Human Decompression Modelling

At present, no decompression algorithm is able to predict safe decompression for all dive scenarios. In practice, empirical adjustments are made by experienced organisations or divers in order to improve decompression profiles for the range of depths and durations needed on any particular dive. Bubble formation and growth in the human body are the fundamental causes of decompression sickness, and it is believed that there is significant scope for incorporating better modelling of these processes into the design of decompression algorithms. VR Technology is a leading supplier of technical dive computers. The company is interested in expanding upon an existing algorithm (the Variable Gradient Model - VGM), which is used to design ascent profiles/decompression schedules and thereby mitigate the risk of decompression sickness in divers. The Study Group took the approach of trying to extend the existing Haldane model to account more explicitly for the formation of bubbles. By extending the model to include bubble dynamics it was expected that some physical understanding could be gained for the existing modifications to some of the parameters. The modelling that occurred consisted of first looking at the Haldane model and then considering a single small isolated bubble in each of the compartments and interpreting the predictions of the model in terms of decompression profiles

Underreamer mechanics

In the oil and gas industry, an underreamer is a tool used to extend and enlarge the diameter of a previously-drilled bore. The problem proposed to the Study Group is to obtain appropriate mathematical models of underreamer dynamics, in forms that will lead to feasible computation. The modes of dynamics of interest are torsional, lateral and axial. This report describes some initial models, two of which are developed in more detail: one for the propagation of torsional waves along the drill string and their reflection from contact points with the well bore; and one for the dynamic coupling between the underreamer and the drill bit during drilling

Detection of the Entropy of the Intergalactic Medium: Accretion Shocks in Clusters, Adiabatic Cores in Groups

The thermodynamics of the diffuse, X-ray emitting gas in clusters of galaxies is linked to the entropy level of the intra cluster medium. In particular, models that successfully reproduce the properties of local X-ray clusters and groups require the presence of a minimum value for the entropy in the center of X-ray halos. Such a minimum entropy is most likely generated by non-gravitational processes, in order to produce the observed break in self-similarity of the scaling relations of X-ray halos. At present there is no consensus on the level, the source or the time evolution of this excess entropy. In this paper we describe a strategy to investigate the physics of the heating processes acting in groups and clusters. We show that the best way to extract information from the local data is the observation of the entropy profile at large radii in nearby X-ray halos (z~0.1), both at the upper and lower extremes of the cluster mass scale. The spatially and spectrally resolved observation of such X-ray halos provides information on the mechanism of the heating. We demonstrate how measurements of the size of constant entropy (adiabatic) cores in clusters and groups can directly constrain heating models, and the minimum entropy value. We also consider two specific experiments: the detection of the shock fronts expected at the virial boundary of rich clusters, and the detection of the isentropic, low surface-brightness emission extending to radii larger than the virial ones in low mass clusters and groups. Such observations will be a crucial probe of both the physics of clusters and the relationship of non-gravitational processes to the thermodynamics of the intergalactic medium.Comment: ApJ accepted, 31 pages including 8 figures. Important material added; references update

Transport and Reaction Processes in Soil

In order to register agrochemicals in Europe it is necessary to have a detailed understanding of the processes in the environment that break down agrochemicals. The existing framework for environmental assessment includes a consideration of soil water movement and microbial breakdown of products in soil and these processes are relatively understood and represented in models. However the breakdown of agrochemicals by the action of light incident on the soil surface by a process termed photolysis is not so well represented in models of environmental fate. The problem brought by Syngenta (one of the worlds leading agrochemical companies) to the workshop was how to include the effects of light degradation of chemicals into predictive models of environmental fate. Photolysis is known to occur in a very thin layer at the surface of soil. The workshop was asked to consider how the very rough nature of the upper surface of a ploughed field might affect the degradation of chemicals by sunlight. The discussions were directed down two avenues: - firstly to determine how the very small distances over which photolysis occurs might be adequately incorporated into models of transport in soils and, - secondly to consider how the rough surface might modify the illumination of the surface and hence alter degradation. The rate of degradation by photolysis is measured in the laboratory by illuminating a thin, typically about 1 or 2 mm, layer of soil with very strong xenon lamps. The amount of chemical is measured at various intervals and is fitted to a first-order process. Field experiments where the chemical is sprayed on a bare field show evidence of photolysis indicated by biphasic degradation patterns and the presence of breakdown products only formed by photolysis. This report addresses methods for mathematically modelling the action of photolysis on particular relevant chemical species. We start with a general discussion of mechanisms that transport chemicals within soil §2. There is an existing computational model exploited by Syngenta for such modelling and we discuss how this performs and the predictions that can be derived using it §3. The particular mechanism of photolysis is then considered. One aspect of this mechanism that is investigated is how the roughness of the surface of the soil could be adequately incorporated into the modelling. Some results relating to this are presented §4.2. Some of the original experimental data used to derive aspects of the model of photolysis are revisited and a simple model of the process presented and shown to fit the data very well §5. By considering photolysis with a constant diffusion coefficient various analytical results are derived and general behaviour of the system outlined. This simple model is then applied to real field-based data and shown to give very good fit when simply extended to account for the moisture variations by utilising moisture dependent diffusion coefficients derived from the existing computational model §5.3. Some consequences of the simple model are then discussed §6

The Evolution of X-ray Clusters and the Entropy of the Intra Cluster Medium

The thermodynamics of the diffuse, X-ray emitting gas in clusters of galaxies is determined by gravitational processes associated with shock heating, adiabatic compression, and non-gravitational processes such as heating by SNe, stellar winds, activity in the central galactic nucleus, and radiative cooling. The effect of gravitational processes on the thermodynamics of the Intra Cluster Medium (ICM) can be expressed in terms of the ICM entropy S ~ ln(T/\rho^{2/3}). We use a generalized spherical model to compute the X-ray properties of groups and clusters for a range of initial entropy levels in the ICM and for a range of mass scales, cosmic epochs and background cosmologies. We find that the statistical properties of the X-ray clusters strongly depend on the value of the initial excess entropy. Assuming a constant, uniform value for the excess entropy, the present-day X-ray data are well fitted for the following range of values K_* = kT/\mu m_p \rho^{2/3} = (0.4\pm 0.1) \times 10^{34} erg cm^2 g^{-5/3} for clusters with average temperatures kT>2 keV; K_* = (0.2\pm 0.1) \times 10^{34} erg cm^2 g^{-5/3} for groups and clusters with average temperatures kT<2 keV. These values correspond to different excess energy per particle of kT \geq 0.1 (K_*/0.4\times 10^{34}) keV. The dependence of K_* on the mass scale can be well reproduced by an epoch dependent external entropy: the relation K_* = 0.8(1+z)^{-1}\times 10^{34} erg cm^2 g^{-5/3} fits the data over the whole temperature range. Observations of both local and distant clusters can be used to trace the distribution and the evolution of the entropy in the cosmic baryons, and ultimately to unveil the typical epoch and the source of the heating processes.Comment: 53 pages, LateX, 19 figures, ApJ in press, relevant comments and references adde

The dependence on environment of Cold Dark Matter Halo properties

High-resolution LCDM cosmological N-body simulations are used to study the properties of galaxy-size dark halos in different environments (cluster, void, and "field"). Halos in clusters and their surroundings have a median spin parameter ~1.3 times lower, and tend to be more spherical and to have less aligned internal angular momentum than halos in voids and the field. For halos in clusters the concentration parameters decrease on average with mass with a slope of ~0.1; for halos in voids these concentrations do not change with mass. For masses <5 10^11 M_sh^-1, halos in clusters are on average ~30-40% more concentrated and have ~2 times higher central densities than halos in voids. When comparing only parent halos, the differences are less pronounced but they are still significant. The Vmax-and Vrms-mass relations are shallower and more scattered for halos in clusters than in voids, and for a given Vmax or Vrms, the mass is smaller at z=1 than at z=0 in all the environments. At z=1, the differences in the halo properties with environment almost dissapear, suggesting this that the differences were stablished mainly after z~1. The halos in clusters undergo more dramatic changes than those in the field or the voids. The differences with environment are owing to (i) the dependence of halo formation time on environment, and (ii) local effects as tidal stripping and the tumultuos histories that halos suffer in high-density regions. We calculate seminumerical models of disk galaxy evolution in halos with the properties found for the different environments. For a given disk mass, the galaxy disks have higher surface density, larger Vd,max and secular bulge-to-disk ratio, lower gas fraction, and are redder as one goes from cluster to void environments, in rough agreement with observations. (abridged)Comment: 28 pages, 13 figures included. To appear in The Astrophysical Journa

Cosmological Constraints from the ROSAT Deep Cluster Survey

The ROSAT Deep Cluster Survey (RDCS) has provided a new large deep sample of X-ray selected galaxy clusters. Observables such as the flux number counts n(S), the redshift distribution n(z) and the X-ray luminosity function (XLF) over a large redshift baseline (z\lesssim 0.8) are used here in order to constrain cosmological models. Our analysis is based on the Press-Schechter approach, whose reliability is tested against N-body simulations. Following a phenomenological approach, no assumption is made a priori on the relation between cluster masses and observed X-ray luminosities. As a first step, we use the local XLF from RDCS, along with the high-luminosity extension provided by the XLF from the BCS, in order to constrain the amplitude of the power spectrum, \sigma_8, and the shape of the local luminosity-temperature relation. We obtain \sigma_8=0.58 +/- 0.06 for Omega_0=1 for open models at 90% confidence level, almost independent of the L-T shape. The density parameter \Omega_0 and the evolution of the L-T relation are constrained by the RDCS XLF at z>0 and the EMSS XLF at z=0.33, and by the RDCS n(S) and n(z) distributions. By modelling the evolution for the amplitude of the L-T relation as (1+z)^A, an \Omega_0=1 model can be accommodated for the evolution of the XLF with 1<A<3 at 90% confidence level, while \Omega_0=0.4^{+0.3}_{-0.2} and \Omega_0<0.6 are implied by a non--evolving L-T for open and flat models, respectively.Comment: 12 pages, 9 colour figures, LateX, uses apj.sty, ApJ, in press, May 20 issu

Populating a cluster of galaxies - I. Results at z=0

We simulate the assembly of a massive rich cluster and the formation of its constituent galaxies in a flat, low-density universe. Our most accurate model follows the collapse, the star-formation history and the orbital motion of all galaxies more luminous than the Fornax dwarf spheroidal, while dark halo structure is tracked consistently throughout the cluster for all galaxies more luminous than the SMC. Within its virial radius this model contains about 2.0e7 dark matter particles and almost 5000 distinct dynamically resolved galaxies. Simulations of this same cluster at a variety of resolutions allow us to check explicitly for numerical convergence both of the dark matter structures produced by our new parallel N-body and substructure identification codes, and of the galaxy populations produced by the phenomenological models we use to follow cooling, star formation, feedback and stellar aging. This baryonic modelling is tuned so that our simulations reproduce the observed properties of isolated spirals outside clusters. Without further parameter adjustment our simulations then produce a luminosity function, a mass-to-light ratio, luminosity, number and velocity dispersion profiles, and a morphology-radius relation which are similar to those observed in real clusters. In particular, since our simulations follow galaxy merging explicitly, we can demonstrate that it accounts quantitatively for the observed cluster population of bulges and elliptical galaxies.Comment: 28 pages, submitted to MNRA

Evolution of bias in different cosmological models

We study the evolution of the halo-halo correlation function and bias in four cosmological models (LCDM, OCDM, tauCDM, and SCDM) using very high-resolution N-body simulations. The high force and mass resolution allows dark matter (DM) halos to survive in the tidal fields of high-density regions and thus prevents the ambiguities related with the ``overmerging problem.'' This allows us to estimate for the first time the evolution of the correlation function and bias at small (down to ~100/h kpc) scales. We find that at all epochs the 2-point correlation function of galaxy-size halos xi_hh is well approximated by a power-law with slope ~1.6-1.8. The difference between the shape of xi_hh and the shape of the correlation function of matter results in the scale-dependent bias at scales <7/h Mpc, which we find to be a generic prediction of the hierarchical models. The bias evolves rapidly from a high value of ~2-5 at z~3-7 to the anti-bias of b~0.5-1 at small <5/h Mpc scales at z=0. We find that our results agree well with existing clustering data at different redshifts. Particularly, we find an excellent agreement in both slope and the amplitude between xi_hh(z=0) in our LCDM simulation and the galaxy correlation function measured using the APM galaxy survey. At high redshifts, the observed clustering of the Lyman-break galaxies is also well reproduced by the models. The agreement with the data at high and low z indicates the general success of the hierarchical models of structure formation in which galaxies form inside the host DM halos. (Abridged)Comment: submitted to the Astrophys.Journal; 21 pages, LaTeX (uses emulateapj.sty); full resolution versions of figs.1 and 2 are available at http://astro.nmsu.edu/~akravtso/GROUP/group_publications.html or at ftp://charon.nmsu.edu/pub/kravtsov/PAPERS/Bias