Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

The sky is the limit? The determinants and constraints of European airports' commercial revenues

This study investigates the determinants of commercial and retail airport revenues as well as revenues from real estate operations. Cross-sectional OLS, 2SLS and robust regression models of European airports identify a number of significant drivers of airport revenues. Aviation revenues per passenger are mainly determined by the national income per capita in which the airport is located, the percentage of leisure travelers and the size of the airport proxied by total aviation revenues. Main drivers of commercial revenues per passenger include the total number of passengers passing through the airport, the ratio of commercial to total revenues, the national income, the share of domestic and leisure travelers and the total number of flights. These results are in line with previous findings of a negative influence of business travelers on commercial revenues per passenger. We also find that a high amount of retail space per passenger is generally associated with lower commercial revenues per square meter confirming decreasing marginal revenue effects. Real estate revenues per passenger are positively associated with national income per capita at airport location, share of intra-EU passengers and percent delayed flights. Overall, aviation and non-aviation revenues appear to be strongly interlinked, underlining the potential for a comprehensive airport management strategy above and beyond mere cost minimization of the aviation sector.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Creep and recovery of magnetorheological fluids: experiments and simulations

A direct comparative study on the creep-recovery behavior of conventional MR fluids is carried out using magnetorheometry and particle-level simulations. Two particle concentrations are investigated (ϕ=0.05 and 0.30) at two different magnetic field strengths (53 kA•m-1 and 173 kA•m-1) in order to match the yield stresses developed in both systems for easier comparison. Simulations are mostly started with random initial structures with some additional tests of using preassembled single chains in the low concentration case. Experimental and simulation data are in good qualitative agreement. The results demonstrate three regions in the creep curves: i) In the initial viscoelastic region, the chain-like (at ϕ=0.05) or percolated three-dimensional network (at ϕ=0.30) structures fill up the gap and the average cluster size remains constant; ii) Above a critical strain of 10 %, in the retardation region, these structures begin to break and rearrange under shear. At large enough imposed stress values, they transform into thin sheet-like or thick lamellar structures, depending on the particle concentration; iii) Finally in the case of larger strain values either the viscosity diverges (at low stress values) or reaches a constant low value (at high stress values), showing a clear bifurcation behavior. For stresses below the bifurcation point the MR fluid is capable to recover the strain by a certain fraction. However, no recovery is observed for large stress values.

Can a native rodent species limit the invasive potential of a non-native rodent species in tropical agroforest habitats?

BACKGROUND Little is known about native and non-native rodent species interactions in complex tropical agro-ecosystems. We hypothesised that the native non-pest rodent Rattus everetti may be competitively dominant over the invasive pest rodent Rattus tanezumi within agroforests. We tested this experimentally by using pulse removal for three consecutive months to reduce populations of R. everetti in agroforest habitat and assessed over 6-months the response of R. tanezumi and other rodent species. RESULTS Following removal, R. everetti individuals rapidly immigrated into removal sites. At the end of the study period, R. tanezumi were larger and there was a significant shift in their microhabitat use with respect to the use of ground vegetation cover following the perturbation of R. everetti. Irrespective of treatment, R. tanezumi selected microhabitat with less tree canopy cover, indicative of severely disturbed habitat, whereas, R. everetti selected microhabitat with a dense canopy. CONCLUSION Our results suggest that sustained habitat disturbance in agroforests favours R. tanezumi, whilst the regeneration of agroforests towards a more natural state would favour native species and may reduce pest pressure in adjacent crops. In addition, the rapid recolonisation of R. everetti suggests this species would be able to recover from non-target impacts of short-term rodent pest control.

Improving a global model from the boundary layer: total turbulent energy and the neutral limit Prandtl number

Model intercomparisons have identified important deficits in the representation of the stable boundary layer by turbulence parametrizations used in current weather and climate models. However, detrimental impacts of more realistic schemes on the large-scale flow have hindered progress in this area. Here we implement a total turbulent energy scheme into the climate model ECHAM6. The total turbulent energy scheme considers the effects of Earth’s rotation and static stability on the turbulence length scale. In contrast to the previously used turbulence scheme, the TTE scheme also implicitly represents entrainment flux in a dry convective boundary layer. Reducing the previously exaggerated surface drag in stable boundary layers indeed causes an increase in southern hemispheric zonal winds and large-scale pressure gradients beyond observed values. These biases can be largely removed by increasing the parametrized orographic drag. Reducing the neutral limit turbulent Prandtl number warms and moistens low-latitude boundary layers and acts to reduce longstanding radiation biases in the stratocumulus regions, the Southern Ocean and the equatorial cold tongue that are common to many climate models.

Limit sets and the Poincare-Bendixson Theorem in impulsive semidynamical systems

We consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy, compactness and connectedness. As a consequence we obtain a version of the Poincare-Bendixson Theorem for impulsive semidynamical systems. (C) 2008 Elsevier Inc. All rights reserved.