Design of a Semi-analytical Method to Describe Plasma-Wall Interactions

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.

Sorting by diffusion: An asymmetric obstacle course for continuous molecular separation

A separation technique employing a microfabricated sieve has been demonstrated by observing the motion of DNA molecules of different size. The sieve consists of a two-dimensional lattice of obstacles whose asymmetric disposition rectifies the Brownian motion of molecules driven through the device, causing them to follow paths that depend on their diffusion coefficient. A nominal 6% resolution by length of DNA molecules in the size range 15–30 kbp may be achieved in a 4-inch (10-cm) silicon wafer. The advantage of this method is that samples can be loaded and sorted continuously, in contrast to the batch mode commonly used in gel electrophoresis.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Co-Permeability of 3H-Labeled Water and 14C-Labeled Organic Acids across Isolated Plant Cuticles1 : Investigating Cuticular Paths of Diffusion and Predicting Cuticular Transpiration

Penetration of 3H-labeled water (3H2O) and the 14C-labeled organic acids benzoic acid ([14C]BA), salicylic acid ([14C]SA), and 2,4-dichlorophenoxyacetic acid ([14C]2,4-D) were measured simultaneously in isolated cuticular membranes of Prunus laurocerasus L., Ginkgo biloba L., and Juglans regia L. For each of the three pairs of compounds (3H2O/[14C]BA, 3H2O/[14C]SA, and 3H2O/[14C]2,4-D) rates of cuticular water penetration were highly correlated with the rates of penetration of the organic acids. Therefore, water and organic acids penetrated the cuticles by the same routes. With the combination 3H2O/[14C]BA, co-permeability was measured with isolated cuticles of nine other plant species. Permeances of 3H2O of all 12 investigated species were highly correlated with the permeances of [14C]BA (r2 = 0.95). Thus, cuticular transpiration can be predicted from BA permeance. The application of this experimental method, together with the established prediction equation, offers the opportunity to answer several important questions about cuticular transport physiology in future investigations.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

An account of Lord Bacon's Novum organon scientiarum, or new method of studying the sciences. The first or introductory part.

Published by authority of the Boston society for the diffusion of useful knowledge.

A PCR method for the identification of methicillin-resistant Staphylococcus aureus (MRSA) from screening swabs

Aim: The aim of this study was to assess the discriminatory power and potential turn around time ( TAT) of a PCR-based method for the detection of methicillin-resistant Staphylococcus aureus (MRSA) from screening swabs. Methods: Screening swabs were examined using the current laboratory protocol of direct culture on mannitol salt agar supplemented with oxacillin (MSAO-direct). The PCR method involved pre-incubation in broth for 4 hours followed by a multiplex PCR with primers directed to mecA and nuc genes of MRSA. The reference standard was determined by pre-incubation in broth for 4 hours followed by culture on MSAO (MSAO-broth). Results: A total of 256 swabs was analysed. The rates of detection of MRSA using MSAO-direct, MSAO-broth and PCR were 10.2, 13.3 and 10.2%, respectively. For PCR, the sensitivity, specificity, positive predictive value and negative predictive values were 66.7% (95% CI 51.9 - 83.3%), 98.6% ( 95% CI 97.1 - 100%), 84.6% ( 95% CI 76.2 - 100%) and 95.2% ( 95% CI 92.4 - 98.0%), respectively, and these results were almost identical to those obtained from MSAO-direct. The agreement between MSAO-direct and PCR was 61.5% ( 95% CI 42.8 - 80.2%) for positive results, 95.6% ( 95% CI 93.0 - 98.2%) for negative results and overall was 92.2% ( 95% CI 88.9 - 95.5%). Conclusions: ( 1) The discriminatory power of PCR and MSAO-direct is similar but the level of agreement, especially for true positive results, is low. ( 2) The potential TAT for the PCR method provides a marked advantage over conventional methods. ( 3) Further modifications to the PCR method such as increased broth incubation time, use of selective broth and adaptation to real-time PCR may lead to improvement in sensitivity and TAT.

Diffusion of linear paraffins in nanoporous silica

The diffusion of hexane, heptane, octane, and decane in nanoporous MCM-41 silica at various temperatures is investigated by the zero-length-column method. The diffusion coefficients are derived by a complete-time-range analysis of desorption curves at different purge flow rates and temperatures. The results show that the calculated low-coverage diffusivity values decrease monotonically, and the derived Henry's law constants increase, as the carbon number of paraffins increases. The study reveals that transport is strongly influenced by intracrystalline diffusion and dominated by the sorbate-sorbent interaction. The diffusion activation energy and adsorption isosteric heat at zero loading increase monotonically with the carbon number of linear paraffins, but their ratio is essentially constant for each adsorbate compound.

Diffusion of n-decane in mesoporous MCM-41 silicas

We investigate here the diffusion of n-decane in nanoporous MCM-41 silicas with pore diameters between 3.0 and 4.3 nm, and at various temperatures and purge flow rates, by the Zero Length Column method. A complete-time-range analysis of desorption curves is used to derive the diffusion coefficient, and the effect of pore size, purge flow rate and temperature on the diffusion character is systematically studied. The results show that the calculated low-coverage diffusivity values are strongly dependent on temperature but only weakly dependent on pore size. The study reveals that transport is controlled by intracrystalline diffusion and dominated by sorbate-sorbent interaction, with the experimental isosteric heat matching the potential energy of flat-lying n-decane molecules on the surface, determined using a united atom model. The diffusion activation energy and adsorption isosteric heat at zero loading for the different pore size MCM-41 samples vary in a narrow range respectively, and their ratio is essentially constant over the pore size range studied. The study shows that the ZLC method is an effective tool to investigate the diffusion kinetics of hydrocarbons in mesoporous MCM-41 materials. (c) 2005 Elsevier Inc. All rights reserved.

Modelling oxygen diffusion and cell growth in a porous, vascularising scaffold for soft tissue engineering applications

Soft tissue engineering presents significant challenges compared to other tissue engineering disciplines such as bone, cartilage or skin engineering. The very high cell density in most soft tissues, often combined with large implant dimensions, means that the supply of oxygen is a critical factor in the success or failure of a soft tissue scaffold. A model is presented for oxygen diffusion in a 15-60 mm diameter dome-shaped scaffold fed by a blood vessel loop at its base. This model incorporates simple models for vascular growth, cell migration and the effect of cell density on the effective oxygen diffusivity. The model shows that the dynamic, homogeneous cell seeding method often employed in small-scale applications is not applicable in the case of larger scale scaffolds such as these. Instead, we propose the implantation of a small biopsy of tissue close to a blood supply within the scaffold as a technique more likely to be successful. Crown Copyright (c) 2005 Published by Elsevier Ltd. All rights reserved.

Effects of adsorbed phase on diffusion of subcritical hydrocarbons in activated carbon at low pressures

Diffusions of free and adsorbed molecules of subcritical hydrocarbons in activated carbon were investigated to study the influence of adsorbed molecules on both diffusion processes at low pressures. A collision reflection factor, defined as the fraction of molecules undergoing collision to the solid surface over reflection from the surface, is incorporated into Knudsen diffusivity and surface diffusivity in meso/macropores. Since the porous structure of activated carbon is bimodal in nature, the diffusion of adsorbed molecules is contributed by that of weakly adsorbed molecules on the meso/macropore surfaces and that of strongly adsorbed molecules in the small confinement of micropores. The mobility of adsorbed molecules on the meso/macropore surface is characterized by the surface diffusivity D-mu 2, while that in the micropore is characterized by D-mu 1. In our study with subcritical hydrocarbons, we have found that the former increases almost linearly with pressure, while the latter exhibits a sharp increase at a very low-pressure region and then decreases beyond a critical pressure. This critical pressure is identified as a pressure at which the micropores are saturated.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behavior of a simple homogeneous Bose gas, finding a very slight increase of the loss rate compared to that obtained by using the standard method.

NMR microscopy: A tool for measuring monomer diffusion in supercritical CO2

The diffusion of styrene into linear low density polyethylene in a solution of supercritical CO2 was investigated using NMR microimaging. For both pure styrene and styrene dissolved in supercritical CO2, the diffusion was found to follow Fickian kinetics. Supercritical CO2 was found to enhance the rate and extent of diffusion of styrene into the substrate by up to three times under the conditions of this investigation, compared to pure styrene. NMR imaging was used to measure the concentration profiles of the styrene penetrants in real time, and the results were fitted to a Fickian model for diffusion. At a CO2 pressure of 150 bar and temperature of 40 degrees C, the diffusion coefficient of a 30 wt-% solution of styrene into LLDPE was calculated to be 1 X 10(-11) m(2). s(-1). This is significantly faster than the diffusion coefficient measured for pure styrene diffusion at 40 degrees C (3 x 10(-12) m(2). s(-1)). The diffusion coefficients determined by gravimetric analysis were slightly higher than those determined by the imaging method. This was probably due to residual styrene and/or polystyrene adhering to the surface of the films in the gravimetric technique.

Estimation of concentration-dependent diffusion coefficient in drying process from the space-averaged concentration versus time with experimental data

The estimation of a concentration-dependent diffusion coefficient in a drying process is known as an inverse coefficient problem. The solution is sought wherein the space-average concentration is known as function of time (mass loss monitoring). The problem is stated as the minimization of a functional and gradient-based algorithms are used to solve it. Many numerical and experimental examples that demonstrate the effectiveness of the proposed approach are presented. Thin slab drying was carried out in an isothermal drying chamber built in our laboratory. The diffusion coefficients of fructose obtained with the present method are compared with existing literature results.