments using isotopically labeled CS2 (i.e., 13CS2), we determined the stoichiometry of nine of the remaining structures. The nine structures are Sn (n = 3-8) and CS3, C2S5, and C4S6. A structure with mass 297.1 amu was also observed in the 12CS2 experiments but was not detected in the 13CS2 experiments. This structure must be C6S7, C14S4, or C22S; given the low carbon content of the other observed carbon species, it is probably C6S7. The shockwaves to which the CS2 molecules were subjected were produced by the detonation of high mass-density solid explosives. The explosives used were either a plastic bonded form of cyclotetramethlylene tetranitramine or pure hexanitrostilbene. Numerical compressible fluid-mechanical simulations were done to estimate the pressures, temperatures, and time scales of the processes that occurred in the shocked CS2. The results obtained in the present experiments are related to earlier work on CS2's chemical reactivity that used both shockwave methods and static techniques to produce very high pressure.     

Conformal Radii for Conformal Loop Ensembles

The conformal loop ensembles CLE _κ , defined for 8/3 ≤ κ ≤ 8, are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compute the expectation dimension of the CLE _κ gasket, which consists of points not surrounded by any loop, to be

Contour lines of the two-dimensional discrete Gaussian free field

We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant λ > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain—with boundary values −λ on one boundary arc and λ on the complementary arc—the zero level line of h joining the endpoints of these arcs converges to SLE(4) as the domain grows larger. If instead the boundary values are −a < 0 on the first arc and b > 0 on the complementary arc, then the convergence is to SLE(4; a/λ - 1, b/λ - 1), a variant of SLE(4).     

Renormalization of Critical Gaussian Multiplicative Chaos and KPZ Relation

Gaussian Multiplicative Chaos is a way to produce a measure on \({\mathbb{R}^d}\) (or subdomain of \({\mathbb{R}^d}\) ) of the form \({e^{\gamma X(x)} dx}\) , where X is a log-correlated Gaussian field and \({\gamma \in [0, \sqrt{2d})}\) is a fixed constant. A renormalization procedure is needed to make this precise, since X oscillates between ?∞ and ∞ and is not a function in the usual sense. This procedure yields the zero measure when \({\gamma = \sqrt{2d}}\) . Two methods have been proposed to produce a non-trivial measure when \({\gamma = \sqrt{2d}}\) . The first involves taking a derivative at \({\gamma = \sqrt{2d}}\) (and was studied in an earlier paper by the current authors), while the second involves a modified renormalization scheme. We show here that the two constructions are equivalent and use this fact to deduce several quantitative properties of the random measure. In particular, we complete the study of the moments of the derivative multiplicative chaos, which allows us to establish the KPZ formula at criticality. The case of two-dimensional (massless or massive) Gaussian free fields is also covered.     

Absolutely minimal Lipschitz extension of tree-valued mappings

We prove that every Lipschitz function from a subset of a locally compact length space to a metric tree has a unique absolutely minimal Lipschitz extension (AMLE). We relate these extensions to a stochastic game called Politics??a generalization of a game called Tug of War that has been used in Peres et?al. (J Am Math Soc 22(1):167?C210, 2009) to study real-valued AMLEs.     

Fixation for distributed clustering processes

We study a discrete‐time resource flow in \input amssym ${\Bbb Z}^d $ where wealthier vertices attract the resources of their less rich neighbors. For any translation‐invariant probability distribution of initial resource quantities, we prove that the flow at each vertex terminates after finitely many steps. This answers (a generalized version of) a question posed by van den Berg and Meester in 1991. The proof uses the mass transport principle and extends to other graphs. © 2010 Wiley Periodicals, Inc.