The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation

We analyse different error propagation mechanisms for conservativeand nonconservative time-integrators of nonlinear Schrödingerequations. We use a geometric approach based on interpretingwaves as relative equilibria.     

Diphosphanes derived from phobane and phosphatrioxa-adamantane: similarities, differences and anomalies

The homodiphosphanes CgP-PCg (1) and PhobP-PPhob (2) and the heterodiphosphanes CgP-PPhob (3), CgP-PPh(2) (4a), CgP-P(o-Tol)(2) (4b), CgP-PCy(2) (4c), CgP-P(t)Bu(2) (4d), PhobP-PPh(2) (5a), PhobP-P(o-Tol)(2) (5b), PhobP-PCy(2) (5c), PhobP-P(t)Bu(2) (5d) where CgP = 6-phospha-2,4,8-trioxa-1,3,5,7-tetramethyladamant-9-yl and PhobP = 9-phosphabicyclo[3.3.1]nonan-9-yl have been prepared from CgP(BH(3))Li or PhobP(BH(3))Li and the appropriate halophosphine. The formation of 1 is remarkably diastereoselective, with the major isomer (97% of the product) assigned to rac-1. Restricted rotation about the P-P bond of the bulky meso-1 is detected by variable temperature (31)P NMR spectroscopy. Diphosphane 3 reacts with BH(3) to give a mixture of CgP(BH(3))-PPhob and CgP-PPhob(BH(3)) which was unexpected in view of the predicted much greater electron-richness of the PhobP site. Each of the diphosphanes was treated with dimethylacetylene dicarboxylate (DMAD) in order to determine their propensity for diphosphination. The homodiphosphanes 1 and 2 did not react with DMAD. The CgP-containing heterodiphosphanes 4a-d all added to DMAD to generate the corresponding cis alkenes CgPCH(CO(2)Me)=CH(CO(2)Me)PR(2) (6a-d) which have been used in situ to form chelate complexes of the type [MCl(2)(diphos)] (7a-d) where M = Pd or Pt. The PhobP-containing heterodiphosphanes 3 and 5a-d react anomalously with DMAD and do not give the products of diphosphination. The X-ray crystal structures of the diphosphanes 2, 3, 4a, and 5a, the monoxide and dioxide of diphosphane 1, and the platinum chelate complex 7c have been determined and their structures are discussed.     

High-resolution studies of tropolone in the S0 and S1 electronic states: isotope driven dynamics in the zero-point energy levels

Rotationally resolved microwave (MW) and ultraviolet (UV) spectra of jet-cooled tropolone have been obtained in S(0) and S(1) electronic states using Fourier-transform microwave and UV-laser/molecular-beam spectrometers. In the ground electronic state, the MW spectra of all heavy-atom isotopomers including one (18)O and four (13)C isotopomers were observed in natural abundance. The OD isotopomer was obtained from isotopically enriched samples. The two lowest tunneling states of each isotopomer except (18)O have been assigned. The observed inversion splitting for the OD isotopomer is 1523.227(5) MHz. For the asymmetric (13)C structures, the magnitudes of tunneling-rotation interactions are found to diminish with decreasing distance between the heavy atom and the tunneling proton. In the limit of closest approach, the 0(+) state of (18)O was well fitted to an asymmetric rotor Hamiltonian, reflecting significant changes in the tautomerization dynamics. Comparisons of the substituted atom coordinates with theoretical predictions at the MP2/aug-cc-pVTZ level of theory suggest the localized 0(+) and 0(-) wave functions of the heavier isotopes favor the C-OH and C=O forms of tropolone, respectively. The only exception occurs for the (13)C-OH and (13)C[Double Bond]O structures which correlate to the 0(-) and 0(+) states, respectively. These preferences reflect kinetic isotope effects as quantitatively verified by the calculated zero-point energy differences between members of the asymmetric atom pairs. From rotationally resolved data of the 0(+) <--0(+) and 0(-) <--0(-) bands in S(1), line-shape fits have yielded Lorentzian linewidths that differ by 12.2(16) MHz over the 19.88(4) cm(-1) interval in S(1). The fluorescence decay rates together with previously reported quantum yield data give nonradiative decay rates of 7.7(5) x 10(8) and 8.5(5) x 10(8) s(-1) for the 0(+) and 0(-) levels of the S(1) state of tropolone.     

A Mössbauer effect study of the Re2Fe14B magnets,where RE is Y,Pr, Nd,and Gd

The Mössbauer spectra of Pr₂Fe₁₄B and Gd₂Fe₁₄B have been measured from 85 to 295 K and fit with a second order approximation in which the angle, ?, between the principal axis of the electric field gradient and the easy-axis of magnetization has been fixed by the positions of the near-neighbor rare-earth atoms. The coordination environment for each of the six iron sites in these materials has been determined from the Wigner-Seitz cell and used in the spectral analysis. The hyperfine parameters resulting from the above fit are in agreement with the structural and electronic properties of these compounds and also agree well with those determined in our earlier studies of Nd₂Fe₁₄B and Y₂Fe₁₄B. The magnetic hyperfine fields for the different sites are similar in the Y, Pr, and Nd compounds but are, as expected, higher in the Gd compound because of the much higher spin-multiplicity associated with Gd. The hyperfine fields on the 8j ₁ and 4c sites, which have the most rare-earth near-neighbors show, as expected, the largest variation with rare-earth atom. The quadrupole interactions are constant with temperature and the absolute value of the quadrupole interactions on the 8j ₂ and 4e site are found to be the largest, as is consistent with the highly distorted environment of these sites With the possible exception of the 4c site, the quadrupole interaction shows little variation with rare-earth atom. The isomer shift for each site in each compound varies linearly with temperature, as expected, for the second-order Doppler shift and gives effective Mössbauer masses between 62 and 67 g/mole. The weighted average isomer shift is similar in each of these compounds, but the isomer shifts associated with some of the specific sites in Gd₂Fe₁₄B are rather different than in the Y, Pr, and Nd compounds.     

Matrix isolation studies and potential function for perfluorocyclobutane

The infrared and Raman spectra of perfluorocyclobutane isolated in argon matrices at 1:100 and 1:200 mole ratios have been measured between 200 and 2000 cm^?1. Although the ring-puckering fundamental (ν₁₆) was not observed directly, an assignment for the 2 ← 1 (30 cm^?1) transition of ν₁₆ has been deduced from sum and difference bands resolved in the infrared spectrum. Potential functions based upon valence force models are considered in detail and correlated with those of similar ring systems. By using the frequency of the 2 ← 1 transition for ν₁₆ and a vibrational reduced mass of 1501 amu, an approximate model potential function calculation yields a slightly puckered equilibrium conformation with a barrier on the order of 124 cm^?1. The vibrational assignment for perfluorocyclobutane is discussed in terms of the new matrix isolation spectra.     

Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow

New families of three-dimensional nonlinear traveling waves are discovered in pipe flow. In contrast with known waves [H. Faisst and B. Eckhardt, Phys. Rev. Lett. 91, 224502 (2003); H. Wedin and R. R. Kerswell, J. Fluid Mech. 508, 333 (2004), they possess no discrete rotational symmetry and exist at a significantly lower Reynolds numbers (Re). First to appear is a mirror-symmetric traveling wave which is born in a saddle node bifurcation at Re=773. As Re increases, "asymmetric" modes arise through a symmetry-breaking bifurcation. These look to be a minimal coherent unit consisting of one slow streak sandwiched between two fast streaks located preferentially to one side of the pipe. Helical and nonhelical rotating waves are also found, emphasizing the richness of phase space even at these very low Reynolds numbers.     

Synthesis and reactivity of dichloroboryl complexes of platinum(II)

The reaction between [Pt(nbe)3] (nbe=norbornene), two equivalents of the phosphines PPh3, PMePh2 or PMe2Ph and 1 equivalent of BCl3 affords the platinum dichloroboryl species [PtCl(BCl2)(PPh3)2], [PtCl(BCl2)(PMePh2)2] and [PtCl(BCl2)(PMe2Ph)2]. All three complexes were characterised by X-ray crystallography and reveal that the boryl group lies trans to the chloride. With PMe3 as the phosphine, the complex [PtCl(BCl2)(PMe3)2] is isolated in high yield as a white crystalline powder although crystals suitable for X-ray crystallography were not obtained. Crystals were obtained of a product shown by X-ray crystallography to be the unusual dinuclear species [Pt2(BCl2)2(PMe3)4(micro-Cl)][BCl4] which reveals an arrangement in which two square planar platinum(II) centres are linked by a single bridging chloride which is trans to a BCl2 group on each platinum centre. The reaction of [PtCl(BCl2)(PMe3)2] with NEt3 or pyridine (py) affords the adducts [PtCl{BCl2(NEt3)}(PMe3)2] and [PtCl{BCl2(py)}(PMe3)2], respectively, both characterised spectroscopically. The reaction between [PtCl(BCl2)(PMe3)2] and either 4 equivalents of NHEt2 or piperidine (pipH) results in the mono-substituted boryl species [PtCl{BCl(NEt2)}(PMe3)2] and [PtCl{BCl(pip)}(PMe3)2], respectively, the former characterised by X-ray crystallography. Treatment of either [PtCl(BCl2)(PMe3)2] (in the presence of excess NEt3) or [PtCl{BCl(NEt2)}(PMe3)2] with catechol affords the B(cat) (cat=catecholate) derivative [PtCl{B(cat)}(PMe3)2] which is also formed in the reaction between [Pt(PMe3)4] and ClB(cat) and also from the slow decomposition of [Pt{B(cat)}2(PMe3)2] in dichloromethane over a period of months. The compound [Pt{B(cat)}2(PMe3)2] was prepared from the reaction between [Pt(PMe3)4] and B2(cat)2.     

Environmental fatigue testing of molded plastics for prosthetic heart valves

A testing machine was designed specifically to study fatigue behavior of molded polymeric materials by subjecting multiple cantilever specimens to vibratory fluid loading. The fluid loading permits aqueous or other environments, facilitates temperature control, and makes possible high testing frequencies. Samples of fifteen to thirty specimens may be tested simultaneously to obtain statistical data. Example results are presented showing Weibull distributions fitted to polymethyl methacrylate fatigue-life data. A statistical criterion was used to verify that scatter, due to the machine and testing technique, was not excessive.     

Integral resource capacity planning for inpatient care services based on bed census predictions by hour

The design and operations of inpatient care facilities are typically largely historically shaped. A better match with the changing environment is often possible, and even inevitable due to the pressure on hospital budgets. Effectively organizing inpatient care requires simultaneous consideration of several interrelated planning issues. Also, coordination with upstream departments like the operating theatre and the emergency department is much-needed. We present a generic analytical approach to predict bed census on nursing wards by hour, as a function of the Master Surgical Schedule and arrival patterns of emergency patients. Along these predictions, insight is gained on the impact of strategic (ie, case mix, care unit size, care unit partitioning), tactical (ie, allocation of operating room time, misplacement rules), and operational decisions (ie, time of admission/discharge). The method is used in the Academic Medical Center Amsterdam as a decision-support tool in a complete redesign of the inpatient care operations.