Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Simulation-based systematic review of imatinib population pharmacokinetics and PK-PD relationships in chronic myeloid leukemia (CML) patients

Objectives: Several population pharmacokinetic (PPK) and pharmacokinetic-pharmacodynamic (PK-PD) analyses have been performed with the anticancer drug imatinib. Inspired by the approach of meta-analysis, we aimed to compare and combine results from published studies in a useful way - in particular for improving the clinical interpretation of imatinib concentration measurements in the scope of therapeutic drug monitoring (TDM). Methods: Original PPK analyses and PK-PD studies (PK surrogate: trough concentration Cmin; PD outcomes: optimal early response and specific adverse events) were searched systematically on MEDLINE. From each identified PPK model, a predicted concentration distribution under standard dosage was derived through 1000 simulations (NONMEM), after standardizing model parameters to common covariates. A "reference range" was calculated from pooled simulated concentrations in a semi-quantitative approach (without specific weighting) over the whole dosing interval. Meta-regression summarized relationships between Cmin and optimal/suboptimal early treatment response. Results: 9 PPK models and 6 relevant PK-PD reports in CML patients were identified. Model-based predicted median Cmin ranged from 555 to 1388 ng/ml (grand median: 870 ng/ml and inter-quartile range: 520-1390 ng/ml). The probability to achieve optimal early response was predicted to increase from 60 to 85% from 520 to 1390 ng/ml across PK-PD studies (odds ratio for doubling Cmin: 2.7). Reporting of specific adverse events was too heterogeneous to perform a regression analysis. The general frequency of anemia, rash and fluid retention increased however consistently with Cmin, but less than response probability. Conclusions: Predicted drug exposure may differ substantially between various PPK analyses. In this review, heterogeneity was mainly attributed to 2 "outlying" models. The established reference range seems to cover the range where both good efficacy and acceptable tolerance are expected for most patients. TDM guided dose adjustment appears therefore justified for imatinib in CML patients. Its usefulness remains now to be prospectively validated in a randomized trial.

Radiocarbon dating of modern groundwater: the role of the unsaturated zone

Biological and physical processes occurring in soils may lead to significant isotopic changes between the isotopic compositions of atmospheric CO2 and of soil CO2. Also, during water and gas transport from the soil surface to the water table, isotopic changes likely occur due to numerous physical processes such as gas production and diffusion, water advection, and gas-water-rock interactions. In most cases, these changes are not included in the correction models developed for groundwater dating, whereas they can significantly impact the calculation of the 14C age. We explore the role of these processes using: i) experimental data from two aquifer sites (Fontainebleau sands and Astian sands, France), ii) a distributed model to simulate the 14C activities of soil CO2, and iii) numerical simulations in order to highlight the role of the physical processes.¦The 13C content in soil CO2 showed seasonal variations and highlighted the competition between CO2 production and CO2 diffusion. Their respective contributions played a significant role in defining the isotopic composition of CO2 at the water table. On both study sites, variations of the 14C activity in soil CO2 reflect the competition between the fluxes of root derived-CO2 and organic matter derived-CO2. Since the nuclear weapon tests in the fifties and sixties, soil CO2 became significantly depleted in 14C compared to modern atmospheric CO2. Models that take into account this 14C depletion in soil CO2 for dating modern groundwater would lead to apparent younger 14C ages than models that only consider the 14C activity in atmospheric CO2. Moreover, since 2000-2005, the inverse effect is observed as soil CO2 is enriched in 14C compared to atmospheric CO2.¦Therefore, we conclude that the isotopic composition of CO2 at the water table have to be taken into account for the dating of modern groundwater. This requires a systematic sampling of soil CO2 and the measurement of its 13C and 14C contents. We used this information in a numerical simulation to calculate the evolution of isotopic composition of CO2 from the soil surface to the water table. This simulation integrated physical processes in the unsaturated zone (e.g. CO2 production and diffusion, water advection, etc.) and gas-water-rock interactions.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Agent based simulation to optimise emergency departments

Nowadays, many of the health care systems are large and complex environments and quite dynamic, specifically Emergency Departments, EDs. It is opened and working 24 hours per day throughout the year with limited resources, whereas it is overcrowded. Thus, is mandatory to simulate EDs to improve qualitatively and quantitatively their performance. This improvement can be achieved modelling and simulating EDs using Agent-Based Model, ABM and optimising many different staff scenarios. This work optimises the staff configuration of an ED. In order to do optimisation, objective functions to minimise or maximise have to be set. One of those objective functions is to find the best or optimum staff configuration that minimise patient waiting time. The staff configuration comprises: doctors, triage nurses, and admissions, the amount and sort of them. Staff configuration is a combinatorial problem, that can take a lot of time to be solved. HPC is used to run the experiments, and encouraging results were obtained. However, even with the basic ED used in this work the search space is very large, thus, when the problem size increases, it is going to need more resources of processing in order to obtain results in an acceptable time.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Artificial Snow Optimization in Winter Sport Destinations Using a Multi-agent Simulation

This paper presents the Juste-Neige system for predicting the snow height on the ski runs of a resort using a multi-agent simulation software. Its aim is to facilitate snow cover management in order to i) reduce the production cost of artificial snow and to improve the profit margin for the companies managing the ski resorts; and ii) to reduce the water and energy consumption, and thus to reduce the environmental impact, by producing only the snow needed for a good skiing experience. The software provides maps with the predicted snow heights for up to 13 days. On these maps, the areas most exposed to snow erosion are highlighted. The software proceeds in three steps: i) interpolation of snow height measurements with a neural network; ii) local meteorological forecasts for every ski resort; iii) simulation of the impact caused by skiers using a multi-agent system. The software has been evaluated in the Swiss ski resort of Verbier and provides useful predictions.

In vitro Comparison of Disk Diffusion and Agar Dilution Antibiotic Susceptibility Test Methods for Neisseria gonorrhoeae

At present, most Neisseria gonorrhoeae testing is done with ß-lactamase and agar dilution tests with common therapeutic agents. Generally, in bacteriological diagnosis laboratories in Argentina, study of antibiotic susceptibility of N.gonorrhoeae is based on ß-lactamase determination and agar dilution method with common therapeutic agents. The National Committee for Clinical Laboratory Standards (NCCLS) has recently described a disk diffusion test that produces results comparable to the reference agar dilution method for antibiotic susceptibility of N.gonorrhoeae, using a dispersion diagram for analyzing the correlation between both techniques. We obtained 57 gonococcal isolates from patients attending a clinic for sexually transmitted diseases in Tucumán, Argentina. Antibiotic susceptibility tests using agar dilution and disk diffusion techniques were compared. The established NCCLS interpretive criteria for both susceptibility methods appeared to be applicable to domestic gonococcal strains. The correlation between the MIC's and the zones of inhibition was studied for penicillin, ampicillin, cefoxitin, spectinomycin, cefotaxime, cephaloridine, cephalexin, tetracycline, norfloxacin and kanamycin. Dispersion diagrams showed a high correlation between both methods.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.