Multiple stationary solutions of an irradiated slab

A mathematical model describing the heat budget of an irradiated medium is introduced. The one-dimensional form of the equations and boundary conditions are presented and analysed. Heat transport at one face of the slab occurs by absorption (and reflection) of an incoming beam of short-wave radiation with a fraction of this radiation penetrating into the body of the slab, a diffusive heat flux in the slab and a prescribed incoming heat flux term. The other face of the slab is immersed in its own melt and is considered to be a free surface. Here, temperature continuity is prescribed and evolution of the surface is determined by a Stefan condition. These boundary conditions are flexible enough to describe a range of situations such as a laser shining on an opaque medium, or the natural environment of polar sea ice or lake ice. A two-stream radiation model is used which replaces the simple Beer’s law of radiation attenuation frequently used for semi-infinite domains. The stationary solutions of the governing equations are sought and it is found that there exists two possible stationary solutions for a given set of boundary conditions and a range of parameter choices. It is found that the existence of two stationary solutions is a direct result of the model of radiation absorption, due to its effect on the albedo of the medium. A linear stability analysis and numerical calculations indicate that where two stationary solutions exist, the solution corresponding to a larger thickness is always stable and the solution corresponding to a smaller thickness is unstable. Numerical simulations reveal that when there are two solutions, if the slab is thinner than the smaller stationary thickness it will melt completely, whereas if the slab is thicker than the smaller stationary thickness it will evolve toward the larger stationary thickness. These results indicate that other mechanisms (e.g. wave-induced agglomeration of crystals) are necessary to grow a slab from zero initial thickness in the parameter regime that yields two stationary solutions.

Conical sedimentary structures, trace fossils or not? Observations, experiments, and review

Conical sedimentary structures are widespread in the geological column. Those that are mediated by organisms (or organic matter) can be attributed to seven principal processes, which are investigated by experiment and/or field observations: (1) sand collapse into a cavity (decomposed body, open shaft, or gallery), (2) upward (escape) or downward locomotion by an organism through the sediment, (3) upward adjustment (equilibration), (4) casting of coelenterates' excavations, (5) organism-mediated soft-sediment deformation in heterolithic sediment, (6) biodeformational small and large excavations by organisms, and (7) fluid (gas or liquid) escape structures. Footprint loading may also be included. Criteria are given to distinguish between these processes. Dewatering pipes are best recognized by a zone of deformed and fluidized sediment at the base, and association with non-life (lethal) facies. Care must be used in assigning specimens to ichnotaxa, and it is generally necessary to slab, and also to carry out stratinomic investigation in the field.

Magnitude of climate variability during middle Pliocene warmth: a palaeoclimate modelling study

The nature and magnitude of climatic variability during the period of middle Pliocene warmth (ca 3.29–2.97 Ma) is poorly understood. We present a suite of palaeoclimate modelling experiments incorporating an advanced atmospheric general circulation model (GCM), coupled to a Q-flux ocean model for 3.29, 3.12 and 2.97 Ma BP. Astronomical solutions for the periods in question were derived from the Berger and Loutre BL2 astronomical solution. Boundary conditions, excluding sea surface temperatures (SSTs) which were predicted by the slab-ocean model, were provided from the USGS PRISM2 2°×2° digital data set. The model results indicate that little annual variation (0.5°C) in SSTs, relative to a ‘control’ experiment, occurred during the middle Pliocene in response to the altered orbital configurations. Annual surface air temperatures also displayed little variation. Seasonally, surface air temperatures displayed a trend of cooler temperatures during December, January and February, and warmer temperatures during June, July and August. This pattern is consistent with altered seasonality resulting from the prescribed orbital configurations. Precipitation changes follow the seasonal trend observed for surface air temperature. Compared to present-day, surface wind strength and wind stress over the North Atlantic, North Pacific and Southern Ocean remained greater in each of the Pliocene experiments. This suggests that wind-driven gyral circulation may have been consistently greater during the middle Pliocene. The trend of climatic variability predicted by the GCM for the middle Pliocene accords with geological data. However, it is unclear if the model correctly simulates the magnitude of the variation. This uncertainty is derived from, (a) the relative insensitivity of the GCM to perturbation in the imposed boundary conditions, (b) a lack of detailed time series data concerning changes to terrestrial ice cover and greenhouse gas concentrations for the middle Pliocene and (c) difficulties in representing the effects of ‘climatic history’ in snap-shot GCM experiments.

Model catalyst studies of the strong metal-support interaction: Surface structure identified by STM on Pd nanoparticles on TiO2(110)

Model catalysts of Pd nanoparticles and films on TiO2 (I 10) were fabricated by metal vapour deposition (MVD). Molecular beam measurements show that the particles are active for CO adsorption, with a global sticking probability of 0.25, but that they are deactivated by annealing above 600 K, an effect indicative of SMSI. The Pd nanoparticles are single crystals oriented with their (I 11) plane parallel to the surface plane of the titania. Analysis of the surface by atomic resolution STM shows that new structures have formed at the surface of the Pd nanoparticles and films after annealing above 800 K. There are only two structures, a zigzag arrangement and a much more complex "pinwheel" structure. The former has a unit cell containing 7 atoms, and the latter is a bigger unit cell containing 25 atoms. These new structures are due to an overlayer of titania that has appeared on the surface of the Pd nanoparticles after annealing, and it is proposed that the surface layer that causes the SMSI effect is a mixed alloy of Pd and Ti, with only two discrete ratios of atoms: Pd/Ti of 1: 1 (pinwheel) and 1:2 (zigzag). We propose that it is these structures that cause the SMSI effect. (c) 2005 Elsevier Inc. All rights reserved.

Changes in the global sulfate burden due to perturbations in global CO2 concentrations

A large ensemble of general circulation model (GCM) integrations coupled to a fully interactive sulfur cycle scheme were run on the climateprediction.net platform to investigate the uncertainty in the climate response to sulfate aerosol and carbon dioxide (CO2) forcing. The sulfate burden within the model (and the atmosphere) depends on the balance between formation processes and deposition (wet and dry). The wet removal processes for sulfate aerosol are much faster than dry removal and so any changes in atmospheric circulation, cloud cover, and precipitation will feed back on the sulfate burden. When CO2 is doubled in the Hadley Centre Slab Ocean Model (HadSM3), global mean precipitation increased by 5%; however, the global mean sulfate burden increased by 10%. Despite the global mean increase in precipitation, there were large areas of the model showing decreases in precipitation (and cloud cover) in the Northern Hemisphere during June–August, which reduced wet deposition and allowed the sulfate burden to increase. Further experiments were also undertaken with and without doubling CO2 while including a future anthropogenic sulfur emissions scenario. Doubling CO2 further enhanced the increases in sulfate burden associated with increased anthropogenic sulfur emissions as observed in the doubled CO2-only experiment. The implications are that the climate response to doubling CO2 can influence the amount of sulfate within the atmosphere and, despite increases in global mean precipitation, may act to increase it.

Conservative upwind difference schemes for the Euler equations for real gas flows in a duct

In a recent paper [P. Glaister, Conservative upwind difference schemes for compressible flows in a Duct, Comput. Math. Appl. 56 (2008) 1787–1796] numerical schemes based on a conservative linearisation are presented for the Euler equations governing compressible flows of an ideal gas in a duct of variable cross-section, and in [P. Glaister, Conservative upwind difference schemes for compressible flows of a real gas, Comput. Math. Appl. 48 (2004) 469–480] schemes based on this philosophy are presented for real gas flows with slab symmetry. In this paper we seek to extend these ideas to encompass compressible flows of real gases in a duct. This will incorporate the handling of additional terms arising out of the variable geometry and the non-ideal nature of the gas.

Synthesis, crystal structure and hydrolysis of a dinuclear copper(II) complex constructed by N2O donor Schiff base and 4,4 '-bipyridine: discrete supra-molecular ensembles vs. oligomers

The tridentate Schiff base ligand, 7-amino-4-methyl-5-aza-3-hepten-2-one (HAMAH), prepared by the mono-condensation of 1,2diaminoethane and acetylacetone, reacts with Cu(BF4)(2) center dot 6H(2)O to produce initially a dinuclear Cu(II) complex, [{Cu(AMAH)}(2) (mu-4,4'-bipyJ](BF4)(2) (1) which undergoes hydrolysis in the reaction mixture and finally produces a linear polymeric chain compound, [Cu(acac)(2)(mu-4,4'-bipy)](n) (2). The geometry around the copper atom in compound 1 is distorted square planar while that in compound 2 is essentially an elongated octahedron. On the other hand, the ligand HAMAH reacts with Cu(ClO4)(2) center dot 6H(2)O to yield a polymeric zigzag chain, [{Cu(acac)(CH3OH)(mu-4,4'-bipy)}(ClO4)](n) (3). The geometry of the copper atom in 3 is square pyramidal with the two bipyridine molecules in the cis equatorial positions. All three complexes have been characterized by elemental analysis, IR and UV-Vis spectroscopy and single crystal X-ray diffraction studies. A probable explanation for the different size and shape of the reported polynuclear complexes formed by copper(II) and 4,4'-bipyridine has been put forward by taking into account the denticity and crystal field strength of the blocking ligand as well as the Jahn-Teller effect in copper(II). (c) 2007 Elsevier Ltd. All rights reserved.

4,4 '-Dipyridyl-N,N '-dioxide complexes of metal-thiocyanate/selenocyanate: pi-stacked molecular rods as three-dimensional support for two-dimensional polymeric sheets and intra/interchain S center dot center dot center dot S interaction dependent architecture of the R-2(2)(8) synthon driven assembly of one-dimensional polymeric chains

Three supramolecular complexes of Co(II) using SCN-/SeCN- in combination with 4,4'-dipyridyl-N,N'-dioxide (dpyo), i.e., {[Co(SCN)(2)(dpyo)(2)].(dpyo)}(n) ( 1), {[Co(SCN)(2)(dpyo)(H2O)(2)].(H2O)}(n) ( 2), {[Co(SeCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 3), have been synthesized and characterized by single-crystal X-ray analysis. Complex 1 is a rare example of a dpyo bridged two-dimensional (2D) coordination polymer, and pi-stacked dpyo supramolecular rods are generated by the lattice dpyo, passing through the rhombic grid of stacked layers, resulting in a three-dimensional (3D) superstructure. Complexes 2 and 3 are isomorphous one-dimensional (1D) coordination polymers [-Co-dpyo-Co-] that undergo self-assembly leading to a bilayer architecture derived through an R-2(2)(8) H-bonding synthon between coordinated water and dpyo oxygen. A reinvestigation of coordination polymers [Mn(SCN)(2)(dpyo)( H2O)(MeOH)](n) ( 4) and {[Fe(SCN)(2)(dpyo)(H2O)(2)]center dot(H2O)}(n) ( 5) reported recently by our group [ Manna et al. Indian J. Chem. 2006, 45A, 1813] reveals brick wall topology rather than bilayer architecture is due to the decisive role of S center dot center dot center dot S/Se center dot center dot center dot Se interactions in determining the helical nature in 4 and 5 as compared to zigzag polymeric chains in 2 and 3, although the same R-2(2)(8) synthon is responsible for supramolecular assembly in these complexes.

Syntheses, structural analyses, and magneto-structural correlations of three polymeric Fe(II) complexes with azide ligand

Three new metal-organic polymeric complexes, [Fe(N-3)(2)(bPP)(2)] (1), [Fe(N-3)(2)(bpe)] (2), and [Fe(N-3)(2)(phen)] (3) [bpp = (1,3-bis(4-pyridyl)-propane), bpe = (1,2-bis(4-pyridyl)-ethane), phen = 1,10-phenanthroline], have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature magnetic measurements in the range 300-2 K. Complexes 1 and 2 crystallize in the monoclinic system, space group C2/c, with the following cell parameters: a = 19.355(4) Angstrom, b = 7.076(2) Angstrom, c = 22.549(4) Angstrom, beta = 119.50(3)degrees, Z = 4, and a = 10.007(14) Angstrom, b = 13.789(18) Angstrom, c = 10.377(14) Angstrom, beta = 103.50(1)degrees, Z = 4, respectively. Complex 3 crystallizes in the triclinic system, space group P (1) over bar, with a = 7.155(12) Angstrom, b = 10.066(14) Angstrom, c = 10.508(14) Angstrom, alpha = 109.57(1)degrees, beta = 104.57(1)degrees, gamma = 105.10(1)degrees, and Z = 2. All coordination polymers exhibit octahedral Fe(II) nodes. The structural determination of 1 reveals a parallel interpenetrated structure of 2D layers of (4,4) topology, formed by Fe(II) nodes linked through bpp ligands, while mono-coordinated azide anions are pendant from the corrugated sheet. Complex 2 has a 2D arrangement constructed through 1D double end-to-end azide bridged iron(11) chains interconnected through bpe ligands. Complex 3 shows a polymeric arrangement where the metal ions are interlinked through pairs of end-on and end-to-end azide ligands exhibiting a zigzag arrangement of metals (Fe-Fe-Fe angle of 111.18degrees) and an intermetallic separation of 3.347 Angstrom (through the EO azide) and of 5.229 Angstrom (EE azide). Variable-temperature magnetic susceptibility data suggest that there is no magnetic interaction between the metal centers in 1, whereas in 2 there is an antiferromagnetic interaction through the end-to-end azide bridge. Complex 3 shows ferro- as well as anti-ferromagnetic interactions between the metal centers generated through the alternating end-on and end-to-end azide bridges. Complex I has been modeled using the D parameter (considering distorted octahedral Fe(II) geometry and with any possible J value equal to zero) and complex 2 has been modeled as a one-dimensional system with classical and/or quantum spin where we have used two possible full diagonalization processes: without and with the D parameter, considering the important distortions of the Fe(II) ions. For complex 3, the alternating coupling model impedes a mathematical solution for the modeling as classical spins. With quantum spin, the modeling has been made as in 2.

Occurrence of ribbons of cyclic water pentamers in a metallo-organic framework formed by spontaneous fixation of CO2

In the reaction of equimolar amounts of copper(II) acetate with 2,2'-dipyridylamine (DPA) in aqueous tetrahydrofuran, in presence of KOH, aerial CO2 is spontaneously fixed to the carbonate anion yielding [Cu(DPA)(CO3)] . 3H(2)O (1). X-ray crystallography shows the presence of zigzag ribbons of cyclic water pentamers in the channels of a chain-like metallo-organic framework. The water ribbons are stabilised by hydrogen bonds to the metallo-organic backbone. Each (H2O)(5) pentamer is approximately planar.

Modelling oil absorption during post-frying cooling - I: model development

Several studies have highlighted the importance of the cooling period in oil absorption in deep-fat fried products. Specifically, it has been established that the largest proportion of oil which ends up into the food, is sucked into the porous crust region after the fried product is removed from the oil bath, stressing the importance of this time interval. The main objective of this paper was to develop a predictive mechanistic model that can be used to understand the principles behind post-frying cooling oil absorption kinetics, which can also help identifying the key parameters that affect the final oil intake by the fried product. The model was developed for two different geometries, an infinite slab and an infinite cylinder, and was divided into two main sub-models, one describing the immersion frying period itself and the other describing the post-frying cooling period. The immersion frying period was described by a transient moving-front model that considered the movement of the crust/core interface, whereas post-frying cooling oil absorption was considered to be a pressure driven flow mediated by capillary forces. A key element in the model was the hypothesis that oil suction would only begin once a positive pressure driving force had developed. The mechanistic model was based on measurable physical and thermal properties, and process parameters with no need of empirical data fitting, and can be used to study oil absorption in any deep-fat fried product that satisfies the assumptions made.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

A similarity solution for a shock reflection problem in isentropic gas dynamics

A one-dimensional shock-reflection test problem in the case of slab, cylindrical, or spherical symmetry is discussed. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankie-Hugoniot shock relations.

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.