On the evolution of two-dimensional patterns in an inviscid liquid sheet

We perform an analysis of the pattern formation for a moving sheet of inviscid fluid. The sheet, which is assumed to have an infinite horizontal extent, moves at some prescribed velocity into a passive surrounding gas. The sheet’s thickness is assumed much smaller than the horizontal scale of the fluid motion. By considering a system that is symmetric with respect to the horizontal planes, long scale asymptotics are used to reduce the full governing equations in three dimensions to a set of three coupled nonlinear partial differential equations for the horizontal components of the velocity field and the height of the interface profile. The interfacial conditions consisting of the kinematic and normal stress balance are incorporated into these evolution equations. Investigations are carried out as function of the sole dimensionless parameter, namely the Weber number. A small amplitude stability analysis around the planar gas–liquid interface reveals that wave patterns in the form of traveling plane waves occur subcritically, and are therefore unstable. The reduced evolution equations are solved numerically for fixed values of the Weber number. Since the reduced system of equations is homogeneous, the wave motion is generated by initial conditions. Five initial conditions have been imposed: one-dimensional rolls, two-dimensional squares, two-dimensional hexagons, two-dimensional ridges, and smooth peaks. The ensuing evolution of the liquid sheet’s shape and corresponding flow fields are described by illustrations of the changes in the sheet’s morphology with time.     

Variation of geometric invariant theory quotients

Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parameterizing isomorphism classes of geometric objects (vector bundles, polarized varieties, etc.). The quotient depends on a choice of an ample linearized line bundle. Two choices are equivalent if they give rise to identical quotients. A priori, there are infinitely many choices since there are infinitely many isomorphism classes of linearized ample line bundles. Hence several natural questions arise. Is the set of equivalence classes, and hence the set of non-isomorphic quotients, finite? How does the quotient vary under change of the equivalence class? In this paper we give partial answers to these questions in the case of actions of reductive algebraic groups on nonsingular projective algebraic varieties. We shall show that among ample line bundles which give projective geometric quotients there are only finitely many equivalence classes. These classes span certain convex subsets (chambers) in a certain convex cone in Euclidean space, and when we cross a wall separating one chamber from another, the corresponding quotient undergoes a birational transformation which is similar to a Mori flip.     

Observation and analysis ofE mesons in\bar p p annihilation at rest in H2 gas

Antiproton-proton annihilation at rest in a gaseous H₂ target at NTP into the final state π⁺ π^? K ^± π^? (K ⁰) with an undetectedK ⁰ or \(\bar K^0 \) has been investigated. We observe theE(1420) resonance in the invariant mass spectrum (K ⁰)_miss K ^± π^? with massM _E =1413±8 MeV/c² and widthГ ^E =62 ± 16MeV/c² and find evidence for the production of thef ₁(1285). The absolute branching ratio of \(\bar p\) p → π⁺ π^? E ⁰,E ⁰ →K ₀ ^L K ^± π ^? at (61±6)%P wave annihilation is (3.0±0.9)·10^?4 of all annihilations. The observed suppression of theE production fromP wave with respect to theS wave together with some simple selection rules suggest that the quantum numbers of theE(1420) areJ ^pc=0^?+ and not I⁺⁺.     

Thermodynamic properties of transition metals in aqueous solution. 2. The enthalpies of mixing of aqueous solutions of CoCl2, CuCl2, and MnCl2 with NaCl at varying ionic strength at 25°C

Enthalpies of mixing (_m H) aqueous solutions of CoCl₂, CuCl₂, and MnCl₂ with NaCl solutions were measured at constant ionic strengths of 0.5, 1.0, and 3.0 molal at 25°C. The excess enthalpy equations of Pitzer were then fit to the resulting _m H data. The resulting parameters are the temperature derivatives of the activity coefficient mixing parameters in the Pitzer system. The heat of mixing data for CoCl₂ and CuCl₂ were in agreement with earlier isomolal results by other workers.     

Nitroxides with two pK values--useful spin probes for pH monitoring within a broad range

A series of 4-dialkylamino-2,5-dihydroimidazole nitroxides with pyridine-4-yl, 4-dimethylaminophenyl or 4-hydroxyphenyl groups in position 2 of the imidazole ring were prepared using the reaction of RMgBr with corresponding 5-dialkylamino-4,4-dimethyl-4H-imidazole 3-oxides. The EPR spectra of the nitroxides were shown to be pH-sensitive due to consecutive protonation of the amidino moiety and the basic group(s) at position 2 of the imidazole ring. The 5,5-dimethyl-4-(dimethylamino)-2-ethyl-2-pyridine-4-yl-2,5-dihydro-1H-imidazol-1-oxyl showed a monotonic increase in the isotropic nitrogen hyperfine (hfi) coupling constant alpha(N) of 1 .4 G over a pH range from 2 to 6.5. Such a broad range of pH-sensitivity could be useful for many biophysical and biomedical applications, including pH-monitoring in the stomach.     

Kinetic studies of some substituted hexarhodium carbonyl clusters

Reactions of the halides X- (X- = chloride, bromide or iodide) with the substituted cluster Rh6(CO)15(PPh3) in oxygen-free chloroform lead to [Rh5(CO)14(PPh3)]-, Rh(CO)2(PPh3)2X and [Rh(CO)2X2]- in the molar ratios 2:1: approximately 13. Oxidation by the solvent is assumed to lead to most of the Rh(I) product, and the stoichiometry for reactions with I- can be defined as 4Rh6(CO)15(PPh3) + 27I- + 12CHCl3 --> 2[Rh5(CO)14(PPh3)]- + Rh(CO)2(PPh3)2I + 13[Rh(CO)2I2]- + 6C2H2Cl4 + 4CO + 12Cl-. This can be rationalized quite simply with the aid of a few generally justifiable assumptions. Rate constants for reactions with bromide increase to a limiting value with increasing [Br-] in a way that shows that breaking of one Rh-Rh bond, with an unusual closo to nido structural change, is rate determining. This opening of the cluster might be spontaneous or solvent induced. To complete the reaction, the bromide has to compete with the reverse nido to closo change. The same closo to nido change is also a major rate determining step for reactions with P(OPh)3 in oxygen-free solutions, and for reactions with bromide in oxygenated solutions in the presence of trifluoroacetic and some other acids. The limiting rates increase slightly with increasing basicity of the ligands P(p-XC6H4)3 along the series X = F3C, Cl, F, H and MeO. Activation parameters for these reactions are reported.     

Trennung, Nachweis und Bestimmung von Benzidin, α- und β-Naphthylamin

Summary Three methods (photometry, TLC, HPLC) are proposed for the separation, detection and determination of the cancerogenic compounds benzidine, - and -naphthylamine in drinking water. The necessary detection limit of 0.1 g/l has been achieved.