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.

Chemical profiling of different hashish seizures by gas chromatography-mass spectrometry and statistical methodology: a case report

Limited information is available regarding the methodology required to characterize hashish seizures for assessing the presence or the absence of a chemical link between two seizures. This casework report presents the methodology applied for assessing that two different police seizures were coming from the same block before this latter one was split. The chemical signature was extracted using GC-MS analysis and the implemented methodology consists in a study of intra- and inter-variability distributions based on the measurement of the chemical profiles similarity using a number of hashish seizures and the calculation of the Pearson correlation coefficient. Different statistical scenarios (i.e., a combination of data pretreatment techniques and selection of target compounds) were tested to find the most discriminating one. Seven compounds showing high discrimination capabilities were selected on which a specific statistical data pretreatment was applied. Based on the results, the statistical model built for comparing the hashish seizures leads to low error rates. Therefore, the implemented methodology is suitable for the chemical profiling of hashish seizures.

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.

Determination of human plasma levels of levo-alpha-acetylmethadol and its metabolites by gas chromatography-mass spectrometry.

A gas chromatography-mass spectrometry (GC-MS) method is presented which allows the simultaneous determination of the plasma concentrations of the levo-alpha-acetylmethadol (LAAM) and of its active metabolites (NorLAAM and DiNorLAAM), after derivatization with the reagent trifluoroacetic anhydride (TFAA). No interferences from endogenous compounds were observed following the extraction of plasma samples from 11 different human subjects. The standard curves were linear over a working range of 5-200ng/ml for the three compounds. Recoveries measured at three concentrations ranged from 47 to 67% for LAAM, from 50 to 69% for NorLAAM and from 28 to 50% for DiNorLAAM. Intra- and interday coefficients of variation determined at three concentrations ranged from 5 to 13% for LAAM, from 3 to 9% for NorLAAM and from 5 to 13% for DiNorLAAM. The limits of quantitation of the method were found to be 4ng/ml for the three compounds. No interference was noted from methadone. This sensitive and specific analytical method could be useful for assessing the in vivo relationship between LAAM's blood levels, clinical efficacy and/or cardiotoxicity

Protein recovery, separation and purification: selection of optimal techniques using an expert system

The paper discusses the utilization of new techniques ot select processes for protein recovery, separation and purification. It describesa rational approach that uses fundamental databases of proteins molecules to simplify the complex problem of choosing high resolution separation methods for multi component mixtures. It examines the role of modern computer techniques to help solving these questions.

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.

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.

Quantitative Measurement of Brain Perfusion with Intravoxel Incoherent Motion MR Imaging.

Purpose: To evaluate the sensitivity of the perfusion parameters derived from Intravoxel Incoherent Motion (IVIM) MR imaging to hypercapnia-induced vasodilatation and hyperoxygenation-induced vasoconstriction in the human brain. Materials and Methods: This study was approved by the local ethics committee and informed consent was obtained from all participants. Images were acquired with a standard pulsed-gradient spin-echo sequence (Stejskal-Tanner) in a clinical 3-T system by using 16 b values ranging from 0 to 900 sec/mm(2). Seven healthy volunteers were examined while they inhaled four different gas mixtures known to modify brain perfusion (pure oxygen, ambient air, 5% CO(2) in ambient air, and 8% CO(2) in ambient air). Diffusion coefficient (D), pseudodiffusion coefficient (D*), perfusion fraction (f), and blood flow-related parameter (fD*) maps were calculated on the basis of the IVIM biexponential model, and the parametric maps were compared among the four different gas mixtures. Paired, one-tailed Student t tests were performed to assess for statistically significant differences. Results: Signal decay curves were biexponential in the brain parenchyma of all volunteers. When compared with inhaled ambient air, the IVIM perfusion parameters D*, f, and fD* increased as the concentration of inhaled CO(2) was increased (for the entire brain, P = .01 for f, D*, and fD* for CO(2) 5%; P = .02 for f, and P = .01 for D* and fD* for CO(2) 8%), and a trend toward a reduction was observed when participants inhaled pure oxygen (although P > .05). D remained globally stable. Conclusion: The IVIM perfusion parameters were reactive to hyperoxygenation-induced vasoconstriction and hypercapnia-induced vasodilatation. Accordingly, IVIM imaging was found to be a valid and promising method to quantify brain perfusion in humans. © RSNA, 2012.

Initial clinical experience with the admiral oxygenator combined with separated suction.

The Admiral, a new microporous membrane oxygenator with a low surface area, decreased priming volume and two separate reservoirs, was tested in 30 adult patients. This study was undertaken to evaluate blood path resistance, gas exchange capabilities and blood trauma in clinical use, with and without shed blood separation. Patients were divided into 3 groups. Group 1 had valve surgery without separation of suction, Group 2 had coronary artery bypass grafting (CABG) with direct blood aspiration and Group 3 had coronary artery bypass grafting with shed blood separation. The suctioned, separated, cardiotomy blood in Group 3 was treated with an autotransfusion device at the end of bypass before being returned to the patient. Theoretical blood flow could be achieved in all cases without problem. The pressure drop through the oxygenator averaged 88 +/- 13 mmHg at 4 l/min and 109 +/- 12 mmHg at 5 l/min. O(2) transfer was 163 +/- 27 ml/min. Free plasma haemoglobin rose in all groups, but significantly less in group 3. Lactate dehydrogenase (LDH) rose significantly in Groups 1 and 2. Platelets decreased in all groups without significant differences. Clinical experience with this new oxygenator was safe, the reduced membrane surface did not impair gas exchange and blood trauma could be minimized easily by separating shed blood, using the second cardiotomy reservoir.