Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean field equations are iterated with Anderson mixing. The different methods are tested on the triply-periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

Illustration of micro-scale advection using grid-pattern mini-lysimeters

Twenty-five small soil-filled perspex boxes arranged in a square, with dwarf sunflowers growing in them, were used to study micro-scale advection. Hydrological heterogeneity was introduced by applying two different amounts of irrigation water (low-irrigation, L, versus high-irrigation, H). The nine central boxes (4 H, 4 L and I bare box) were precision weighing lysimeters, yielding diurnal measurements of evaporation. After the onset of soil water stress, a large difference in latent heat flux (up to 4-fold) was observed between the lysimeters of the H and L treatments, mainly caused by large differences between H and L stomatal conductance values. This resulted in micro-advection, causing H soil-sunflower systems to evaporate well above equilibrium latent heat flux. The occurrence of micro-advective enhancement was reflected in large values of the Priestley-Taylor constant (often larger than 2.0) and generally negative values of sensible heat flux for the H treatment. (c) 2005 Elsevier B.V. All rights reserved.

On the time for fold surfaces to order during the crystallization of polyethylene from the melt and its dependence on molecular parameters

New experiments underpin the interpretation of the basic division in crystallization behaviour of polyethylene in terms of whether or not there is time for the fold surface to order before the next molecular layer is added at the growth front. For typical growth rates, in Regime 11, polyethylene lamellae form with disordered {001} fold surfaces then transform, with lamellar thickening and twisting, towards the more-ordered condition found for slower crystallization in Regime 1, in which lamellae form with and retain {201} fold surfaces. Several linear and linear-low-density polyethylenes have been used to show that, for the same polymer crystallized alone or in a blend, the growth rate at which the change in initial lamellar condition occurs is reasonably constant thereby supporting the concept of a specific time for surfaces to attain the ordered {201}) state. This specific time, in the range from milliseconds to seconds, increases with molecular length, and in linear-low-density polymer, for higher branch contents. (c) 2006 Elsevier Ltd. All rights reserved.

Parameter estimation using a particle method: inferring mixing coefficients from sea level observations

This paper presents a first attempt to estimate mixing parameters from sea level observations using a particle method based on importance sampling. The method is applied to an ensemble of 128 members of model simulations with a global ocean general circulation model of high complexity. Idealized twin experiments demonstrate that the method is able to accurately reconstruct mixing parameters from an observed mean sea level field when mixing is assumed to be spatially homogeneous. An experiment with inhomogeneous eddy coefficients fails because of the limited ensemble size. This is overcome by the introduction of local weighting, which is able to capture spatial variations in mixing qualitatively. As the sensitivity of sea level for variations in mixing is higher for low values of mixing coefficients, the method works relatively well in regions of low eddy activity.

Architectural effect on the surface tension of an ABA triblock copolymer melt

The excess surface energy of lamellae formed by an ABA triblock copolymer melt oriented parallel to a neutral surface is evaluated using self-consistent field theory (SCFT). Consistent with experiments and previous SCFT calculations, we find a preference for the A-rich domains at the surface, which can only be attributed to the architectural asymmetry between the A and B blocks. The behavior was previously attributed to a loss of bridging configurations that occurs when the B-domain resides at the surface. Here we demonstrate that it is actually the presence of chain ends that reduces the excess surface energy of an A-rich domain relative that of a B-rich domain.

Variation of the mixing state of Saharan dust particles with atmospheric transport

Mineral dust is an important aerosol species in the Earth’s atmosphere and has a major source within North Africa, of which the Sahara forms the major part. Aerosol Time of Flight Mass Spectrometry (ATOFMS) is first used to determine the mixing state of dust particles collected from the land surface in the Saharan region, showing low abundance of species such as nitrate and sulphate internally mixed with the dust mineral matrix. These data are then compared with the ATOFMS single particle mass spectra of Saharan dust particles detected in the marine atmosphere in the vicinity of the Cape Verde islands, which are further compared with those from particles with longer atmospheric residence sampled at a coastal station at Mace Head, Ireland. Saharan dust particles collected near the Cape Verde Islands showed increased internally mixed nitrate but no sulphate, whilst Saharan dust particles collected on the coast of Ireland showed a very high degree of internally mixed secondary species including nitrate, sulphate and methanesulphonate. This uptake of secondary species will change the pH and hygroscopic properties of the aerosol dust and thus can influence the budgets of other reactive gases, as well as influencing the radiative properties of the particles and the availability of metals for dissolution.

Sewage effluent clean-up reduces phosphorus but not phytoplankton in lowland chalk stream (River Kennet, UK) impacted by water mixing from adjacent canal

Information is provided on phosphorus in the River Kennet and the adjacent Kennet and Avon Canal in southern England to assess their interactions and the changes following phosphorus reductions in sewage treatment work (STW) effluent inputs. A step reduction in soluble reactive phosphorus (SRP) concentration within the effluent (5 to 13 fold) was observed from several STWs discharging to the river in the mid-2000s. This translated to over halving of SRP concentrations within the lower Kennet. Lower Kennet SRP concentrations change from being highest under base-flow to highest under storm-flow conditions. This represented a major shift from direct effluent inputs to a within-catchment source dominated system characteristic of the upper part to the catchment. Average SRP concentrations in the lower Kennet reduced over time towards the target for good water quality. Critically, there was no corresponding reduction in chlorophyll-a concentration, the waters remaining eutrophic when set against standards for lakes. Following the up gradient input of the main water and SRP source (Wilton Water), SRP concentrations in the canal reduced down gradient to below detection limits at times near its junction with the Kennet downstream. However, chlorophyll concentrations in the canal were in an order of magnitude higher than in the river. This probably resulted from long water residence times and higher temperatures promoting progressive algal and suspended sediment generations that consumed SRP. The canal acted as a point source for sediment, algae and total phosphorus to the river especially during the summer months when boat traffic disturbed the canal's bottom sediments and the locks were being regularly opened. The short-term dynamics of this transfer was complex. For the canal and the supply source at Wilton Water, conditions remained hypertrophic when set against standards for lakes even when SRP concentrations were extremely low.

Melt structure and its transformation by sequential crystallization of the two blocks within poly(L-lactide)-block-poly(epsilon-caprolactone) double crystalline diblock copolymers

Sequential crystallization of poly(L-lactide) (PLLA) followed by poly(epsilon-caprolactone) (PCL) in double crystalline PLLA-b-PCL diblock copolymers is studied by differential scanning calorimetry (DSC), polarized optical microscopy (POM), wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS). Three samples with different compositions are studied. The sample with the shortest PLLA block (32 wt.-% PLLA) crystallizes from a homogeneous melt, the other two (with 44 and 60% PLLA) from microphase separated structures. The microphase structure of the melt is changed as PLLA crystallizes at 122 degrees C (a temperature at which the PCL block is molten) forming spherulites regardless of composition, even with 32% PLLA. SAXS indicates that a lamellar structure with a different periodicity than that obtained in the melt forms (for melt segregated samples). Where PCL is the majority block, PCL crystallization at 42 degrees C following PLLA crystallization leads to rearrangement of the lamellar structure, as observed by SAXS, possibly due to local melting at the interphases between domains. POM results showed that PCL crystallizes within previously formed PLLA spherulites. WAXS data indicate that the PLLA unit cell is modified by crystallization of PCL, at least for the two majority PCL samples. The PCL minority sample did not crystallize at 42 degrees C (well below the PCL homopolymer crystallization temperature), pointing to the influence of pre-crystallization of PLLA on PCL crystallization, although it did crystallize at lower temperature. Crystallization kinetics were examined by DSC and WAXS, with good agreement in general. The crystallization rate of PLLA decreased with increase in PCL content in the copolymers. The crystallization rate of PCL decreased with increasing PLLA content. The Avrami exponents were in general depressed for both components in the block copolymers compared to the parent homopolymers. Polarized optical micrographs during isothermal crystalli zation of (a) homo-PLLA, (b) homo-PCL, (c) and (d) block copolymer after 30 min at 122 degrees C and after 15 min at 42 degrees C.

Phase mixing and phase separation accompanying the catalytic oxidation of CO on Ir{100}

The co-adsorption of CO and O on the unreconstructed (1 x 1) phase of Ir {100} was examined by low energy electron diffraction (LEED) and temperature programmed desorption (TPD). When CO is adsorbed at 188 K onto the Ir{100} surface precovered with 0.5 ML O, a mixed c(4 x 2)-(2O + CO) overlayer is formed. All CO is oxidised upon heating and desorbs as CO2 in three distinct stages at 230 K, 330 K and 430 K in a 2:1:2 ratio. The excess oxygen left on the surface after all CO has reacted forms an overlayer with a LEED pattern with p(2 x 10) periodicity. This overlayer consists of stripes with a local p(2 x 1)-O arrangement of oxygen atoms separated by stripes of uncovered It. When CO is adsorbed at 300 K onto the surface precovered with 0.5 ML O an apparent (2 x 2) LEED pattern is observed. LEED IV analysis reveals that this pattern is a superposition of diffraction patterns from islands of c(2 x 2)-CO and p(2 x 1)-O structures on the surface. Heating this co-adsorbed overlayer leads to the desorption of CO, in two stages at 330 K and 430 K; the excess CO (0.1 ML) desorbs at 590 K. LEED IV structural analysis of the mixed c(4 x 2) O and CO overlayer shows that both the CO molecules and the O atoms occupy bridge sites. The O atoms show significant lateral displacements of 0.14 angstrom away from the CO molecules; the C-O bond is slightly expanded with respect to the gas phase (1.19 angstrom); the modifications of the Ir substrate with respect to the bulk-terminated surface are very small. (c) 2006 Elsevier B.V. All rights reserved.