Truncation errors in finite difference models for solute transport equation with first-order reaction

The truncation errors associated with finite difference solutions of the advection-dispersion equation with first-order reaction are formulated from a Taylor analysis. The error expressions are based on a general form of the corresponding difference equation and a temporally and spatially weighted parametric approach is used for differentiating among the various finite difference schemes. The numerical truncation errors are defined using Peclet and Courant numbers and a new Sink/Source dimensionless number. It is shown that all of the finite difference schemes suffer from truncation errors. Tn particular it is shown that the Crank-Nicolson approximation scheme does not have second order accuracy for this case. The effects of these truncation errors on the solution of an advection-dispersion equation with a first order reaction term are demonstrated by comparison with an analytical solution. The results show that these errors are not negligible and that correcting the finite difference scheme for them results in a more accurate solution. (C) 1999 Elsevier Science B.V. All rights reserved.

Building better wildlife-habitat models

Wildlife-habitat models are an important tool in wildlife management toda?, and by far the majority of these predict aspects of species distribution (abundance or presence) as a proxy measure of habitat quality. Unfortunately, few are tested on independent data, and of those that are, few show useful predictive st;ill. We demonstrate that six critical assumptions underlie distribution based wildlife-habitat models, all of which must be valid for the model to predict habitat quality. We outline these assumptions in a mete-model, and discuss methods for their validation. Even where all sis assumptions show a high level of validity, there is still a strong likelihood that the model will not predict habitat quality. However, the meta-model does suggest habitat quality can be predicted more accurately if distributional data are ignored, and variables more indicative of habitat quality are modelled instead.

Growth and lactic acid production in batch culture of Lactobacillus rhamnosus in a defined medium

To facilitate metabolic analysis, batch fermentations of Lactobacillus rhamnosus were carried out in a new defined medium. Biomass at 10.5 g/l and lactic acid at 67 g/l with a Y-P/S of 0.84 were achieved. The maximum specific growth rate and the average productivity were 0.49/h and 2.48 g/l.h, respectively. These are comparable to those of this organism and related organisms in complex media. Preliminary amino acid studies were also conducted, highlighting the importance of serine, asparagine, glutamine and cysteine. Kinetic analysis revealed that lactic acid production was predominantly growth-associated with growth associated and non-growth associated lactic acid constants of 0.389 mol/g-cell and 0.0025 mol/g-cell.h, respectively. Finally a kinetic model has been included to describe the fermentation of L. rhamnosus.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Control of fed-batch fermentations

Fed-batch fermentation is used to prevent or reduce substrate-associated growth inhibition by controlling nutrient supply. Here we review the advances in control of fed-batch fermentations. Simple exponential feeding and inferential methods are examined, as are newer methods based on fuzzy control and neural networks. Considerable interest has developed in these more advanced methods that hold promise for optimizing fed-batch techniques for complex fermentation systems. (C) 1999 Elsevier Science Inc. All rights reserved.

Comparison of coherent and weakly incoherent transport models for the interlayer magnetoresistance of layered Fermi liquids

The interlayer magnetoresistance of layered metals in a tilted magnetic field is calculated for two distinct models for the interlayer transport. The first model involves coherent interlayer transport, and makes use of results of semiclassical or Bloch-Boltzmann transport theory. The second model involves weakly incoherent interlayer transport where the electron is scattered many times within a layer before tunneling into the next layer. The results are relevant to the interpretation of experiments on angular-dependent magnetoresistance oscillations (AMRO) in quasi-one- and quasi-two-dimensional organic metals. We find that the dependence of the magnetoresistance on the direction of the magnetic field is identical for both models except when the field is almost parallel to the layers. An important implication of this result is that a three-dimensional Fermi surface is not necessary for the observation of the Yamaji and Danner oscillations seen in quasi-two- and quasi-one-dimensional metals, respectively. A universal expression is given for the dependence of the resistance at AMRO maxima and minima on the magnetic field and scattering time (and thus the temperature). We point out three distinctive features of coherent interlayer transport: (i) a beat frequency in the magnetic oscillations of quasi-two-dimensional systems, (ii) a peak in the angular-dependent magnetoresistance when the field is sufficiently large and parallel to the layers, and (iii) a crossover from a linear to a quadratic field dependence for the magnetoresistance when the field is parallel to the layers. Properties (i) and (ii) are compared with published experimental data for a range of quasi-two-dimensional organic metals. [S0163-1829(99)02236-5].

Approach to designing rotating drum bioreactors for solid-state fermentation on the basis of dimensionless design factors

The development of large-scale solid-stale fermentation (SSF) processes is hampered by the lack of simple tools for the design of SSF bioreactors. The use of semifundamental mathematical models to design and operate SSF bioreactors can be complex. In this work, dimensionless design factors are used to predict the effects of scale and of operational variables on the performance of rotating drum bioreactors. The dimensionless design factor (DDF) is a ratio of the rate of heat generation to the rate of heat removal at the time of peak heat production. It can be used to predict maximum temperatures reached within the substrate bed for given operational variables. Alternatively, given the maximum temperature that can be tolerated during the fermentation, it can be used to explore the combinations of operating variables that prevent that temperature from being exceeded. Comparison of the predictions of the DDF approach with literature data for operation of rotating drums suggests that the DDF is a useful tool. The DDF approach was used to explore the consequences of three scale-up strategies on the required air flow rates and maximum temperatures achieved in the substrate bed as the bioreactor size was increased on the basis of geometric similarity. The first of these strategies was to maintain the superficial flow rate of the process air through the drum constant. The second was to maintain the ratio of volumes of air per volume of bioreactor constant. The third strategy was to adjust the air flow rate with increase in scale in such a manner as to maintain constant the maximum temperature attained in the substrate bed during the fermentation. (C) 2000 John Wiley & Sons, Inc.

Subgroup relations: A comparison of mutual intergroup differentiation and common ingroup identity models of prejudice reduction

Two studies examined relations between groups (humanities and math-science students) that implicitly or explicitly share a common superordinate category (university student). In Experiment 1, 178 participants performed a noninteractive decision-making task during which category salience was manipulated in a 2 (superordinate category salience) x 2 (subordinate category salience) between-groups design. Consistent with the mutual intergroup differentiation model, participants for whom both categories were salient exhibited the lowest levels of bias, whereas bias was strongest when the superordinate category alone was made salient. This pattern of results was replicated in Experiment 2 (N = 135). In addition, Experiment 2 demonstrated that members of subgroups that are nested within a superordinate category are more sensitive to how the superordinate category is represented than are members of subgroups that extend beyond the boundaries of the superordinate category.

Incorporating phase retardation effects into radiofrequency resonator models: application to magnetic resonance microscopy

A method is presented for including path propagation effects into models of radiofrequency resonators for use in magnetic resonance imaging. The method is based on the use of Helmholtz retarded potentials and extends our previous work on current density models of resonators based on novel inverse finite Hilbert transform solutions to the requisite integral equations. Radiofrequency phase retardation effects are most pronounced at high field strengths (frequencies) as are static field perturbations due to the magnetic materials in the resonators themselves. Both of these effects are investigated and a novel resonator structure presented for use in magnetic resonance microscopy.

Empirical catchment-wide rainfall erosivity models for two rivers in the humid tropics of Australia

The concept of rainfall erosivity is extended to the estimation of catchment sediment yield and its variation over time. Five different formulations of rainfall erosivity indices, using annual, monthly and daily rainfall data, are proposed and tested on two catchments in the humid tropics of Australia. Rainfall erosivity indices, using simple power functions of annual and daily rainfall amounts, were found to be adequate in describing the interannual and seasonal variation of catchment sediment yield. The parameter values of these rainfall erosivity indices for catchment sediment yield are broadly similar to those for rainfall erosivity models in relation to the R-factor in the Universal Soil Loss Equation.

Integrable Kondo impurities in one-dimensional extended Hubbard models

Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are presented as a nontrivial realization of the graded reflection equation algebras acting in a (2s alpha + 1)-dimensional impurity Hilbert space. Furthermore, these models are solved using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Swapping space for time and unfair tests of ecological models

Testing ecological models for management is an increasingly important part of the maturation of ecology as an applied science. Consequently, we need to work at applying fair tests of models with adequate data. We demonstrate that a recent test of a discrete time, stochastic model was biased towards falsifying the predictions. If the model was a perfect description of reality, the test falsified the predictions 84% of the time. We introduce an alternative testing procedure for stochastic models, and show that it falsifies the predictions only 5% of the time when the model is a perfect description of reality. The example is used as a point of departure to discuss some of the philosophical aspects of model testing.

Structured modeling of recombinant protein production in batch and fed-batch culture of baculovirus-infected insect cells

The infection of insect cells with baculovirus was described in a mathematical model as a part of the structured dynamic model describing whole animal cell metabolism. The model presented here is capable of simulating cell population dynamics, the concentrations of extracellular and intracellular viral components, and the heterologous product titers. The model describes the whole processes of viral infection and the effect of the infection on the host cell metabolism. Dynamic simulation of the model in batch and fed-batch mode gave good agreement between model predictions and experimental data. Optimum conditions for insect cell culture and viral infection in batch and fed-batch culture were studied using the model.