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

Radiator deployment actuator Patent

Hydraulic actuator design for space deployment of heat radiator

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

Physics case of the very high energy electron--proton collider, VHEeP

The possibility of a very high energy electron-proton (VHEeP) collider with a centre-of-mass energy of 9 TeV has been presented at previous workshops. These proceedings briefly summarise the VHEeP concept, which was recently published, and developments since then, as well as future directions. At the VHEeP collider, with a centre-of-mass energy 30 times greater than HERA, parton momentum fractions, $x$, down to about $10^{-8}$ are accessible for photon virtualities, $Q^2$, of 1 GeV$^2$. This extension in the kinematic range to low $x$ complements proposals for other electron-proton or electron-ion colliders.Comment: 6 pages, 2 figures, for proceedings of DIS 2017 worksho

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

Low-power radio galaxy environments in the Subaru/XMM-Newton Deep Field at z~0.5

We present multi-object spectroscopy of galaxies in the immediate (Mpc-scale) environments of four low-power (L_1.4 GHz < 10^25 W/Hz) radio galaxies at z~0.5, selected from the Subaru/XMM-Newton Deep Field. We use the spectra to calculate velocity dispersions and central redshifts of the groups the radio galaxies inhabit, and combined with XMM-Newton (0.3-10 keV) X-ray observations investigate the L_X--sigma_v and T_X--sigma_v scaling relationships. All the radio galaxies reside in moderately rich groups -- intermediate environments between poor groups and rich clusters, with remarkably similar X-ray properties. We concentrate our discussion on our best statistical example that we interpret as a low-power (FRI) source triggered within a sub-group, which in turn is interacting with a nearby group of galaxies, containing the bulk of the X-ray emission for the system -- a basic scenario which can be compared to more powerful radio sources at both high (z>4) and low (z<0.1) redshifts. This suggests that galaxy-galaxy interactions triggered by group mergers may play an important role in the life-cycle of radio galaxies at all epochs and luminosities.Comment: 12 pages, 7 figures, accepted for publication in MNRAS. High resolution version available upon reques

An experimental study of surface pressure fluctuations in a separating turbulent boundary layer

Measurements of streamwise velocity fluctuation and surface pressure fluctuation spectra and wavespeeds are reported for a well-documented separating turbulent boundary layer. Because a portion of the acoustic pressure fluctuations is the same across the nominally two-dimensional turbulent flow, it is possible to decompose two microphone signals and obtain directly the turbulent flow contributions to the surface pressure spectra. The rms surface pressure fluctuation p' and spectra phi(omega) increase through the adverse pressure gradient attached flow region and the detached flow zone and scale on the maximum turbulent shearing stress tau(M); p'/tau(M) increases to the detachment location and decreases downstream due to the rapid movement of the pressure-fluctuation-producing motions away from the wall after the beginning of intermittent backflow. At lower frequencies for the attached flow phi(omega) is approximately omega to the -0.7 while phi(omega) is approximately omega to the -3 at higher frequencies. After the beginning of intermittent backflow, phi(omega) varies with omega at low frequencies and omega to the -3 at high frequencies; farther downstream the lower frequency range varies with omega to the 2.4. The surface pressure fluctuation celerity for the attached flow increases with frequency and agrees with the semi-logarithmic overlap equation of Panton and Linebarger. After the beginning of the separation process, the wavespeed decreases because of the oscillation of the instantaneous wavespeed direction and the streamwise coherence decreases drastically

Experimental atmospheric absorption values from aircraft flyover noise signals

Analysis of aircraft noise recordings to determine experimental values of atmospheric sound absorptio