Ice crystals growing from vapor in supercooled clouds between −2.5° and −22°C: testing current parameterization methods using laboratory data

The physical and empirical relationships used by microphysics schemes to control the rate at which vapor is transferred to ice crystals growing in supercooled clouds are compared with laboratory data to evaluate the realism of various model formulations. Ice crystal growth rates predicted from capacitance theory are compared with measurements from three independent laboratory studies. When the growth is diffusion- limited, the predicted growth rates are consistent with the measured values to within about 20% in 14 of the experiments analyzed, over the temperature range −2.5° to −22°C. Only two experiments showed significant disagreement with theory (growth rate overestimated by about 30%–40% at −3.7° and −10.6°C). Growth predictions using various ventilation factor parameterizations were also calculated and compared with supercooled wind tunnel data. It was found that neither of the standard parameterizations used for ventilation adequately described both needle and dendrite growth; however, by choosing habit-specific ventilation factors from previous numerical work it was possible to match the experimental data in both regimes. The relationships between crystal mass, capacitance, and fall velocity were investigated based on the laboratory data. It was found that for a given crystal size the capacitance was significantly overestimated by two of the microphysics schemes considered here, yet for a given crystal mass the growth rate was underestimated by those same schemes because of unrealistic mass/size assumptions. The fall speed for a given capacitance (controlling the residence time of a crystal in the supercooled layer relative to its effectiveness as a vapor sink, and the relative importance of ventilation effects) was found to be overpredicted by all the schemes in which fallout is permitted, implying that the modeled crystals reside for too short a time within the cloud layer and that the parameterized ventilation effect is too strong.

The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

Interactions between different convection modes can be investigated using an energy–cycle description under a framework of mass–flux parameterization. The present paper systematically investigates this system by taking a limit of two modes: shallow and deep convection. Shallow convection destabilizes itself as well as the other convective modes by moistening and cooling the environment, whereas deep convection stabilizes itself as well as the other modes by drying and warming the environment. As a result, shallow convection leads to a runaway growth process in its stand–alone mode, whereas deep convection simply damps out. Interaction between these two convective modes becomes a rich problem, even when it is limited to the case with no large–scale forcing, because of these opposing tendencies. Only if the two modes are coupled at a proper level can a self–sustaining system arise, exhibiting a periodic cycle. The present study establishes the conditions for self–sustaining periodic solutions. It carefully documents the behaviour of the two mode system in order to facilitate the interpretation of global model behaviours when this energy–cycle is implemented as a closure into a convection parameterization in future.

The coevolution of two phytoplankton species on a single resource: allelopathy as a pseudo-mixotrophy

Without the top-down effects and the external/physical forcing, a stable coexistence of two phytoplankton species under a single resource is impossible — a result well known from the principle of competitive exclusion. Here I demonstrate by analysis of a mathematical model that such a stable coexistence in a homogeneous media without any external factor would be possible, at least theoretically, provided (i) one of the two species is toxin producing thereby has an allelopathic effect on the other, and (ii) the allelopathic effect exceeds a critical level. The threshold level of allelopathy required for the coexistence has been derived analytically in terms of the parameters associated with the resource competition and the nutrient recycling. That the extra mortality of a competitor driven by allelopathy of a toxic species gives a positive feed back to the algal growth process through the recycling is explained. And that this positive feed back plays a pivotal role in reducing competition pressures and helping species succession in the two-species model is demonstrated. Based on these specific coexistence results, I introduce and explain theoretically the allelopathic effect of a toxic species as a ‘pseudo-mixotrophy’—a mechanism of ‘if you cannot beat them or eat them, just kill them by chemical weapons’. The impact of this mechanism of species succession by pseudo-mixotrophy in the form of alleopathy is discussed in the context of current understanding on straight mixotrophy and resource-species relationship among phytoplankton species.

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.

Similarity solutions describing the melting of a mushy layer

A model of the melting of a mushy region in the absence of fluid flow is presented. Similarity solutions are obtained which are used to describe melting from a hot plate with and without the generation of a completely molten region. These solutions are extended to describe the melting of a mushy region in contact with a hot liquid. A significant feature of melting mushy regions is that the phase change occurs internally by dissolution. Our solutions for melting of a mushy region are used to investigate this internal phase change and are compared with the classical Neumann solutions for melting of a pure substance.

Salt forms of Amides: protonation and polymorphism of Carbamazepine and Cytenamide

In situ generation of HCl or HBr in alcohol leads to O-protonation of the amide group of carbamazepine. Six salt phases have been produced using this method and their crystal structures determined by single crystal diffraction. A new polymorph of carbamazepine hydrochloride is described as are two polymorphs of carbamazepine hydrobromide. All are protonated at the amide O atom to give RC(OH)NH2 cations. Prolonged exposure to air results in addition of water to the solid salt forms. Such hydration of carbamazepine hydrobromide simply gives a monohydrated phase, but similar treatment of the equivalent hydrochloride results in partial loss of HCl and the transfer of the remaining proton from the amide group to water to give [carbamazepine][H3O]0.5[Cl]0.5·H2O. A similar hydronium chloride species is the only product isolated after reaction of the carbamazepine analogue cytenamide with HCl generated in methanol.

Salt and ionic cocrystalline forms of amides: protonation of carbamazepine in aqueous media

The products of reactions of the pharmaceutical amide carbamazepine (CBZ) with strong acids under aqueous conditions were investigated by both powder and single crystal X-ray diffraction. Despite previous claims to the contrary, it was found that salt forms with CBZ protonated at the amide O atom could be isolated from reactions with both HCl and HBr. These forms include the newly identified hydrate phase [CBZ(H)][Cl]·H O. Reactions with other mineral acids (HI and HBF ) gave ionic cocrystalline (ICC) forms (CBZ· [acridinium][I ]·2.5I and CBZ·[H O ] [BF ] ·H O) as well as the salt form CBZ·[CBZ(H)][BF ]·0.5H O. Reaction 2 4 3 2 5 2 0.25 4 0.25 2 4 2 of CBZ with a series of sulfonic acids also gave salt forms, namely, [CBZ(H)][O SC H ], [CBZ(H)][O SC H (OH)]· 3 6 5 3 6 4 0.5H O, [CBZ(H)] [O SCH CH SO ], and [CBZ(H)][O SC H (OH) (COOH)]·H O. CBZ and protonated CBZ(H) 2 2 3 2 2 3 3 6 3 2 moieties can be differentiated in the solid state both by changes to molecular geometry and by differing packing preferences

Synthesis of a catechol-based poly(ether ether ketone) ("o-PEEK") by classical step-growth polymerization and by entropically driven ring-opening polymerization of macrocyclic oligomers

An amorphous, catechol-based analogue of PEEK ("o-PEEK") has been prepared by a classical step-growth polymerization reaction between catechol and 4,4'-difluorobenzophenone and shown to be readily soluble in a range of organic solvents. Copolymers with p-PEEK have been investigated, including an amorphous 50: 50 composition and a semicrystalline though still organic-soluble material comprising 70% p-PEEK. o-PEEK has also been obtained by entropy-driven ring-opening polymerization of the macrocyclic oligomers (MCO's) formed by cyclo-condensation of catechol with 4,4'-difluorobenzophenone under pseudo-high-dilution conditions. The principal products of this latter reaction were the cyclic dimer 3a (20 wt %), cyclic trimer 3b (16%) cyclic tetramer 3c (14%), cyclic pentamer 3d (13%) and cyclic hexamer 3e (12%). Macrocycles 3a-c were isolated as pure compounds by gradient column chromatography, and the structures of the cyclic dimer 3a and cyclic tetramer 3c were analyzed by single-crystal X-ray diffraction. A mixture of MCO's, 3, of similar composition, was obtained by cyclodepolymerization of high molar mass o-PEEK in dilute soluion.

The role of Ti3+ interstitials in TiO2(110) reduction and oxidation

Here we describe results which teach us much about the mechanism of the reduction and oxidation of TiO2(110) by the application of scanning tunnelling microscopy imaging at high temperatures. Titania reduces at high temperature by thermal oxygen loss to leave localized (i.e. Ti3+) and delocalized electrons on the lattice Ti, and a reduced titania interstitial that diffuses into the bulk of the crystal. The interstitial titania can be recalled to the surface by treatment in very low pressures of oxygen, occurring at a significant rate even at 573 K. This re-oxidation occurs by re-growth of titania layers in a Volmer-Weber manner, by a repeating sequence in which in-growth of extra titania within the cross-linked (1 x 2) structure completes the (1 x 1) bulk termination. The next layer then initiates with the nucleation of points and strings which extend to form islands of cross-linked (1 x 2), which once again grow and fill in to reform the (1 x 1). This process continues in a cyclical manner to form many new layers of well-ordered titania. The details of the mechanism and kinetics of the process are considered.

Effect of culture medium and cryoprotectants on the growth and survival of probiotic lactobacilli during freeze drying

To investigate the effects of the medium and cryoprotective agents used on the growth and survival of Lactobacillus plantarum and Lactobacillus rhamnosus GG during freeze drying. A complex medium was developed consisting primarily of glucose, yeast extract and vegetable-derived peptone. Trehalose, sucrose and sorbitol were examined for their ability to protect the cells during freeze drying. Using standardized amount of cells and the optimized freeze drying media, the effect of the growth medium on cell survival during freeze drying was investigated. The results showed that glucose and yeast extract were the most important growth factors, while sucrose offered better protection than trehalose and sorbitol during freeze drying. When the cells were grown under carbon limiting conditions, their survival during freeze drying was significantly decreased. A clear relationship was observed between cell growth and the ability of the cells to survive during the freeze drying process. The survival of probiotic strains during freeze drying was shown to be dependent on the cryoprotectant used and the growth medium.

Predicting the thermal inactivation of bacteria in a solid matrix: simulation studies on the relative effects of microbial thermal resistance parameters and process conditions

A combined mathematical model for predicting heat penetration and microbial inactivation in a solid body heated by conduction was tested experimentally by inoculating agar cylinders with Salmonella typhimurium or Enterococcus faecium and heating in a water bath. Regions of growth where bacteria had survived after heating were measured by image analysis and compared with model predictions. Visualisation of the regions of growth was improved by incorporating chromogenic metabolic indicators into the agar. Preliminary tests established that the model performed satisfactorily with both test organisms and with cylinders of different diameter. The model was then used in simulation studies in which the parameters D, z, inoculum size, cylinder diameter and heating temperature were systematically varied. These simulations showed that the biological variables D, z and inoculum size had a relatively small effect on the time needed to eliminate bacteria at the cylinder axis in comparison with the physical variables heating temperature and cylinder diameter, which had a much greater relative effect. (c) 2005 Elsevier B.V All rights reserved.

Modelling the uptake and growth kinetics of Penicillium glabrum in a tannic acid-containing solid-state fermentation for tannase production

A mathematical growth model for the batch solid-state fermentation process for fungal tannase production was developed and tested experimentally. The unstructured model describes the uptake and growth kinetics of Penicillium glabrum in an impregnated polyurethane foam substrate system. In general, good agreement between the experimental data and model simulations was obtained. Biomass, tannase and spore production are described by logistic kinetics with a time delay between biomass production and tannase and spore formation. Possible induction mechanisms for the latter are proposed. Hydrolysis of tannic acid, the main carbon source in the substrate system, is reasonably well described with Michaelis-Menten kinetics with time-varying enzyme concentration but a more complex reaction mechanism is suspected. The metabolism of gallic acid, a tannase-hydrolysis product of tannic acid, was shown to be growth limiting during the main growth phase. (c) 2004 Elsevier Ltd. All rights reserved.

Seasonal changes in olive fruit characteristics and oil accumulation during ripening process

Olive fruits of three of the most important Spanish and Italian cultivars, 'Picual', `Hojiblanca' and 'Frantoio', were harvested at bi-weekly periods during three crop seasons to study their development and ripening process. Fresh and dry weights and ripening index were determined for fruit, while dry matter, oil and moisture contents were determined in both fruit and pulp (flesh). Fruit growth rate and oil accumulation were calculated. Each olive cultivar showed a different ripening pattern, 'Hojiblanca' being the last one to maturate. Fruit weight increased, decreasing its growth rate from the middle of November. Dry matter and moisture contents decreased during ripening in pulp and fruit, 'Hojiblanca' showing the highest values for both. Oil content, when expressed on a fresh weight basis, increased in all cultivars, although for the last time period showed variations due to climatic conditions. During ripening, oil content on a dry weight basis increased in fruit, but oil biosynthesis in flesh ceased from November. Olive fruits presented lower oil and higher dry matter contents in the year of lowest rainfall. Therefore fruit harvesting should be carried out from the middle of November in order to obtain the highest oil yield and avoid natural fruit drop. (C) 2004 Society of Chemical Industry.

Crosstalk with insulin and dependence on PI3K/Akt/mTOR rather than MAPK pathways in upregulation of basal growth following long-term oestrogen deprivation in three human breast cancer cell lines

Background: MCF-7, T-47-D, ZR-75-1 human breast cancer cell lines are dependent on oestrogen for growth but can adapt to grow during long-term oestrogen deprivation. This serves as a model for identification of therapeutic targets in endocrine-resistant breast cancer. Methods: An overlooked complication of this model is that it involves more than non-addition of oestrogen, and inadequate attention has been given to separating molecular events associated with each of the culture manipulations. Results: Insulin and oestradiol were shown to protect MCF-7 cells against upregulation of basal growth, demonstrating a crosstalk in the growth adaptation process. Increased phosphorylation of p44/42MAPK and c-Raf reflected removal of insulin from the medium and proliferation of all three cell lines was inhibited to a lesser extent by PD98059 and U0126 following long-term oestrogen/insulin withdrawal, demonstrating a reduced dependence on the MAPK pathway. By contrast, long-term oestrogen/insulin deprivation did not alter levels of phosphorylated Akt and did not alter the dose-response of growth inhibition with LY294002 in any of the three cell lines. The IGF1R inhibitor picropodophyllin inhibited growth of all MCF-7 cells but only in the long-term oestrogen/insulin-deprived cells was this paralleled by reduction in phosphorylated p70S6K, a downstream target of mTOR. Long-term oestrogen/insulin-deprived MCF-7 cells had higher levels of phosphorylated p70S6K and developed increased sensitivity to growth inhibition by rapamycin. Conclusions: The greater sensitivity to growth inhibition by rapamycin in all three cell lines following long-term oestrogen/insulin deprivation suggests rapamycin-based therapies might be more effective in breast cancers with acquired oestrogen resistance. Keywords Akt, breast cancer cells, endocrine resistance, insulin, MAPK, MCF-7 cells, mTOR, oestrogen, oestrogen-deprived, PI3K, picropodophyllin, rapamycin, T-47-D cells, ZR-75-1 cells

The growth of private property vehicles in the UK: causes and conditions

The UK private indirect real estate market has seen a rapid growth in the last seven years. The gross asset value (GAV) of the private property vehicle (PPV) market has about tripled from a GAV of £22.6bn in 1998 to a GAV of £67.1 billion at the end of 2005 (OPC, 2006). Although this trend of growing syndication of real estate is not only a UK phenomenon, the rate of growth has been significantly faster in the UK. For example the German open-ended funds have grown over the same period from €50.4bn to €85.1bn (BVI, 2006). In the US the market capitalization of equity real estate investment trusts (REIT) has grown 155% since 1999 to US$ 301bn (NAREIT, 2006). Each jurisdiction is offering different formats to invest indirectly into real estate but at the core all these vehicles are the same in that they provide a different route for investors to access real estate. In the UK, although the range of ‘products’ is now quite diverse, all structures have in common the ‘wrapping’ of property assets into a multi-investor vehicle. This paper examines the nature, pattern and process of market growth in PPVs and constructs a series of associations between causes and effects to explain this market shift.