From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Aspects of particle filtering in high-dimensional spaces

Nonlinear data assimilation is high on the agenda in all fields of the geosciences as with ever increasing model resolution and inclusion of more physical (biological etc.) processes, and more complex observation operators the data-assimilation problem becomes more and more nonlinear. The suitability of particle filters to solve the nonlinear data assimilation problem in high-dimensional geophysical problems will be discussed. Several existing and new schemes will be presented and it is shown that at least one of them, the Equivalent-Weights Particle Filter, does indeed beat the curse of dimensionality and provides a way forward to solve the problem of nonlinear data assimilation in high-dimensional systems.

On the use of a time sequence of surface pressures in four-dimensional data assimilation

The possibility of using a time sequence of surface pressure observations in four-dimensional data assimilation is being investigated. It is shown that a linear multilevel quasi-geostrophic model can be updated successfully with surface data alone, provided the number of time levels are at least as many as the number of vertical levels. It is further demonstrated that current statistical analysis procedures are very inefficient to assimilate surface observations, and it is shown by numerical experiments that the vertical interpolation must be carried out using the structure of the most dominating baroclinic mode in order to obtain a satisfactory updating. Different possible ways towards finding a practical solution are being discussed.

Nonlinear stability of Euler flows in two-dimensional periodic domains

The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.

Assessing the discourses and practices of urban regeneration in a growing region

Most research on the discourses and practices of urban regeneration in-the UK has examined case studies located in areas of relative socio-economic distress. Less research has been undertaken on regeneration projects and agendas in areas characterise by strong economic growth. Yet, it is in such places that some of the best examples of the discourses, practices and impacts of contemporary urban regeneration can be. found. In some areas of high demand regeneration projects have used inner urban brownfield sites as locations for new investment. With the New Labour government's urban policy agendas targeting similar forms of regeneration, an examination of completed or on-going schemes is timely and relevant to debates over the direction that policy should take. This paper, drawing on a study of urban regeneration in one of England's, fastest growing towns, Reading in Berkshire, examines the discourses, practices and impacts of redevelopment schemes during the 1990s and 2000s. Reading's experiences have received national attention and have been hailed as a model for other urban areas to follow. The research documents the discursive and concrete aspects of local regeneration and examines the ways in which specific priorities and defined problems have come to dominate agendas. Collectively, the study argues that market-driven objectives come to dominate regeneration agendas, even in areas of strong demand where development agencies wield a relatively high degree of influence. Such regeneration plays a symbolic and practical role in creating new forms of exclusion and interpretations of place. (C) 2003 Elsevier Science Ltd. All rights reserved.

An insight into the mechanism of protein separation by colloidal gas aphrons (CGA) generated from ionic surfactants

Colloidal gas aphrons (CGA), which are surfactant stabilised microbubbles, have been previously applied for the recovery of proteins from model mixtures and a few studies have demonstrated the potential of these dispersions for the selective recovery of proteins from complex mixtures. However there is a lack of understanding of the mechanism of separation and forces governing the selectivity of the separation. In this paper a mechanistic study is carried out to determine the main factors and forces influencing the selectivity of separation of whey proteins with CGA generated from ionic surfactants. Two different separation strategies were followed: (i) separation of lactoferrin and lactoperoxidase by anionic CGA generated from a solution of sodium bis-(2-ethyl hexyl) sulfosuccinate (AOT); (ii) separation of beta-lactoglobulin by cationic CGA generated from a solution of cetyltrimethylammonium bromide (CTAB). Separation results indicate that electrostatic interactions are the main forces determining the selectivity however these could not completely explain the selectivities obtained following both strategies. Protein-surfactant interactions were studied by measuring the zeta potential changes on individual proteins upon addition of surfactant and at varying pH. Interestingly strongest electrostatic interactions were measured at those pH and surfactant to protein mass ratios which were optimum for protein separation. Effect of surfactant on protein conformation was determined by measuring the change in fluorescence intensity upon addition of surfactant at varying pH. Differences in the fluorescence patterns were detected among proteins which were correlated to differences in their conformational features which could in turn explain their different separation behaviour. The effect of conformation on selectivity was further proven by experiments in which conformational changes were induced by pre-treatment of whey (heating) and by storage at 4 degrees C. Overall it can be concluded that separation of proteins by ionic CGA is driven mainly by electrostatic interactions however conformational features will finally determine the selectivity of the separation with competitive adsorption having also an effect. (c) 2006 Elsevier B.V. All rights reserved.

Non-steady state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on: the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow-which spans the whole Brillouin zone-and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

The decomposition of some RDX and HMX based materials in the one dimensional time to explosion apparatus. Part 2. Estimating the violence of the cook-off event

Various methods of assessment have been applied to the One Dimensional Time to Explosion (ODTX) apparatus and experiments with the aim of allowing an estimate of the comparative violence of the explosion event to be made. Non-mechanical methods used were a simple visual inspection, measuring the increase in the void volume of the anvils following an explosion and measuring the velocity of the sound produced by the explosion over 1 metre. Mechanical methods used included monitoring piezo-electric devices inserted in the frame of the machine and measuring the rotational velocity of a rotating bar placed on the top of the anvils after it had been displaced by the shock wave. This last method, which resembles original Hopkinson Bar experiments, seemed the easiest to apply and analyse, giving relative rankings of violence and the possibility of the calculation of a “detonation” pressure.

The decomposition of some RDX and HMX based materials in the one-dimensional time to explosion apparatus. Part 1. Time to explosion and apparent activation energy

A One-Dimensional Time to Explosion (ODTX) apparatus has been used to study the times to explosion of a number of compositions based on RDX and HMX over a range of contact temperatures. The times to explosion at any given temperature tend to increase from RDX to HMX and with the proportion of HMX in the composition. Thermal ignition theory has been applied to time to explosion data to calculate kinetic parameters. The apparent activation energy for all of the compositions lay between 127 kJ mol−1 and 146 kJ mol−1. There were big differences in the pre-exponential factor and this controlled the time to explosion rather than the activation energy for the process.

Comparison of polar ozone loss rates simulated by one-dimensional and three-dimensional models with Match observations in recent Antarctic and Arctic winters

Simulations of ozone loss rates using a three-dimensional chemical transport model and a box model during recent Antarctic and Arctic winters are compared with experimental loss rates. The study focused on the Antarctic winter 2003, during which the first Antarctic Match campaign was organized, and on Arctic winters 1999/2000, 2002/2003. The maximum ozone loss rates retrieved by the Match technique for the winters and levels studied reached 6 ppbv/sunlit hour and both types of simulations could generally reproduce the observations at 2-sigma error bar level. In some cases, for example, for the Arctic winter 2002/2003 at 475 K level, an excellent agreement within 1-sigma standard deviation level was obtained. An overestimation was also found with the box model simulation at some isentropic levels for the Antarctic winter and the Arctic winter 1999/2000, indicating an overestimation of chlorine activation in the model. Loss rates in the Antarctic show signs of saturation in September, which have to be considered in the comparison. Sensitivity tests were performed with the box model in order to assess the impact of kinetic parameters of the ClO-Cl2O2 catalytic cycle and total bromine content on the ozone loss rate. These tests resulted in a maximum change in ozone loss rates of 1.2 ppbv/sunlit hour, generally in high solar zenith angle conditions. In some cases, a better agreement was achieved with fastest photolysis of Cl2O2 and additional source of total inorganic bromine but at the expense of overestimation of smaller ozone loss rates derived later in the winter.

Formation of a one-dimensional helical alignment of water molecules within a water-mediated supramolecular helix using molecular self-assembly of a water-soluble short pseudopeptide

The reported pseudopeptide 1 adopts a double turn molecular conformation consisting of an intramolecular 9-membered turn together with a water-mediated 11-atom turn and this pseudopeptide 1 self-assembles to form a water-mediated supramolecular helical structure with internal water molecules, which are aligned in a ID helical array. (c) 2006 Elsevier Ltd. All rights reserved.