Dynamics of precipitation pattern formation at geothermal hot springs

We formulate and model the dynamics of spatial patterns arising during the precipitation of calcium carbonate from a supersaturated shallow water flow. The model describes the formation of travertine deposits at geothermal hot springs and rimstone dams of calcite in caves. We find explicit solutions for travertine domes at low flow rates, identify the linear instabilities which generate dam and pond formation on sloped substrates, and present simulations of statistical landscape evolution

Migration paths saturations in meta-epidemic systems

In this paper we consider a simple two-patch model in which a population affected by a disease can freely move. We assume that the capacity of the interconnected paths is limited, and thereby influencing the migration rates. Possible habitat disruptions due to human activities or natural events are accounted for. The demographic assumptions prevent the ecosystem to be wiped out, and the disease remains endemic in both populated patches at a stable equilibrium, but possibly also with an oscillatory behavior in the case of unidirectional migrations. Interestingly, if infected cannot migrate, it is possible that one patch becomes disease-free. This fact could be exploited to keep disease-free at least part of the population

Interaction, Pair Formation and Force of Infection Terms in Sexually Transmitted Diseases

15 pages, 1 article*Interaction, Pair Formation and Force of Infection Terms in Sexually Transmitted Diseases* (Busenberg, Stavros; Castillo-Chavez, Carlos) 15 page

A General Solution of the Problem of Mixing of Subpopulations, and its Application to Risk- and Age- Structured Epidemic Models for the Spread of AIDS

35 pages, 1 article*A General Solution of the Problem of Mixing of Subpopulations, and its Application to Risk- and Age- Structured Epidemic Models for the Spread of AIDS* (Busenberg, Stavros; Castillo-Chavez, Carlos) 35 page

Pair Formation in Structured Populations

This issue was undated. The date given is an estimate.26 pages, 1 article*Pair Formation in Structured Populations* (Castillo-Chavez, Carlos; Busenberg, Stavros; Gerow, Ken) 26 page

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with two examples arising from cancer invasion

Computational Approaches and Analysis for a Spatio-Structural-Temporal Invasive Carcinoma Model

Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.PostprintPeer reviewe

Molecular diffusion of CF\u3csub\u3e3\u3c/sub\u3eSF\u3csub\u3e5\u3c/sub\u3e in pure water and artificial seawater

We have experimentally determined the diffusion coefficient for trifluoromethyl sulfur pentafluoride (CF3SF5) in pure water and artificial seawater over a temperature range of − 2.0 °C to 30.0 °C. A working gas standard containing known concentrations of CF3SF5 and sulfur hexafluoride (SF6) was prepared. The working standard was allowed to diffuse across a water barrier, stabilized with agar gel, and the diffused gas was swept into a gas chromatograph with an electron-capture detector to measure the resulting gas mixing ratio. The mixing ratios for both CF3SF5 and SF6 were measured to determine the diffusivity for each species. The diffusion coefficient for SF6 was determined during these experiments as a check against existing literature values and to validate our experimental setup. The experimental data were fit to the Arrhenius equation to yield the following equations DCF3SF5 = 0.0015 exp (-12.9/RT) and DSF6 = 0.037 exp (-19.8/RT), where R is the gas constant in units of kilojoules per mole per kelvin and T is the temperature in kelvin. At the mean temperature of the ocean, 18 °C, DCF3SF5 = 7.02 × 10-6 ± 9.9% and DSF6 = 1.03 × 10-5 ± 13.8 % cm2/s. The diffusion coefficients for SF6 matched the literature data within 4.3% for all temperatures

Flow and geochemistry of groundwater beneath a back-barrier lagoon : the subterranean estuary at Chincoteague Bay, Maryland, USA

This paper is not subject to U.S. copyright. The definitive version was published in Marine Chemistry 113 (2009): 78-92, doi:10.1016/j.marchem.2009.01.004.To better understand large-scale interactions between fresh and saline groundwater beneath an Atlantic coastal estuary, an offshore drilling and sampling study was performed in a large barrier-bounded lagoon, Chincoteague Bay, Maryland, USA. Groundwater that was significantly fresher than overlying bay water was found in shallow plumes up to 8 m thick extending more than 1700 m offshore. Groundwater saltier than bay surface water was found locally beneath the lagoon and the barrier island, indicating recharge by saline water concentrated by evaporation prior to infiltration. Steep salinity and nutrient gradients occur within a few meters of the sediment surface in most locations studied, with buried peats and estuarine muds acting as confining units. Groundwater ages were generally more than 50 years in both fresh and brackish waters as deep as 23 m below the bay bottom. Water chemistry and isotopic data indicate that freshened plumes beneath the estuary are mixtures of water originally recharged on land and varying amounts of estuarine surface water that circulated through the bay floor, possibly at some distance from the sampling location. Ammonium is the dominant fixed nitrogen species in saline groundwater beneath the estuary at the locations sampled. Isotopic and dissolved-gas data from one location indicate that denitrification within the subsurface flow system removed terrestrial nitrate from fresh groundwater prior to discharge along the western side of the estuary. Similar situations, with one or more shallow semi-confined flow systems where groundwater geochemistry is strongly influenced by circulation of surface estuary water through organic-rich sediments, may be common on the Atlantic margin and elsewhere.Primary funding was provided by USGS (Coastal and Marine Geology Program and National Research Program in Water Resources) with additional material support from the National Park Service (C. Zimmerman) and the University of Toledo