A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Cell compartmentalisation in planctomycetes: novel types of structural organisation for the bacterial cell

The organisation of cells of the planctomycete species Pirellula marina, Isosphaera pallida, Gemmata obscuriglobus, Planctomyces mat-is and Candidatus Brocadia anammoxidans was investigated based on ultrastructure derived from thin-sections of cryosubstituted cells, freeze-fracture replicas, and in the case of Gemmata obscuriglobus and Pirellllla marina, computer-aided 3-D reconstructions from serial sections of cryosubstituted cells. All planctomycete cells display a peripheral ribosome-free region, termed here the paryphoplasm, surrounding the perimeter of the cell, and an interior region including any nucleoid regions as well as ribosome-like particles, bounded by a single intracytoplasmic membrane (ICM), and termed the pirellulosome in Pirellula species. Immunogold labelling and RNase-gold cytochemistry indicates that in planctomycetes all the cell DNA is contained wholly within the interior region bounded by the ICM, and the paryphoplasm contains no DNA but at least some of the cell's RNA. The ICM in Isosphaera pallida and Planctomyces mat-is is invaginated such that the paryphoplasm forms a major portion of the cell interior in sections, but in other planctomycetes it remains as a peripheral zone. In the anaerobic ammonium-oxidising (anammox process) chemoautotroph Candidatus Brocadia anammoxidans the interior region bounded by ICM contains a further internal single-membrane-bounded region, the anam-moxosome. In Gemmata obscuriglobus. the interior ICM-bounded region contains the nuclear body, a double-membrane-bounded region containing the cell's nucleoid and all genomic DNA in addition to some RNA. Shared features of cell compartmentalisation in different planctomycetes are consistent with the monophyletic nature of the planctomycetes as a distinct division of the Bacteria. The shared organisational plan for the planctomycete cell constitutes a new type not known in cells of other bacteria.

Structural and morphological anomalies in magnetosomes: possible biogenic origin for magnetite in ALH84001

We report biogenic magnetite whiskers, with axial ratios of 6: 1, elongated in the [1 1 1]. [1 1 2] and [1 0 0] directions, resembling the magnetite whiskers detected in the Martian meteorite ALH84001 by Bradley ct nl., and interpreted by those authors as evidence of vapour-phase (abiogenic) growth. Magnetosomal whiskers with extended defects consistent with screw dislocations and magnetosomes resembling flattened twinned platelets, as well as other twinning phenomena and other structural defects, are also reported here. Magnetosomes with teardrop-shaped. cuboidal. irregular and jagged structures similar to those detected in ALH84001 by McKay et al.. coprecipitation of magnetite possibly with amorphous calcium carbonate, coprecipitation of magnetite possibly with amorphous silica, the incorporation of titanium in volutin inclusions and disoriented arrays of magnetosomes are also described. These observations demonstrate that the structures of the magnetite particles in ALH84001. their spatial arrange ment and coprecipitation with carbonates and proximity to silicates are consistent with being biogenic. Electron-beam-induced flash-melting of magnetosomes produced numerous screw dislocations in the (1 1 1). (1 0 0) and (1 1 0) lattice planes and induced fusion of platelets. From this, the lack of screw dislocations reported in the magnetite particles in ALH84001 (McKay et al.. and Bradley et al.) indicates that they have a low-temperature origin.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

A nanometre-scale non-periodic structural variation in high temperature superconducting ceramics and the implications for properties

Non-periodic structural variation has been found in the high T-c cuprates, YBa2Cu3O7-x and Hg0.67Pb0.33Ba2Ca2Cu3O8+delta, by image analysis of high resolution transmission electron microscope (HRTEM) images. We use two methods for analysis of the HRTEM images. The first method is a means for measuring the bending of lattice fringes at twin planes. The second method is a low-pass filter technique which enhances information contained by diffuse-scattered electrons and reveals what appears to be an interference effect between domains of differing lattice parameter in the top and bottom of the thin foil. We believe that these methods of image analysis could be usefully applied to the many thousands of HRTEM images that have been collected by other workers in the high temperature superconductor field. This work provides direct structural evidence for phase separation in high T-c cuprates, and gives support to recent stripes models that have been proposed to explain various angle resolved photoelectron spectroscopy and nuclear magnetic resonance data. We believe that the structural variation is a response to an opening of an electronic solubility gap where holes are not uniformly distributed in the material but are confined to metallic stripes. Optimum doping may occur as a consequence of the diffuse boundaries between stripes which arise from spinodal decomposition. Theoretical ideas about the high T-c cuprates which treat the cuprates as homogeneous may need to be modified in order to take account of this type of structural variation.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Should optional properties be used in conceptual modelling? A theory and three empirical tests

An important feature of some conceptual modelling grammars is the features they provide to allow database designers to show real-world things may or may not possess a particular attribute or relationship. In the entity-relationship model, for example, the fact that a thing may not possess an attribute can be represented by using a special symbol to indicate that the attribute is optional. Similarly, the fact that a thing may or may not be involved in a relationship can be represented by showing the minimum cardinality of the relationship as zero. Whether these practices should be followed, however, is a contentious issue. An alternative approach is to eliminate optional attributes and relationships from conceptual schema diagrams by using subtypes that have only mandatory attributes and relationships. In this paper, we first present a theory that led us to predict that optional attributes and relationships should be used in conceptual schema diagrams only when users of the diagrams require a surface-level understanding of the domain being represented by the diagrams. When users require a deep-level understanding, however, optional attributes and relationships should not be used because they undermine users' abilities to grasp important domain semantics. We describe three experiments which we then undertook to test our predictions. The results of the experiments support our predictions.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

A dynamic model with on-line identification for rotary sugar drying processes

A dynamic modelling methodology, which combines on-line variable estimation and parameter identification with physical laws to form an adaptive model for rotary sugar drying processes, is developed in this paper. In contrast to the conventional rate-based models using empirical transfer coefficients, the heat and mass transfer rates are estimated by using on-line measurements in the new model. Furthermore, a set of improved sectional solid transport equations with localized parameters is developed in this work to reidentified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.place the global correlation for the computation of solid retention time. Since a number of key model variables and parameters are identified on-line using measurement data, the model is able to closely track the dynamic behaviour of rotary drying processes within a broad range of operational conditions. This adaptive model is validated against experimental data obtained from a pilot-scale rotary sugar dryer. The proposed modelling methodology can be easily incorporated into nonlinear model based control schemes to form a unified modelling and control framework.

Structural Dynamics in (ND4)2[Cu(D2O)6](SO4)2

The extended X-ray absorption fine structure spectroscopy (EXAFS) of (ND4)(2)[CU(D2O)(6)](SO4)(2) at 5, 14,100, 200, and 298 K is reported. This indicates that the Cu-O bond lengths of the Cu(D2O)(6)(2+) ion do not change significantly within this temperature range, which contrasts with EPR results and X-ray and neutron diffraction experiments, which imply that two of the Cu-(D2O) bonds converge in length as the temperature is raised. The EXAFS measurements thus confirm that the bond distances yielded by the diffraction experiments refer to the average positions of ligands involved in a dynamic equilibrium in which the directions of the long and intermediate bonds of the Jahn-Teller distorted Cu(D2O)(6)(2+) ion are interchanged in the crystal lattice. Analysis of the displacement parameters is consistent with this interpretation, as are the wave functions calculated using a model involving Jahn-Teller vibronic coupling and the influence of lattice strain interactions.

Ni(II)-doped CsCdBrCl2: Variation of spectral and structural properties via mixed-halide coordination

A new addition to the family of single-molecule magnets is reported: an Fete cage stabilized with benzoate and pyridonate ligands. Monte Carlo methods have been used to derive exchange parameters within the cage, and hence model susceptibility behavior.

Design, modelling and analysis of a six component force balance for hypervelocity wind tunnel testing

A combination of modelling and analysis techniques was used to design a six component force balance. The balance was designed specifically for the measurement of impulsive aerodynamic forces and moments characteristic of hypervelocity shock tunnel testing using the stress wave force measurement technique. Aerodynamic modelling was used to estimate the magnitude and distribution of forces and finite element modelling to determine the mechanical response of proposed balance designs. Simulation of balance performance was based on aerodynamic loads and mechanical responses using convolution techniques. Deconvolution was then used to assess balance performance and to guide further design modifications leading to the final balance design. (C) 2001 Elsevier Science Ltd. All rights reserved.