Linear Kinetic Model Research Articles

Kinetic water-bag model of global collisional drift waves and ion temperature gradient instabilities in cylindrical geometry

Collisional drift waves and ion temperature gradient (ITG) instabilities are studied using a linear water-bag kinetic model [P. Morel et al., Phys. Plasmas 14, 112109 (2007)]. An efficient spectral method, already validated in the case of drift waves instabilities [E. Gravier et al., Eur. Phys. J. D 67, 7 (2013)], allows a fast solving of the global linear problem in cylindrical geometry. The comparison between the linear ITG instability properties thus computed and the ones given by the COLUMBIA experiment [R. G. Greaves et al., Plasma Phys. Controlled Fusion 34, 1253 (1992)] shows a qualitative agreement. Moreover, the transition between collisional drift waves and ITG instabilities is studied theoretically as a function of the ion temperature profile.

Quercetin solid lipid microparticles: A flavonoid for inhalation lung delivery

PurposeThe aim of the present work was to develop solid lipid microparticles (SLMs), as dry powders containing quercetin for direct administration to the lung. MethodsQuercetin microparticles were prepared by o/w emulsification via a phase inversion technique, using tristearin as the lipid component and phosphatidylcholine as an emulsifier. The quercetin SLMs were characterised for morphology, drug loading (15.5%±0.6, which corresponded to an encapsulation efficiency of 71.4%), particle size distribution, response to humidity, crystallinity, thermal behaviour and in vitro respirable fraction. Furthermore, the toxicity and the in vitro transport of the SLMs on an air liquid interface model of the Calu-3 cell line were also investigated using a modified twin-stage impinger apparatus. ResultsResults showed that quercetin SLMs could be formulated as dry powder suitable for inhalation drug delivery (20.5±3.3% fine particle fraction ⩽4.46μm) that was absorbed, via a linear kinetic model across the Calu-3 monolayer (22.32±1.51% over 4h). In addition, quercetin SLMs were shown to be non-toxic at the concentrations investigated. Interestingly, no apical to basolateral transport of the micronised quercetin was observed over the period of study. ConclusionsThese observations suggest quercetin diffusion was enhanced by the presence of the lipid/emulsifying excipients in the SLMs; however further studies are necessary to elucidate the exact mechanisms.

Direct Estimation of Kinetic Parametric Images for Dynamic PET

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed.

Experimental analysis of heat transfer between a heated wire and a rarefied gas in an annular gap with high diameter ratio

In this paper a first experimental attempt is performed to measure heat conduction through rarefied air at rest contained between two concentric cylinders. The heat transfer between a heated platinum wire having a diameter (d) of 0.15 mm, disposed along the axis of a cylindrical shell in stainless steel having an inner diameter (D) of 100 mm, and a surrounded rarefied gas has been studied experimentally and numerically. The ratio between the outer and inner diameter of the annular region filled by the gas is large (D/d=667). In the annular region filled with air the pressure was varied by using a vacuum pump from atmospheric value down to 10−3 mbar. Temperature differences between the wire and the external stainless steel wall in the range 50-125 K were imposed and the heat power transferred from the wire to the surround was measured as a function of the gas pressure starting from air at atmospheric conditions down to 10−3 mbar. The experimental results obtained in these tests were compared with the numerical results obtained by using the linear and nonlinear Shakhov kinetic models.

Towards a unified linear kinetic transport model with the trace ion module for EIRENE

Linear kinetic Monte Carlo particle transport models are frequently employed in fusion plasma simulations to quantify atomic and surface effects on the main plasma flow dynamics. Separate codes are used for transport of neutral particles (incl. radiation) and charged particles (trace impurity ions). Integration of both modules into main plasma fluid solvers provides then self-consistent solutions, in principle. The required interfaces are far from trivial, because rapid atomic processes in particular in the edge region of fusion plasmas require either smoothing and resampling, or frequent transfer of particles from one into the other Monte Carlo code. We propose a different scheme here, in which despite the inherently different mathematical form of kinetic equations for ions and neutrals (e.g. Fokker–Planck vs. Boltzmann collision integrals) both types of particle orbits can be integrated into one single code. We show that the approximations and shortcomings of this “single sourcing” concept (e.g., restriction to explicit ion drift orbit integration) can be fully tolerable in a wide range of typical fusion edge plasma conditions, and be overcompensated by the code-system simplicity, as well as by inherently ensured consistency in geometry (one single numerical grid only) and (the common) atomic and surface process modules.

Design of steady-state isothermal gas distribution systems consisting of long tubes in the whole range of the Knudsen number

A novel algorithm is developed to solve steady-state isothermal vacuum gas dynamics flows through pipe networks consisting of long tubes based on linear kinetic theory. For a pipe network of known geometry the algorithm is capable of computing the mass flow rates (or the conductance) through the pipes as well as the pressure heads at the nodes of the network. The pressure distribution along each pipe element may also be found. Since a linear kinetic approach is implemented the analysis is valid and the results are accurate in the whole range of the Knudsen number, provided that the local pressure gradient along each tube of the network is small. This latter condition is satisfied when the channel is sufficiently long. The involved computational effort is very small. This is achieved by successfully integrating the linear kinetic results for the single tubes into the general solver for designing the gas pipe network. To demonstrate the feasibility of the approach two typical piping systems one in the range of small and a second one in the range of moderate Knudsen numbers are simulated. The proposed algorithm simulates, in an exact manner, low-speed gas distribution systems under any vacuum conditions based on linear kinetic modeling and constitutes a significant advancement tool in vacuum technology.

Human biokinetic data and a new compartmental model of zirconium — A tracer study with enriched stable isotopes

Biokinetic models describing the uptake, distribution and excretion of trace elements are an essential tool in nutrition, toxicology, or internal dosimetry of radionuclides. Zirconium, especially its radioisotope 95Zr, is relevant to radiation protection due to its production in uranium fission and neutron activation of nuclear fuel cladding material. We present a comprehensive set of human data from a tracer study with stable isotopes of zirconium. The data are used to refine a biokinetic model of zirconium. Six female and seven male healthy adult volunteers participated in the study. It includes 16 complete double tracer investigations with oral ingestion and intravenous injection, and seven supplemental investigations. Tracer concentrations were measured in blood plasma and urine collected up to 100 d after tracer administration. The four data sets (two chemical tracer forms in plasma and urine) each encompass 105–240 measured concentration values above detection limits. Total fractional absorption of ingested zirconium was found to be 0.001 for zirconium in citrate-buffered drinking solution and 0.007 for zirconium oxalate solution. Biokinetic models were developed based on the linear first-order kinetic compartmental model approach used by the International Commission on Radiological Protection (ICRP). The main differences of the optimized systemic model of zirconium to the current ICRP model are (1) recycling into the transfer compartment made necessary by the observed tracer clearance from plasma, (2) different parameters related to fractional absorption for each form of the ingested tracer, and (3) a physiologically based excretion pathway to urine. The study considerably expands the knowledge on the biokinetics of zirconium, which was until now dominated by data from animal studies. The proposed systemic model improves the existing ICRP model, yet is based on the same principles and fits well into the ICRP radiation protection approach.

Inégalités de Poincaré cinétiques

In this Note we prove Poincaré type inequalities for a family of kinetic equations. We apply this inequality to the variational solution of a linear kinetic model by generalizing the STILS method (Azerad, 1996 [1]; Azerad and Pousin, 1996 [2]) to a kinetic setting.

Chalcopyrite leaching in sulfate–chloride media at ambient pressure

In this article, experimental results on the leaching of a chalcopyrite concentrate with oxygen at ambient pressure in H 2SO 4–NaCl solutions are discussed taking into account the evolution of the solution redox potential and the concentration of ferric ions during leaching. The results indicate that leaching of chalcopyrite concentrate with particle size 12.3 μm in sulfate–chloride solutions was rapid. Over 90% copper was dissolved in 180 min at 100 °C. The results also showed that 17.7 g/l (0.5 M) of chloride ions in the leaching solution affected significantly the leaching rate as compared to leaching without chloride. The addition of 3 g/l of ferric ions to the leaching system produced a large increase in the solution potential which in turn affected negatively the leaching rate of chalcopyrite. The leaching of chalcopyrite in H 2SO 4–NaCl–O 2 media depends largely on the temperature, and the linear kinetics model 1−(1−X) 1/3 = kt represents the copper dissolution well. An activation energy value of 91.2 kJ/mol was determined for the temperature range of 80 to 100 °C.

Prediction of the plasma concentration profiles of orally administered drugs in rats on the basis of gastrointestinal transit kinetics and absorbability.

A new method based on gastrointestinal transit kinetics has been developed for estimation of the absorption profiles of drugs administered orally as aqueous solutions. The utility of the method was evaluated in rats. The gastrointestinal transit profile for each segment was estimated by in-vivo studies using phenol red, an unabsorbable marker. The gastrointestinal transit profile of phenol red was well explained by a linear gastrointestinal transit kinetic model with eight segments. We also introduced the absorption process into the gastrointestinal transit kinetic model and the plasma profile was predicted by the convolution method. The absorbability of drugs in each segment was assessed by an in-situ absorption study. The validity of the model was evaluated for model drugs with different absorption characteristics. The plasma profiles predicted for ampicillin, theophylline and cephalexin were in good agreement with those observed. The overestimated plasma profile of propranolol suggests that the low bioavailability of propranolol is a result of first-pass metabolism by the intestine wall and the liver, because the calculated absolute absorption is almost perfect. This proposed model is also suitable for estimation of segmental absorption, which is useful for the development of drug delivery systems. We have demonstrated that the plasma profile of orally administered drugs can be predicted by use of gastrointestinal transit and segmental absorbability information and that this method is especially useful for estimating separately the effect of absolute absorption and first-pass metabolism on the bioavailability of drugs.

Calculation of the total lethality of conductive heat in cylindrical cans sterilization using linear and non linear survival kinetic models

There is growing evidence suggesting that inactivation of bacterial spores may follow the Weibullian model, of which the log linear relationship between survival ratio and time is just a special case. Where true, the time and not only the temperature dependence of the rate must be taken into account. Also, it is of interest to estimate spores survival not only at the coldest point but also throughout the whole container's volume. Numerical calculation on changing survival ratios was performed by combining the conductive heat transfer model with that of the nonlinear inactivation kinetics. Results are based on published linear and non linear inactivation parameters of Clostridium botulinum spores, typical thermal properties of solid foods and realistic thermal processing conditions. Results could be used to quantify the efficacy of thermal processes of solid products in terms of spores' residual survival ratio at the coldest point and in the container as a whole.

Kinetic linear model of the interaction of helical magnetic perturbations with cylindrical plasmas

The linear kinetic model of the interaction of helical rotating magnetic perturbations (resonant and nonresonant) with a tokamak plasma developed in [M. F. Heyn et al., Nucl. Fusion 46, S159 (2006)] is extended by a Galilean invariant collision operator and a different finite Larmor radius expansion scheme of particle current density. The model is applied to study the plasma screening effect on resonant magnetic perturbations and the resulting torques acting on the plasma at various orders of Larmor radius expansion.

Three-dimensional structure of electron density fluctuations in the Hall thruster plasma: E¯×B¯ mode

Collective scattering measurements have been conducted on the plasma of a Hall thruster, in which the electron density fluctuations are fully characterized by the dynamic form factor. The dynamic form factor amplitude distribution has been measured depending on the k-vector spatial and frequency components at different locations. Fluctuations are seen as propagating waves. The largest amplitude mode propagates nearly along the cross-field direction but at a phase velocity that is much smaller than the E¯×B¯ drift velocity. Refined directional analysis of this largest amplitude mode shows a thin angular emission diagram with a mean direction that is not strictly along the E¯×B¯ direction but at small angles near it. The deviation is oriented toward the anode in the (E¯,E¯×B¯) plane and toward the exterior of the thruster channel in the (B¯,E¯×B¯) plane. The density fluctuation rate is on the order of 1%. These experimentally determined directional fluctuation characteristics are discussed with regard to the linear kinetic theory model and particle-in-cell simulation results.

A Kinetic Study of Aluminium(III) and Chromium(III) Adsorption by Silica Gel <i>Chaetoceros calcitrans</i> Biomass Immobilized on Silica Gel

The kinetics of aluminium(III) and chromium(III) adsorption in an adsorbent prepared by immobilization of Chaetoceros calcitrans biomass on silica ge has been investigated. The functional groups which were probable involved in the adsorption processes also identified. Experimentally, the adsorption was conducted by coloumn and batch method. In this work atomic adsorption spectrophotometric techniques was applied indirectly to determine of the metal ion adsorpted, and infra red spectroscopic technique was used for the identification of functional groups present in the adsorbent. The study included two parts of experiment, i.e. 1) the determination of rate of adsorption and 2) the determination of capacity and energy of adsorption. Results showed that the AI(III) and Cr(III) adsorption data fit quiet well with non linear kinetics model proposed by Langmuir-Hinshelwood giving a first order rate constant, (k1) of 8.65.10-3 min-1 for AI(III) and 9.92.10-4 min' for Cr(III) when the immobilized biomass used as the adsorbent in agreement with the activation energy calculation giving values of 1.184 kcal/mole for Al(111) and 1.877 kcal/mole for Cr (Ill). It was concluded that the adsorption of Al(III) and Cr(III) on Chaetoceros calcitrans immobilized and free Chaetoceros calcitrans adsorbents, may be classified as chemical adsorption, involving entalphi of adsorption in the range of 6-17 kcal/mole. And the infra red spectroscopic data indicated that the functional groups i.e.: carboxylate (-COO), hydroxyl (-OH) silanol (SI-OH), siloksil (SI-O-Si) and amine (NH2) are present in free Chaetoceros calcitrans biomass and silanol (Si-OH), siloksil (Si-O-Si), hydroxyl (-OH)and C-H metilene (-CH2) are present in immobilized biomass Chatoceros calcitrans, while only siloksil (Si-O-Si) and silanol (Si-OH) in silica gel.

Contaminant transport in groundwater in the presence of colloids and bacteria: Model development and verification

Colloids and bacteria (microorganisms) naturally exist in groundwater aquifers and can significantly impact contaminant migration rates. A conceptual model is first developed to account for the different physiochemical and biological processes, reaction kinetics, and different transport mechanisms of the combined system (contaminant–colloids–bacteria). All three constituents are assumed to be reactive with the reactions taking place between each constituent and the porous medium and also among the different constituents. A general linear kinetic reaction model is assumed for all reactive processes considered. The mathematical model is represented by fourteen coupled partial differential equations describing mass balance and reaction processes. Two of these equations describe colloid movement and reactions with the porous medium, four equations describe bacterial movement and reactions with colloids and the porous medium, and the remaining eight equations describe contaminant movement and its reactions with bacteria, colloids, and the porous medium. The mass balance equations are numerically solved for two-dimensional groundwater systems using a third-order, total variance-diminishing scheme (TVD) for the advection terms. Due to the complex coupling of the equations, they are solved iteratively each time step until a convergence criterion is met. The model is tested against experimental data and the results are favorable.

Effect of pH on Inactivation of Escherichia coli K12 by Sonication, Manosonication, Thermosonication, and Manothermosonication

The effect of pH on inactivation of Escherichia coli K12 by sonication at 100 kPa/40 degrees C, manosonication (MS) at 400 kPa/40 degrees C, thermosonication (TS) at 100 kPa/61 degrees C, and manothermosonication (MTS) at 400 kPa/61 degrees C at acoustic energy density of 3 W/mL and 6 W/mL was investigated. Five linear and nonlinear kinetic models were used to examine the inactivation kinetics. At all pH levels, the inactivation rates of E. coli K12 in a buffer by TS and MTS were significantly higher than those by sonication and MS. A 5 log reduction of E. coli K12 population by TS and MTS was achieved in 0.5 and 0.25 min, respectively. With an initial count of 10(8) CFU/mL, no colonies were detected at pH 3 after a 0.25-min MTS treatment. The lethal effect of MTS was enhanced at low pH (pHs 3 and 4), whereas at nonlethal temperature of 40 degrees C, no increased killing was observed. Regardless of pH, the treatment by MTS, TS, and MS exhibited a rapid initial reduction followed by tailing-off on the inactivation curves. The biphasic linear, log-logistic, and modified Gompertz kinetic models allowed better fitting of the inactivation data for MTS, TS, and MS treatments than the 1st-order and Weibull models. The survival counts of sonication-treated E. coli K12 at all pH levels fitted well to a 1st-order kinetic model.

Adsorption of palladium(II) from chloride solutions on Amberlyst A 29 and Amberlyst A 21 resins

Two anion exchange resins – strongly basic Amberlyst A 29 and weakly basic Amberlyst A 21 – were applied to the adsorption of palladium(II) complexes from HCl-NaCl solutions over a range of acid concentrations (0.1–2.0 M) in 1.0 and 2.0 M NaCl using static and dynamic methods. The breakthrough curves of Pd(II) were used to calculate the ion exchange capacity, weight and bed distribution coefficients. Kinetic studies applied the Legergren's equation, the pseudo-second order and the inter-particle diffusion kinetic models to calculate kinetic parameters. It was observed that Amberlyst A 21 is more promising for adsorbing palladium(II) chloro-complexes from acidic chloride solutions than Amberlyst A 29. Furthermore, the type 1, pseudo-second order linear kinetic model has the highest correlation coefficient and gives the best fit between the experimental and predicted data.

Robust simplifications of multiscale biochemical networks

BackgroundCellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.ResultsWe propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in [1]. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-κB pathway.ConclusionOur approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.

Pseudo-second-order kinetic models for the sorption of Hg(II) onto dead biomass of marine Aspergillus niger: Comparison of linear and non-linear methods

A comparison between linear least-squares method and non-linear regression method of the widely used pseudo-second-order kinetic model, for the sorption of Hg(II) onto dead biomass of marine Aspergillus niger was examined. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from four kinetic linear equations using the linear method differed but they were the same when non-linear method was used. Type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a superior way to obtain the kinetic parameters.

Electric Potential Around an Absorbing Body in Plasmas: Effect of Ion-Neutral Collisions

A simple linear kinetic model is used to investigate the combined effect of plasma absorption and ion-neutral collisions on the electric potential around a small absorbing body in weakly ionized plasmas. It is demonstrated that far from the body the potential decays considerably slower than the conventional Debye-Hückel potential. Moreover, at distances exceeding approximately the ion mean free path, the potential approaches an unscreened Coulomb-like asymptote. Some important consequences of this result are discussed in the context of complex (dusty) plasmas.