The quasi-nondispersive regimes of long extratropical baroclinic rossby waves over (slowly varying) topography

Actual energy paths of long, extratropical baroclinic Rossby waves in the ocean are difficult to describe simply because they depend on the meridional-wavenumber-to-zonal-wavenumber ratio tau, a quantity that is difficult to estimate both observationally and theoretically. This paper shows, however, that this dependence is actually weak over any interval in which the zonal phase speed varies approximately linearly with tau, in which case the propagation becomes quasi-nondispersive (QND) and describable at leading order in terms of environmental conditions (i.e., topography and stratification) alone. As an example, the purely topographic case is shown to possess three main kinds of QND ray paths. The first is a topographic regime in which the rays follow approximately the contours f/h(alpha c) = a constant (alpha(c) is a near constant fixed by the strength of the stratification, f is the Coriolis parameter, and h is the ocean depth). The second and third are, respectively, "fast" and "slow" westward regimes little affected by topography and associated with the first and second bottom-pressure-compensated normal modes studied in previous work by Tailleux and McWilliams. Idealized examples show that actual rays can often be reproduced with reasonable accuracy by replacing the actual dispersion relation by its QND approximation. The topographic regime provides an upper bound ( in general a large overestimate) of the maximum latitudinal excursions of actual rays. The method presented in this paper is interesting for enabling an optimal classification of purely azimuthally dispersive wave systems into simpler idealized QND wave regimes, which helps to rationalize previous empirical findings that the ray paths of long Rossby waves in the presence of mean flow and topography often seem to be independent of the wavenumber orientation. Two important side results are to establish that the baroclinic string function regime of Tyler and K se is only valid over a tiny range of the topographic parameter and that long baroclinic Rossby waves propagating over topography do not obey any two-dimensional potential vorticity conservation principle. Given the importance of the latter principle in geophysical fluid dynamics, the lack of it in this case makes the concept of the QND regimes all the more important, for they are probably the only alternative to provide a simple and economical description of general purely azimuthally dispersive wave systems.

Dinuclear complexes of M-II thiocyanate (M = Ni and Cu) containing a tridentate Schiff-base ligand: synthesis, structural diversity and magnetic properties

A dinuclear Ni-II complex, [Ni-2(L)(2)(H2O)(NCS)(2)]center dot 3H(2)O (1) in which the metal atoms are bridged by one water molecule and two mu(2)-phenolate ions, and a thiocyanato-bridged dimeric Cull complex, [Cu(L)NCS](2) (2) [L = tridentate Schiff-base ligand, N-(3-aminopropyl)salicylaldimine, derived from 1:1 condensation of salicylaldehyde and 1,3-diaminopropane], have been synthesized and characterized by IR and UV/Vis spectroscopy, cyclic voltammetry and single-crystal X-ray diffraction studies. The structure of 1 consists of dinuclear units with crystallographic C-2 symmetry in which each Ni-II atom is in a distorted octahedral environment. The Ni-O distance and the Ni-O-Ni angle, through the bridged water molecule, are 2.240(11) angstrom and 82.5(5)degrees, respectively. The structure of 2 consists of dinuclear units bridged asymmetrically by di-mu(1,3)-NCS ions; each Cull ion is in a square-pyramidal environment with tau = 0.25. Variable-temperature magnetic susceptibility studies indicate the presence of dominant ferromagnetic exchange coupling in complex 1 with J = 3.1 cm(-1), whereas complex 2 exhibits weak antiferromagnetic coupling between the Cu-II centers with J = -1.7 cm(-1). ((c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2005)

Synthesis, characterization, and anion selectivity of copper(II) complexes with a tetradentate Schiff base ligand

A new mononuclear Cu(II) complex, [CuL(ClO4)(2)] (1) has been derived from symmetrical tetradentate di-Schiff base, N,N'-bis-(1-pyridin-2-yl-ethylidene)-propane-1,3-diamine (L) and characterized by X-ray crystallography. The copper atom assumes a tetragonally distorted octahedral geometry with two perchlorate oxygens coordinated very weakly in the axial positions. Reactions of I with sodium azide, ammonium thiocyanate or sodium nitrite solution yielded compounds [CuL(N-3)]ClO4 (2), [CuL(SCN)ClO4 (3) or [CuL(NO2)]-ClO4 (4), respectively, all of which have been characterized by X-ray analysis. The geometries of the penta-coordinated copper(H) in complexes 2-4 are intermediate between square pyramid and trigonal bipyramid (tbp) having the Addition parameters (tau) 0.47, 0.45 and 0.58, respectively. In complex 4, the nitrite ion is coordinated as a chelating ligand and essentially both the 0 atoms of the nitrite occupy one axial site. Complex 1 shows distinct preference for the anion in the order SCN- > N-3(-) > NO2- in forming the complexes 24 when treated with a SCN-/N-3(-)/NO2- mixture. Electrochemical electron transfer study reveals (CuCuI)-Cu-II reduction in acetonitrile solution. (c) 2006 Elsevier B.V.. All rights reserved.

Photochemical, photophysical and redox properties of novel fulgimide derivatives with attached 2,2 '-bipyridine (bpy) and [M(bpy)(3)](2+) (M = Ru and Os) moieties

Fulgimides monosubstituted with [M(bpy)(3)](2+) (M = Ru, Os; bpy = 2,2'-bipyridine) chromophore units and with a single bpy group were synthesized and investigated as components of conceivable dinuclear photochromic switches of luminescence. The E-, Z- and closed-ring (C) photoisomer forms of the bpy-bound fulgimide were successfully separated by semi-preparative HPLC. The same procedure failed, however, in the case of the [M(bpy)(3)](2+)-substituted fulgimides. Energy transfer from the excited photochromic unit to the metal-bpy centre competes with the fulgimide cyclization, reducing the photocyclization quantum yields by approximately one order of magnitude compared to the non-complexed fulgimide-bpy ligand (phi(EC) = 0.17, phi(EZ) = 0.071, phi(ZE) = 0.15 at lambda(exc) = 334 nm). The cycloreversion of the fulgimide-bpy ligand is less efficient (phi(CE) = 0.047 at lambda(exc) = 520 nm). The intensity of the (MLCT)-M-3-based luminescence of the metal-bpy chromophore (in MeCN, phi(deaer) = 6.6 x 10(-2) and tau(deaer) = 1.09 mu s for Ru; phi(deaer) = 6.7 x 10(-3) and tau(deaer) = 62 ns for Os) is not affected by the fulgimide photoconversion. These results and supporting spectro-electrochemical data reveal that the lowest triplet excited states of the photochromic fulgimide moiety in all its E-, Z- and closed-ring forms lie above the lowest 3MLCT levels of the attached ruthenium and osmium chromophores. The actual components are therefore unlikely to form a triad acting as functional switch of energy transfer from [Ru(bpy)(3)](2+) to [Os(bpy)(3)](2+) through the photochromic fulgimide bridge.

Synthesis, crystal structure and reactivity of copper(II) complexes of tetradentate N2S2 donor ligands

Two new hexa-coordinated mononuclear copper(II) complexes of two ligands L-1 and L-2 containing NSSN donor sets formulated as [Cu(L)(H2O)(2)](NO3)(2) [1a, L = 1,2-bis(2-pyridylmethylthio)ethane (L-1), 1b L = 1,3-bis(2-pyridyl-methylthio)propane (L-2)] were synthesized and characterized by physico-chemical and spectroscopic methods. In 1a the single crystal X-ray crystallography analysis showed a distorted octahedral geometry about copper(II) ion. The crystal packing evidences pairs of complexes arranged about a center of symmetry and connected through a H-bond occurring between aquo ligands and nitrate anions. On reaction with chloride and pseudohalides (N-3(-) and SCN-), in acetonitrile at ambient temperature. complexes 1 changed to monocationic penta-coordinated mononuclear copper(H) species formulated as [Cu(L)(Cl)]NO3 (2), [Cu(L)(N-3)]NO3 (3). and [Cu(L)(SCN)]NO3 (4). These copper(II) complexes have been isolated in pure form from the reaction mixtures and characterized by physico-chemical and spectroscopic tools. The solid-state structure of 2a, established by X-ray crystallography, shows a trigonal bipyramidal geometry about the metal ion with a trigonality index (tau) of 0.561. (C) 2009 Elsevier B.V. All rights reserved.

Critical flux in ultrafiltration of skimmed milk

he best operating conditions, using the critical flux concept during ultrafiltration of skimmed milk, were evaluated for tubular membranes. It was found that irreversible fouling was greatly reduced by operating at or below the critical flux, but was not totally eliminated. The critical flux of skimmed milk was found to be the weak form. The critical flux at cross flow velocity 3.4 in s(-1) for MWCO 200 kDa membrane was 56.9 kg m(-2) h(-1) while for MWCO 25 kDa membranes it was 45 kg m(2) h(-1) suggesting that membrane pore size influenced the flux. The critical flux increased with increasing wall shear stress and decreased with increasing protein concentration. Empirical equations, for predicting the critical flux (J(crit)) for skimmed milk with a protein concentration (c(b)) in the range 3-7% w/w and wall shear stress (tau(w)) in the range 7-60 Pa for MWCO 200 kDa and 25 kDa membranes were J(crit) = 5.1 (tau(w)/c(b)) and J(crit) = 4.0 (tau(w)/c(b)) respectively. In general, the rejections of protein and lactose at the critical flux were not affected by protein concentration, wall shear stress and membrane used, and they were similar to those found when operating at the limiting flux.

Stress relaxation behavior of wheat dough, gluten, and gluten protein fractions

Relaxation behavior was measured for dough, gluten and gluten protein fractions obtained from the U.K. biscuitmaking flour, Riband, and the U.K. breadmaking flour, Hereward. The relaxation spectrum, in which relaxation times (tau) are related to polymer molecular size, for dough showed a broad molecular size distribution, with two relaxation processes: a major peak at short times and a second peak at times longer than 10 sec, which is thought to correspond to network structure, and which may be attributed to entanglements and physical cross-links of polymers. Relaxation spectra of glutens were similar to those for the corresponding doughs from both flours. Hereward gluten clearly showed a much more pronounced second peak in relaxation spectrum and higher relaxation modulus than Riband gluten at the same water content. In the gluten protein fractions, gliadin and acetic acid soluble glutenin only showed the first relaxation process, but gel protein clearly showed both the first and second relaxation processes. The results show that the relaxation properties of dough depend on its gluten protein and that gel protein is responsible for the network structure for dough and gluten.

The effect of vessel diameter on time dependent gas hold-up variations in highly viscous impeller agitated liquids

Time dependent gas hold-up generated in the 0.3 and 0.6 m diameter vessels using high viscosity castor oil and carboxy methyl cellulose (CMC) solution was compared on the basis of impeller speed (N) and gas velocity (V-G). Two types of hold-up were distinguished-the hold-up due to tiny bubbles (epsilon(ft)) and total hold-up (epsilon(f)), which included large and tiny bubbles. It was noted that vessel diameter (i.e. the scale of operation) significantly influences (i) the trends and the values of epsilon(f) and epsilon(ft), and (ii) the values of tau (a constant reflecting the time dependency of hold-up). The results showed that a scale independent correlation for gas hold-up of the form epsilon(f) or epsilon(ft) = A(N or P-G/V)(a) (V-G)(b), where "a" and "b" are positive constants is not appropriate for viscous liquids. This warrants further investigations into the effect of vessel diameter on gas hold-up in impeller agitated high viscosity liquids (mu or mu(a) > 0.4 Pa s). (C) 2003 Elsevier B.V. All rights reserved.

Interceptive timing: prior knowledge matters

Fast interceptive actions, such as catching a ball, rely upon accurate and precise information from vision. Recent models rely on flexible combinations of visual angle and its rate of expansion of which the tau parameter is a specific case. When an object approaches an observer, however, its trajectory may introduce bias into tau-like parameters that render these computations unacceptable as the sole source of information for actions. Here we show that observer knowledge of object size influences their action timing, and known size combined with image expansion simplifies the computations required to make interceptive actions and provides a route for experience to influence interceptive action.

Motorcycle accident risk could be inflated by a time to arrival illusion

Purpose. Drivers adopt smaller safety margins when pulling out in front of motorcycles compared with cars. This could partly account for why the most common motorcycle/car accident involves a car violating a motorcyclist's right of way. One possible explanation is the size-arrival effect in which smaller objects are perceived to arrive later than larger objects. That is, drivers may estimate the time to arrival of motorcycles to be later than cars because motorcycles are smaller. Methods. We investigated arrival time judgments using a temporal occlusion paradigm. Drivers recruited from the student population (n = 28 and n = 33) saw video footage of oncoming vehicles and had to press a response button when they judged that vehicles would reach them. Results. In experiment 1, the time to arrival of motorcycles was estimated to be significantly later than larger vehicles (a car and a van) for different approach speeds and viewing times. In experiment 2, we investigated an alternative explanation to the size-arrival effect: that the smaller size of motorcycles places them below the threshold needed for observers to make an accurate time to arrival judgment using tau. We found that the motorcycle/car difference in arrival time estimates was maintained for very short occlusion durations when tau could be estimated for both motorcycles and cars. Conclusions. Results are consistent with the size-arrival effect and are inconsistent with the tau threshold explanation. Drivers estimate motorcycles will reach them later than cars across a range of conditions. This could have safety implications.

Efficient on the fly calculation of time correlation functions in computer simulations

Time correlation functions yield profound information about the dynamics of a physical system and hence are frequently calculated in computer simulations. For systems whose dynamics span a wide range of time, currently used methods require significant computer time and memory. In this paper, we discuss the multiple-tau correlator method for the efficient calculation of accurate time correlation functions on the fly during computer simulations. The multiple-tau correlator is efficacious in terms of computational requirements and can be tuned to the desired level of accuracy. Further, we derive estimates for the error arising from the use of the multiple-tau correlator and extend it for use in the calculation of mean-square particle displacements and dynamic structure factors. The method described here, in hardware implementation, is routinely used in light scattering experiments but has not yet found widespread use in computer simulations.

Heterosite effects in novel heteronuclear clusters [OS2Ru(CO)(11)(PPh3)] and Os2Ru(CO)(10)(2-acetylpyridine-N-isopropylimine)]

A new synthetic route towards the mixed-metal cluster [OS2Ru(CO)(12)] is described together with the syntheses of its PPh3 and iPr-AcPy (iPr-AcPy = 2-acetylpyridine-N-isopropylimine) derivatives. The molecular structures of the novel clusters [Os2Ru(CO)(11)(PPh3)] and [Os2Ru(CO)(10)(iPr-AcPy)] were determined on the basis of crystalline solid solutions of the Os2Ru and corresponding Os-3 species. The structures reveal that coordination of the Lewis bases occurs exclusively at the ruthenium site of [Os2Ru(CO)(12)], which is in agreement with density functional theory (DFT) calculations on several structural isomers of these compounds. According to the time-dependent DFT results, the lowest optically accessible excited state of [Os2Ru(CO)(10)(iPr-AcPy)] has a prevailing sigma(Ru-Os-2)pi*(iPr-AcPy) character, with a partial sigma sigma*(Ru-Os-2) contribution. In weakly coordinating 2-chlorobutane, the excited state has a lifetime tau = 10.4 +/- 1.2 ps and produces biradicals considerably faster than observed for [Os-3(CO)10(iPr-AcPy) (tau = 25.3 +/- 0.7ps)]. In coordinating acetonitrile, the excited state of [Os2Ru(CO)(10)(iPr-AcPy)] decays mono-exponentially with a lifetime tau = 2.1 +/- 0.2 ps. In contrast to [Os-3(CO)(10)(iPr-AcPy)] that forms biradicals as the main primary photoproduct even in strongly coordinating solvents, zwitterion formation from the solvated lowest excited state is observed for the heterometallic cluster. This is concluded from time-resolved absorption studies in the microsecond time domain. Due to the lower tendency of the coordinatively unsaturated Ru+(CO)(2)(iPr-AcPy-/0) moiety to bind a Lewis base, the heteronuclear biradical and zwitterionic photoproducts live significantly shorter than their triosmium counterparts. The influence of the weaker Os-2-Ru(iPr-AcPy) bond on the redox reactivity is clearly reflected in very reactive radical anions formed upon electrochemical reduction of [Os2Ru(CO)(10)(iPr-AcPy)]. The dimer [-OS(CO)(4)-Os(CO)(4)-Ru(CO)(2)(iPr-AcPy)](2)(2-) is the only IR-detectable intermediate reduction product. The dinuclear complex [Os-2(CO)(8)](2-) and insoluble [Ru(CO)(2)(iPr-AcPy)](n), are the ultimate reduction products, proving fragmentation of the OS2Ru core.

Luminescence of a new Ru(II) polypyridine complex controlled by a redox-responsive protonable anthra[1,10]phenanthrolinequinone

Redox-controlled luminescence quenching is presented for a new Ru(II)-bipyridine complex [Ru(bpy)(2)(1)](2+) where ligand 1 is an anthra[1,10] phenanthrolinequinone. The complex emits from a short-lived metal-to-ligand charge transfer, (MLCT)-M-3 state (tau = 5.5 ns in deaerated acetonitrile) with a low luminescence quantum yield (5 x 10(-4)). The emission intensity becomes significantly enhanced when the switchable anthraquinone unit is reduced to corresponding hydroquinone. On the contrary, chemical one-electron reduction of the anthraquinone moiety to semiquinone in aprotic tetrahydrofuran results in total quenching of the emission.