Kinetic Model

This paper is organized as follows. In § 2, the Rykov kinetic model of the Boltzmann equation for non-vibrating diatomic gases is introduced, and then extended to polyatomic gases. A new kinetic model for non-vibrating polyatomic gases, which recovers the elastic velocity-dependent collision frequency, is then proposed. In § 3, the kinetic model equations are solved by the fast spectral method and the discrete velocity method. Numerical results for normal shock waves and planar Fourier/Couette flows are compared with DSMC results and experimental data. In § 4, the mass and heat flow rates in Poiseuille and thermal creep flows of polyatomic gases are calculated. In § 5, the spectra of both spontaneous and coherent Rayleigh–Brillouin scattering (RBS) in polyatomic gases are obtained, and the influence of the molecular model is analysed. We conclude in § 6.

Thermal cracking of light hydrocarbons was studied in which a molecular kinetic model for light hydrocarbons, and their mixture was developed. Required kinetic parameters were calculated and tuned by error minimization between several real reactors measured data and results of their simulation. Reactors were simulated as a one-dimensional plug flow reactor. Simulation consists of a reactor model and heat transfer from an external hot surface of the reactor. Nonlinear regression method was used to minimize the errors of simulation results and optimization of the kinetic model parameters. The kinetic and reactor models were verified by comparing their results with the measured data of several real reactors. Required experimental data were collected through the literature survey. Accuracy of the simulation results showed that the developed kinetic model and the reactor simulation can be applied for the operational analysis of cracking furnaces, operating parameters optimization, and industrial plant profitability improvement.

The study of fermentation kinetic parameters is crucial to understand the effect of the environmental factors on biohydrogen production. The fermentation process of palm oil mill effluent involves the conversion of organic compounds to liquid organics and biogas, which is relatively complex. Furthermore, kinetic parameters, coupled with the mathematical model, can be used to predict the substrate utilization, cell concentration, and biohydrogen productio n rate during steady-state. This paper aimed to present a kinetic model for the thermophilic POME fermentation in an anaerobic sequential batch reactor (ASBR) by a mixed culture. The model can be used for understanding the behavior of the anaerobic digestion under most related environmental conditions for biohydrogen production. The weighted least-squares parameter estimation method was used to compute the kinetic model parameters from the previous literature data. Mathematical models base on Monod’s equation accounting for substrate inhibition were developed to predict hydrogen fermentation.

The most rigorous kinetic model considering the difference between the interfacial and bulk concentrations of the enzyme, substrates and products, and the interfacial enzymatic reaction mechanism was proposed in this model [71]. The model describing the stepwise hydrolysis of triglyceride by nonspecific lipase in the biphasic oil-water system was formulated on the basis of the following assumptions:

ABSTRACT The precise details of how myosin-V coordinates the biochemical reactions and mechanical motions of its two head elements to engineer effective processive molecular motion along actin filaments remain unresolved. We compare a quantitative kinetic model of the myosin-V walk, consisting of five basic states augmented by two further states to allow for futile hydrolysis and detachments, with experimental results for run lengths, velocities, and dwell times and their dependence on bulk nucleotide concentrations and external loads in both directions. The model reveals how myosin-V can use the internal strain in the molecule to synchronize the motion of the head elements. Estimates for the rate constants in the reaction cycle and the internal strain energy are obtained by a computational comparison scheme involving an extensive exploration of the large parameter space. This scheme exploits the fact that we have obtained analytic results for our reaction network, e.g., for the velocity but also the run length, diffusion constant, and fraction of backward steps. The agreement with experiment is often reasonable but some open problems are highlighted, in particular the inability of such a general model to reproduce the reported dependence of run length on ADP concentration. The novel way that our approach explores parameter space means that any confirmed discrepancies should give new insights into the reaction network model.

The kinetic model of TBP revealed the possibility of a range of potential behaviours. For parameter values where the system exhibits bistability, one of the steady states is the zero-state and the other is a high-TBP state corresponding to a total TBP concentration in the 10 nanomolar range. It is seen that a physiological state resulting in low total TBP concentration (below ~0.1 nanomolar) will be in the zone of attraction of the zero- state and hence lead to cell death. Studies have shown that mRNA of many of the proteins involved in basic processes of gene expresion are maternally inherited [21,22] since the egg cell is transcriptionally silent but translationally active [23]. These maternally inherited proteins help the growth of zygote during first few cycles of cell division. The model predicts that a certain amount of TBP is needed to “ jump start ” its own tran- scription. These properties may also explain the reason for the maternal inheritance of TBP [24].

In this study, pickles were used as the research objects, the shelf life of the pickles during storage at different temperatures (25 ℃、 30 ℃ or 37 ℃ ) was studied, the changes of sensory quality and the total number of colonies during storage were determined. The results showed that the sensory score declined with storage time increased, the higher the storage temperature, the greater the rate of change; with the increased of storage time , the total number of colonies increased ,the higher the storage temperature , the higher the rate of change , this conformed to the first-order kinetics model. Kinetic model of the total number of colonies was established , through the analysis, obtained a Arrhenius equation and the first-order (chemical reaction) , the correlation coefficient of which were greater than 0.9, showing a high goodness of fit; and a shelf life prediction kinetic model was obtained as follows: y = 224.73 e -0. 0791 x (R 2 = 0.9999). Experiments showed that the kinetics model of pickles quality changes had a high fitting accuracy, it can exhibit a good reliability in predicting the shelf life of pickles.

Cancer growth has been modeled as the growth as an ex- isting tumor and metastasis resulting in interaction be- tween the existing tumor and plasma viewed as two independent but interacting compartments. The cells present in plasma, thereafter attach to another tissue and grow into a new tumor mass. The new tumor mass in- creases in size due to cell growth and cell uptake from plasma. However, once the cell concentration reaches a steady state concentration, this tumor mass also becomes a source for new tumor masses, i.e. it forms another stage for cancer growth. Further, two different cancer therapies- EGFR inhibitor therapy and adoptive therapy- were ana- lyzed using this kinetic model. The results point to the im- portance of targeting the specific growth rate as well as the plasma clearance rate in the system. Thus, this model helps study the efficacy of the cancer treatment therapies, and also helps determine the critical factors, which may be targeted. However, these results are strongly dependent on the parameter values, which should be appropriately taken and analyzed for specific case; but this model is use- ful in focussing and improving a cancer therapy in order to make it more effective.

The Vlasov equation describes a large collection of particles as a continuum. Charged continua typically do not suffer from the pathologies associated with radiating point particles and since the Maxwell-Vlasov system satisfies the energy and momentum conservation laws that led to (1) it may seem that it does not need modifying to describe radiation reaction. However, the continuum comprises “particles” with infinitesimal mass and charge, (q, m) → 0 with q/m fixed, in which limit (1 ) becomes the usual Lorentz force equation. To describe a collection of real electrons with finite q and m, the Vlasov equation must be modified so that elements of the continuum follow trajectories of the Lorentz-Dirac Eq. (1). Such a kinetic equation was introduced previously; 26 however, in that work the physical phase space was not identified, so the 1-particle distribution is required to be distributional (in the sense of Schwartz). As well as impeding the physical interpretation, this has led to a number of errors, for example, in calculating the rate of change of entropy.

Earlier, mathematical expressions pertaining to analytical concentration and current for limiting cases in a conducting polymer film were calculated by Bartlett and Whitaker [11]. Somasundrum et al. [20] suggested a mathematical model of the steady state current and the function and optimization of metal particles deposited in a conducting polymer for the limiting cases only (high and low substrate concentration). However, to the best of our knowledge, till date no simple analytical results for the concentrations of substrate and hydrogen peroxide for all values of the parameters have been reported. The purpose of this communication is to derive analytical expressions for concentrations of substrate and hydrogen peroxide in a conducting film containing metal microparticles using new Homotopy perturbation method. This method is very easy compared to all other asymptotic methods. This simple analytical expression of concentrations of substrate, hydrogen peroxide and flux is very much useful to the electrochemical scientists for the analysis of experimental data. The analytical results have been extended numerically and are to be in good agreement with each other.

Main combustion product species concentra­ tions (Rjo, 0 2, NO) were measured with gas analysers in the laboratory for combustion cham­ bers at the Aerospace Department of FH-Aachen, and the results were used to validate our theore­ tical model. The H2 concentration was monitored with an analyser based on the detection of diffe­ rent gas thermal conductivities, the 0 2 concentra­ tion with a gas analyser of a magnetic mechanical type and NO with a chemoluminescent NO-NOx analyser. The water concentration was computed at each measuring point, applying the following balance equation:

The kinetic theory of matter states that the tiny particles that make up matter are always in continuous random motion.. kinetic theory of matter.[r]

In summary, we have analyzed a quasi-chemical kinetic model which provides very good fits to experimental data collected from various bacteria species under different environmental conditions. However, we have shown that although the QCM model has great flexibility, it often results in an ill-posed problem, or estimated parameter values with little statistical significance. We illustrated that using statistical model reduction techniques provide a way in which to reduce the uncertainty in model parameters for cases where the data does not exhibit the complex behavior the QCM was designed to capture. Additionally, we developed surrogate models, which at the very least provide alternatives for the QCM model, and in the case of the hybrid food chemistry model, can be used to estimate a subset of the QCM model parameters. Finally, we proposed an adaptive optimal design method for selecting the sampling times. However, we noted that due to the locality of the optimal design methods combined with the fact that the two of the four parameters in the QCM model are not sensitive during the lag and growth phases, these methods do not provide a significant reduction of uncertainty over linear spaced sampling.

To describe the adsorption mechanism Pseudo–first-order, Pseudo-second-order, Elovich and Intra-particle diffusion [19-22] were tested as a kinetics models for the adsorption of dye on CKD. Figs. (8-11) showed the plots of kinetic model equations at different dye concentrations. Table2 listed the kinetic models equations and the rate constants and correlation coefficients for the dye adsorption onto CKD.

In this study, we quantified the bio-kinetics of Cs and Cd in Penaeus monodon is one of marine organism which has been suggested to be useful bio-monitors for radionuclides. A trend kinetic model was then developed through identify and understand it accordingly to influx and efflux processes for parameter estimation. Finally, the model with the estimated parameters was used to predict Cs-134 and Cd-109 accumulation in the Penaeus monodon under waterborne exposure pathway scenarios. This study was conducted with an aim to quantify the uptake and loss/depuration of these two radionuclides in the Penaeus monodon and to understand the kinetic trend of their bio-accumulation via waterborne exposure pathway.

The kinetic model of the pseudo-first order, also called the Lagergen model, was firstly used to describe the adsorption at the solid-liquid interface. The basis of this model is the capacity of the solid. Derivation from the Lagergren equation requires that the concentration of the two ions is time-independent and, therefore, the constant should correspond to the linear combination of both concentration values. The Lagergren equation represents the adsorption in the case of diffusion across the liquid phase boundary to a solid sorbent. The constant of the equation varies depending on the particle size and surface film thickness, where the constant is dependent on the concentration of ions in the solution and the process temperature in the case of chemisorption. The particle size does not affect adsorption [19]. The pseudo-first order equation can be expressed by (3):

Abstract. In the present study, a kinetic model of nitration between glycerol and nitric acid was developed. The presented model describes three controlling reactions model used elementary reactions consisting of three reversible reactions. The model utilizes first order reaction according to each reactant. The nitration of glycerol was modelled by fitting the kinetic model with 6 parameters, the rate constant at an average temperature and the activation energy. The reaction rate is assumed to be governed by three reactions, i.e. the formation of MNG (mononitroglycerin), the formation of DNG (dinitroglycerin) and the formation of TNG (nitroglycerin). The aim of this work is compare two models: seven controlling reactions model and three controlling reactions model. Two models have the similar trend. The three controlling reactions model gives better fit than seven controlling reactions model. The accuracy of three controlling reactions model is higher. The advantage of the seven controlling reactions model is this model can predict all products of nitration. So this model can be used at preliminary design plant. Three controlling reactions model can be used at next step, as design of reactor.

Batch adsorption experiment using the bottle point method was performed at temperatures ranging from 15˚C to 35˚C for adsorption Isotherm test, varying weights of the granular activated carbon (0.05 g - 0.8 g) were added to 200 ml of E2 and EE2 aqueous solutions in 250 ml plugged conical flasks. The experiments were conducted at pHs 4, 6, 7, 8 and 10. The aqueous mixtures were agi- tated at a constant rate of 250 rpm. The experiments were conducted for 180 mins initially and subsequently for 120 mins. Samples were withdrawn at fixed time inter- vals for chemical analysis. The experimental data ob- tained were analysed using various kinetic models: Leger- gren pseudo first-order kinetics, pseudo second order kinetics, intra-particle diffusion kinetic model and the Langmuir and Freundlich adsorption isotherm models. The thermodynamic parameters which include Gibb’s free energy, enthalpy and entropy were also investigated. 2.3. Analytical Procedures

paper is aimed at comparison of different sources of chlorophyll and their extraction rate from various natural materials. A kinetic model of chlorophyll extraction from leaves, needles and microalgae is depicted and extraction process according to different materials and solvent used is described. This method enables proper selection of material and solvent to produce high amount of chlorophyll in the shortest possible time. Microalgae seem to be the most promising alternative source for chlorophyll.

It should be noted that the kinetic parameters k and m calculated from the Avrami – Erofe'ev kinetic model are rea- sonably consistent and within appropriate ranges, even though several factors may have influenced their accuracy during the experimental and data analysis stages. This includes, but not limited to, the complex nature of sol – gel used, EDXRD data collection over few visits to SRS station 16.4, possible variations in stirring speed of different cells used, detection of small diffraction peaks and errors in induction time due to the lower detection limits intrinsic to the EDXRD technique, 28 and errors in integration of the peak