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This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.
The jurisprudence of Robert P. George is twofold, in that he is one of the most important public law, and especially constitutional law, scholars of the late twentieth and so far in the twenty-first centuries, and, at the same time, he is America’s leading legal exponent of natural law. He is a devout Roman Catholic. But the relationship between his religious convictions and his jurisprudence will strike some readers as paradoxical. George writes: “I want to show that Christians and other believers are right to defend their positions on key moral issues as rationally superior to the alternatives proposed by secular liberals and those within the religious denominations who have abandoned traditional moral principles in favor of secularist morality.” “My criticism of secular liberal views is not that they are contrary to faith; it is that they fail the test of reason.” This chapter explains how the “paradox” is merely apparent.
A new x-ray spectrometer has been constructed which incorporates a novel large area, low capacitance Si(Li) detector and a low noise JFET (junction field effect transistor) preamplifier. The spectrometer operates at high count Tates without the conventional compromise in energy resolution. For example, at an amplifier peaking time of 1 p.sec and a throughput count rate of 145,000 counts sec-1, the energy resolution at 5.9 keV is 220 eV FWHM. Commercially available spectrometers utilizing conventional geometry Si(Li) detectors with areas equivalent to the new detector have resolutions on the order of 540 eV under the same conditions. Conventional x-ray spectrometers offering high energy resolution must employ detectors with areas one-tenth the size of the new LBL detector (20 mm2 compared with 200 mm2). However, even with the use of the smaller area detectors, the energy resolution of a commercial system is typically limited to approximately 300 eV (again, at 1 μsec and 5.9 keV) due to the noise of the commercially available JFET's. The new large area detector is useful in high count rate applications, but is also useful in the detection of weak photon signals, in which it is desirable to subtend as large an angle of the available photon flux as possible, while still maintaining excellent energy resolution. X-ray fluorescence data from die new spectrometer is shown in comparison to a commercially available system in the analysis of a dilute muhi-element material, and also in conjunction with high count rate synchrotron EXAFS applications.
Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary waves generated are exponentially small in the surface tension, and are determined using the theory of exponential asymptotics. In the steady problem, capillary waves are found to extend upstream from the source, switching on across curves on the free surface known as Stokes lines. Asymptotic predictions are compared with computational solutions for the position of the free surface. In the unsteady problem, transient effects cause the solution to display more complicated asymptotic behaviour, such as higher-order Stokes lines. The theory of exponential asymptotics is applied to show how the capillary waves evolve over time, and eventually tend to the steady solution.
Numerous experimental studies have documented that injecting low-salinity water into an oil reservoir can increase the amount of oil recovered. However, owing to the complexity of the chemical interactions involved in this process, there has been much debate over the dominant mechanism causing this effect. In order to further understand one proposed mechanism, multicomponent ionic exchange, we study the motion of an oil slug through a clay pore throat filled with saline water. The pore throat is modelled as a capillary tube connecting two bulk regions of water. We assume that the surfaces of the oil and the capillary are negatively charged and that, due to repulsion between these surfaces, the oil slug is separated from the capillary surface by a thin film of water. Ion interactions at the oil–water and clay–water interfaces are modelled using the law of mass action. By using lubrication theory to describe the thin-film flow in the water layer separating the oil from the clay surface, and the macroscopic flow through the capillary, we derive expressions for the thickness of the wetting film, and the velocity of the oil slug, given a pressure difference across the ends of the capillary. Numerical results show that the thickness of the water layer and the velocity of the oil slug increase as the salinity of the water is reduced, suggesting that this mechanism contributes to the low-salinity effect. An analytical solution is presented in the limit in which the applied pressure is small.
One method to grow artificial body tissue is to place a porous scaffold seeded with cells, known as a tissue construct, into a rotating bioreactor filled with a nutrient-rich fluid. The flow within the bioreactor is affected by the movement of the construct relative to the bioreactor which, in turn, is affected by the hydrodynamical and gravitational forces the construct experiences. The construct motion is thus coupled to the flow within the bioreactor. Over the time scale of a few hours, the construct appears to move in a periodic orbit but, over tens of hours, the construct drifts from periodicity. In the biological literature, this effect is often attributed to the change in density of the construct that occurs via tissue growth. In this paper, we show that weak inertia can cause the construct to drift from its periodic orbit over the same time scale as tissue growth. We consider the coupled flow and construct motion problem within a rotating high-aspect-ratio vessel bioreactor. Using an asymptotic analysis, we investigate the case where the Reynolds number is large but the geometry of the bioreactor yields a small reduced Reynolds number, resulting in a weak inertial effect. In particular, to accurately couple the bioreactor and porous flow regions, we extend the nested boundary layer analysis of Dalwadi et al. (J. Fluid Mech., vol. 798, 2016, pp. 88–139) to include moving walls and the thin region between the porous construct and the bioreactor wall. This allows us to derive a closed system of nonlinear ordinary differential equations for the construct trajectory, from which we show that neglecting inertia results in periodic orbits; we solve the inertia-free problem analytically, calculating the periodic orbits in terms of the system parameters. Using a multiple-scale analysis, we then systematically derive a simpler system of nonlinear ordinary differential equations that describe the long-time drift of the construct due to the effect of weak inertia. We investigate the bifurcations of the construct trajectory behaviour, and the limit cycles that appear when the construct is less dense than the surrounding fluid and the rotation rate is large enough. Thus, we are able to predict when the tissue construct will drift towards a stable limit cycle within the bioreactor and when it will drift out until it hits the bioreactor edge.
Background: It is unclear as to the extent to which psychological interventions focusing specifically on depression and anxiety are helpful for people with physical health conditions, with respect to mood and condition management. Aims: To evaluate the effectiveness of a modified evidence-based psychological intervention focusing on depression and anxiety for people with type 2 diabetes mellitus (T2DM), compared with a control intervention. Method: Clients (n = 140) who experienced mild to moderate depression and/or anxiety and had a diagnosis of T2DM were allocated to either diabetes specific treatment condition (n = 52) or standard intervention (control condition, n = 63), which were run in parallel. Each condition received a group intervention offering evidence-based psychological interventions for people with depression and anxiety. Those running the diabetes specific treatment group received additional training and supervision on working with people with T2DM from a clinical health psychologist and a general practitioner. The diabetes specific treatment intervention helped patients to link mood with management of T2DM. Results: Both conditions demonstrated improvements in primary outcomes of mood and secondary outcome of adjustment [95% confidence interval (CI) between 0.25 and 5.06; p < 0.05 in all cases]. The diabetes specific treatment condition also demonstrated improvements in secondary outcomes of self-report management of T2DM for diet, checking blood and checking feet, compared with the control condition (95% CIs between 0.04 and 2.05; p < 0.05 in all cases) and in glycaemic control (95% CI: 0.67 to 8.22). The findings also suggested a non-significant reduction in NHS resources in the diabetes specific treatment condition. These changes appeared to be maintained in the diabetes specific treatment condition. Conclusions: It is concluded that a modified intervention, with input from specialist services, may offer additional benefits in terms of improved diabetic self-management and tighter glycaemic control.
Because of the metastability of the 23S level of He I, a variety of effects can change the line strengths from pure recombination values in Seyfert galaxies (see Feldman and MacAlpine 1978). This occurs because the population which builds up in the 23S level can be collisionally excited to the 23P level, enhancing λ10830. The expected ratios of λ10830/λ5876 can be altered by internal or external reddening and vary with temperature, density and optical depth.
The aim of this work is to better understand fluid displacement mechanisms at the pore scale in relation to capillary-filling rules. Using specifically designed micro-models we investigate the role of pore body shape on fluid displacement during drainage and imbibition via quasi-static and spontaneous experiments at ambient conditions. The experimental results are directly compared to lattice Boltzmann (LB) simulations. The critical pore-filling pressures for the quasi-static experiments agree well with those predicted by the Young–Laplace equation and follow the expected filling events. However, the spontaneous imbibition experimental results differ from those predicted by the Young–Laplace equation; instead of entering the narrowest available downstream throat the wetting phase enters an adjacent throat first. Thus, pore geometry plays a vital role as it becomes the main deciding factor in the displacement pathways. Current pore network models used to predict displacement at the field scale may need to be revised as they currently use the filling rules proposed by Lenormand et al. (J. Fluid Mech., vol. 135, 1983, pp. 337–353). Energy balance arguments are particularly insightful in understanding the aspects affecting capillary-filling rules. Moreover, simulation results on spontaneous imbibition, in excellent agreement with theoretical predictions, reveal that the capillary number itself is not sufficient to characterise the two phase flow. The Ohnesorge number, which gives the relative importance of viscous forces over inertial and capillary forces, is required to fully describe the fluid flow, along with the viscosity ratio.
We have conducted tests of the Canadian Land Surface Scheme (CLASS V2.5) for
Arctic tundra applications. Our tests emphasize sensitivities to initial
conditions, external forcings and internal parameters, and focus on the
Alaskan North Slope during the summer of 1992. Observational data from the
National Science foundation (NSF), Arctic Systems Science (ARCSS),
Land/Atmosphere/Ice Interactions (LAII) Flux Study is available to serve as
forcing and validation for our simulations.
Comparisons of the runs show strong sensitivities to the composition and
depth of the soil layers, and we find that a minimum total soil depth of 5.0
m is needed to maintain permafrost. The response of the soil to diurnal
variations in forcing is strong, while sensitivities to other internal
parameters, as well as to precipitation, were relatively small. Some
sensitivity to air temperatures and radiative fluxes, particularly the
incoming shortwave flux, was also present. Significant sensitivity to the
specification of the initial water and ice contents of the soil was found,
while the sensitivity to initial soil temperature was somewhat less.
Different vegetation models impact the atmospheric response of a regional
climate model in different ways, and hence have an impact upon the ability
of that model to match an observed climatology. Using a multivariate
principal-component analysis, we investigate the relationships between
several land-surface models (BATS, LSM) coupled to a regional climate model,
and observed climate parameters over the North Slope of Alaska. In this
application, annual cycle simulations at 20 km spatial resolution are
compared with European Centre for Medium-Range Weather Forecasts (ECMWF)
climatology. Initial results demonstrate broad agreement between all models;
however, small-scale regional variations between land-surface models
indicate the strengths and weaknesses of the land-surface treatments in a
climate system model. Specifically, we found that the greater
surface-moisture availability and temperature-dependent albedo formulation
of the LSM model allow for a higher proportion of low-level cloud, and a
later, more rapid transition from the winter to the summer regime. Crucial
to this transition is the seasonal cycle of incoming solar radiation. These
preliminary results indicate the importance of the land-surface hydrologic
cycle in modelling the seasonal transitions.
Background: There are currently no national standards for clinical electromyography (EMG) training for residents in neurology and physiatry in Canada. The purpose of this study was to obtain demographic and qualitative data pertaining to EMG residency training in Canada, with the goal of facilitating discourse that could lead to national standards for EMG training. Methods: An online survey was distributed to senior neurology and physiatry residents (post-graduate years 3-5), at seven tertiary Canadian centres. The study authors, who are trainees and consultants with a broad range of EMG expertise (junior and senior resident, clinical neuromuscular fellows, senior physiatrist and neuromuscular neurologists), developed pertinent demographic and qualitative questions. Results: Thirty-eight residents completed the survey (23 neurology, 15 physiatry). There was inter-program variation in quantity of the training experience, content of the curriculum, access to expertise (including technologists) and goals for future training and practice. Similarly, differences were identified between the training experiences of neurology and physiatry residents. Conclusions: Inter-program variability in EMG training was identified. Additionally, differences were identified between neurology and physiatry resident training. This data provides evidence of training discrepancies across the country and can be used to establish national training standards for EMG in Canada.
The method of matched asymptotic expansions is used to study the canonical problem of steady laminar flow through a narrow two-dimensional channel blocked by a tight-fitting finite-length highly permeable porous obstacle. We investigate the behaviour of the local flow close to the interface between the single-phase and porous regions (governed by the incompressible Navier–Stokes and Darcy flow equations, respectively). We solve for the flow in these inner regions in the limits of low and high Reynolds number, facilitating an understanding of the nature of the transition from Poiseuille to plug to Poiseuille flow in each of these limits. Significant analytical progress is made in the high Reynolds number limit, and we explore in detail the rich boundary layer structure that occurs. We derive general results for the interfacial stress and for the conditions that couple the flow in the outer regions away from the interface. We consider the three-dimensional generalization to unsteady laminar flow through and around a tight-fitting highly permeable cylindrical porous obstacle within a Hele-Shaw cell. For the high Reynolds number limit, we give the coupling conditions and interfacial stress in terms of the outer flow variables, allowing information from a nonlinear three-dimensional problem to be obtained by solving a linear two-dimensional problem. Finally, we illustrate the utility of our analysis by considering the specific example of time-dependent forced far-field flow in a Hele-Shaw cell containing a porous cylinder with a circular cross-section. We determine the internal stress within the porous obstacle, which is key for tissue engineering applications, and the interfacial stress on the boundary of the porous obstacle, which has applications to biofilm erosion. In the high Reynolds number limit, we demonstrate that the fluid inertia can result in the cylinder experiencing a time-independent net force, even when the far-field forcing is periodic with zero mean.
The period covered by this report, 1984 July to 1987 June, was of extraordinary importance for the progress of cometary physics. For the first time in the history, special space probes were launched to comets. Vega 1, Vega 2 and Giotto encountered P/Halley, providing us with the first close-up pictures of a cometary nucleus, its surface features, and with the first in situ measurements of the matter escaping from it. ICE, Suisei and Sakigake carried out measurements relevant to P/Giacobini-Zinner and P/Halley in interplanetary space. Unprecedented worldwide campaigns of ground-based observations, with the participation of about 1000 professional and 2000 amateur astronomers, were coordinated in 8 sections of the International Halley Watch. Additional measurements were made from artificial satellites, sounding rockets, and highflying airplanes. The wealth of data collected in this way, to a major extent thanks to an excellent international cooperation, represents a milestone in cometary astronomy. Another important step was the progress in processing the extensive 1983 IRAS observations of minor planets and comets, including the discovery of asteroid dust bands and cometary dust trails.
Periodicity and new properties of the frequency curve. Bruno Hanisch uses the method of autocorrelation introduced by W. Pollack in geophysics for the discovery of periods in the frequency series of sunspots from 1794 to 1925. Dividing the whole interval into three sections he finds an eleven- and an eight-year period common to the three sections, whereas other periods found in the three sections differ widely from each other. The new method gives for the length of the main period II-8 years for the interval 1880 to 1925. This result agrees strikingly with the revolution period of Jupiter (Gerlands Beiträge zur Geophysik, 46, 1935).
III Zw 35 is a pair of galaxies characterised by intense OH maser emission, and powerful far-infrared and radio continuum. We have made a detailed study of the galaxy pair based on optical, infrared and radio observations. The brighter northern component is identified as a LINER or Seyfert galaxy and contains an active nuclear region from which radio continuum, OH maser and thermal dust emission are detected. We propose that the northern component has a compact active nucleus deeply embedded in an obscured region of diameter ~ 210 pc within which enhanced star-formation occurs. The lower luminosity, southern component is of low mass and is undergoing starburst activity over an extended region of diameter ~ 5.5 kpc. The origin of the starburst and non-thermal activity appears to be an interaction between the two components.