Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description

Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation & travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape

Perceptions of healthy eating and physical activity in an ethnically diverse sample of young children and their parents: the DEAL prevention of obesity study

Background: Ethnicity is a consistent correlate of obesity; however, little is known about the perceptions and beliefs that may influence engagement with obesity prevention programmes among ethnic minority children. Barriers to (and facilitators of) healthy lifestyles were examined in the qualitative arm of the London (UK) DiEt and Active Living (DEAL) study. Methods: Children aged 8–13 years and their parents, from diverse ethnic groups, were recruited through schools and through places of worship. Thirteen focus group sessions were held with 70 children (n = 39 girls) and eight focus groups and five interviews with 43 parents (n = 34 mothers). Results: Across ethnic groups, dislike of school meals, lack of knowledge of physical activity guidelines for children and negativity towards physical education at school among girls, potentially hindered healthy living. Issues relating to families' wider neighbourhoods (e.g. fast food outlets; lack of safety) illustrated child and parental concerns that environments could thwart intentions for healthy eating and activity. By contrast, there was general awareness of key dietary messages and an emphasis on dietary variety and balance. For ethnic minorities, places of worship were key focal points for social support. Discourse around the retention of traditional practices, family roles and responsibilities, and religion highlighted both potential facilitators (e.g. the importance of family meals) and barriers (reliance on convenience stores for traditional foods). Socio-economic circumstances intersected with key themes, within and between ethnic groups. Conclusions: Several barriers to (and facilitators of) healthy lifestyles were common across ethnic groups. Diversity of cultural frameworks not only were more nuanced, but also shaped lifestyles for minority children.</p

Gravitational waves from black hole collisions via an eclectic approach

We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular, we address the problem of combining the close-limit approximation describing ringing black holes and full numerical relativity, required for essentially nonlinear interactions. We demonstrate the effectiveness of our approach using general methods for a model problem, the head-on collision of black holes. Our method allows a more direct physical understanding of these collisions indicating clearly when non-linear methods are important. The success of this method supports our expectation that this unified approach will be able to provide astrophysically relevant results for black hole binaries in time to assist gravitational wave observations.Comment: 4 pages, 3 eps figures, Revte

Omnidirectional joint Patent

Cord restraint system for pressure suit joint

The turing model comes of molecular age

Molecular analysis of hair follicle formation provide evidence to support the most well-known mathematical model for biological pattern formation

Effective String Theory of Vortices and Regge Trajectories

Starting from a field theory containing classical vortex solutions, we obtain an effective string theory of these vortices as a path integral over the two transverse degrees of freedom of the string. We carry out a semiclassical expansion of this effective theory, and use it to obtain corrections to Regge trajectories due to string fluctuations.Comment: 27 pages, revtex, 3 figures, corrected an error with the cutoff in appendix E (was previously D), added more discussion of Fig. 3, moved some material in section 9 to a new appendi

Models of collective cell spreading with variable cell aspect ration: a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models

The impact of scatterometer wind data on global weather forecasting

The impact of SEASAT-A scatterometer (SASS) winds on coarse resolution atmospheric model forecasts was assessed. The scatterometer provides high resolution winds, but each wind can have up to four possible directions. One wind direction is correct; the remainder are ambiguous or "aliases'. In general, the effect of objectively dealiased-SASS data was found to be negligible in the Northern Hemisphere. In the Southern Hemisphere, the impact was larger and primarily beneficial when vertical temperature profile radiometer (VTPR) data was excluded. However, the inclusion of VTPR data eliminates the positive impact, indicating some redundancy between the two data sets

Analytical description of spin-Rabi oscillation controlled electronic transitions rates between weakly coupled pairs of paramagnetic states with S=1/2

We report on an analytical description of spin-dependent electronic transition rates which are controlled by a radiation induced spin-Rabi oscillation of weakly spin-exchange and spin-dipolar coupled paramagnetic states (S=1/2). The oscillation components (the Fourier content) of the net transition rates within spin-pair ensembles are derived for randomly distributed spin resonances with account of a possible correlation between the two distributions that correspond to the two individual pair partners. The results presented here show that when electrically or optically detected Rabi spectroscopy is conducted under an increasing driving field B_ 1, the Rabi spectrum evolves from a single resonance peak at s=\Omega_R, where \Omega_R=\gamma B_1 is the Rabi frequency (\gamma is the gyromagnetic ratio), to three peaks at s= \Omega_R, s=2\Omega_R, and at low s<< \Omega_R. The crossover between the two regimes takes place when \Omega_R exceeds the expectation value \delta_0 of the difference of the Zeeman energies within the pairs, which corresponds to the broadening of the magnetic resonance lines in the presence of disorder caused by hyperfine field or distributions of Lande g-factors. We capture this crossover by analytically calculating the shapes of all three peaks at arbitrary relation between \Omega_R and \delta_0. When the peaks are well-developed their widths are \Delta s ~ \delta_0^2/\Omega_R.Comment: 10 page, 5 figure