Figaro, S; Avril, J P; Brouers, F; Ouensanga, A; Gaspard, S
2009-01-30
Adsorption kinetic of molasses wastewaters after anaerobic digestion (MSWD) and melanoidin respectively on activated carbon was studied at different pH. The kinetic parameters could be determined using classical kinetic equations and a recently published fractal kinetic equation. A linear form of this equation can also be used to fit adsorption data. Even with lower correlation coefficients the fractal kinetic equation gives lower normalized standard deviation values than the pseudo-second order model generally used to fit adsorption kinetic data, indicating that the fractal kinetic model is much more accurate for describing the kinetic adsorption data than the pseudo-second order kinetic model.
Controllability in hybrid kinetic equations modeling nonequilibrium multicellular systems.
Bianca, Carlo
2013-01-01
This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation.
Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence
Aupoix, B.; Blaisdell, G. A.; Reynolds, William C.; Zeman, Otto
1990-01-01
The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.
Numerical Comparison of Solutions of Kinetic Model Equations
Directory of Open Access Journals (Sweden)
A. A. Frolova
2015-01-01
Full Text Available The collision integral approximation by different model equations has created a whole new trend in the theory of rarefied gas. One widely used model is the Shakhov model (S-model obtained by expansion of inverse collisions integral in a series of Hermite polynomials up to the third order. Using the same expansion with another value of free parameters leads to a linearized ellipsoidal statistical model (ESL.Both model equations (S and ESL have the same properties, as they give the correct relaxation of non-equilibrium stress tensor components and heat flux vector, the correct Prandtl number at the transition to the hydrodynamic regime and do not guarantee the positivity of the distribution function.The article presents numerical comparison of solutions of Shakhov equation, ESL- model and full Boltzmann equation in the four Riemann problems for molecules of hard spheres.We have considered the expansion of two gas flows, contact discontinuity, the problem of the gas counter-flows and the problem of the shock wave structure. For the numerical solution of the kinetic equations the method of discrete ordinates is used.The comparison shows that solution has a weak sensitivity to the form of collision operator in the problem of expansions of two gas flows and results obtained by the model and the kinetic Boltzmann equations coincide.In the problem of the contact discontinuity the solution of model equations differs from full kinetic solutions at the point of the initial discontinuity. The non-equilibrium stress tensor has the maximum errors, the error of the heat flux is much smaller, and the ESL - model gives the exact value of the extremum of heat flux.In the problems of gas counter-flows and shock wave structure the model equations give significant distortion profiles of heat flux and non-equilibrium stress tensor components in front of the shock waves. This behavior is due to fact that in the models under consideration there is no dependency of the
Kinetic equations modelling wealth redistribution: a comparison of approaches.
Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe
2008-11-01
Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply, e.g., to the market model with risky investments [S. Cordier, L. Pareschi, and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.
Marczewski, Adam W
2010-10-05
In the article, a new integrated kinetic Langmuir equation (IKL) is derived. The IKL equation is a simple and easy to analyze but complete analytical solution of the kinetic Langmuir model. The IKL is compared with the nth-order, mixed 1,2-order, and multiexponential kinetic equations. The impact of both equilibrium coverage θ(eq) and relative equilibrium uptake u(eq) on kinetics is explained. A newly introduced Langmuir batch equilibrium factor f(eq) that is the product of both parameters θ(eq)u(eq) is used to determine the general kinetic behavior. The analysis of the IKL equation allows us to understand fully the Langmuir kinetics and explains its relation with respect to the empirical pseudo-first-order (PFO, i.e., Lagergren), pseudo-second-order (PSO), and mixed 1,2-order kinetic equations, and it shows the conditions of their possible application based on the Langmuir model. The dependence of the initial adsorption rate on the system properties is analyzed and compared to the earlier published approximate equations.
Kinetic equations: computation
Pareschi, Lorenzo
2013-01-01
Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity.
Some Aspects of Extended Kinetic Equation
Directory of Open Access Journals (Sweden)
Dilip Kumar
2015-09-01
Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Kinetic energy equations for the average-passage equation system
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Generalization of the Analytical Exponential Model for Homogeneous Reactor Kinetics Equations
Directory of Open Access Journals (Sweden)
Abdallah A. Nahla
2012-01-01
Full Text Available Mathematical form for two energy groups of three-dimensional homogeneous reactor kinetics equations and average one group of the precursor concentration of delayed neutrons is presented. This mathematical form is called “two energy groups of the point kinetics equations.” We rewrite two energy groups of the point kinetics equations in the matrix form. Generalization of the analytical exponential model (GAEM is developed for solving two energy groups of the point kinetics equations. The GAEM is based on the eigenvalues and the corresponding eigenvectors of the coefficient matrix. The eigenvalues of the coefficient matrix are calculated numerically using visual FORTRAN code, based on Laguerre’s method, to calculate the roots of an algebraic equation with real coefficients. The eigenvectors of the coefficient matrix are calculated analytically. The results of the GAEM are compared with the traditional methods. These comparisons substantiate the accuracy of the results of the GAEM. In addition, the GAEM is faster than the traditional methods.
Maulidah, Rifa'atul; Purqon, Acep
2016-08-01
Mendong (Fimbristylis globulosa) has a potentially industrial application. We investigate a predictive model for heat and mass transfer in drying kinetics during drying a Mendong. We experimentally dry the Mendong by using a microwave oven. In this study, we analyze three mathematical equations and feed forward neural network (FNN) with back propagation to describe the drying behavior of Mendong. Our results show that the experimental data and the artificial neural network model has a good agreement and better than a mathematical equation approach. The best FNN for the prediction is 3-20-1-1 structure with Levenberg- Marquardt training function. This drying kinetics modeling is potentially applied to determine the optimal parameters during mendong drying and to estimate and control of drying process.
Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation
Institute of Scientific and Technical Information of China (English)
LI; Zhihui; ZHANG; Hanxin; FU; Song
2005-01-01
The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS.
Energy Technology Data Exchange (ETDEWEB)
Gelß, Patrick, E-mail: p.gelss@fu-berlin.de; Matera, Sebastian, E-mail: matera@math.fu-berlin.de; Schütte, Christof, E-mail: schuette@mi.fu-berlin.de
2016-06-01
In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.
Bayesian inference for kinetic models of biotransformation using a generalized rate equation.
Ying, Shanshan; Zhang, Jiangjiang; Zeng, Lingzao; Shi, Jiachun; Wu, Laosheng
2017-03-06
Selecting proper rate equations for the kinetic models is essential to quantify biotransformation processes in the environment. Bayesian model selection method can be used to evaluate the candidate models. However, comparisons of all plausible models can result in high computational cost, while limiting the number of candidate models may lead to biased results. In this work, we developed an integrated Bayesian method to simultaneously perform model selection and parameter estimation by using a generalized rate equation. In the approach, the model hypotheses were represented by discrete parameters and the rate constants were represented by continuous parameters. Then Bayesian inference of the kinetic models was solved by implementing Markov Chain Monte Carlo simulation for parameter estimation with the mixed (i.e., discrete and continuous) priors. The validity of this approach was illustrated through a synthetic case and a nitrogen transformation experimental study. It showed that our method can successfully identify the plausible models and parameters, as well as uncertainties therein. Thus this method can provide a powerful tool to reveal more insightful information for the complex biotransformation processes.
Modeling Adsorption Kinetics of Magnesium and Phosphate Ions on Goethite by Empirical Equations
Directory of Open Access Journals (Sweden)
Malihe Talebi Atouei
2017-06-01
Full Text Available Introduction: Natural environments, including soils and sediments, are open and complex systems in which physico-chemical reactions are in semi equilibrium state. In these systems, bioavailability of plant nutrients, like phosphate, is influenced by environmental conditions and concentrations of other ions such as calcium and magnesium. Magnesium is a dominant cation in irrigation water and in the soil solution of calcareous soils. Recent evidences show relative increase in the concentration of magnesium in irrigation water. Because of the importance of chemical kinetics in controlling concentrations of these ions in the soil solution and for understanding their effects of adsorption kinetics of magnesium and phosphate ions, in this research, adsorption kinetics of these two ions on goethite is investigated as function of time and pH in single ion and binary ion systems. The experimental data are described by using the adsorption kinetics equations. These data are of the great importance in better understanding adsorption interactions and ion adsorption mechanism.With respect to the importance of these interactions from both economical and environmental point of view, in this research, the kinetics and thermodynamics of phosphate and Mg2adsorption interactions were investigated as function of pH on soil model mineral goethite in both single and binary ion systems. Materials and Methods: Kinetics experiments were performed in the presence of 0.2 mM magnesium and 0.4 mM phosphate in 0.1 M NaCl background solution and 3 g L-1 goethite concentration as function of pH and time (1, 5, 14, 24, 48. 72 and 168 h in single ion and binary ion systems. After reaction time, the suspensions were centrifuged and a sample of supernatant was taken for measuring ions equilibrium concentrations.Phosphate concentration was measured calorimetrically with the ammonium molybdate blue method by spectrophotometer (Jenway-6505 UV/Vis. Magnesium concentration was
On the Rate of Relaxation for the Landau Kinetic Equation and Related Models
Bobylev, Alexander; Gamba, Irene M.; Zhang, Chenglong
2017-08-01
We study the rate of relaxation to equilibrium for Landau kinetic equation and some related models by considering the relatively simple case of radial solutions of the linear Landau-type equations. The well-known difficulty is that the evolution operator has no spectral gap, i.e. its spectrum is not separated from zero. Hence we do not expect purely exponential relaxation for large values of time t>0. One of the main goals of our work is to numerically identify the large time asymptotics for the relaxation to equilibrium. We recall the work of Strain and Guo (Arch Rat Mech Anal 187:287-339 2008, Commun Partial Differ Equ 31:17-429 2006), who rigorously show that the expected law of relaxation is \\exp (-ct^{2/3}) with some c > 0. In this manuscript, we find an heuristic way, performed by asymptotic methods, that finds this "law of two thirds", and then study this question numerically. More specifically, the linear Landau equation is approximated by a set of ODEs based on expansions in generalized Laguerre polynomials. We analyze the corresponding quadratic form and the solution of these ODEs in detail. It is shown that the solution has two different asymptotic stages for large values of time t and maximal order of polynomials N: the first one focus on intermediate asymptotics which agrees with the "law of two thirds" for moderately large values of time t and then the second one on absolute, purely exponential asymptotics for very large t, as expected for linear ODEs. We believe that appearance of intermediate asymptotics in finite dimensional approximations must be a generic behavior for different classes of equations in functional spaces (some PDEs, Boltzmann equations for soft potentials, etc.) and that our methods can be applied to related problems.
Turbulence kinetic energy equation for dilute suspensions
Abou-Arab, T. W.; Roco, M. C.
1989-01-01
A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-01-01
Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904
DEFF Research Database (Denmark)
Costa, Rafael S.; Machado, Daniel; Rocha, Isabel
2010-01-01
, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action...... using the hybrid model composed of Michaelis–Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown....
Li, Zhihui; Wu, Junlin; Ma, Qiang; Jiang, Xinyu; Zhang, Hanxin
2014-12-01
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
Energy Technology Data Exchange (ETDEWEB)
Li, Zhihui; Ma, Qiang [Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O.Box 211, Mianyang 621000, China and National Laboratory for Computational Fluid Dynamics, No.37 Xueyuan Road, Beijing 100191 (China); Wu, Junlin; Jiang, Xinyu [Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, P.O.Box 211, Mianyang 621000 (China); Zhang, Hanxin [National Laboratory for Computational Fluid Dynamics, No.37 Xueyuan Road, Beijing 100191 (China)
2014-12-09
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
Spectrum Analysis of Some Kinetic Equations
Yang, Tong; Yu, Hongjun
2016-11-01
We analyze the spectrum structure of some kinetic equations qualitatively by using semigroup theory and linear operator perturbation theory. The models include the classical Boltzmann equation for hard potentials with or without angular cutoff and the Landau equation with {γ≥q-2}. As an application, we show that the solutions to these two fundamental equations are asymptotically equivalent (mod time decay rate {t^{-5/4}}) as {tto∞} to that of the compressible Navier-Stokes equations for initial data around an equilibrium state.
Hypocoercivity for linear kinetic equations conserving mass
Dolbeault, Jean
2015-02-03
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining potential, so that the solution relaxes towards a unique equilibrium state. Our goal is to evaluate in an appropriately weighted $ L^2$ norm the exponential rate of convergence to the equilibrium. The method covers various models, ranging from diffusive kinetic equations like Vlasov-Fokker-Planck equations, to scattering models or models with time relaxation collision kernels corresponding to polytropic Gibbs equilibria, including the case of the linear Boltzmann model. In this last case and in the case of Vlasov-Fokker-Planck equations, any linear or superlinear growth of the potential is allowed. - See more at: http://www.ams.org/journals/tran/2015-367-06/S0002-9947-2015-06012-7/#sthash.ChjyK6rc.dpuf
Costa, Rafael S; Machado, Daniel; Rocha, Isabel; Ferreira, Eugénio C
2010-05-01
The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown. 2010 Elsevier Ireland Ltd. All rights reserved.
Kinetic Boltzmann, Vlasov and Related Equations
Sinitsyn, Alexander; Vedenyapin, Victor
2011-01-01
Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in
A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations
Liu, Chang; Xu, Kun; Sun, Quanhua; Cai, Qingdong
2016-06-01
Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier-Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region
Directory of Open Access Journals (Sweden)
Marta Cecilia Quicazán
2012-12-01
Full Text Available Legume soaking is an important practice in food processing; the characteristics of beverages and tofu mainly depend on this operation regarding soybeans. Peleg’s equation has been used in this work to describe the kinetics of water absorption and solid loss during soaking at 20°C, 40°C and 80°C. The moisture content of grain and solids in the remaining water was measured for 10 hours. Variance analysis and principal components analysis showed high fitting of kinetics to Peleg's equation for predicting both transference phenomena. This work found that the value of k1 (rate depended on temperature according to a polynomial function while k2 (capacity did not, meaning that the value of equilibrium moisture content was independent of soaking temperature. k1 had the minimum value for the migration of solids to soaking water at 40°C; this was related to lost solids’ high speed and the microbial degradation of carbohydrates; the values obtained for k2, showed that it was possible to lose total soluble solids at 20°C, while further migration of insoluble compounds occurred at 80°C.
Thermostatted kinetic equations as models for complex systems in physics and life sciences.
Bianca, Carlo
2012-12-01
Statistical mechanics is a powerful method for understanding equilibrium thermodynamics. An equivalent theoretical framework for nonequilibrium systems has remained elusive. The thermodynamic forces driving the system away from equilibrium introduce energy that must be dissipated if nonequilibrium steady states are to be obtained. Historically, further terms were introduced, collectively called a thermostat, whose original application was to generate constant-temperature equilibrium ensembles. This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities. The introduction of deterministic thermostats allows to model the onset of nonequilibrium stationary states that are typical of most real-world complex systems. The first part of the paper is focused on a general presentation of the main physical and mathematical definitions and tools: nonequilibrium phenomena, Gauss least constraint principle and Gaussian thermostats. The second part provides a review of a variety of thermostatted mathematical models in physics and life sciences, including Kac, Boltzmann, Jager-Segel and the thermostatted (continuous and discrete) kinetic for active particles models. Applications refer to semiconductor devices, nanosciences, biological phenomena, vehicular traffic, social and economics systems, crowds and swarms dynamics.
CHARACTERIZATIONS ON THE THIXOTROPY-LOOP TESTS USING UCM MODEL WITH A RATE-TYPE KINETIC EQUATION
Institute of Scientific and Technical Information of China (English)
Shu-xin Huang; Chuan-jing Lu
2006-01-01
The theoretical characterizations on the triangular-form thixotropy-loop tests of an LDPE melt (PE-FSB23D022/Q200) were conducted in the present paper by using a new thixotropy model, which is constituted by the upper convected Maxwell model and a rate-type kinetic equation. The new thixotropic Maxwell model can partially describe well three reported thixotropy-loop experiments by comparison with the previous calculations of the variant form of the thixotropy-type Huang model. It is noted that the stress deviations between the experiments and the predictions of the new thixotropic Maxwell model are much slighter than those deviations obtained by using the variant Huang model at the same condition, although both models include five parameters. The constitution of the new thixotropic Maxwell model is more reasonable than that of the variant Huang model.
Sánchez, Ana; Vázquez, José A; Quinteiro, Javier; Sotelo, Carmen G
2013-04-10
Real-time PCR is the most sensitive method for detection and precise quantification of specific DNA sequences, but it is not usually applied as a quantitative method in seafood. In general, benchmark techniques, mainly cycle threshold (Ct), are the routine method for quantitative estimations, but they are not the most precise approaches for a standard assay. In the present work, amplification data from European hake (Merluccius merluccius) DNA samples were accurately modeled by three sigmoid reparametrized equations, where the lag phase parameter (λc) from the Richards equation with four parameters was demonstrated to be the perfect substitute for Ct for PCR quantification. The concentrations of primers and probes were subsequently optimized by means of that selected kinetic parameter. Finally, the linear correlation among DNA concentration and λc was also confirmed.
Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.
2008-12-01
Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.
Maslov, Lev A.; Chebotarev, Vladimir I.
2017-02-01
The generalized logistic equation is proposed to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. This equation has the form dN(A)/dA = s dot (1-N(A)) dot N(A)q dot A-α, q>0q>0 and A>0A>0 is the size of an element of a structure, and α≥0. The equation contains two exponents α and q taking into account two important properties of elements of a system: their fractal geometry, and their ability to interact either to enhance or to damp the process of aggregation. The function N(A)N(A) can be understood as an approximation to the number of elements the size of which is less than AA. The function dN(A)/dAdN(A)/dA where N(A)N(A) is the general solution of this equation for q=1 is a product of an increasing bounded function and power-law function with stretched exponential cut-off. The relation with Tsallis non-extensive statistics is demonstrated by solving the generalized logistic equation for q>0q>0. In the case 01q>1 it models sub-additive structures. The Gutenberg-Richter (G-R) formula results from interpretation of empirical data as a straight line in the area of stretched exponent with small α. The solution is applied for modeling distribution of foreshocks and aftershocks in the regions of Napa Valley 2014, and Sumatra 2004 earthquakes fitting the observed data well, both qualitatively and quantitatively.
Wu, Zhen; Zhang, Xian; Zhou, Chunjiao; Pang, Jing-Lin; Zhang, Panyue
2017-02-22
Single-molecule aluminum salt AlCl3, medium polymerized polyaluminum chloride (PAC), and high polymerized polyaluminum chloride (HPAC) were prepared in a laboratory. The characteristics and coagulation properties of these prepared aluminum salts were investigated. The Langmuir, Freundlich, and Sips adsorption isotherms were first used to describe the adsorption neutralization process in coagulation, and the Boltzmann equation was used to fit the reaction kinetics of floc growth in flocculation. It was novel to find that the experimental data fitted well with the Sips and Boltzmann equation, and the significance of parameters in the equations was discussed simultaneously. Through the Sips equation, the adsorption neutralization reaction was proved to be spontaneous and the adsorption neutralization capacity was HPAC > PAC > AlCl3. Sips equation also indicated that the zeta potential of water samples would reach a limit with the increase of coagulant dosage, and the equilibrium zeta potential values were 30.25, 30.23, and 27.25 mV for AlCl3, PAC, and HPAC, respectively. The lower equilibrium zeta potential value of HPAC might be the reason why the water sample was not easy to achieve restabilization at a high coagulant dosage. Through the Boltzmann equation modeling, the maximum average floc size formed by AlCl3, PAC, and HPAC were 196.0, 188.0, and 203.6 μm, respectively, and the halfway time of reactions were 31.23, 17.08, and 9.55 min, respectively. The HPAC showed the strongest floc formation ability and the fastest floc growth rate in the flocculation process, which might be caused by the stronger adsorption and bridging functions of Alb and Alc contained in HPAC.
A novel fractional technique for the modified point kinetics equations
Directory of Open Access Journals (Sweden)
Ahmed E. Aboanber
2016-10-01
Full Text Available A fractional model for the modified point kinetics equations is derived and analyzed. An analytical method is used to solve the fractional model for the modified point kinetics equations. This methodical technique is based on the representation of the neutron density as a power series of the relaxation time as a small parameter. The validity of the fractional model is tested for different cases of step, ramp and sinusoidal reactivity. The results show that the fractional model for the modified point kinetics equations is the best representation of neutron density for subcritical and supercritical reactors.
Generalized Bloch-Wangsness-Redfield Kinetic Equations
Fatkullin, Nail
2011-01-01
We present a compact and general derivation of the generalized Bloch-Wangsness-Redfield kinetic equations for systems with the static spin Hamiltonian utilizing the concept of the Liouville space. We show that the assumptions of short correlation times and large heat capacity of the lattice are sufficient to derive the kinetic equations without the use of perturbation theory for the spin-lattice interaction operator. The perturbation theory is only applied for calculation of the kinetic coeff...
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.
Onsager reciprocity principle for kinetic models and kinetic schemes
Mahendra, Ajit Kumar
2013-01-01
Boltzmann equation requires some alternative simpler kinetic model like BGK to replace the collision term. Such a kinetic model which replaces the Boltzmann collision integral should preserve the basic properties and characteristics of the Boltzmann equation and comply with the requirements of non equilibrium thermodynamics. Most of the research in development of kinetic theory based methods have focused more on entropy conditions, stability and ignored the crucial aspect of non equilibrium thermodynamics. The paper presents a new kinetic model formulated based on the principles of non equilibrium thermodynamics. The new kinetic model yields correct transport coefficients and satisfies Onsager's reciprocity relationship. The present work also describes a novel kinetic particle method and gas kinetic scheme based on this linkage of non-equilibrium thermodynamics and kinetic theory. The work also presents derivation of kinetic theory based wall boundary condition which complies with the principles of non-equili...
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
A Pseudo-Kinetic Approach for Helmholtz Equation
Institute of Scientific and Technical Information of China (English)
Radjesvarane ALEXANDRE; Jie LIAO
2013-01-01
A lattice Boltzmann type pseudo-kinetic model for a non-homogeneous Helmholtz equation is derived in this paper.Numerical results for some model problems show the robustness and efficiency of this lattice Boltzmann type pseudo-kinetic scheme.The computation at each site is determined only by local parameters,and can be easily adapted to solve multiple scattering problems with many scatterers or wave propagation in nonhomogeneous medium without increasing the computational cost.
Fractional neutron point kinetics equations for nuclear reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Espinosa-Paredes, Gilberto, E-mail: gepe@xanum.uam.mx [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico); Polo-Labarrios, Marco-A. [Area de Ingenieria en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico); Espinosa-Martinez, Erick-G. [Retorno Quebec 6, Col. Burgos de Cuernavaca 62580, Temixco, Mor. (Mexico); Valle-Gallegos, Edmundo del [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Av. Instituto Politecnico Nacional s/n, Col. San Pedro Zacatenco, Mexico, D.F. 07738 (Mexico)
2011-02-15
The fractional point-neutron kinetics model for the dynamic behavior in a nuclear reactor is derived and analyzed in this paper. The fractional model retains the main dynamic characteristics of the neutron motion in which the relaxation time associated with a rapid variation in the neutron flux contains a fractional order, acting as exponent of the relaxation time, to obtain the best representation of a nuclear reactor dynamics. The physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. The numerical approximation to the solution of the fractional neutron point kinetics model, which can be represented as a multi-term high-order linear fractional differential equation, is calculated by reducing the problem to a system of ordinary and fractional differential equations. The numerical stability of the fractional scheme is investigated in this work. Results for neutron dynamic behavior for both positive and negative reactivity and for different values of fractional order are shown and compared with the classic neutron point kinetic equations. Additionally, a related review with the neutron point kinetics equations is presented, which encompasses papers written in English about this research topic (as well as some books and technical reports) published since 1940 up to 2010.
Modeling of Reactor Kinetics and Dynamics
Energy Technology Data Exchange (ETDEWEB)
Matthew Johnson; Scott Lucas; Pavel Tsvetkov
2010-09-01
In order to model a full fuel cycle in a nuclear reactor, it is necessary to simulate the short time-scale kinetic behavior of the reactor as well as the long time-scale dynamics that occur with fuel burnup. The former is modeled using the point kinetics equations, while the latter is modeled by coupling fuel burnup equations with the kinetics equations. When the equations are solved simultaneously with a nonlinear equation solver, the end result is a code with the unique capability of modeling transients at any time during a fuel cycle.
Genuinely Multidimensional Kinetic Scheme For Euler Equations
Tiwari, Praveer
2015-01-01
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using polar coordinates. The aim is to develop a framework which is genuinely multidimensional and can be implemented with different methodologies, no matter whether it is in finite difference, finite volume or finite element form. There is a considerable improvement in capturing shocks and other discontinuities. Also, since the method is multidimensional, the flow features are captured isotropically. The method is further extended to second order using 'Arc of Approach' concept. The framework is developed as a finite difference method (called as GINEUS) and is tested on the benchmark test cases. The results are compared against Kinetic Flux Vector Splitting Method.
Berglund, Martin; Sunnåker, Mikael; Adiels, Martin; Jirstrand, Mats; Wennberg, Bernt
2012-12-01
Non-linear mixed effects (NLME) models represent a powerful tool to simultaneously analyse data from several individuals. In this study, a compartmental model of leucine kinetics is examined and extended with a stochastic differential equation to model non-steady-state concentrations of free leucine in the plasma. Data obtained from tracer/tracee experiments for a group of healthy control individuals and a group of individuals suffering from diabetes mellitus type 2 are analysed. We find that the interindividual variation of the model parameters is much smaller for the NLME models, compared to traditional estimates obtained from each individual separately. Using the mixed effects approach, the population parameters are estimated well also when only half of the data are used for each individual. For a typical individual, the amount of free leucine is predicted to vary with a standard deviation of 8.9% around a mean value during the experiment. Moreover, leucine degradation and protein uptake of leucine is smaller, proteolysis larger and the amount of free leucine in the body is much larger for the diabetic individuals than the control individuals. In conclusion, NLME models offers improved estimates for model parameters in complex models based on tracer/tracee data and may be a suitable tool to reduce data sampling in clinical studies.
Kiviharju, Kristiina; Salonen, Kalle; Leisola, Matti; Eerikäinen, Tero
2006-11-10
This study focuses on comparing different kinetic growth models and the use of neural networks in the batch cultivation of Streptomyces peucetius var. caesius producing epsilon-rhodomycinone. Contois, Monod and Teissier microbial growth models were used as well as the logistic growth modeling approach, which was found best in the simulations of growth and glucose consumption in the batch growth phase. The lag phase was included in the kinetic model with a CO2 trigger and a delay factor. Substrate consumption and product formation were included as Luedeking-Piret and logistic type equations, respectively. Biomass formation was modeled successfully with a 6-8-2 network, and the network was capable of biomass prediction with an R2-value of 0.983. Epsilon-rhodomycinone production was successfully modeled with a recursive 8-3-1 network capable of epsilon-rhodomycinone prediction with an R2-value of 0.903. The predictive power of the neural networks was superior to the kinetic models, which could not be used in predictive modeling of arbitrary batch cultivations.
Avissar, Roni; Chen, Fei
1993-01-01
Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes
Avissar, Roni; Chen, Fei
1993-01-01
Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes
Abedi-Varaki, Mehdi; Ganjovi, Alireza; Shojaei, Fahimeh; Hassani, Zahra
2015-01-01
In this work, a zero-dimensional kinetics model is used to study the temporal behavior of different species such as charged particles, radicals and excited states inside a Dielectric Barrier Discharge plasma reactor. It is shown that, the reactor significantly reduces the concentration of nitrogen monoxide as an environmental pollutant. After a drastic increase, a decrease in the concentration of the NO2 molecules inside the reactor is seen. Nitrogen monoxide molecules with a very low concentration are produced inside the reactor and its quick conversion to other products is proved. The obtained results are compared with the existing experimental and simulation findings, whenever possible.
Directory of Open Access Journals (Sweden)
Czerw Katarzyna
2016-01-01
Full Text Available The aim of this study was to investigate the ability of kinetic equations to describe the sorption kinetics and expansion rate of solid coal samples. In order to address his issue the sorption kinetics of methane and carbon dioxide on bituminous coals were studied. At the same time, the changes occurring in the sample’s overall dimensions, which accompanied sorption processes, were monitored. Experiments were carried out at high pressure by means of the volumetric method on a cubicoid solid samples. Several literature-based modeling approaches and equations are proposed to fit the kinetic curves of gas deposition, as well as the adequate kinetics of coal swelling. First equation represents the traditional approach to interpret experimental data in terms of fast and slow sorption process and consider the combination of two first-order rate functions. The other empirical kinetic equations are: the pseudo-second-order kinetic equation (PSOE, Elovich equation and the stretched exponential equation (SE. Two of the four equations are suitable to describe the kinetics of methane and carbon dioxide sorption and have been successfully used to quantify the observed dilatometric phenomena rates. The stretched exponential equation gave the best fit to the experimental data.
Similarities and Differences Between Freundlich Kinetic Equation and Two—Constant Equation
Institute of Scientific and Technical Information of China (English)
ZHANGZENGQIANG; ZHANGYIPING
1999-01-01
A mathematical expression of Freundlich kinetic equation,lnS=A'+B'lnt,is presented,and the physical meanings of its parameters are indicated.Although the Freundlich kinetic equation and the two-constant equation are the same in the form,the derivation of the Freundlich kinetic equation is precise,while the derivation of the two-constant equation has some contradictions and is unreasonable,And it is suggested that the Freundlich kinetic equation should have prority over the two-constant equation to be used.
Neutrino quantum kinetic equations: The collision term
Blaschke, Daniel N.; Cirigliano, Vincenzo
2016-08-01
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.
Neutrino Quantum Kinetic Equations: The Collision Term
Blaschke, Daniel N
2016-01-01
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.
Probability representation of kinetic equation for open quantum system
Man'ko, V I; Shchukin, E V
2003-01-01
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
A relativistic correlationless kinetic equation with radiation reaction fully incorporated
Lai, H. M.
1984-06-01
The Landau-Lifshitz expression for the Lorentz-Dirac equation is used to derive a relativistic correlationless kinetic equation for a system of electrons with radiation reaction fully incorporated. Various situations and possible applications are discussed.
Herschlag, Gregory J; Mitran, Sorin; Lin, Guang
2015-06-21
We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finite-range spatial correlation. Each approximation within the hierarchy is a set of ordinary differential equations that considers spatial correlations of varying lattice distance; the assumption is that the full system will have finite spatial correlations and thus the behavior of the models within the hierarchy will approach that of the full system. We provide evidence of this convergence in the context of one- and two-dimensional numerical examples. Lower levels within the hierarchy that consider shorter spatial correlations are shown to be up to three orders of magnitude faster than traditional kinetic Monte Carlo methods (KMC) for one-dimensional systems, while predicting similar system dynamics and steady states as KMC methods. We then test the hierarchy on a two-dimensional model for the oxidation of CO on RuO2(110), showing that low-order truncations of the hierarchy efficiently capture the essential system dynamics. By considering sequences of models in the hierarchy that account for longer spatial correlations, successive model predictions may be used to establish empirical approximation of error estimates. The hierarchy may be thought of as a class of generalized phenomenological kinetic models since each element of the hierarchy approximates the master equation and the lowest level in the hierarchy is identical to a simple existing phenomenological kinetic models.
Institute of Scientific and Technical Information of China (English)
M. Rafizadeh; H. Ghasemi; V. Haddadi-Asl
2006-01-01
Due to its mechanical properties and ease of use, vinyl ester resin is enjoying increasing consideration. This resin normally is produced by reaction between epoxy resin and unsaturated carboxylic acid. In the present study, bis-phenol A based epoxy resin and methacrylic acid was used to produce vinyl ester resin. The reaction was conducted under both stoichiometric and non-stoichiometric conditions in the presence of triphenylphosphine as catalyst. The stoichiometric and non-stoichiometric experiments were conducted at 95, 100, 105 and 110℃ and at 90 and 95℃, respectively. The first order rate equation and mechanism based rate equation were examined. Parameters are evaluated by least square method. A comparison of mechanism based rate equation and experimental data show an excellent agreement. Finally, Arrhenius equation and activation energy were presented.
On Some Properties of the Landau Kinetic Equation
Bobylev, Alexander; Gamba, Irene; Potapenko, Irina
2015-12-01
We discuss some general properties of the Landau kinetic equation. In particular, the difference between the "true" Landau equation, which formally follows from classical mechanics, and the "generalized" Landau equation, which is just an interesting mathematical object, is stressed. We show how to approximate solutions to the Landau equation by the Wild sums. It is the so-called quasi-Maxwellian approximation related to Monte Carlo methods. This approximation can be also useful for mathematical problems. A model equation which can be reduced to a local nonlinear parabolic equation is also constructed in connection with existence of the strong solution to the initial value problem. A self-similar asymptotic solution to the Landau equation for large v and t is discussed in detail. The solution, earlier confirmed by numerical experiments, describes a formation of Maxwellian tails for a wide class of initial data concentrated in the thermal domain. It is shown that the corresponding rate of relaxation (fractional exponential function) is in exact agreement with recent mathematically rigorous estimates.
Modelling heart rate kinetics.
Zakynthinaki, Maria S
2015-01-01
The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise). Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual's cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects) but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women).
Modelling heart rate kinetics.
Directory of Open Access Journals (Sweden)
Maria S Zakynthinaki
Full Text Available The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise. Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual's cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women.
Zakynthinaki, Maria S.
2015-01-01
The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise). Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual’s cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects) but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women). PMID:25876164
Regularized Structural Equation Modeling.
Jacobucci, Ross; Grimm, Kevin J; McArdle, John J
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.
Jahandar Lashaki, Masoud; Fayaz, Mohammadreza; Niknaddaf, Saeid; Hashisho, Zaher
2012-11-30
This paper investigates the effect of the kinetic diameter (KD) of the reference adsorbate on the accuracy of the Dubinin-Radushkevich (D-R) equation for predicting the adsorption isotherms of organic vapors on microporous activated carbon. Adsorption isotherms for 13 organic compounds on microporous beaded activated carbon were experimentally measured, and predicted using the D-R model and affinity coefficients. The affinity coefficients calculated based on molar volumes, molecular polarizabilities, and molecular parachors were used to predict the isotherms based on four reference compounds (4.3≤KD≤6.8 Å). The results show that the affinity coefficients are independent of the calculation method if the reference and test adsorbates are from the same organic group. Choosing a reference adsorbate with a KD similar to that of the test adsorbate results in better prediction of the adsorption isotherm. The relative error between the predicted and the measured adsorption isotherms increases as the absolute difference in the kinetic diameters of the reference and test adsorbates increases. Finally, the proposed hypothesis was used to explain reports of inconsistent findings among published articles. The results from this study are important because they allow a more accurate prediction of adsorption capacities of adsorbents which allow for better design of adsorption systems.
Kinetic equation for a gas with attractive forces as a functional equation
Directory of Open Access Journals (Sweden)
Ryszard Wojnar
2009-04-01
Full Text Available Diffusion problems studied in the time scale comparable with time of particles collision lead to kinetic equations which for step-wise potentials are functional equations in the velocity space. After a description of meaning of diffusion in biology and survey of derivation of kinetic equations by projective operator method, we pay an attention to the Lorentz gas with step potential. The gas is composed of $N$ particles: $N-1$ of which are immovable between $N-1$ immovable particles-scatterers, particle number 1 is moving, and we describe its movement by means of one-particle distribution function satisfying a kinetic equation. Solutions of the kinetic equation for some simple potentials are given. We derive also a kinetic equation for one-dimensional Lorentz gas, which is a functional equation.
A boundary matching micro/macro decomposition for kinetic equations
Lemou, Mohammed
2010-01-01
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distribution fonction $f$ in all its domain as the sum of a Maxwellian adapted to the boundary (which is not the usual Maxwellian associated with $f$) and a reminder kinetic part. This Maxwellian is defined such that its 'incoming' velocity moments coincide with the 'incoming' velocity moments of the distribution function. Important consequences of this strategy are the following. i) No artificial boundary condition is needed in the micro/macro models and the exact boundary condition on $f$ is naturally transposed to the macro part of the model. ii) It provides a new class of the so-called 'Asymptotic preserving' (AP) numerical schemes: such schemes are consistent with the original kinetic equation for all fixed positive value of the Knudsen number $\\eps$, and if $\\eps \\to 0 $ with fixed numerical parameters then these schemes degenerate into ...
On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity
Directory of Open Access Journals (Sweden)
Nikolai N. Bogoliubov (Jr.
2007-01-01
Full Text Available A two-component particle model of Boltzmann-Vlasov type kinetic equations in the form of special nonlinear integro-differential hydrodynamic systems on an infinite-dimensional functional manifold is discussed. We show that such systems are naturally connected with the nonlinear kinetic Boltzmann-Vlasov equations for some one-dimensional particle flows with pointwise interaction potential between particles. A new type of hydrodynamic two-component Benney equations is constructed and their Hamiltonian structure is analyzed.
Metamaterial characterization using Boltzmann's kinetic equation for electrons
DEFF Research Database (Denmark)
Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.
2013-01-01
Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows the r...
Conformational Nonequilibrium Enzyme Kinetics: Generalized Michaelis-Menten Equation.
Piephoff, D Evan; Wu, Jianlan; Cao, Jianshu
2017-08-03
In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. On the basis of a discrete kinetic network model, we use an integrated probability flux balance method to derive the cNESS turnover rate for a conformation-modulated enzymatic reaction. The traditional Michaelis-Menten (MM) rate equation is extended to a generalized form, which includes non-MM corrections induced by conformational population currents within combined cyclic kinetic loops. When conformational detailed balance is satisfied, the turnover rate reduces to the MM functional form, explaining its general validity. For the first time, a one-to-one correspondence is established between non-MM terms and combined cyclic loops with unbalanced conformational currents. Cooperativity resulting from nonequilibrium conformational dynamics can be achieved in enzymatic reactions, and we provide a novel, rigorous means of predicting and characterizing such behavior. Our generalized MM equation affords a systematic approach for exploring cNESS enzyme kinetics.
Kinetic derivation of a Hamilton-Jacobi traffic flow model
Borsche, Raul; Kimathi, Mark
2012-01-01
Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow equations leads to different types of equations: in certain situations modified Aw-Rascle equations are obtained. On the other hand, for several choices of kinetic parameters new Hamilton-Jacobi type traffic equations are found. Associated microscopic models are discussed and numerical experiments are presented discussing several situations for highway traffic and comparing the different models.
Solution of the reactor point kinetics equations by MATLAB computing
Directory of Open Access Journals (Sweden)
Singh Sudhansu S.
2015-01-01
Full Text Available The numerical solution of the point kinetics equations in the presence of Newtonian temperature feedback has been a challenging issue for analyzing the reactor transients. Reactor point kinetics equations are a system of stiff ordinary differential equations which need special numerical treatments. Although a plethora of numerical intricacies have been introduced to solve the point kinetics equations over the years, some of the simple and straightforward methods still work very efficiently with extraordinary accuracy. As an example, it has been shown recently that the fundamental backward Euler finite difference algorithm with its simplicity has proven to be one of the most effective legacy methods. Complementing the back-ward Euler finite difference scheme, the present work demonstrates the application of ordinary differential equation suite available in the MATLAB software package to solve the stiff reactor point kinetics equations with Newtonian temperature feedback effects very effectively by analyzing various classic benchmark cases. Fair accuracy of the results implies the efficient application of MATLAB ordinary differential equation suite for solving the reactor point kinetics equations as an alternate method for future applications.
Fractional Diffusion Limit for Collisional Kinetic Equations
Mellet, Antoine
2010-08-20
This paper is devoted to diffusion limits of linear Boltzmann equations. When the equilibrium distribution function is a Maxwellian distribution, it is well known that for an appropriate time scale, the small mean free path limit gives rise to a diffusion equation. In this paper, we consider situations in which the equilibrium distribution function is a heavy-tailed distribution with infinite variance. We then show that for an appropriate time scale, the small mean free path limit gives rise to a fractional diffusion equation. © 2010 Springer-Verlag.
Kinetic Equations for Describing Phosphorus Transport
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
@@Studies on kinetics of adsorption and release of phosphorus by soil,a new field in soil chemistry,began only over ten years ago (He et al.,1989; Wang and Zhu,1988;Zhang and Zhang,1991; Lin,1989; Lin and Xue,1989; Jiang,1993; Xue et al.,1995;LU et al.,1997).
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Oxidative desulfurization: kinetic modelling.
Dhir, S; Uppaluri, R; Purkait, M K
2009-01-30
Increasing environmental legislations coupled with enhanced production of petroleum products demand, the deployment of novel technologies to remove organic sulfur efficiently. This work represents the kinetic modeling of ODS using H(2)O(2) over tungsten-containing layered double hydroxide (LDH) using the experimental data provided by Hulea et al. [V. Hulea, A.L. Maciuca, F. Fajula, E. Dumitriu, Catalytic oxidation of thiophenes and thioethers with hydrogen peroxide in the presence of W-containing layered double hydroxides, Appl. Catal. A: Gen. 313 (2) (2006) 200-207]. The kinetic modeling approach in this work initially targets the scope of the generation of a superstructure of micro-kinetic reaction schemes and models assuming Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) mechanisms. Subsequently, the screening and selection of above models is initially based on profile-based elimination of incompetent schemes followed by non-linear regression search performed using the Levenberg-Marquardt algorithm (LMA) for the chosen models. The above analysis inferred that Eley-Rideal mechanism describes the kinetic behavior of ODS process using tungsten-containing LDH, with adsorption of reactant and intermediate product only taking place on the catalyst surface. Finally, an economic index is presented that scopes the economic aspects of the novel catalytic technology with the parameters obtained during regression analysis to conclude that the cost factor for the catalyst is 0.0062-0.04759 US $ per barrel.
Kinetic equation for nonlinear resonant wave-particle interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
Metamaterial characterization using Boltzmann's kinetic equation for electrons
DEFF Research Database (Denmark)
Novitsky, Andrey; Zhukovsky, Sergei; Novitsky, D.;
2013-01-01
Statistical properties of electrons in metals are taken into consideration to describe the microscopic motion of electrons. Assuming degenerate electron gas in metal, we introduce the Boltzmann kinetic equation to supplement Maxwell's equations. The solution of these equations clearly shows the r...... the resonant behavior of electronic response to an external electromagnetic field. We demonstrate the approach for planar and circular geometries of the metamolecules....
Introduction to Kinetic Model Equations
2011-01-01
application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 ∗Dipartimento di Matematica del Politecnico di Milano Piazza Leonardo da Vinci 32...NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Dipartimento di Matematica del Politecnico di Milano Piazza Leonardo da Vinci 32, 20133 Milano
Kinetic and hydrodynamic models of chemotactic aggregation
Chavanis, Pierre-Henri
2007-01-01
We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean field Fokker-Planck equation governing the evolution of the distribution function of the system in phase space. By taking the successive moments of this kinetic equation and using a local thermodynamic equilibrium condition, we derive a set of hydrodynamic equations involving a damping term. In the limit of small frictions, we obtain a hyperbolic model describing the formation of network patterns (filaments) and in the limit of strong frictions we obtain a parabolic model which is a generalization of the standard Keller-Segel model describing the formation of clusters (clumps). Our approach connects and generalizes several models introduced in the chemotactic literature. We discuss the anal...
Directory of Open Access Journals (Sweden)
Sheidaei Behnaz
2015-06-01
Full Text Available In this work, a design equation was presented for a batch-recirculated photoreactor composed of a packed bed reactor (PBR with immobilised TiO2-P25 nanoparticle thin films on glass beads, and a continuous-flow stirred tank (CFST. The photoreactor was studied in order to remove C.I. Acid Orange 7 (AO7, a monoazo anionic dye from textile industry, by means of UV/TiO2 process. The effect of different operational parameters such as the initial concentration of contaminant, the volume of solution in CFST, the volumetric flow rate of liquid, and the power of light source in the removal efficiency were examined. A rate equation for the removal of AO7 is obtained by mathematical kinetic modelling. The results of reaction kinetic analysis indicate the conformity of removal kinetics with Langmuir-Hinshelwood model (kL-H = 0.74 mg L-1 min-1, Kads = 0.081 mg-1 L. The represented design equation obtained from mathematical kinetic modelling can properly predict the removal rate constant of the contaminant under different operational conditions (R2 = 0.963. Thus the calculated and experimental results are in good agreement with each other.
A nondissipative simulation method for the drift kinetic equation
Energy Technology Data Exchange (ETDEWEB)
Watanabe, Tomo-Hiko; Sugama, Hideo; Sato, Tetsuya
2001-07-01
With the aim to study the ion temperature gradient (ITG) driven turbulence, a nondissipative kinetic simulation scheme is developed and comprehensively benchmarked. The new simulation method preserving the time-reversibility of basic kinetic equations can successfully reproduce the analytical solutions of asymmetric three-mode ITG equations which are extended to provide a more general reference for benchmarking than the previous work [T.-H. Watanabe, H. Sugama, and T. Sato: Phys. Plasmas 7 (2000) 984]. It is also applied to a dissipative three-mode system, and shows a good agreement with the analytical solution. The nondissipative simulation result of the ITG turbulence accurately satisfies the entropy balance equation. Usefulness of the nondissipative method for the drift kinetic simulations is confirmed in comparisons with other dissipative schemes. (author)
Retarded versus time-nonlocal quantum kinetic equations
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Spicka, V.; Lipavsky, P. [Institute of Physics, Academy of Sciences, Praha (Czech Republic)
2000-07-01
The finite duration of the collisions in Fermionic systems as expressed by the retardation time in the non-Markovian Levinson equation is discussed in the quasiclassical limit. The separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levison equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other. (authors)
Modeling in applied sciences a kinetic theory approach
Pulvirenti, Mario
2000-01-01
Modeling complex biological, chemical, and physical systems, in the context of spatially heterogeneous mediums, is a challenging task for scientists and engineers using traditional methods of analysis Modeling in Applied Sciences is a comprehensive survey of modeling large systems using kinetic equations, and in particular the Boltzmann equation and its generalizations An interdisciplinary group of leading authorities carefully develop the foundations of kinetic models and discuss the connections and interactions between model theories, qualitative and computational analysis and real-world applications This book provides a thoroughly accessible and lucid overview of the different aspects, models, computations, and methodology for the kinetic-theory modeling process Topics and Features * Integrated modeling perspective utilized in all chapters * Fluid dynamics of reacting gases * Self-contained introduction to kinetic models * Becker–Doring equations * Nonlinear kinetic models with chemical reactions * Kinet...
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Enzyme Kinetics and the Michaelis-Menten Equation
Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee
2010-01-01
The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…
Gaussian kinetic model for granular gases.
Dufty, James W; Baskaran, Aparna; Zogaib, Lorena
2004-05-01
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal "homogeneous cooling solution" after a few collisions. The homogeneous cooling solution (HCS) is studied in some detail and the exact solution is compared with known results for the hard sphere Boltzmann equation. It is shown that all qualitative features of the HCS, including the nature of overpopulation at large velocities, are reproduced by the kinetic model. It is also shown that all the transport coefficients are in excellent agreement with those from the Boltzmann equation. Also, the model is specialized to one having a velocity independent collision frequency and the resulting HCS and transport coefficients are compared to known results for the Maxwell model. The potential of the model for the study of more complex spatially inhomogeneous states is discussed.
Energy Technology Data Exchange (ETDEWEB)
Westbrook, C.K.; Pitz, W.J. [Lawrence Livermore National Laboratory, CA (United States)
1993-12-01
This project emphasizes numerical modeling of chemical kinetics of combustion, including applications in both practical combustion systems and in controlled laboratory experiments. Elementary reaction rate parameters are combined into mechanisms which then describe the overall reaction of the fuels being studied. Detailed sensitivity analyses are used to identify those reaction rates and product species distributions to which the results are most sensitive and therefore warrant the greatest attention from other experimental and theoretical research programs. Experimental data from a variety of environments are combined together to validate the reaction mechanisms, including results from laminar flames, shock tubes, flow systems, detonations, and even internal combustion engines.
Bai, Shirong; Skodje, Rex T
2017-08-17
A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H2 combustion model.
Kinetic Equations of Potassium Desorption and the Application of Equation Constants
Institute of Scientific and Technical Information of China (English)
LUEXIAO－NAN; LUYUN－FU
1995-01-01
Elovich,parabolic diffusion,power function and exponential equations were used to describe K desorption kinetics of 12 soils in a constant electric field of electro-ultrafiltration(EUF),Results showed that the Elovich,parabolic diffusion and power function equations could describe K desorption kinetics well owing to their high correlation coefficients and low standard errors;but the exponential equation was not suitable to be used in this study due to its relatively low correlation coefficients and relatively high standard errors.This work established successfully the relationships between the constants(slope or intercept)of kinetic equations and the barley responses to K fertilizer in the multiple-site field experiments and K-supplying status of soilsk,the constants of Elovich,parabolic diffusion and power function equations were very significantly or significantly correlated to the soil available K,relative yield of barley and K uptake of barley in NP plot.It was suggested that the kinetic equation constants could be used to estimate K-supplying power of soils.
Energy Technology Data Exchange (ETDEWEB)
Silva, Milena Wollmann da; Vilhena, Marco Tullio M.B.; Bodmann, Bardo Ernst J.; Vasques, Richard, E-mail: milena.wollmann@ufrgs.br, E-mail: vilhena@mat.ufrgs.br, E-mail: bardobodmann@ufrgs.br, E-mail: richard.vasques@fulbrightmail.org [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2015-07-01
The neutron point kinetics equation, which models the time-dependent behavior of nuclear reactors, is often used to understand the dynamics of nuclear reactor operations. It consists of a system of coupled differential equations that models the interaction between (i) the neutron population; and (II) the concentration of the delayed neutron precursors, which are radioactive isotopes formed in the fission process that decay through neutron emission. These equations are deterministic in nature, and therefore can provide only average values of the modeled populations. However, the actual dynamical process is stochastic: the neutron density and the delayed neutron precursor concentrations vary randomly with time. To address this stochastic behavior, Hayes and Allen have generalized the standard deterministic point kinetics equation. They derived a system of stochastic differential equations that can accurately model the random behavior of the neutron density and the precursor concentrations in a point reactor. Due to the stiffness of these equations, this system was numerically implemented using a stochastic piecewise constant approximation method (Stochastic PCA). Here, we present a study of the influence of stochastic fluctuations on the results of the neutron point kinetics equation. We reproduce the stochastic formulation introduced by Hayes and Allen and compute Monte Carlo numerical results for examples with constant and time-dependent reactivity, comparing these results with stochastic and deterministic methods found in the literature. Moreover, we introduce a modified version of the stochastic method to obtain a non-stiff solution, analogue to a previously derived deterministic approach. (author)
A tool model for predicting atmospheric kinetics with sensitivity analysis
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A package( a tool model) for program of predicting atmospheric chemical kinetics with sensitivity analysis is presented. The new direct method of calculating the first order sensitivity coefficients using sparse matrix technology to chemical kinetics is included in the tool model, it is only necessary to triangularize the matrix related to the Jacobian matrix of the model equation. The Gear type procedure is used to integrate amodel equation and its coupled auxiliary sensitivity coefficient equations. The FORTRAN subroutines of the model equation, the sensitivity coefficient equations, and their Jacobian analytical expressions are generated automatically from a chemical mechanism. The kinetic representation for the model equation and its sensitivity coefficient equations, and their Jacobian matrix is presented. Various FORTRAN subroutines in packages, such as SLODE, modified MA28, Gear package, with which the program runs in conjunction are recommended.The photo-oxidation of dimethyl disulfide is used for illustration.
Institute of Scientific and Technical Information of China (English)
CHEN Ping; LU Zu-shun; YU Da-shu; HU Li-jiang
2005-01-01
Based on three typical mechanisms (second-order, third-order and competitive mechanisms) for the curing reactions of the epoxy resins with amines, a pair of the kinetic equations (for primary and secondary aminations) was presented to explain the uniformity and relationship among the three different kinetic mechanisms of the reactions. The presented macro-equations were deduced from the kinetic micro-equations by the statistics method. And the constitutive equations were verified by experimental data at different reaction times and temperatures (95℃, 60℃ and 39℃), taking diglycidyl ether of bisphenol A (DGEBA) /ethyleneamine (EA) as a model.
Bifurcation in kinetic equation for interacting Fermi systems
Morawetz, Klaus
2003-06-01
The recently derived nonlocal quantum kinetic equation for dense interacting Fermi systems combines time derivatives with finite time stepping known from the logistic mapping. This continuous delay differential equation is a consequence of the microscopic delay time representing the dynamics of the deterministic chaotic system. The responsible delay time is explicitly calculated and discussed for short-range correlations. As a novel feature oscillations in the time evolution of the distribution function itself appear and bifurcations up to chaotic behavior occur. The temperature and density conditions are presented where such oscillations and bifurcations arise indicating an onset of phase transition.
On the drift kinetic equation driven by plasma flows
Energy Technology Data Exchange (ETDEWEB)
Shaing, K C [Plasma and Space Science Center and ISAPS, National Cheng Kung University, Tainan 70101, Taiwan (China); Department of Engineering Physics, University of Wisconsin, Madison, WI 53706 (United States)
2010-07-15
A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators. (brief communication)
Directory of Open Access Journals (Sweden)
Pavithra Sivasamy
Full Text Available A mathematical model of biotransformation of D-methionine into L-methionine in the cascade of the enzymes such as, D-amino acid oxidase (D-AAO, L-phenylalanine dehydrogenase (L-PheDH and formate dehydrogenase (FDH is discussed. The model is based on a system of coupled nonlinear reaction equations under non steady-state conditions for biochemical reactions occurring in the batch reactor that describes the substrate and product concentration within the catalyst. Simple analytical expressions for the concentration of substrate and product have been derived for all values of reaction parameters using the new homotopy perturbation method (NHPM. Enzyme reaction rate in terms of concentration and kinetic parameters are also reported. The analytical results are also compared with experimental and numerical ones and a good agreement is obtained. The graphical procedure for estimating the kinetic parameters is also reported.
Açıkyıldız, Metin; Gürses, Ahmet; Güneş, Kübra; Yalvaç, Duygu
2015-11-01
The present study was designed to compare the linear and non-linear methods used to check the compliance of the experimental data corresponding to the isotherm models (Langmuir, Freundlich, and Redlich-Peterson) and kinetics equations (pseudo-first order and pseudo-second order). In this context, adsorption experiments were carried out to remove an anionic dye, Remazol Brillant Yellow 3GL (RBY), from its aqueous solutions using a commercial activated carbon as a sorbent. The effects of contact time, initial RBY concentration, and temperature onto adsorbed amount were investigated. The amount of dye adsorbed increased with increased adsorption time and the adsorption equilibrium was attained after 240 min. The amount of dye adsorbed enhanced with increased temperature, suggesting that the adsorption process is endothermic. The experimental data was analyzed using the Langmuir, Freundlich, and Redlich-Peterson isotherm equations in order to predict adsorption isotherm. It was determined that the isotherm data were fitted to the Langmuir and Redlich-Peterson isotherms. The adsorption process was also found to follow a pseudo second-order kinetic model. According to the kinetic and isotherm data, it was found that the determination coefficients obtained from linear method were higher than those obtained from non-linear method.
SBMLsqueezer: A CellDesigner plug-in to generate kinetic rate equations for biochemical networks
Directory of Open Access Journals (Sweden)
Schröder Adrian
2008-04-01
Full Text Available Abstract Background The development of complex biochemical models has been facilitated through the standardization of machine-readable representations like SBML (Systems Biology Markup Language. This effort is accompanied by the ongoing development of the human-readable diagrammatic representation SBGN (Systems Biology Graphical Notation. The graphical SBML editor CellDesigner allows direct translation of SBGN into SBML, and vice versa. For the assignment of kinetic rate laws, however, this process is not straightforward, as it often requires manual assembly and specific knowledge of kinetic equations. Results SBMLsqueezer facilitates exactly this modeling step via automated equation generation, overcoming the highly error-prone and cumbersome process of manually assigning kinetic equations. For each reaction the kinetic equation is derived from the stoichiometry, the participating species (e.g., proteins, mRNA or simple molecules as well as the regulatory relations (activation, inhibition or other modulations of the SBGN diagram. Such information allows distinctions between, for example, translation, phosphorylation or state transitions. The types of kinetics considered are numerous, for instance generalized mass-action, Hill, convenience and several Michaelis-Menten-based kinetics, each including activation and inhibition. These kinetics allow SBMLsqueezer to cover metabolic, gene regulatory, signal transduction and mixed networks. Whenever multiple kinetics are applicable to one reaction, parameter settings allow for user-defined specifications. After invoking SBMLsqueezer, the kinetic formulas are generated and assigned to the model, which can then be simulated in CellDesigner or with external ODE solvers. Furthermore, the equations can be exported to SBML, LaTeX or plain text format. Conclusion SBMLsqueezer considers the annotation of all participating reactants, products and regulators when generating rate laws for reactions. Thus, for
Seidi, M.; Behnia, S.; Khodabakhsh, R.
2014-09-01
Point reactor kinetics equations with one group of delayed neutrons in the presence of the time-dependent external neutron source are solved analytically during the start-up of a nuclear reactor. Our model incorporates the random nature of the source and linear reactivity variation. We establish a general relationship between the expectation values of source intensity and the expectation values of neutron density of the sub-critical reactor by ignoring the term of the second derivative for neutron density in neutron point kinetics equations. The results of the analytical solution are in good agreement with the results obtained with numerical solution.
Kinetic models with randomly perturbed binary collisions
Bassetti, Federico; Toscani, Giuseppe
2010-01-01
We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules, which include as particular cases models for wealth redistribution in an agent-based market or models for granular gases with a background heat bath. Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. We show that the characterization of these stationary solutions is of independent interest, since the same profiles are shown to be solutions of different evolution problems, both in the econophysics context and in the kinetic theory of rarefied gases.
Energy Technology Data Exchange (ETDEWEB)
Misguich, J.H
2004-04-01
As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.
Directory of Open Access Journals (Sweden)
Vijay K. Garg
1998-01-01
reason for the discrepancy on the pressure surface could be the presence of unsteady effects due to stator-rotor interaction in the experiments which are not modeled in the present computations. Prediction using the two-equation model is in general poorer than that using the zero-equation model, while the former requires at least 40% more computational resources.
Arino, O; Kimmel, M
1989-01-01
A model of cell cycle kinetics is proposed, which includes unequal division of cells, and a nonlinear dependence of the fraction of cells re-entering proliferation on the total number of cells in the cycle. The model is described by a nonlinear functional-integral equation. It is analyzed using the operator semigroup theory combined with classical differential equations approach. A complete description of the asymptotic behavior of the model is provided for a relatively broad class of nonlinearities. The nonnegative solutions either tend to a stable steady state, or to zero. The simplicity of the model makes it an interesting step in the analysis of dynamics of nonlinear structure populations.
Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation
Institute of Scientific and Technical Information of China (English)
Zhihui Li; Hanxin Zhang
2007-01-01
A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuumflow regimes can be presented on the basis of the kinetic Boltzmann-Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integration method can be developed and adopted to attack complex flows with different Mach numbers. HPF parallel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarily with massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuillechannel flow and pressure-driven gas flows in twodimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of microscale gas flows occuring in the Micro-Electro-Mechanical System (MEMS).
The H-theorem for the physico-chemical kinetic equations with explicit time discretization
Adzhiev, S. Z.; Melikhov, I. V.; Vedenyapin, V. V.
2017-09-01
There is demonstrated in the present paper, that the H-theorem in the case of explicit time discretization of the physico-chemical kinetic equations, generally speaking, is not valid. We prove the H-theorem, when the system of the physico-chemical kinetic equations with explicit time discretization has the form of non-linear analogue of the Markov process with doubly stochastic matrix, and for more general cases. In these cases the proof is reduced to the proof of the H-theorem for Markov chains. The simplest discrete velocity models of the Boltzmann equation with explicit time discretization -the Carleman and Broadwell models are discussed and the H-theorem for them in the case of discrete time is proved.
Causal kinetic equation of non-equilibrium plasmas
Directory of Open Access Journals (Sweden)
R. A. Treumann
2017-05-01
Full Text Available Statistical plasma theory far from thermal equilibrium is subject to Liouville's equation, which is at the base of the BBGKY hierarchical approach to plasma kinetic theory, from which, in the absence of collisions, Vlasov's equation follows. It is also at the base of Klimontovich's approach which includes single-particle effects like spontaneous emission. All these theories have been applied to plasmas with admirable success even though they suffer from a fundamental omission in their use of the electrodynamic equations in the description of the highly dynamic interactions in many-particle conglomerations. In the following we extend this theory to taking into account that the interaction between particles separated from each other at a distance requires the transport of information. Action needs to be transported and thus, in the spirit of the direct-interaction theory as developed by Wheeler and Feynman (1945, requires time. This is done by reference to the retarded potentials. We derive the fundamental causal Liouville equation for the phase space density of a system composed of a very large number of charged particles. Applying the approach of Klimontovich (1967, we obtain the retarded time evolution equation of the one-particle distribution function in plasmas, which replaces Klimontovich's equation in cases when the direct-interaction effects have to be taken into account. This becomes important in all systems where the distance between two points |Δq| ∼ ct is comparable to the product of observation time and light velocity, a situation which is typical in cosmic physics and astrophysics.
Kinetic equation for strongly interacting dense Fermi systems
Lipavsky, P; Spicka, V
2001-01-01
We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions. The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landau's quasiparticles in metals. The collisions are non-local in the spirit of Enskog's theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems. In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and th...
Kinetics Modeling of Cancer Immunology.
1986-05-09
CANCER IMMUNOLOGY -1 DTICS ELECTED SEP 9 8 UNITED STATES NAVAL ACADEMY ANNAPOLIS, MARYLAND V ,1986 %,e docment ha le approved for public A." I and sale...1986 4. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED KINETICS MODELING OF CANCER IMMUNOLOGY Final: 1985/1986 6. PERFORMING ORG. REPORT...137 (1986) "Kinetics Modeling of Cancer Immunology " A Trident Scholar Project Report by Midn I/C Scott Helmers, Class of 1986 United States Naval
Hybrid fluid/kinetic model for parallel heat conduction
Energy Technology Data Exchange (ETDEWEB)
Callen, J.D.; Hegna, C.C.; Held, E.D. [Univ. of Wisconsin, Madison, WI (United States)
1998-12-31
It is argued that in order to use fluid-like equations to model low frequency ({omega} < {nu}) phenomena such as neoclassical tearing modes in low collisionality ({nu} < {omega}{sub b}) tokamak plasmas, a Chapman-Enskog-like approach is most appropriate for developing an equation for the kinetic distortion (F) of the distribution function whose velocity-space moments lead to the needed fluid moment closure relations. Further, parallel heat conduction in a long collision mean free path regime can be described through a combination of a reduced phase space Chapman-Enskog-like approach for the kinetics and a multiple-time-scale analysis for the fluid and kinetic equations.
SBMLsqueezer 2: context-sensitive creation of kinetic equations in biochemical networks
DEFF Research Database (Denmark)
Draeger, Andreas; Zielinski, Daniel C.; Keller, Roland
2015-01-01
Background: The size and complexity of published biochemical network reconstructions are steadily increasing, expanding the potential scale of derived computational models. However, the construction of large biochemical network models is a laborious and error-prone task. Automated methods have...... during kinetic model construction would thus benefit from automated methods for rate law assignment. Results: We present a high-throughput algorithm to automatically suggest and create suitable rate laws based upon reaction type according to several criteria. The criteria for choices made...... simplified the network reconstruction process, but building kinetic models for these systems is still a manually intensive task. Appropriate kinetic equations, based upon reaction rate laws, must be constructed and parameterized for each reaction. The complex test-and-evaluation cycles that can be involved...
An equation of state for purely kinetic k-essence inspired by cosmic topological defects
Cordero, Ruben; Queijeiro, Alfonso
2016-01-01
We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter $w$ and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. Furthermore, we analyze the evolution of the luminosity distance $d_{L}$ with redshift $z$ by comparing (normalizing) it with the $\\Lambda$CDM model. Since the equation of state parameter is $z$-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczy\\'{n}ski test.
An equation of state for purely kinetic k-essence inspired by cosmic topological defects
Energy Technology Data Exchange (ETDEWEB)
Cordero, Ruben; Gonzalez, Eduardo L.; Queijeiro, Alfonso [Instituto Politecnico Nacional, Departamento de Fisica, Escuela Superior de Fisica y Matematicas, Ciudad de Mexico (Mexico)
2017-06-15
We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter w and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. We study the evolution of the scale factor and address the question of the possible existence of finite-time future singularities. Furthermore, we analyze the evolution of the luminosity distance d{sub L} with redshift z by comparing (normalizing) it with the ΛCDM model. Since the equation of state parameter is z-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczynski test. (orig.)
An equation of state for purely kinetic k-essence inspired by cosmic topological defects
Cordero, Rubén; González, Eduardo L.; Queijeiro, Alfonso
2017-06-01
We investigate the physical properties of a purely kinetic k-essence model with an equation of state motivated in superconducting membranes. We compute the equation of state parameter w and discuss its physical evolution via a nonlinear equation of state. Using the adiabatic speed of sound and energy density, we restrict the range of parameters of the model in order to have an acceptable physical behavior. We study the evolution of the scale factor and address the question of the possible existence of finite-time future singularities. Furthermore, we analyze the evolution of the luminosity distance dL with redshift z by comparing (normalizing) it with the Λ CDM model. Since the equation of state parameter is z-dependent the evolution of the luminosity distance is also analyzed using the Alcock-Paczyński test.
Crystallization Kinetics within a Generic Modelling Framework
DEFF Research Database (Denmark)
Meisler, Kresten Troelstrup; von Solms, Nicolas; Gernaey, Krist
2013-01-01
An existing generic modelling framework has been expanded with tools for kinetic model analysis. The analysis of kinetics is carried out within the framework where kinetic constitutive models are collected, analysed and utilized for the simulation of crystallization operations. A modelling...... procedure is proposed to gain the information of crystallization operation kinetic model analysis and utilize this for faster evaluation of crystallization operations....
Directory of Open Access Journals (Sweden)
Quevedo María
2010-10-01
Full Text Available Abstract Background Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease. Methods The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type. Results The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced. Conclusion The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.
Ocean swell within the kinetic equation for water waves
Badulin, Sergei I
2016-01-01
Effects of wave-wave interactions on ocean swell are studied. Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation at long times up to $10^6$ seconds are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring are discussed. Essential drop of wave energy (wave height) due to wave-wave interactions is found to be pronounced at initial stages of swell evolution (of order of 1000 km for typical parameters of the ocean swell). At longer times wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions.
Coupling coefficients and kinetic equation for Rossby waves in multi-layer ocean
Directory of Open Access Journals (Sweden)
T. Soomere
2003-01-01
Full Text Available The kinetic description of baroclinic Rossby waves in multi-layer model ocean is analysed. Explicit analytical expressions for the coupling coefficients describing energy exchange intensity between different modes are obtained and their main properties are established for the three-layer model. It is demonstrated that several types of interactions vanish in the case of simple vertical structures of the ocean, e.g. when all layers have equal depth. These cases correspond to a zero component of the eigenvectors of the potential vorticity equations. The kinetic equation always possesses a fully barotropic solution. If energy is concentrated in the baroclinic modes, the barotropic mode will necessarily be generated. Motion systems consisting of a superposition of the barotropic and a baroclinic mode always transfer energy to other baroclinic modes.
Generalized fractional kinetic equations involving generalized Struve function of the first kind
Directory of Open Access Journals (Sweden)
K.S. Nisar
2016-04-01
Full Text Available In recent paper Dinesh Kumar et al. developed a generalized fractional kinetic equation involving generalized Bessel function of first kind. The object of this paper is to derive the solution of the fractional kinetic equation involving generalized Struve function of the first kind. The results obtained in terms of generalized Struve function of first kind are rather general in nature and can easily construct various known and new fractional kinetic equations.
Directory of Open Access Journals (Sweden)
Grima Ramon
2009-10-01
Full Text Available Abstract Background Classical descriptions of enzyme kinetics ignore the physical nature of the intracellular environment. Main implicit assumptions behind such approaches are that reactions occur in compartment volumes which are large enough so that molecular discreteness can be ignored and that molecular transport occurs via diffusion. Though these conditions are frequently met in laboratory conditions, they are not characteristic of the intracellular environment, which is compartmentalized at the micron and submicron scales and in which active means of transport play a significant role. Results Starting from a master equation description of enzyme reaction kinetics and assuming metabolic steady-state conditions, we derive novel mesoscopic rate equations which take into account (i the intrinsic molecular noise due to the low copy number of molecules in intracellular compartments (ii the physical nature of the substrate transport process, i.e. diffusion or vesicle-mediated transport. These equations replace the conventional macroscopic and deterministic equations in the context of intracellular kinetics. The latter are recovered in the limit of infinite compartment volumes. We find that deviations from the predictions of classical kinetics are pronounced (hundreds of percent in the estimate for the reaction velocity for enzyme reactions occurring in compartments which are smaller than approximately 200 nm, for the case of substrate transport to the compartment being mediated principally by vesicle or granule transport and in the presence of competitive enzyme inhibitors. Conclusion The derived mesoscopic rate equations describe subcellular enzyme reaction kinetics, taking into account, for the first time, the simultaneous influence of both intrinsic noise and the mode of transport. They clearly show the range of applicability of the conventional deterministic equation models, namely intracellular conditions compatible with diffusive transport
Ocean swell within the kinetic equation for water waves
Badulin, Sergei I.; Zakharov, Vladimir E.
2017-06-01
Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation for long durations of up to 2 × 106 s are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov-Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring is discussed. Essential drop in wave energy (wave height) due to wave-wave interactions is found at the initial stages of swell evolution (on the order of 1000 km for typical parameters of the ocean swell). At longer times, wave-wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (synthetic aperture radar) data. At the same time, the relatively fast weakening of wave-wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow in relatively light winds.
Chemical kinetics and combustion modeling
Energy Technology Data Exchange (ETDEWEB)
Miller, J.A. [Sandia National Laboratories, Livermore, CA (United States)
1993-12-01
The goal of this program is to gain qualitative insight into how pollutants are formed in combustion systems and to develop quantitative mathematical models to predict their formation rates. The approach is an integrated one, combining low-pressure flame experiments, chemical kinetics modeling, theory, and kinetics experiments to gain as clear a picture as possible of the process in question. These efforts are focused on problems involved with the nitrogen chemistry of combustion systems and on the formation of soot and PAH in flames.
Comparison of Seven Kinetic Equations for K Release and Application of Kinetic Parameters
Institute of Scientific and Technical Information of China (English)
L(U) Xiao-Nan; XU Jian-Ming; MA Wan-Zhu; LU Yun-Fu
2007-01-01
Corn field experiments with two treatments, NP and NPK, where N in the form of urea, P in the form of calcium phosphate, and K in the form of KC1 were applied at rates of 187.5, 33.3, and 125 kg ha-1, respectively, on soils derived from Quaternary red clay were conducted in the hilly red soil region of Zhejiang Province, China. Plant grains and stalks were collected for determination of K content. Seven equations were used to describe the kinetics of K release from surface soil samples taken before the corn experiments under electric field strengths of 44.4 and 88.8 V cm-1 by means of electro-ultrafiltration (EUF) and to determine if their parameters had a practical application. The second-order and Elovich equations excellently described K release; the first-order, power function, and parabolic diffusion equations also described K release well; but the zero-order and exponential equations were not so good at reflecting K release. Five reference standards from the field experiments, including relative grain yield (yield of the NP treatment/yield of the NPK treatment), relative dry matter yield (dry matter of the NP treatment/dry matter of the NPK treatment), quantity of K uptake in the NP treatment (no K application), soil exchangeable K, and soil HNO3-soluble K, were used to test the effectiveness of equation parameters obtained from the slope or intercept of these equations. Correlations of the ymax (the maximum desorbable quantity of K) in the second-order equation and the constant b in the first-order and E lovich equations to all five reference standards were highly significant (P ≤ 0.01). The constant a in the power function equation was highly significant (P ≤ 0.01) for four of the five reference standards with the fifth being significant (P ≤ 0.05). The constant b in the parabolic equation was also significantly correlated (P ≤ 0.05) to the relative grain yield and soil HNO3-solublc K. These suggested that all of these parameters could be used to
Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation
Frost, W.; Harper, W. L.; Fichtl, G. H.
1975-01-01
Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Mean-flow results are compared with those given in a previous paper where the same problem was attacked using a Prandtl mixing-length hypothesis. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow. They highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient.
Kinetic Modeling of Biological Systems
Energy Technology Data Exchange (ETDEWEB)
Resat, Haluk; Petzold, Linda; Pettigrew, Michel F.
2009-04-21
The dynamics of how its constituent components interact define the spatio-temporal response of a natural system to stimuli. Modeling the kinetics of the processes that represent a biophysical system has long been pursued with the aim of improving our understanding of the studied system. Due to the unique properties of biological systems, in addition to the usual difficulties faced in modeling the dynamics of physical or chemical systems, biological simulations encounter difficulties that result from intrinsic multiscale and stochastic nature of the biological processes. This chapter discusses the implications for simulation of models involving interacting species with very low copy numbers, which often occur in biological systems and give rise to significant relative fluctuations. The conditions necessitating the use of stochastic kinetic simulation methods and the mathematical foundations of the stochastic simulation algorithms are presented. How the well-organized structural hierarchies often seen in biological systems can lead to multiscale problems, and possible ways to address the encountered computational difficulties are discussed. We present the details of the existing kinetic simulation methods, and discuss their strengths and shortcomings. A list of the publicly available kinetic simulation tools and our reflections for future prospects are also provided.
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
Proton-pumping mechanism of cytochrome c oxidase: A kinetic master-equation approach
Kim, Young C.; Hummer, Gerhard
2011-01-01
Cytochrome c oxidase (CcO) is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, CcO translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in CcO. Basic principles of the CcO proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the ative-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for CcO provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. PMID:21946020
Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach.
Kim, Young C; Hummer, Gerhard
2012-04-01
Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .
A bin integral method for solving the kinetic collection equation
Wang, Lian-Ping; Xue, Yan; Grabowski, Wojciech W.
2007-09-01
A new numerical method for solving the kinetic collection equation (KCE) is proposed, and its accuracy and convergence are investigated. The method, herein referred to as the bin integral method with Gauss quadrature (BIMGQ), makes use of two binwise moments, namely, the number and mass concentration in each bin. These two degrees of freedom define an extended linear representation of the number density distribution for each bin following Enukashvily (1980). Unlike previous moment-based methods in which the gain and loss integrals are evaluated for a target bin, the concept of source-bin pair interactions is used to transfer bin moments from source bins to target bins. Collection kernels are treated by bilinear interpolations. All binwise interaction integrals are then handled exactly by Gauss quadrature of various orders. In essence the method combines favorable features in previous spectral moment-based and bin-based pair-interaction (or flux) methods to greatly enhance the logic, consistency, and simplicity in the numerical method and its implementation. Quantitative measures are developed to rigorously examine the accuracy and convergence properties of BIMGQ for both the Golovin kernel and hydrodynamic kernels. It is shown that BIMGQ has a superior accuracy for the Golovin kernel and a monotonic convergence behavior for hydrodynamic kernels. Direct comparisons are also made with the method of Berry and Reinhardt (1974), the linear flux method of Bott (1998), and the linear discrete method of Simmel et al. (2002).
An integral representation of functions in gas-kinetic models
Perepelitsa, Misha
2016-08-01
Motivated by the theory of kinetic models in gas dynamics, we obtain an integral representation of lower semicontinuous functions on {{{R}}^d,} {d≥1}. We use the representation to study the problem of compactness of a family of the solutions of the discrete time BGK model for the compressible Euler equations. We determine sufficient conditions for strong compactness of moments of kinetic densities, in terms of the measures from their integral representations.
Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation
Ölschläger, M.; Wirth, G.; Smith, C. Morais; Hemmerich, A.
2010-01-01
Approximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas-Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-equation with this property and definite values of the kinetic energy, which suggests the term "kinetic Thomas-Fermi" (KTF) solutions. We point out that a large class of light-shift potentials gives ...
Construction of the simplest model to explain complex receptor activation kinetics
DEFF Research Database (Denmark)
Bywater, RP; Sorensen, A; Røgen, Peter;
2002-01-01
We study the mathematical solutions to the kinetic equations arising from various simple ligand-reactor models. Focusing on the prediction of the various models for the activity vs. concentration curve, we find that solutions to the kinetic equations arising from the so-called dimer model exibit...
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
From Langmuir kinetics to first- and second-order rate equations for adsorption.
Liu, Yu; Shen, Liang
2008-10-21
So far, the first- and second-order kinetic equations have been most frequently employed to interpret adsorption data obtained under various conditions, whereas the theoretical origins of these two equations still remain unknown. Using the Langmuir kinetics as a theoretical basis, this study showed that the Langmuir kinetics can be transformed to a polynomial expression of dtheta t /d t = k 1(theta e - theta t ) + k 2(theta e - theta t ) (2), a varying-order rate equation. The sufficient and necessary conditions for simplification of the Langmuir kinetics to the first- and second-order rate equations were put forward, which suggested that the relative magnitude of theta e over k 1/ k 2 governs the simplification of the Langmuir kinetics. In cases where k 1/ k 2 is greater than theta e or k 1/ k 2 is very close to theta e, adsorption kinetics would be reasonably described by the first-order rate equation, whereas the Langmuir kinetics would be reduced to the second-order equation only at k 1/ k 2 Langmuir kinetics indeed is determined by C 0. Detailed C 0-depedent boundary conditions for simplifying the Langmuir kinetics were also established and were verified by experimental data.
Kinetic Formulation of the Kohn-Sham Equations for ab initio Electronic Structure Calculations
Mendoza, M; Herrmann, H J
2013-01-01
We introduce a new approach to density functional theory based on kinetic theory, showing that the Kohn-Sham equations can be derived as a macroscopic limit of a suitable Boltzmann kinetic equation in the limit of small mean free path versus the typical scale of density gradients (Chapman-Enskog expansion). To derive the approach, we first write the Schr\\"odinger equation as a special case of a Boltzmann equation for a gas of quasi-particles, with the potential playing the role of an external source that generates and destroys particles, so as to drive the system towards the ground state. The ions are treated as classical particles, using the Born-Oppenheimer dynamics, or by imposing concurrent evolution with the electronic orbitals. In order to provide quantitative support to our approach, we implement a discrete (lattice) model and compute, the exchange and correlation energies of simple atoms, and the geometrical configuration of the methane molecule. Excellent agreement with values in the literature is fo...
A kinetic model for chemical neurotransmission
Ramirez-Santiago, Guillermo; Martinez-Valencia, Alejandro; Fernandez de Miguel, Francisco
Recent experimental observations in presynaptic terminals at the neuromuscular junction indicate that there are stereotyped patterns of cooperativeness in the fusion of adjacent vesicles. That is, a vesicle in hemifusion process appears on the side of a fused vesicle and which is followed by another vesicle in a priming state while the next one is in a docking state. In this talk we present a kinetic model for this morphological pattern in which each vesicle state previous to the exocytosis is represented by a kinetic state. This chain states kinetic model can be analyzed by means of a Master equation whose solution is simulated with the stochastic Gillespie algorithm. With this approach we have reproduced the responses to the basal release in the absence of stimulation evoked by the electrical activity and the phenomena of facilitation and depression of neuromuscular synapses. This model offers new perspectives to understand the underlying phenomena in chemical neurotransmission based on molecular interactions that result in the cooperativity between vesicles during neurotransmitter release. DGAPA Grants IN118410 and IN200914 and Conacyt Grant 130031.
Generalized kinetics of overall phase transition in terms of logistic equation
Avramov, I
2015-01-01
We summarize and to discuss briefly the geometrical practice of modeling attitudes so far popular in treating reaction kinetics of solid-state processes. The model equations existing in the literature have been explored to describe the thermal decomposition and crystallization data and are deeply questioned and analyzed showing that under such a simple algebraic representation, the reacting system is thus classified as a set of geometrical bodies (spheres) where each and every one reaction interface is represented by similar and smooth characteristics of reaction curve. It brings an unsolved question whether the sharp and even boundary factually exists or if it resides jointly just inside the global whole of the sample entirety preventing individual particles from having their individual reaction front. Most of the derived expressions are specified in an averaged generalization in terms of the three and two parameters equation (so called JMAK and SB models) characterized by a combination of power exponents m,...
Kinetic modelling of enzymatic starch hydrolysis
Bednarska, K.A.
2015-01-01
Kinetic modelling of enzymatic starch hydrolysis – a summary K.A. Bednarska The dissertation entitled ‘Kinetic modelling of enzymatic starch hydrolysis’ describes the enzymatic hydrolysis and kinetic modelling of liquefaction and saccharification of wheat starch. A
Some models for the adsorption kinetics of pesticides in soil
Leistra, M.; Dekkers, W.A.
1977-01-01
Three models describing adsorption‐desorption kinetics of pesticides in soil, that could be incorporated into computer programs on pesticide movement in soil, were discussed, the first model involved single first‐order rate equations for adsorption and desorption. Results from an analytical and a
3D Building Model Fitting Using A New Kinetic Framework
Brédif, Mathieu; Pierrot-Deseilligny, Marc; Maître, Henri
2008-01-01
We describe a new approach to fit the polyhedron describing a 3D building model to the point cloud of a Digital Elevation Model (DEM). We introduce a new kinetic framework that hides to its user the combinatorial complexity of determining or maintaining the polyhedron topology, allowing the design of a simple variational optimization. This new kinetic framework allows the manipulation of a bounded polyhedron with simple faces by specifying the target plane equations of each of its faces. It proceeds by evolving continuously from the polyhedron defined by its initial topology and its initial plane equations to a polyhedron that is as topologically close as possible to the initial polyhedron but with the new plane equations. This kinetic framework handles internally the necessary topological changes that may be required to keep the faces simple and the polyhedron bounded. For each intermediate configurations where the polyhedron looses the simplicity of its faces or its boundedness, the simplest topological mod...
Comparative Study on the Kinetic Equations of Potassium Release from Soils
Institute of Scientific and Technical Information of China (English)
LUXIAO－NAN; LUYUN－FU
1993-01-01
Elovich,two-constant,parabolic diffusion,exponential,second-order,first-order and zero-order equations were used to describe the kinetic characteristics of potassium desorption from six paddy soils of Zhejiang Province in a constant electric field (44.4V/cm) of EUF.Results showed that the second-order and Elovich equations could describe the potassium desorption kinetics best,as evidenced by the highest correlation coefficients (r) and the lowest standard errors (SE).The first-order,two-constant and parabolic diffusion equations also described the K desorption kinetics well,as showed by the relatively high correlation coefficients and relatively low standard errors.The zero-order equation did not describe the K desorption satisfactorily with a relatively low correlation coefficient and relatively high standard error.However,the exponential equation could not be used to describe the K desorption kinetics,due to the lowest correlation coefficient and the highest standarderror.
Kinetic equation for internal oxidation of Cu-Al alloy cylinders
Institute of Scientific and Technical Information of China (English)
Kexing Song; Jiandong Xing; Baohong Tian; Ping Liu; Qiming Dong
2005-01-01
The kinetics of internal oxidation of Cu-Al alloy cylinders, containing up to 2.214mol% Al, were investigated in the temperature range of 1023 K to 1273 K, and the depth of internal oxidation was measured in the microscopy. A kinetic equation was derived to describe the internal oxidation of Cu-Al alloy cylinders. For the internal oxidation of Cu-Al alloys employed in the synthesis of alumina dispersion strengthened copper, the kinetic equation can be simplified. The derived equation was checked experimentally by means of oxidation depth measurements and the results show that the derived equation is exact enough to describe the kinetics of internal oxidation of Cu-Al alloy cylinders. Based on this equation and the oxidation depth measurements, the permeability of oxygen in solid copper was obtained. Investigation also shows that there is no evidence for preferential diffusion along grain boundaries in the process of internal oxidation.
Energy Technology Data Exchange (ETDEWEB)
Schramm, Marcelo; Bodmann, Bardo E.J.; Vilhena, Marco T.M.B., E-mail: marceloschramm@hotmail.com, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Departamento de Engenharia Mecanica; Petersen, Claudio Z., E-mail: claudiopetersen@yahoo.com.br [Universidade Federal de Pelotas (UFPel), RS (Brazil). Departamento de Matematica; Alvim, Antonio C.M., E-mail: alvim@nuclear.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto Alberto Luiz Coimbra de Pos-Graduacao e Pesquisa em Engenharia
2013-07-01
Following the quest to find analytical solutions, we extend the methodology applied successfully to timely fractional neutron point kinetics (FNPK) equations by adding the effects of temperature. The FNPK equations with temperature feedback correspond to a nonlinear system and “stiff” type for the neutron density and the concentration of delayed neutron precursors. These variables determine the behavior of a nuclear reactor power with time and are influenced by the position of control rods, for example. The solutions of kinetics equations provide time information about the dynamics in a nuclear reactor in operation and are useful, for example, to understand the power fluctuations with time that occur during startup or shutdown of the reactor, due to adjustments of the control rods. The inclusion of temperature feedback in the model introduces an estimate of the transient behavior of the power and other variables, which are strongly coupled. Normally, a single value of reactivity is used across the energy spectrum. Especially in case of power change, the neutron energy spectrum changes as well as physical parameters such as the average cross sections. However, even knowing the importance of temperature effects on the control of the reactor power, the character of the set of nonlinear equations governing this system makes it difficult to obtain a purely analytical solution. Studies have been published in this sense, using numerical approaches. Here the idea is to consider temperature effects to make the model more realistic and thus solve it in a semi-analytical way. Therefore, the main objective of this paper is to obtain an analytical representation of fractional neutron point kinetics equations with temperature feedback, without having to resort to approximations inherent in numerical methods. To this end, we will use the decomposition method, which has been successfully used by the authors to solve neutron point kinetics problems. The results obtained will
The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models
Hesse, Michael; Birn, Joachim
2011-01-01
Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.
Double perturbation series in the differential equations of enzyme kinetics
Fraser, Simon J.
1998-07-01
The connection between combined singular and ordinary perturbation methods and slow-manifold theory is discussed using the Michaelis-Menten model of enzyme catalysis as an example. This two-step mechanism is described by a planar system of ordinary differential equations (ODEs) with a fast transient and a slow "steady-state" decay mode. The systems of scaled nonlinear ODEs for this mechanism contain a singular (η) and an ordinary (ɛ) perturbation parameter: η multiplies the velocity component of the fast variable and dominates the fast-mode perturbation series; ɛ controls the decay toward equilibrium and dominates the slow-mode perturbation series. However, higher order terms in both series contain η and ɛ. Finite series expansions partially decouple the system of ODEs into fast-mode and slow-mode ODEs; infinite series expansions completely decouple these ODEs. Correspondingly, any slow-mode ODE approximately describes motion on M, the linelike slow manifold of the system, and in the infinite series limit this description is exact. Thus the perturbation treatment and the slow-manifold picture of the system are closely related. The functional equation for M is solved automatically with the manipulative language MAPLE. The formal η and ɛ single perturbation expansions for the slow mode yield the same double (η,ɛ) perturbation series expressions to given order. Generalizations of this procedure are discussed.
Is it appropriate to model turbidity currents with the Three-Equation Model?
Hu, Peng; He, Zhiguo
2015-01-01
The Three-Equation Model (TEM) was developed in the 1980s to model turbidity currents (TCs) and has been widely used ever since. However, its physical justification was questioned because self-accelerating TCs simulated with the steady TEM seemed to violate the turbulent kinetic energy balance. This violation was considered as a result of very strong sediment erosion that consumes more turbulent kinetic energy than is produced. To confine bed erosion and thus remedy this issue, the Four-Equation Model (FEM) was introduced by assuming a proportionality between the bed shear stress and the turbulent kinetic energy. Here we analytically proof that self-accelerating TCs simulated with the original steady TEM actually never violate the turbulent kinetic energy balance, provided that the bed drag coefficient is not unrealistically low. We find that stronger bed erosion, surprisingly, leads to more production of turbulent kinetic energy due to conversion of potential energy of eroded material into kinetic energy of ...
Kinetic models of conjugated metabolic cycles
Ershov, Yu. A.
2016-01-01
A general method is developed for the quantitative kinetic analysis of conjugated metabolic cycles in the human organism. This method is used as a basis for constructing a kinetic graph and model of the conjugated citric acid and ureapoiesis cycles. The results from a kinetic analysis of the model for these cycles are given.
A Review of Kinetic Modeling Methodologies for Complex Processes
Directory of Open Access Journals (Sweden)
de Oliveira Luís P.
2016-05-01
Full Text Available In this paper, kinetic modeling techniques for complex chemical processes are reviewed. After a brief historical overview of chemical kinetics, an overview is given of the theoretical background of kinetic modeling of elementary steps and of multistep reactions. Classic lumping techniques are introduced and analyzed. Two examples of lumped kinetic models (atmospheric gasoil hydrotreating and residue hydroprocessing developed at IFP Energies nouvelles (IFPEN are presented. The largest part of this review describes advanced kinetic modeling strategies, in which the molecular detail is retained, i.e. the reactions are represented between molecules or even subdivided into elementary steps. To be able to retain this molecular level throughout the kinetic model and the reactor simulations, several hurdles have to be cleared first: (i the feedstock needs to be described in terms of molecules, (ii large reaction networks need to be automatically generated, and (iii a large number of rate equations with their rate parameters need to be derived. For these three obstacles, molecular reconstruction techniques, deterministic or stochastic network generation programs, and single-event micro-kinetics and/or linear free energy relationships have been applied at IFPEN, as illustrated by several examples of kinetic models for industrial refining processes.
Fully implicit kinetic modelling of collisional plasmas
Energy Technology Data Exchange (ETDEWEB)
Mousseau, V.A.
1996-05-01
This dissertation describes a numerical technique, Matrix-Free Newton Krylov, for solving a simplified Vlasov-Fokker-Planck equation. This method is both deterministic and fully implicit, and may not have been a viable option before current developments in numerical methods. Results are presented that indicate the efficiency of the Matrix-Free Newton Krylov method for these fully-coupled, nonlinear integro-differential equations. The use and requirement for advanced differencing is also shown. To this end, implementations of Chang-Cooper differencing and flux limited Quadratic Upstream Interpolation for Convective Kinematics (QUICK) are presented. Results are given for a fully kinetic ion-electron problem with a self consistent electric field calculated from the ion and electron distribution functions. This numerical method, including advanced differencing, provides accurate solutions, which quickly converge on workstation class machines. It is demonstrated that efficient steady-state solutions can be achieved to the non-linear integro-differential equation, obtaining quadratic convergence, without incurring the large memory requirements of an integral operator. Model problems are presented which simulate plasma impinging on a plate with both high and low neutral particle recycling typical of a divertor in a Tokamak device. These model problems demonstrate the performance of the new solution method.
On Generalized Fractional Kinetic Equations Involving Generalized Bessel Function of the First Kind
Directory of Open Access Journals (Sweden)
Dinesh Kumar
2015-01-01
Full Text Available We develop a new and further generalized form of the fractional kinetic equation involving generalized Bessel function of the first kind. The manifold generality of the generalized Bessel function of the first kind is discussed in terms of the solution of the fractional kinetic equation in the paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably new results.
Generalized Klein-Gordon and Dirac Equations from Nonlocal Kinetic Approach
El-Nabulsi, Rami Ahmad
2016-09-01
In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens's nonlocal-in-time kinetic energy approach, which is motivated from Feynman's kinetic energy functional formalism where the position differences are shifted with respect to one another. I proved that these generalized equations are similar to those obtained in literature in the presence of minimal length based on the Quesne-Tkachuk algebra.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations
Shiuhong, Lui; Xu, Jun
1999-01-01
Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.
Development of simple kinetic models and parameter estimation for ...
African Journals Online (AJOL)
PANCHIGA
Key words: Exponential feed, growth modeling, Monod kinetic equation, Pichia pastoris, recombinant human ... Author(s) agree that this article remains permanently open access under the terms of the Creative Commons .... Methanol was the only energy and carbon source ..... A potential explanation for the decline in cell.
Energy Technology Data Exchange (ETDEWEB)
Thompson, A.S.; Thompson, B.R.
1988-09-01
The analytical model of nuclear reactor transients, incorporating both mechanical and nuclear effects, simulates reactor kinetics. Linear analysis shows the stability borderline for small power perturbations. In a stable system, initial power disturbances die out with time. With an unstable combination of nuclear and mechanical characteristics, initial disturbances persist and may increase with time. With large instability, oscillations of great magnitude occur. Stability requirements set limits on the power density at which particular reactors can operate. The limiting power density depends largely on the product of two terms: the fraction of delayed neutrons and the frictional damping of vibratory motion in reactor core components. As the fraction of delayed neutrons is essentially fixed, mechanical damping largely determines the maximum power density. A computer program, based on the analytical model, calculates and plots reactor power as a nonlinear function of time in response to assigned values of mechanical and nuclear characteristics.
Directory of Open Access Journals (Sweden)
Bambang Rusdiarso
2016-12-01
Full Text Available Extraction and purification of humic acid from dry horse dung powder (HD-HA was performed successfully and the purified HD-HA was then applied as sorbent to adsorb Zn2+. Extraction and purification were performed based on procedure of Stevenson (1994 under atmospheric air. Parameters investigated in this work consist of effect of medium sorption acidity, sorption rate (ka and desorption rate constant (kd, Langmuir (monolayer and Freundlich (multilayer sorption capacities, and energy (E of sorption. The ka and kd were determined according to the kinetic model of second order sorption reaching equilibrium, monolayer sorption capacity (b and energy (E were determined according to Langmuir isotherm model, and multilayer sorption capacity (B was determined based on Freundlich isotherm model. Sorption of Zn2+ on purified HD-HA was maximum at pH 5.0. The novel kinetic expression resulted from proposed kinetic model has been shown to be more applicable than the commonly known Lagergren equation obtained from the pseudo-first order sorption model. The application of the equation revealed that the intercept of Lagergren equation, ln qe was more complex function of initial concentration of Zn2+ (a, Langmuir sorption capacity (b, and sorbed Zn2+ at equilibrium (xe.
Salhoumi, A.; Galenko, P. K.
2017-04-01
Rapidly moving solid-liquid interface is treated analytically and numerically. Derivation and qualitative analysis of interface propagation kinetics is presented. Quantitative predictions of solutions, which follow from the Kinetic Rate Theory and the solution of Gibbs-Thomson-type equation, are compared with Molecular Dynamics simulation data (MD-data) on crystallization and melting of fcc-lattice of nickel. It is shown in the approximation of a linear behavior of the interface velocity versus undercooling that the Gibbs-Thomson-type equation and kinetic rate theory describe MD-data well enough, in the range of small growth velocity and within the range of relatively small undercooling, with a relative error for the obtained values of kinetic coefficient of the order 1.1%. Within the small-and long range of undercooling, in nonlinear behavior of the interface velocity versus undercooling, the kinetic rate theory disagrees sharply with MD-data, qualitatively and quantitatively, unlike to the Gibbs-Thomson-type equation which is in a good agreement with MD-data within the whole range of undercooling and crystal growth velocity.
COMPARISON BETWEEN BOUSSINESQ EQUATIONS AND MILD-SLOPE EQUATIONS MODEL
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, the Boussinesq equations and mild-slope equation of wave transformation in near-shore shallow water were introduced and the characteristics of the two forms of equations were compared and analyzed. Meanwhile, a Boussinesq wave model which includes effects of bottom friction, wave breaking and subgrid turbulent mixing is established, slot technique dealing with moving boundary and damping layer dealing with absorbing boundary were established. By adopting empirical nonlinear dispersion relation and including nonlinear term, the mild-slope equation model was modified to take nonlinear effects into account. The two types of models were validated with the experiment results given by Berkhoff and their accuracy was analysed and compared with that of correlated methods.
Kinetics model for lutate dosimetry
Energy Technology Data Exchange (ETDEWEB)
Lima, M.F.; Mesquita, C.H., E-mail: mflima@ipen.br, E-mail: chmesqui@ipen.br [Instituto de Pesquisas Energeticas (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2013-11-01
The use of compartmental analysis to predict the behavior of drugs in the organism is considered the better option among numerous methods employed in pharmacodynamics. A six compartments model was developed to determinate the kinetic constants of 177Lu-DOTATATO biodistribution using data from one published study with 67 patients treated by PRRT (Peptide receptor radionuclide therapy) and followed by CT during 68,25 hours. The compartmental analysis was made using the software AnaComp Registered-Sign . The influence of the time pos-injection over the dose assessment was studied taking into account the renal excretion management by aminoacid coinfusion, whose direct effects persist in the first day. The biodistribution curve was split in five sectors: 0-0.25h; 0-3.25h; 3.25-24.25h; 24.25-68.25h and 3.25-68.25h. After the examination of that influence, the study was concentrated in separate the biodistribution curve in two phases. Phase 1: governed by uptake from the blood, considering the time pos-injection until 3.25h and phase 2: governed by renal excretion, considering the time pos-injection from 3.25h to 68.25h. The model considered the organs and tissues superposition in the CT image acquisition by sampling parameters as the contribution of the the activity concentration in blood and relation between the sizes of the whole body and measured organs. The kinetic constants obtained from each phase (1 and 2) were used in dose assessment to patients in 26 organs and tissues described by MIRD. Dosimetry results were in agreement with the available results from literature, restrict to whole body, kidneys, bone marrow, spleen and liver. The advantage of the proposed model is the compartmental method quickness and power to estimate dose in organs and tissues, including tumor that, in the most part, were not discriminate by voxels of phantoms built using CT images. (author)
Crystallization Kinetics within a Generic Modeling Framework
DEFF Research Database (Denmark)
Meisler, Kresten Troelstrup; von Solms, Nicolas; Gernaey, Krist V.
2014-01-01
to the modeling of various kinetic phenomena like nucleation, growth, agglomeration, and breakage are discussed in terms of model forms, model parameters, their availability and/or estimation, and their selection and application for specific crystallization operational scenarios under study. The advantages......A new and extended version of a generic modeling framework for analysis and design of crystallization operations is presented. The new features of this framework are described, with focus on development, implementation, identification, and analysis of crystallization kinetic models. Issues related...... of employing a well-structured model library for storage, use/reuse, and analysis of the kinetic models are highlighted. Examples illustrating the application of the modeling framework for kinetic model discrimination related to simulation of specific crystallization scenarios and for kinetic model parameter...
Kinetic theory the Chapman-Enskog solution of the transport equation for moderately dense gases
Brush, S G
1972-01-01
Kinetic Theory, Volume 3: The Chapman-Enskog Solution of the Transport Equation for Moderately Dense Gases describes the Chapman-Enskog solution of the transport equation for moderately dense gases. Topics covered range from the propagation of sound in monatomic gases to the kinetic theory of simple and composite monatomic gases and generalizations of the theory to higher densities. The application of kinetic theory to the determination of intermolecular forces is also discussed. This volume is divided into two sections and begins with an introduction to the work of Hilbert, Chapman, and Ensko
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Jagtap, Ameya Dilip
2015-01-01
A novel explicit and implicit Kinetic Streamlined-Upwind Petrov Galerkin (KSUPG) scheme is presented for hyperbolic equations such as Burgers equation and compressible Euler equations. The proposed scheme performs better than the original SUPG stabilized method in multi-dimensions. To demonstrate the numerical accuracy of the scheme, various numerical experiments have been carried out for 1D and 2D Burgers equation as well as for 1D and 2D Euler equations using Q4 and T3 elements. Furthermore, spectral stability analysis is done for the explicit 2D formulation. Finally, a comparison is made between explicit and implicit versions of the KSUPG scheme.
Population balance modeling of antibodies aggregation kinetics.
Arosio, Paolo; Rima, Simonetta; Lattuada, Marco; Morbidelli, Massimo
2012-06-21
The aggregates morphology and the aggregation kinetics of a model monoclonal antibody under acidic conditions have been investigated. Growth occurs via irreversible cluster-cluster coagulation forming compact, fractal aggregates with fractal dimension of 2.6. We measured the time evolution of the average radius of gyration, , and the average hydrodynamic radius, , by in situ light scattering, and simulated the aggregation kinetics by a modified Smoluchowski's population balance equations. The analysis indicates that aggregation does not occur under diffusive control, and allows quantification of effective intermolecular interactions, expressed in terms of the Fuchs stability ratio (W). In particular, by introducing a dimensionless time weighed on W, the time evolutions of measured under various operating conditions (temperature, pH, type and concentration of salt) collapse on a single master curve. The analysis applies also to data reported in the literature when growth by cluster-cluster coagulation dominates, showing a certain level of generality in the antibodies aggregation behavior. The quantification of the stability ratio gives important physical insights into the process, including the Arrhenius dependence of the aggregation rate constant and the relationship between monomer-monomer and cluster-cluster interactions. Particularly, it is found that the reactivity of non-native monomers is larger than that of non-native aggregates, likely due to the reduction of the number of available hydrophobic patches during aggregation.
Breakdown parameter for kinetic modeling of multiscale gas flows.
Meng, Jianping; Dongari, Nishanth; Reese, Jason M; Zhang, Yonghao
2014-06-01
Multiscale methods built purely on the kinetic theory of gases provide information about the molecular velocity distribution function. It is therefore both important and feasible to establish new breakdown parameters for assessing the appropriateness of a fluid description at the continuum level by utilizing kinetic information rather than macroscopic flow quantities alone. We propose a new kinetic criterion to indirectly assess the errors introduced by a continuum-level description of the gas flow. The analysis, which includes numerical demonstrations, focuses on the validity of the Navier-Stokes-Fourier equations and corresponding kinetic models and reveals that the new criterion can consistently indicate the validity of continuum-level modeling in both low-speed and high-speed flows at different Knudsen numbers.
Luo, Songting; Payne, Nicholas
2017-07-01
We present an effective asymptotic method for approximating the density of particles for kinetic equations with a Bhatnagar-Gross-Krook (BGK) relaxation operator in the large scale hyperbolic limit. The density of particles is transformed via a Hopf-Cole transformation, where the phase function is expanded as a power series with respect to the Knudsen number. The expansion terms can be determined by solving a sequence of equations. In particular, it has been proved in [3] that the leading order term is the viscosity solution of an effective Hamilton-Jacobi equation, and we show that the higher order terms can be formally determined by solving a sequence of transport equations. Both the effective Hamilton-Jacobi equation and the transport equations are independent of the Knudsen number, and are formulated in the physical space, where the effective Hamiltonian is obtained as the solution of a nonlinear equation that is given as an integral in the velocity variable, and the coefficients of the transport equations are given as integrals in the velocity variable. With appropriate Gauss quadrature rules for evaluating these integrals effectively, the effective Hamilton-Jacobi equation and the transport equations can be solved efficiently to obtain the expansion terms for approximating the density function. In this work, the zeroth, first and second order terms in the expansion are used to obtain second order accuracy with respect to the Knudsen number. The proposed method balances efficiency and accuracy, and has the potential to deal with kinetic equations with more general BGK models. Numerical experiments verify the effectiveness of the proposed method.
Reaction Kinetic Equation for Char Combustion of Underground Coal Gasification
Institute of Scientific and Technical Information of China (English)
YU Hong-guan; YANG Lan-he; FENG Wei-min; LIU Shu-qin; SONG Zhen-qi
2006-01-01
Based on the quasi-steady-state approximation, the dynamic equation of char combustion in the oxidation zone of underground coal gasification (UCG) was derived. The parameters of the dynamic equation were determined at 900℃ using a thermo-gravimetric (TG) analyzer connected to a flue gas analyzer and this equation. The equation was simplified for specific coals, including high ash content, low ash content, and low ash fusibility ones. The results show that 1) the apparent reaction rate constant increases with an increase in volatile matter value as dry ash-free basis, 2) the effective coefficient of diffusion decreases with an increase in ash as dry basis, and 3) the mass transfer coefficient is independent of coal quality on the whole. The apparent reaction rate constant, mass-transfer coefficient and effective coefficient of diffusion of six char samples range from 7.51×104 m/s to 8.98×104 m/s, 3.05×106 m/s to 3.23×106 m/s and 5.36×106 m2/s to 8.23×106 m2/s at 900℃, respectively.
Kinetic model for hydroisomerization reaction of C8-aromatics
Institute of Scientific and Technical Information of China (English)
Ouguan XU; Hongye SU; Xiaoming JIN; Jian CHU
2008-01-01
Based on the reported reaction networks, a novel six-component hydroisomerization reaction net-work with a new lumped species including C8-naphthenes and Cs-paraffins is proposed and a kinetic model for a commercial unit is also developed. An empirical catalyst deactivation function is incorporated into the model accounting for the loss in activity because of coke forma-tion on the catalyst surface during the long-term opera-tion. The Runge-Kutta method is used to solve the ordinary differential equations of the model. The reaction kinetic parameters are benchmarked with several sets of balanced plant data and estimated by the differential vari-able metric optimization method (BFGS). The kinetic model is validated by an industrial unit with sets of plant data under different operating conditions and simulation results show a good agreement between the model predic-tions and the plant observations.
Modelling atypical CYP3A4 kinetics: principles and pragmatism.
Houston, J Brian; Galetin, Aleksandra
2005-01-15
The Michaelis-Menten model, and the existence of a single active site for the interaction of substrate with drug metabolizing enzyme, adequately describes a substantial number of in vitro metabolite kinetic data sets for both clearance and inhibition determination. However, in an increasing number of cases (involving most notably, but not exclusively, CYP3A4), atypical kinetic features are observed, e.g., auto- and heteroactivation; partial, cooperative, and substrate inhibition; concentration-dependent effector responses (activation/inhibition); limited substrate substitution and inhibitory reciprocity necessitating sub-group classification. The phenomena listed above cannot be readily interpreted using single active site models and the literature indicates that three types of approaches have been adopted. First the 'nai ve' approach of using the Michaelis-Menten model regardless of the kinetic behaviour, second the 'empirical' approach (e.g., employing the Hill or uncompetitive inhibition equations to model homotropic phenomena of sigmoidicity and substrate inhibition, respectively) and finally, the 'mechanistic' approach. The later includes multisite kinetic models derived using the same rapid equilibrium/steady-state assumptions as the single-site model. These models indicate that 2 or 3 binding sites exist for a given CYP3A4 substrate and/or effector. Multisite kinetic models share common features, depending on the substrate kinetics and the nature of the effector response observed in vitro, which allow a generic model to be proposed. Thus although more complex than the other two approaches, they show more utility and can be comprehensively applied in relatively simple versions that can be readily generated from generic model. Multisite kinetic features, observed in isolated hepatocytes as well as in microsomes from hepatic tissue and heterologous expression systems, may be evident in substrate depletion-time profiles as well as in metabolite formation rates
Kinetic Model of Hypophosphite Oxidation on a Nickel Electrode in D2O Solution
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Kinetic model of hypophosphite oxidation on a nickel electrode was studied in D2Osolution in order to reach a better understanding of the oxidation mechanism. In the model the electrooxidation of hypophosphite undergo a H abstraction of hypophosphite from the P-H bond to form the phosphorus-centered radical PHO2-, which subsequently is electrochemically reacted with water to form the final product, phosphite. The kinetic equations were derived, and the kinetic parameters were obtained from a comparison of experimental results and the kinetic equations. The process of hypophosphite electrooxidation could be well simulated by this model
About and beyond the Henri-Michaelis-Menten rate equation for single-substrate enzyme kinetics.
Bajzer, Zeljko; Strehler, Emanuel E
2012-01-20
For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S](0). In our formula the rate is already expressed through [S](0), and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S](0). Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S](0). Copyright © 2011 Elsevier Inc. All rights reserved.
A Note on Two-Equation Closure Modelling of Canopy Flow
DEFF Research Database (Denmark)
Sogachev, Andrey
2009-01-01
The note presents a rational approach to modelling the source/sink due to vegetation or buoyancy effects that appear in the turbulent kinetic energy, E, equation and a supplementary equation for a length-scale determining variable, φ, when two-equation closure is applied to canopy and atmospheric...
A Note on Two-Equation Closure Modelling of Canopy Flow
DEFF Research Database (Denmark)
Sogachev, Andrey
2009-01-01
The note presents a rational approach to modelling the source/sink due to vegetation or buoyancy effects that appear in the turbulent kinetic energy, E, equation and a supplementary equation for a length-scale determining variable, φ, when two-equation closure is applied to canopy and atmospheric...
Directory of Open Access Journals (Sweden)
Pedro L. Valencia
2017-04-01
Full Text Available We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974. The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis–Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax, Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
Valencia, Pedro L; Astudillo-Castro, Carolina; Gajardo, Diego; Flores, Sebastián
2017-04-01
We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974). The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis-Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax , Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].
Improving Solution of Euler Equations by a Gas-Kinetic BGK Method
Institute of Scientific and Technical Information of China (English)
Liu Ya; Gao Chao; F. Liu
2009-01-01
Aim. The well known JST(Jameson-Schmidt-Turkel) scheme requires the use of a dissipation term. We propose using gas-kinetic BGK (Bhatnagar-Gross-Krook) method, which is based on the more fundamental Boltzmann equation, in order to obviate the use of dissipation term and obtain, we believe, an improved solution. Section 1 deals essentially with three things: (1) as analytical solution of molecular probability density function at the ceil interface has been obtained by the Bohzmann equation with BGK model, we can compute the flux term by integrating the density function in the phase space; eqs. (8) and (11) require careful attention; (2) the integrations can be expressed as the moments of Maxwellian distribution with different limits according to the analytical solution; eqs. (9) and (10) require careful attention; (3) the discrete equation by finite volume method can be solved using the time marching method. Computations are performed by the BGK method for the Sod's shock tube problem and a two-dimensional shock reflection problem. The results are compared with those of the conventional JST scheme in Figs. 1 and 2. The BGK method provides better resolution of shock waves and other features of the flow fields.
Solution of fractional kinetic equation by a class of integral transform of pathway type
Kumar, Dilip
2013-04-01
Solutions of fractional kinetic equations are obtained through an integral transform named Pα-transform introduced in this paper. The Pα-transform is a binomial type transform containing many class of transforms including the well known Laplace transform. The paper is motivated by the idea of pathway model introduced by Mathai [Linear Algebra Appl. 396, 317-328 (2005), 10.1016/j.laa.2004.09.022]. The composition of the transform with differential and integral operators are proved along with convolution theorem. As an illustration of applications to the general theory of differential equations, a simple differential equation is solved by the new transform. Being a new transform, the Pα-transform of some elementary functions as well as some generalized special functions such as H-function, G-function, Wright generalized hypergeometric function, generalized hypergeometric function, and Mittag-Leffler function are also obtained. The results for the classical Laplace transform is retrieved by letting α → 1.
Study on Kinetics for Desulfurization of Model Diesel
Institute of Scientific and Technical Information of China (English)
Qian Jianhua; Zhou Yuenan; Liu Lin; Wang Yue; Xing Jinjuan; Lü Hong
2009-01-01
In this study, by means of the experiments for desulfurization of model diesel through oxi-dative extraction, the changes associated with the rate of desulfurization of diesel and the mechanism for oxidation of sulfides in diesel were explored. Through studying the mechanism for oxidation of sulfides and the principle of solvent extraction, the kinetic equation of desulfurization via oxidative extraction were determined. By means of the evaluation of model parameters and curve fitting, the reaction order between organic sulfide and sulfone, the intrinsic oxidation rate constant of organic sulfide and sulfone, and the equilibrium constant between suifone in model diesel and extractive sol-vent were determined. The experimental values of the desulfurization rate and the theoretical values of the corresponding model equation had closely demonstrated that the desulfurization reaction rate had high accuracy. And the reaction kinetics could provide an important basis for diesel desulfurization process in the future.
Enzymatic hydrolysis of protein:mechanism and kinetic model
Institute of Scientific and Technical Information of China (English)
Qi Wei; He Zhimin
2006-01-01
The bioreaction mechanism and kinetic behavior of protein enzymatic hydrolysis for preparing active peptides were investigated to model and characterize the enzymatic hydrolysis curves.Taking into account single-substrate hydrolysis,enzyme inactivation and substrate or product inhibition,the reaction mechanism could be deduced from a series of experimental results carried out in a stirred tank reactor at different substrate concentrations,enzyme concentrations and temperatures based on M-M equation.An exponential equation dh/dt = aexp(-bh) was also established,where parameters a and b have different expressions according to different reaction mechanisms,and different values for different reaction systems.For BSA-trypsin model system,the regressive results agree with the experimental data,i.e.the average relative error was only 4.73%,and the reaction constants were determined as Km = 0.0748 g/L,Ks = 7.961 g/L,kd = 9.358/min,k2 =38.439/min,Ea= 64.826 kJ/mol,Ed= 80.031 kJ/mol in accordance with the proposed kinetic mode.The whole set of exponential kinetic equations can be used to model the bioreaction process of protein enzymatic hydrolysis,to calculate the thermodynamic and kinetic constants,and to optimize the operating parameters for bioreactor design.
Chemical Kinetic Modeling of 2-Methylhexane Combustion
Mohamed, Samah Y.
2015-03-30
Accurate chemical kinetic combustion models of lightly branched alkanes (e.g., 2-methylalkanes) are important for investigating the combustion behavior of diesel, gasoline, and aviation fuels. Improving the fidelity of existing kinetic models is a necessity, as new experiments and advanced theories show inaccuracy in certain portions of the models. This study focuses on updating thermodynamic data and kinetic model for a gasoline surrogate fuel, 2-methylhexane, with recently published group values and rate rules. These update provides a better agreement with rapid compression machine measurements of ignition delay time, while also strengthening the fundamental basis of the model.
Kinetic Equation for Internal Oxidation of Cu-Al Alloy Spheres
Institute of Scientific and Technical Information of China (English)
SONG Kexing; GAO Jianxin; XU Xiaofeng; LI Peiquan; TIAN Baohong; GUO Xiuhua
2007-01-01
The kinetics of internal oxidation of Cu-Al alloy spheres, containing up to 2.214% mole fraction Al was investigated in the temperature range 1 023 K to 1 273 K, and the depth of internal oxidation was measured in the microscopy. A kinetic equation was derived to describe the internal oxidation of Cu-Al alloy spheres, which was checked experimentally by means of oxidation depth measurements. The results show that the derived equation is exact enough to describe the kinetics of internal oxidation of Cu-Al alloy spheres.Based on this equation and the oxidation depth measurements, the permeability of oxygen in solid copper has been obtained. Investigation also shows that in the process of internal oxidation, there is no evidence for preferential diffusion along grain boundaries.
Kinetic model for microbial growth and desulphurisation with Enterobacter sp.
Liu, Long; Guo, Zhiguo; Lu, Jianjiang; Xu, Xiaolin
2015-02-01
Biodesulphurisation was investigated by using Enterobacter sp. D4, which can selectively desulphurise and convert dibenzothiophene into 2-hydroxybiphenyl (2-HBP). The experimental values of growth, substrate consumption and product generation were obtained at 95 % confidence level of the fitted values using three models: Hinshelwood equation, Luedeking-Piret and Luedeking-Piret-like equations. The average error values between experimental values and fitted values were less than 10 %. These kinetic models describe all the experimental data with good statistical parameters. The production of 2-HBP in Enterobacter sp. was by "coupled growth".
Small velocity and finite temperature variations in kinetic relaxation models
Markowich, Peter
2010-01-01
A small Knuden number analysis of a kinetic equation in the diffusive scaling is performed. The collision kernel is of BGK type with a general local Gibbs state. Assuming that the flow velocity is of the order of the Knudsen number, a Hilbert expansion yields a macroscopic model with finite temperature variations, whose complexity lies in between the hydrodynamic and the energy-transport equations. Its mathematical structure is explored and macroscopic models for specific examples of the global Gibbs state are presented. © American Institute of Mathematical Sciences.
Reproducing Phenomenology of Peroxidation Kinetics via Model Optimization
Ruslanov, Anatole D.; Bashylau, Anton V.
2010-06-01
We studied mathematical modeling of lipid peroxidation using a biochemical model system of iron (II)-ascorbate-dependent lipid peroxidation of rat hepatocyte mitochondrial fractions. We found that antioxidants extracted from plants demonstrate a high intensity of peroxidation inhibition. We simplified the system of differential equations that describes the kinetics of the mathematical model to a first order equation, which can be solved analytically. Moreover, we endeavor to algorithmically and heuristically recreate the processes and construct an environment that closely resembles the corresponding natural system. Our results demonstrate that it is possible to theoretically predict both the kinetics of oxidation and the intensity of inhibition without resorting to analytical and biochemical research, which is important for cost-effective discovery and development of medical agents with antioxidant action from the medicinal plants.
Stochastic effects in a discretized kinetic model of economic exchange
Bertotti, M. L.; Chattopadhyay, A. K.; Modanese, G.
2017-04-01
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing random fluctuations into the kinetic model based on Langevin and Fokker-Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggest a growing inequality with increasing income. Further analysis shows, in the presence of a conserved total wealth, a simultaneous decrease in inequality as social mobility increases, in conformity with economic data.
Kinetic modelling of krypton fluoride laser systems
Energy Technology Data Exchange (ETDEWEB)
Jancaitis, K.S.
1983-11-01
A kinetic model has been developed for the KrF* rare gas halide laser system, specifically for electron-beam pumped mixtures of krypton, fluorine, and either helium or argon. The excitation produced in the laser gas by the e-beam was calculated numerically using an algorithm checked by comparing the predicted ionization yields in the pure rare gases with their experimental values. The excitation of the laser media by multi-kilovolt x-rays was also modeled and shown to be similar to that produced by high energy electrons. A system of equations describing the transfer of the initial gas excitation into the laser upper level was assembled using reaction rate constants from both experiment and theory. A one-dimensional treatment of the interaction of the laser radiation with the gas was formulated which considered spontaneous and stimulated emission and absorption. The predictions of this model were in good agreement with the fluorescence signals and gain and absorption measured experimentally.
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...
Kinetic theory of spatially homogeneous systems with long-range interactions: II. Basic equations
Chavanis, Pierre-Henri
2013-01-01
We provide a short historic of the early development of kinetic theory in plasma physics and synthesize the basic kinetic equations describing the evolution of systems with long-range interactions derived in Paper I. We describe the evolution of the system as a whole and the relaxation of a test particle in a bath at equilibrium or out-of-equilibrium. We write these equations for an arbitrary long-range potential of interaction in a space of arbitrary dimension d. We discuss the scaling of th...
Applications of nonlinear science and kinetic equations to the spread of epidemics
Macinnis, David Robert
The study of the spread of epidemics is currently growing into a successful subfield of a combination of nonlinear science and statistical mechanics. Topics studied in this field include kinetic and mean field levels of epidemiological models. This thesis consists of the analysis of such topics and specifically directed at the Hantavirus, West Nile virus, and the Bubonic Plague. A successful reaction-diffusion equation approach developed recently by Abramson and Kenkre was able to describe spatiotemporal patterns of the Hantavirus model. From measurements of the parameters of their model it was found that the mice, the carriers of the infection, must be regarded as moving diffusively within attractive potentials representative of home ranges. Several attempts have been made to incorporate home ranges into their model. Two of these attempts are discussed within this thesis. A model to explain the transmission of the West Nile virus within bird and mosquito populations was recently developed by Kenkre, Parmenter, Peixoto, and Sadasiv who showed how spatially resolved issues could be discussed but restricted their analysis to mean field considerations. This thesis extends that study by investigating spatial resolution of the infected populations. Traveling waves of the bird and mosquito populations are found in the West Nile context. Infection control of various epidemics has become increasingly important to limit the potential force of infection into the human population. This thesis contains a quantitative attempt at a theory of such control (for the West Nile virus) via spraying of the mosquito population. Mean field and kinetic level models are proposed in this thesis to describe the transmission of the Bubonic Plague which involves flea and mammal populations. The various populations are found to undergo a variety of bifurcations as well as hysteresis in their steady state regime. Spatially resolved analysis of the populations is also presented.
Modeling inhomogeneous DNA replication kinetics.
Directory of Open Access Journals (Sweden)
Michel G Gauthier
Full Text Available In eukaryotic organisms, DNA replication is initiated at a series of chromosomal locations called origins, where replication forks are assembled proceeding bidirectionally to replicate the genome. The distribution and firing rate of these origins, in conjunction with the velocity at which forks progress, dictate the program of the replication process. Previous attempts at modeling DNA replication in eukaryotes have focused on cases where the firing rate and the velocity of replication forks are homogeneous, or uniform, across the genome. However, it is now known that there are large variations in origin activity along the genome and variations in fork velocities can also take place. Here, we generalize previous approaches to modeling replication, to allow for arbitrary spatial variation of initiation rates and fork velocities. We derive rate equations for left- and right-moving forks and for replication probability over time that can be solved numerically to obtain the mean-field replication program. This method accurately reproduces the results of DNA replication simulation. We also successfully adapted our approach to the inverse problem of fitting measurements of DNA replication performed on single DNA molecules. Since such measurements are performed on specified portion of the genome, the examined DNA molecules may be replicated by forks that originate either within the studied molecule or outside of it. This problem was solved by using an effective flux of incoming replication forks at the model boundaries to represent the origin activity outside the studied region. Using this approach, we show that reliable inferences can be made about the replication of specific portions of the genome even if the amount of data that can be obtained from single-molecule experiments is generally limited.
Phu, Jack; Al-Saleem, Noha; Kalloniatis, Michael; Khuu, Sieu K
2016-11-01
In the present study, we measured the extent of statokinetic dissociation (SKD) in normal observers and then equated the psychophysical tasks into a two-interval forced choice (2IFC) procedure. In Experiment 1, we used the Humphrey visual field analyzer in static perimetry and automated kinetic perimetry modes to measure contrast sensitivity thresholds and the Goldmann manual kinetic perimeter to measure isopters. This was carried out using a Goldmann size II target. Goldmann kinetic perimetry was performed manually with both inward (peripheral to center) and outward (center to periphery) directions of movement to deduce an "average" isopter. This revealed the presence of SKD when superimposed upon the map of static contrast threshold results. There was no evidence of any contribution of examiner technique or instrument-specific differences to SKD. In Experiment 2, we determined the psychometric curves plotting proportion seen as a function of stimulus eccentricity with static and kinetic stimuli with a 2IFC procedure and method of constant stimuli. In an additional experiment, we also showed that subjects were able to reliably discriminate whether a stimulus was static, moving inward, or moving outward, and hence, comparisons could be made between static and kinetic perimetry tasks. Overall, by making the task objective and reducing criterion bias, eccentricity thresholds were equated across static and kinetic perimetry methods; hence, no evidence of SKD was seen. We suggest SKD is inherent to the differences in methodology of threshold measurement in conventional static and kinetic perimetry and individual criterion bias.
Serov, S A
2013-01-01
In the article correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert's and Enskog's methods are discussed. The equations system of multicomponent non-equilibrium gas dynamics is derived, that corresponds to the first order in the approximate (asymptotic) method for solution of the system of kinetic Boltzmann equations. It is shown, that the velocity distribution functions of particles, obtained by the proposed method and by Enskog's method, within Enskog's approach, are equivalent up to the infinitesimal first order terms of the asymptotic expansion, but, generally speaking, differ in the next order. Interpretation of turbulent gas flow is proposed, as stratified on components gas flow, which is described by the derived equations system of multicomponent non-equilibrium gas dynamics.
Kinetic Flux Vector Splitting Method for the Shallow Water Wave Equations
Institute of Scientific and Technical Information of China (English)
施卫平; WeiShyy
2003-01-01
Based on the analogy to gas dynamics,the kinetic flux flux vector splitting (KFVS) method is used to stimulate the shallow water wave equations,The flus vectors of the equations are split on the basis of the local equilibrium Maxwell-Boltzmann distribution One dimensional examples including a dam breaking wave and flows over a ridge are calcualted.The solutions exhibit second-order accuracy with no spurious oscillation.
BRIEF COMMUNICATION: On the drift kinetic equation driven by plasma flows
Shaing, K. C.
2010-07-01
A drift kinetic equation that is driven by plasma flows has previously been derived by Shaing and Spong 1990 (Phys. Fluids B 2 1190). The terms that are driven by particle speed that is parallel to the magnetic field B have been neglected. Here, such terms are discussed to examine their importance to the equation and to show that these terms do not contribute to the calculations of plasma viscosity in large aspect ratio toroidal plasmas, e.g. tokamaks and stellarators.
A simple kinetic model for growth and biosynthesis of polyhydroxyalkanoate in Bacillus flexus.
Divyashree, M Somashekara; Rastogi, Navin K; Shamala, T Ramachandriah
2009-10-01
Polyhydroxyalkanoate (PHA), which is produced by several bacteria, is a biodegradable polymer that has many industrial and medical applications. This study deals with development of a simple kinetic model and modification of the logistic equation that can provide an adequate description of PHA formation process by Bacillus flexus. The parameters studied were kinetics of microbial growth, substrate consumption, and product formation. The microbial growth was described by simplification of Monod's model. A simplified Luedeking-Piret type model could be employed to represent the product kinetics. The kinetic constants were evaluated on the basis of non-linear regression and the differential equations were solved using Runge-Kutta algorithm and MATLAB software. A good agreement was found between the experimental and predicted values, which indicated that the model differential equations could describe the PHA formation and fermentation process. In this study, a modification of the logistic equation has also been attempted for describing the growth of B. flexus.
DIFFUSIVE-DISPERSIVE TRAVELING WAVES AND KINETIC RELATIONS IV.COMPRESSIBLE EULER EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
The authors consider the Euler equations for a compressible fluid in one space dimensionwhen the equation of state of the fluid does not fulfill standard convexity assumptions andviscosity and capillarity effects are taken into account. A typical example of nonconvex con-stitutive equation for fluids is Van der Waals' equation. The first order terms of these partialdifferential equations form a nonlinear system of mixed (hyperbolic-elliptic) type. For a class ofnonconvex equations of state, an existence theorem of traveling waves solutions with arbitrarylarge amplitude is established here. The authors distinguish between classical (compressive) andnonclassical (undercompressive) traveling waves. The latter do not fulfill Lax shock inequali-ties, and are characterized by the so-called kinetic relation, whose properties are investigatedin this paper.
Structural Equation Modeling of Travel Choice Dynamics
Golob, Thomas F.
1988-01-01
This research has two objectives. The first objective is to explore the use of the modeling tool called "latent structural equations" (structural equations with latent variables) in the general field of travel behavior analysis and the more specific field of dynamic analysis of travel behavior. The second objective is to apply a latent structural equation model in order to determine the causal relationships between income, car ownership, and mobility. Many transportation researchers ...
Discrete Surface Modelling Using Partial Differential Equations.
Xu, Guoliang; Pan, Qing; Bajaj, Chandrajit L
2006-02-01
We use various nonlinear partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting. The nonlinear equations used include two second order flows, two fourth order flows and two sixth order flows. These nonlinear equations are discretized based on discrete differential geometry operators. The proposed approach is simple, efficient and gives very desirable results, for a range of surface models, possibly having sharp creases and corners.
Modelling conjugation with stochastic differential equations.
Philipsen, K R; Christiansen, L E; Hasman, H; Madsen, H
2010-03-07
Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared to the model without plate conjugation. The modelling approach described in this article can be applied generally when modelling dynamical systems.
Two corrections to the drift-wave kinetic equation in the context of zonal-flow physics
Ruiz, D E; Shi, E L; Dodin, I Y
2016-01-01
The drift-wave (DW) kinetic equation, that is commonly used in studies of zonal flows (ZF), excludes the exchange of enstrophy between DW and ZF and also effects beyond the geometrical-optics limit. Using the quasilinear approximation of the generalized Hasegawa--Mima model, we propose a modified theory that accounts for these effects within a wave kinetic equation (WKE) of the Wigner--Moyal type, which is commonly known in quantum mechanics. In the geometrical-optics limit, this theory features additional terms beyond the traditional WKE that ensure exact conservation of the \\textit{total} enstrophy and energy in the DW-ZF system. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed theory can be viewed as a reformulation of the second-order cumulant expansion (also known as the CE2) in a more intuitive manner, namely, in terms of canonical phase-space variables.
Frost, W.; Harper, W. L.
1975-01-01
Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.
An equilibrium and kinetic modeling
African Journals Online (AJOL)
SERVER
2007-06-18
Jun 18, 2007 ... Potato dextrose agar medium was prepared by taking 200 g of peeled and sliced potato with .... of glucose as carbon source and ammonium chloride as nitrogen source each. .... Pore and solid diffusion kinetics in fixed bed ...
Institute of Scientific and Technical Information of China (English)
陈振兴; 李洪桂; 王零森
2004-01-01
The method to calculate internal surface effective factor of cylinder-type vanadium catalyst Ls-9 was given. Based on hypothesis of subjunctive one dimension diffusion and combined shape adjustment factor with threestep catalytic mechanism model, the macroscopic kinetic model equation about SO2 oxidation on Ls-9 was deduced.With fixed-bed integral reactor and under the conditions of temperature 350 - 410 ℃, space velocity 1 800 - 5 000h-1, SO2 inlet content 7 %- 12%, the macroscopic kinetic data were detected. Through model parameter estimation,the macroscopic kinetic model equation was obtained.
Kinetic Description for a Suspension of Inelastic Spheres - Boltzmann and BGK Equations
2007-11-02
Kinetic description for a suspension of inelastic spheres - Boltzmann and BGK equations Cedric Croizet and Renee Gatignol Laboratoire de Modelisation ...Organization Name(s) and Address(es) Laboratoire de Modelisation en Mecanique - Universite Pierre et Marie Curie (Paris 6) et CNRS UMR 7607 - 4) place
Quantum-kinetic equations for time correlation functions in higher-order perturbation theory
Leermakers, M.C.J.; Suttorp, L.G.
1981-01-01
The memory kernel of the kinetic equation for the time correlation function of a quantum fluid is determined both in third order of the interaction strength and in the low-density approximation. The results are obtained with the help of a diagram representation for the kernel. The connection with
Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation
Ölschläger, M.; Wirth, G.; de Morais Smith, C.; Hemmerich, Andreas
2009-01-01
Approximate solutions of the Gross–Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas–Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the
Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation
Ölschläger, M.; Wirth, G.; de Morais Smith, C.; Hemmerich, Andreas
2009-01-01
Approximate solutions of the Gross–Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas–Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-eq
Kinetic exchange models for social opinion formation
Lallouache, Mehdi; Chakrabarti, Bikas K
2010-01-01
We propose a minimal model for the collective dynamics of opinion formation in the society, by modifying kinetic exchange dynamics studied in the context of income, money or wealth distributions in a society.
Explicit Kinetic Flux Vector Splitting Scheme for the 2-D Shallow Water Wave Equations
Institute of Scientific and Technical Information of China (English)
施卫平; 黄明游; 王婷; 张小江
2004-01-01
Originally, the kinetic flux vector splitting (KFVS) scheme was developed as a numerical method to solve gas dynamic problems. The main idea in the approach is to construct the flux based on the microscopical description of the gas. In this paper, based on the analogy between the shallow water wave equations and the gas dynamic equations, we develop an explicit KFVS method for simulating the shallow water wave equations. A 1D steady flow and a 2D unsteady flow are presented to show the robust and accuracy of the KFVS scheme.
A multi-dimensional kinetic-based upwind solver for the Euler equations
Eppard, W. M.; Grossman, B.
1993-01-01
A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.
Solutions of the chemical kinetic equations for initially inhomogeneous mixtures.
Hilst, G. R.
1973-01-01
Following the recent discussions by O'Brien (1971) and Donaldson and Hilst (1972) of the effects of inhomogeneous mixing and turbulent diffusion on simple chemical reaction rates, the present report provides a more extensive analysis of when inhomogeneous mixing has a significant effect on chemical reaction rates. The analysis is then extended to the development of an approximate chemical sub-model which provides much improved predictions of chemical reaction rates over a wide range of inhomogeneities and pathological distributions of the concentrations of the reacting chemical species. In particular, the development of an approximate representation of the third-order correlations of the joint concentration fluctuations permits closure of the chemical sub-model at the level of the second-order moments of these fluctuations and the mean concentrations.
Interacting multiagent systems kinetic equations and Monte Carlo methods
Pareschi, Lorenzo
2014-01-01
The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics. Applied mathematics is concerned with the construction, analysis and interpretation of mathematical models that can shed light on significant problems of the natural sciences as well as our daily lives. To this set of problems belongs the description of the collective behaviours of complex systems composed by a large enough number of individuals. Examples of such systems are interacting agents in a financial market, potential voters during political elections, or groups of animals with a tendency to flock or herd. Among other possible approaches, this book provides a step-by-step introduction to the mathematical modelling based on a mesoscopic description and the construction of efficient simulation algorithms by Monte Carlo methods. The ar...
Constructing stochastic models from deterministic process equations by propensity adjustment
Directory of Open Access Journals (Sweden)
Wu Jialiang
2011-11-01
Full Text Available Abstract Background Gillespie's stochastic simulation algorithm (SSA for chemical reactions admits three kinds of elementary processes, namely, mass action reactions of 0th, 1st or 2nd order. All other types of reaction processes, for instance those containing non-integer kinetic orders or following other types of kinetic laws, are assumed to be convertible to one of the three elementary kinds, so that SSA can validly be applied. However, the conversion to elementary reactions is often difficult, if not impossible. Within deterministic contexts, a strategy of model reduction is often used. Such a reduction simplifies the actual system of reactions by merging or approximating intermediate steps and omitting reactants such as transient complexes. It would be valuable to adopt a similar reduction strategy to stochastic modelling. Indeed, efforts have been devoted to manipulating the chemical master equation (CME in order to achieve a proper propensity function for a reduced stochastic system. However, manipulations of CME are almost always complicated, and successes have been limited to relative simple cases. Results We propose a rather general strategy for converting a deterministic process model into a corresponding stochastic model and characterize the mathematical connections between the two. The deterministic framework is assumed to be a generalized mass action system and the stochastic analogue is in the format of the chemical master equation. The analysis identifies situations: where a direct conversion is valid; where internal noise affecting the system needs to be taken into account; and where the propensity function must be mathematically adjusted. The conversion from deterministic to stochastic models is illustrated with several representative examples, including reversible reactions with feedback controls, Michaelis-Menten enzyme kinetics, a genetic regulatory motif, and stochastic focusing. Conclusions The construction of a stochastic
Study on kinetic model of microwave thermocatalytic treatment of biomass tar model compound.
Anis, Samsudin; Zainal, Z A
2014-01-01
Kinetic model parameters for toluene conversion under microwave thermocatalytic treatment were evaluated. The kinetic rate constants were determined using integral method based on experimental data and coupled with Arrhenius equation for obtaining the activation energies and pre-exponential factors. The model provides a good agreement with the experimental data. The kinetic model was also validated with standard error of 3% on average. The extrapolation of the model showed a reasonable trend to predict toluene conversion and product yield both in thermal and catalytic treatments. Under microwave irradiation, activation energy of toluene conversion was lower in the range of 3-27 kJ mol(-1) compared to those of conventional heating reported in the literatures. The overall reaction rate was six times higher compared to conventional heating. As a whole, the kinetic model works better for tar model removal in the absence of gas reforming within a level of reliability demonstrated in this study.
Chemical Kinetic Modeling of Advanced Transportation Fuels
Energy Technology Data Exchange (ETDEWEB)
PItz, W J; Westbrook, C K; Herbinet, O
2009-01-20
Development of detailed chemical kinetic models for advanced petroleum-based and nonpetroleum based fuels is a difficult challenge because of the hundreds to thousands of different components in these fuels and because some of these fuels contain components that have not been considered in the past. It is important to develop detailed chemical kinetic models for these fuels since the models can be put into engine simulation codes used for optimizing engine design for maximum efficiency and minimal pollutant emissions. For example, these chemistry-enabled engine codes can be used to optimize combustion chamber shape and fuel injection timing. They also allow insight into how the composition of advanced petroleum-based and non-petroleum based fuels affect engine performance characteristics. Additionally, chemical kinetic models can be used separately to interpret important in-cylinder experimental data and gain insight into advanced engine combustion processes such as HCCI and lean burn engines. The objectives are: (1) Develop detailed chemical kinetic reaction models for components of advanced petroleum-based and non-petroleum based fuels. These fuels models include components from vegetable-oil-derived biodiesel, oil-sand derived fuel, alcohol fuels and other advanced bio-based and alternative fuels. (2) Develop detailed chemical kinetic reaction models for mixtures of non-petroleum and petroleum-based components to represent real fuels and lead to efficient reduced combustion models needed for engine modeling codes. (3) Characterize the role of fuel composition on efficiency and pollutant emissions from practical automotive engines.
Extended master equation models for molecular communication networks
Chou, Chun Tung
2012-01-01
We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signalling molecules, which are diffused over the medium, to the receiver to realise the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time sequences specify the emission patterns of signalling molecules, while diffusion in the medium and chemical reactions at the receivers are modelled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show ho...
Kinetic models for irreversible processes on a lattice
Energy Technology Data Exchange (ETDEWEB)
Wolf, N.O.
1979-04-01
The development and application of kinetic lattice models are considered. For the most part, the discussions are restricted to lattices in one-dimension. In Chapter 1, a brief overview of kinetic lattice model formalisms and an extensive literature survey are presented. A review of the kinetic models for non-cooperative lattice events is presented in Chapter 2. The development of cooperative lattice models and solution of the resulting kinetic equations for an infinite and a semi-infinite lattice are thoroughly discussed in Chapters 3 and 4. The cooperative models are then applied to the problem of theoretically dtermining the sticking coefficient for molecular chemisorption in Chapter 5. In Chapter 6, other possible applications of these models and several model generalizations are considered. Finally, in Chapter 7, an experimental study directed toward elucidating the mechanistic factors influencing the chemisorption of methane on single crystal tungsten is reported. In this it differs from the rest of the thesis which deals with the statistical distributions resulting from a given mechanism.
Hard-sphere kinetic models for inert and reactive mixtures
Polewczak, Jacek
2016-10-01
I consider stochastic variants of a simple reacting sphere (SRS) kinetic model (Xystris and Dahler 1978 J. Chem. Phys. 68 387-401, Qin and Dahler 1995 J. Chem. Phys. 103 725-50, Dahler and Qin 2003 J. Chem. Phys. 118 8396-404) for dense reacting mixtures. In contrast to the line-of-center models of chemical reactive models, in the SRS kinetic model, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justified. In the SRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard sphere-like. I consider a four component mixture A, B, A *, B *, in which the chemical reactions are of the type A+B\\rightleftharpoons {{A}\\ast}+{{B}\\ast} , with A * and B * being distinct species from A and B. This work extends the joined works with George Stell to the kinetic models of dense inert and reactive mixtures. The idea of introducing smearing-type effect in the collisional process results in a new class of stochastic kinetic models for both inert and reactive mixtures. In this paper the important new mathematical properties of such systems of kinetic equations are proven. The new results for stochastic revised Enskog system for inert mixtures are also provided.
Directory of Open Access Journals (Sweden)
V.V.Ignatyuk
2004-01-01
Full Text Available Non-Markovian kinetic equations in the second Born approximation are derived for a two-zone semiconductor excited by a short laser pulse. Both collision dynamics and running nonequilibrium correlations are taken into consideration. The energy balance and relaxation of the system to equilibrium are discussed. Results of numerical solution of the kinetic equations for carriers and phonons are presented.
Kinetic model of induced codeposition of Ni-Mo alloys
Institute of Scientific and Technical Information of China (English)
ZENG, Yue; MA, Ming; XIAO, Xiao-Ming; LI, Ze-Lin; LIAN, Shi-Xun; ZHOU, Shao-Min
2000-01-01
The kinetic model of induced codeposition of nickel-molybdenum alloys from ammoniun citrate solution was studied on rotating disk electrodes to predict the behavior of the electrodeposition. Ihe molybdate (MoO42-) could be firstly electrochemically reduced to MoO2, and subsequently undergoes a chemical reduction with atomic hydrogen previously adsorbed on the inducing metal nickel to form molybdenum in alloys.The kinetic equations were derived, and the kinetic parameters were obtained from a comparison of experimental results and the kinetic equations. The electrochemical rate constants for discharge of nickel, molybdenum and water could been expressed as k1 ( E ) = 1. 23 × 10-9 CNexp( - 0. 198FE/ RT )mol/(dm2. s), k2 (E) = 3.28 × 10-10 CMoexp ( - 0.208FE/RT) mol/(dm2·s) and k3(E) = 1.27 × 10-6exp( - 0.062FE/RT) mol/(dm2 ·s), where CN and CMo are the concentrations of the nickel ion and molybdate, respectively, and E is the applied potential vs, saturated calornel electrode (SCE).The codeposition process could be well simulated by this model.
Modeling helicity dissipation-rate equation
Yokoi, Nobumitsu
2016-01-01
Transport equation of the dissipation rate of turbulent helicity is derived with the aid of a statistical analytical closure theory of inhomogeneous turbulence. It is shown that an assumption on the helicity scaling with an algebraic relationship between the helicity and its dissipation rate leads to the transport equation of the turbulent helicity dissipation rate without resorting to a heuristic modeling.
Structural Equation Modeling of Multivariate Time Series
du Toit, Stephen H. C.; Browne, Michael W.
2007-01-01
The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…
Stochastic differential equation model to Prendiville processes
Energy Technology Data Exchange (ETDEWEB)
Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)
2015-10-22
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
Stochastic differential equation model to Prendiville processes
Granita, Bahar, Arifah
2015-10-01
The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.
KINETIC FLUX VECTOR SPLITTING FOR THE EULER EQUATIONS WITH GENERAL PRESSURE LAWS
Institute of Scientific and Technical Information of China (English)
Hua-zhong Tang
2004-01-01
This paper attempts to develop kinetic flux vector splitting (KFVS) for the Euler equations with general pressure laws. It is well known that the gas distribution function for the local equilibrium state plays an important role in the construction of the gas-kinetic schemes. To recover the Euler equations with a general equation of state (EOS), a new local equilibrium distribution is introduced with two parameters of temperature approximation decided uniquely by macroscopic variables. Utilizing the well-known connection that the Euler equations of motion are the moments of the Boltzmann equation whenever the velocity distribution function is a local equilibrium state, a class of high resolution MUSCL-type KFVS schemes are presented to approximate the Euler equations of gas dynamics with a general EOS. The schemes are finally applied to several test problems for a general EOS. In comparison with the exact solutions, our schemes give correct location and more accurate resolution of discontinuities. The extension of our idea to multidimensional case is natural.
Properties-preserving high order numerical methods for a kinetic eikonal equation
Luo, Songting; Payne, Nicholas
2017-02-01
For the BGK (Bhatnagar-Gross-Krook) equation in the large scale hyperbolic limit, the density of particles can be transformed as the Hopf-Cole transformation, where the phase function converges uniformly to the viscosity solution of an effective Hamilton-Jacobi equation, referred to as the kinetic eikonal equation. In this work, we present efficient high order finite difference methods for numerically solving the kinetic eikonal equation. The methods are based on monotone schemes such as the Godunov scheme. High order weighted essentially non-oscillatory techniques and Runge-Kutta procedures are used to obtain high order accuracy in both space and time. The effective Hamiltonian is determined implicitly by a nonlinear equation given as integrals with respect to the velocity variable. Newton's method is applied to solve the nonlinear equation, where integrals with respect to the velocity variable are evaluated either by a Gauss quadrature formula or as expansions with respect to moments of the Maxwellian. The methods are designed such that several key properties such as the positivity of the viscosity solution and the positivity of the effective Hamiltonian are preserved. Numerical experiments are presented to demonstrate the effectiveness of the methods.
A first course in structural equation modeling
Raykov, Tenko
2012-01-01
In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...
A kinetic model for predicting biodegradation.
Dimitrov, S; Pavlov, T; Nedelcheva, D; Reuschenbach, P; Silvani, M; Bias, R; Comber, M; Low, L; Lee, C; Parkerton, T; Mekenyan, O
2007-01-01
Biodegradation plays a key role in the environmental risk assessment of organic chemicals. The need to assess biodegradability of a chemical for regulatory purposes supports the development of a model for predicting the extent of biodegradation at different time frames, in particular the extent of ultimate biodegradation within a '10 day window' criterion as well as estimating biodegradation half-lives. Conceptually this implies expressing the rate of catabolic transformations as a function of time. An attempt to correlate the kinetics of biodegradation with molecular structure of chemicals is presented. A simplified biodegradation kinetic model was formulated by combining the probabilistic approach of the original formulation of the CATABOL model with the assumption of first order kinetics of catabolic transformations. Nonlinear regression analysis was used to fit the model parameters to OECD 301F biodegradation kinetic data for a set of 208 chemicals. The new model allows the prediction of biodegradation multi-pathways, primary and ultimate half-lives and simulation of related kinetic biodegradation parameters such as biological oxygen demand (BOD), carbon dioxide production, and the nature and amount of metabolites as a function of time. The model may also be used for evaluating the OECD ready biodegradability potential of a chemical within the '10-day window' criterion.
Energy Technology Data Exchange (ETDEWEB)
Zhidkov, A.B.; Smirnov, E.P.
1989-02-01
This work is devoted to the study of the kinetics of the reaction of titanium tetrachloride with the hydride functional groups of diamond. The research was performed on submicron powders of ASM 0.7/0.3 grade synthetic diamond with a specific surface area of 8.0 m/sup 2//g as measured from the adsorption of nitrogen. The reaction was carried out in a flow-through quartz reactor in a flow of dry He. The content of the titanium in the samples was determined by a photocolorimetric method. A kinetic equation for the reaction of diamond with titanium tetrachloride was found on the basis of a statistical approach.
Trigonometric Fourier-series solutions of the point reactor kinetics equations
Energy Technology Data Exchange (ETDEWEB)
Hamada, Yasser Mohamed, E-mail: yaser_abdelsatar@ci.suez.edu.eg
2015-01-15
Highlights: • A new method based on Fourier series expansion is introduced. • The method provides accurate approximations to the point kinetics equations. • Vandermonde matrix is used to determine the coefficients of the Fourier series. • A new formula is introduced to determine the inverse of the Vandermonde matrix. • The obtained results agree well with those obtained with other conventional codes. - Abstract: In this paper, a new method based on the Fourier series is introduced to obtain approximate solutions to the systems of the point kinetics equations. These systems are stiff involving equations with slowly and rapidly varying components. They are solved numerically using Fourier series expansion over a partition of the total time interval. Approximate solution requires determining the series coefficients over each time step in that partition. These coefficients are determined using the high order derivatives of the dependent variables at the beginning of the time step introducing a system of linear algebraic equations to be solved at each step. The obtained algebraic system is similar to the Vandermonde system. Evaluation of the inverse of the Vandermonde matrix is required to determine the coefficients of the Fourier series. Because the obtained Vandermonde matrix has a special structure, due to the properties of the sine and cosine functions, a new formula is introduced to determine its inverse using standard computations. The new method solves the general linear and non-linear kinetics problems with six groups of delayed neutrons. The validity of the algorithm is tested with five different types of reactivities including step reactivity insertion, ramp input, oscillatory reactivity changes, a reactivity as a function of the neutron density and finally temperature feedback reactivity. Comparisons are made with analytical and conventional numerical methods used to solve the point kinetics equations. The results confirm the theoretical analysis
Partial Differential Equations Modeling and Numerical Simulation
Glowinski, Roland
2008-01-01
This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...
Structural equation modeling methods and applications
Wang, Jichuan
2012-01-01
A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...
Modified Heisenberg Ferromagnet Model and Integrable Equation
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We investigate some integrable modified Heisenberg ferromagnet models by using the prolongation structure theory. Through associating them with the motion of curve in Minkowski space, the corresponding coupled integrable equations are presented.
Invariance principle and model reduction for the Fokker-Planck equation
Karlin, I. V.
2016-11-01
The principle of dynamic invariance is applied to obtain closed moment equations from the Fokker-Planck kinetic equation. The analysis is carried out to explicit formulae for computation of the lowest eigenvalue and of the corresponding eigenfunction for arbitrary potentials. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
Linear causal modeling with structural equations
Mulaik, Stanley A
2009-01-01
Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal
Combat modeling with partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Protopopescu, V.; Santoro, R.T.; Dockery, J.; Cox, R.L.; Barnes, J.M.
1987-11-01
A new analytic model based on coupled nonlinear partial differential equations is proposed to describe the temporal and spatial evolution of opposing forces in combat. Analytic descriptions of combat have been developed previously using relatively simpler models based on ordinary differential equations (.e.g, Lanchester's equations of combat) that capture only the global temporal variation of the forces, but not their spatial movement (advance, retreat, flanking maneuver, etc.). The rationale for analytic models and, particularly, the motivation for the present model are reviewed. A detailed description of this model in terms of the mathematical equations together with the possible and plausible military interpretation are presented. Numerical solutions of the nonlinear differential equation model for a large variety of parameters (battlefield length, initial force ratios, initial spatial distribution of forces, boundary conditions, type of interaction, etc.) are implemented. The computational methods and computer programs are described and the results are given in tabular and graphic form. Where possible, the results are compared with the predictions given by the traditional Lanchester equations. Finally, a PC program is described that uses data downloaded from the mainframe computer for rapid analysis of the various combat scenarios. 11 refs., 10 figs., 5 tabs.
Kinetic models for historical processes of fast invasion and aggression
Aristov, Vladimir V.; Ilyin, Oleg V.
2015-04-01
In the last few decades many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological, and historical processes. In the present paper we suggest a model of the Nazi Germany invasion of Poland, France, and the USSR based on kinetic theory. We simulate this process with the Cauchy boundary problem for two-element kinetic equations. The solution of the problem is given in the form of a traveling wave. The propagation velocity of a front line depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be expressed in terms of quadratures and elementary functions. Finally it is shown that the front-line velocities agree with the historical data.
Modelling of an ASR countercurrent pyrolysis reactor with nonlinear kinetics
Energy Technology Data Exchange (ETDEWEB)
Chiarioni, A.; Reverberi, A.P.; Dovi, V.G. [Universita degli Studi di Genova (Italy). Dipartimento di Ingegneria Chimica e di Processo ' G.B. Bonino' ; El-Shaarawi, A.H. [National Water Research Institute, Burlington, Ont. (Canada)
2003-10-01
The main objective of this work is focused on the modelling of a steady-state reactor where an automotive shredder residue (ASR) is subject to pyrolysis. The gas and solid temperature inside the reactor and the relevant density profiles of both phases are simulated for fixed values of the geometry of the apparatus and a lumped kinetic model is adopted to take into account the high heterogeneity of the ASR material. The key elements for the simulation are the inlet solid temperature and the outlet gas temperature. The problem is modelled by a system of first-order boundary-value ordinary differential equations and it is solved by means of a relaxation technique owing to the nonlinearities contained in the chemical kinetic expression. (author)
Energy Technology Data Exchange (ETDEWEB)
Silva, Milena W. Da; Vilhena, Marco T. de; Bodmann, Bardo E., E-mail: milena.wollmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardobodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Leite, Sergio B., E-mail: bogado@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RS (Brazil)
2013-07-01
In this work, we report on an analytical representation for the solution of the neutron point kinetics equation, free of stiffness and assuming that the reactivity is a continuous or sectionally continuous function of time. To this end, we cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix into a diagonal matrix plus a matrix that contains the remaining terms. Expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, allows one to construct a recursive system, in form of a first order matrix differential equation with source. The initialization of the recursion procedure is of diagonal form and has no source, but satisfies the initial conditions. The remaining equations are subject to null initial conditions and include the time dependent diagonal elements together with the off diagonal elements as a source term. The solution is obtained in analytical representation which may be evaluated for any time value, because it is free of stiffness. We present numerical simulations and comparisons against results from the literature, for a constant, a step, a ramp, a quadratic and sine shaped reactivity function. (author)
Numerical solution of point kinetic equations by matrix decomposition and T series expansions
Energy Technology Data Exchange (ETDEWEB)
Silva, Jeronimo J.A.; Alvim, Antonio C.M., E-mail: shaolin.jr@gmail.com, E-mail: alvim@nuclear.ufrj.br [Coordenacao dos Programas de Pos-Graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil); Vilhena, Marco T.M.B., E-mail: vilhena@pq.cnpq.br [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2013-07-01
Recently, an analytical solution of the Point Kinetics equations free from stiffness problems has been presented. The equations, cast in matrix form are split into diagonal plus off-diagonal matrices and a series expansion of neutron density and precursor concentrations is done, producing a recurrent system which is then solved analytically. In this paper, a numerical finite differences equivalent of this decomposition plus expansion method is derived and applied to the same problems tested in the analytical case. As a result, the number of terms in the expansions needed for holding steady state is obtained, as well as results for the transient cases, with good agreement between solutions. (author)
Validation of the point kinetic neutronic model of the PBMR / Deon Marais
Marais, Deon
2007-01-01
This study introduces a new method for the validation of the point kinetic neutronic model of the PBMR. In this study the diffusion equation solution, as implemented in the TlNTE PBMR 268 MW reactor model, replaces the point kinetic model, as implemented in the Flownex V502 PBMR plant model. An indirect coupling method is devised and implemented in an external program called Flownex-Tinte-Interface (FTI) to facilitate the data exchange between these two codes. The validation...
An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit
Wang, Li; Yan, Bokai
2016-05-01
We present a new asymptotic-preserving scheme for the linear Boltzmann equation which, under appropriate scaling, leads to a fractional diffusion limit. Our scheme rests on novel micro-macro decomposition to the distribution function, which splits the original kinetic equation following a reshuffled Hilbert expansion. As opposed to classical diffusion limit, a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter. Our idea is, while solving the macro-micro part in a truncated velocity domain (truncation only depends on numerical accuracy), to incorporate an integrated tail over the velocity space that is beyond the truncation, and its major component can be precomputed once with any accuracy. Such an addition is essential to drive the solution to the correct asymptotic limit. Numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes.
Chiba, G.; Tsuji, M.; Narabayashi, T.
2014-04-01
In order to better predict a kinetic behavior of a nuclear fission reactor, an improvement of the delayed neutron parameters is essential. The present paper specifies important nuclear data for a reactor kinetics: Fission yield and decay constant data of 86Ge, some bromine isotopes, 94Rb, 98mY and some iodine isotopes. Their importance is quantified as sensitivities with a help of the adjoint kinetic equation, and it is found that they are dependent on an inserted reactivity (or a reactor period). Moreover, dependence of sensitivities on nuclear data files is also quantified using the latest files. Even though the currently evaluated data are used, there are large differences among different data files from a view point of the delayed neutrons.
Structural Equation Modeling in Special Education Research.
Moore, Alan D.
1995-01-01
This article suggests the use of structural equation modeling in special education research, to analyze multivariate data from both nonexperimental and experimental research. It combines a structural model linking latent variables and a measurement model linking observed variables with latent variables. (Author/DB)
Multiplicity Control in Structural Equation Modeling
Cribbie, Robert A.
2007-01-01
Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…
Directory of Open Access Journals (Sweden)
Yang Xue
2009-01-01
Full Text Available The fourth order Rosenbrock method with an automatic step size control feature was described and applied to solve the reactor point kinetics equations. A FORTRAN 90 program was developed to test the computational speed and algorithm accuracy. From the results of various benchmark tests with different types of reactivity insertions, the Rosenbrock method shows high accuracy, high efficiency and stable character of the solution.
The heat flux from a relativistic kinetic equation with a simplified collision kernel
Sandoval-Villalbazo, A; García-Colin, L S
2009-01-01
We show how using a special relativistic kinetic equation with a BGK- like collision operator the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so-called "first order in the gradients theories" contend. Here we calculate explicitly the ensuing transport coefficients and compare them with the results obtained by other authors.
Chemical Kinetic Models for Advanced Engine Combustion
Energy Technology Data Exchange (ETDEWEB)
Pitz, William J. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Mehl, Marco [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Westbrook, Charles K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2014-10-22
The objectives for this project are as follows: Develop detailed chemical kinetic models for fuel components used in surrogate fuels for compression ignition (CI), homogeneous charge compression ignition (HCCI) and reactivity-controlled compression-ignition (RCCI) engines; and Combine component models into surrogate fuel models to represent real transportation fuels. Use them to model low-temperature combustion strategies in HCCI, RCCI, and CI engines that lead to low emissions and high efficiency.
Study of carbon dioxide gas treatment based on equations of kinetics in plasma discharge reactor
Abedi-Varaki, Mehdi
2017-08-01
Carbon dioxide (CO2) as the primary greenhouse gas, is the main pollutant that is warming earth. CO2 is widely emitted through the cars, planes, power plants and other human activities that involve the burning of fossil fuels (coal, natural gas and oil). Thus, there is a need to develop some method to reduce CO2 emission. To this end, this study investigates the behavior of CO2 in dielectric barrier discharge (DBD) plasma reactor. The behavior of different species and their reaction rates are studied using a zero-dimensional model based on equations of kinetics inside plasma reactor. The results show that the plasma reactor has an effective reduction on the CO2 density inside the reactor. As a result of reduction in the temporal variations of reaction rate, the speed of chemical reactions for CO2 decreases and very low concentration of CO2 molecules inside the plasma reactor is generated. The obtained results are compared with the existing experimental and simulation findings in the literature.
Global identifiability of linear structural equation models
Drton, Mathias; Sullivant, Seth
2010-01-01
Structural equation models are multivariate statistical models that are defined by specifying noisy functional relationships among random variables. We consider the classical case of linear relationships and additive Gaussian noise terms. We give a necessary and sufficient condition for global identifiability of the model in terms of a mixed graph encoding the linear structural equations and the correlation structure of the error terms. Global identifiability is understood to mean injectivity of the parametrization of the model and is fundamental in particular for applicability of standard statistical methodology.
Basics of Structural Equation Modeling
Maruyama, Dr Geoffrey M
1997-01-01
With the availability of software programs, such as LISREL, EQS, and AMOS, modeling (SEM) techniques have become a popular tool for formalized presentation of the hypothesized relationships underlying correlational research and test for the plausibility of hypothesizing for a particular data set. Through the use of careful narrative explanation, Maruyama's text describes the logic underlying SEM approaches, describes how SEM approaches relate to techniques like regression and factor analysis, analyzes the strengths and shortcomings of SEM as compared to alternative methodologies, and explores
String Field Equations from Generalized Sigma Model
Energy Technology Data Exchange (ETDEWEB)
Bardakci, K.; Bernardo, L.M.
1997-01-29
We propose a new approach for deriving the string field equations from a general sigma model on the world-sheet. This approach leads to an equation which combines some of the attractive features of both the renormalization group method and the covariant beta function treatment of the massless excitations. It has the advantage of being covariant under a very general set of both local and non-local transformations in the field space. We apply it to the tachyon, massless and first massive level, and show that the resulting field equations reproduce the correct spectrum of a left-right symmetric closed bosonic string.
Kinetics approach to modeling of polymer additive degradation in lubricants
Institute of Scientific and Technical Information of China (English)
llyaI.KUDISH; RubenG.AIRAPETYAN; Michael; J.; COVITCH
2001-01-01
A kinetics problem for a degrading polymer additive dissolved in a base stock is studied.The polymer degradation may be caused by the combination of such lubricant flow parameters aspressure, elongational strain rate, and temperature as well as lubricant viscosity and the polymercharacteristics (dissociation energy, bead radius, bond length, etc.). A fundamental approach tothe problem of modeling mechanically induced polymer degradation is proposed. The polymerdegradation is modeled on the basis of a kinetic equation for the density of the statistical distribu-tion of polymer molecules as a function of their molecular weight. The integrodifferential kineticequation for polymer degradation is solved numerically. The effects of pressure, elongational strainrate, temperature, and lubricant viscosity on the process of lubricant degradation are considered.The increase of pressure promotes fast degradation while the increase of temperature delaysdegradation. A comparison of a numerically calculated molecular weight distribution with an ex-perimental one obtained in bench tests showed that they are in excellent agreement with eachother.
Kinetic model of metabolic network for xiamenmycin biosynthetic optimisation.
Xu, Min-juan; Chen, Yong-cong; Xu, Jun; Ao, Ping; Zhu, Xiao-mei
2016-02-01
Xiamenmycins, a series of prenylated benzopyran compounds with anti-fibrotic bioactivities, were isolated from a mangrove-derived Streptomyces xiamenensis. To fulfil the requirements of pharmaceutical investigations, a high production of xiamenmycin is needed. In this study, the authors present a kinetic metabolic model to evaluate fluxes in an engineered Streptomyces lividans with xiamenmycin-oriented genetic modification based on generic enzymatic rate equations and stability constraints. Lyapunov function was used for a viability optimisation. From their kinetic model, the flux distributions for the engineered S. lividans fed on glucose and glycerol as carbon sources were calculated. They found that if the bacterium can utilise glucose simultaneously with glycerol, xiamenmycin production can be enhanced by 40% theoretically, while maintaining the same growth rate. Glycerol may increase the flux for phosphoenolpyruvate synthesis without interfering citric acid cycle. They therefore believe this study demonstrates a possible new direction for bioengineering of S. lividans.
Pratt, D. T.; Radhakrishnan, K.
1986-01-01
The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.
Entropic lattice Boltzmann model for Burgers's equation.
Boghosian, Bruce M; Love, Peter; Yepez, Jeffrey
2004-08-15
Entropic lattice Boltzmann models are discrete-velocity models of hydrodynamics that possess a Lyapunov function. This feature makes them useful as nonlinearly stable numerical methods for integrating hydrodynamic equations. Over the last few years, such models have been successfully developed for the Navier-Stokes equations in two and three dimensions, and have been proposed as a new category of subgrid model of turbulence. In the present work we develop an entropic lattice Boltzmann model for Burgers's equation in one spatial dimension. In addition to its pedagogical value as a simple example of such a model, our result is actually a very effective way to simulate Burgers's equation in one dimension. At moderate to high values of viscosity, we confirm that it exhibits no trace of instability. At very small values of viscosity, however, we report the existence of oscillations of bounded amplitude in the vicinity of the shock, where gradient scale lengths become comparable with the grid size. As the viscosity decreases, the amplitude at which these oscillations saturate tends to increase. This indicates that, in spite of their nonlinear stability, entropic lattice Boltzmann models may become inaccurate when the ratio of gradient scale length to grid spacing becomes too small. Similar inaccuracies may limit the utility of the entropic lattice Boltzmann paradigm as a subgrid model of Navier-Stokes turbulence.
A kinetic model of zircon thermoluminescence
Turkin, A.A.; Es, H.J. van; Vainshtein, D.I.; Hartog, H.W. den
A kinetic model of zircon thermoluminescence (TL) has been constructed to simulate the processes and stages relevant to thermoluminescent dating such as: filling of electron and hole traps during the excitation stage both for natural and laboratory irradiation; the time dependence of fading after
Kinetic modeling of reactions in Foods
Boekel, van M.A.J.S.
2008-01-01
The level of quality that food maintains as it travels down the production-to-consumption path is largely determined by the chemical, biochemical, physical, and microbiological changes that take place during its processing and storage. Kinetic Modeling of Reactions in Foods demonstrates how to effec
Energy Technology Data Exchange (ETDEWEB)
Kolobov, Vladimir [CFD Research Corporation, Huntsville, AL 35805, USA and The University of Alabama in Huntsville, Huntsville, AL 35805 (United States); Arslanbekov, Robert [CFD Research Corporation, Huntsville, AL 35805 (United States); Frolova, Anna [Computing Center of the Russian Academy of Sciences, Moscow, 119333 (Russian Federation)
2014-12-09
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
Kinetics model development of cocoa bean fermentation
Kresnowati, M. T. A. P.; Gunawan, Agus Yodi; Muliyadini, Winny
2015-12-01
Although Indonesia is one of the biggest cocoa beans producers in the world, Indonesian cocoa beans are oftenly of low quality and thereby frequently priced low in the world market. In order to improve the quality, adequate post-harvest cocoa processing techniques are required. Fermentation is the vital stage in series of cocoa beans post harvest processing which could improve the quality of cocoa beans, in particular taste, aroma, and colours. During the fermentation process, combination of microbes grow producing metabolites that serve as the precursors for cocoa beans flavour. Microbial composition and thereby their activities will affect the fermentation performance and influence the properties of cocoa beans. The correlation could be reviewed using a kinetic model that includes unstructured microbial growth, substrate utilization and metabolic product formation. The developed kinetic model could be further used to design cocoa bean fermentation process to meet the expected quality. Further the development of kinetic model of cocoa bean fermentation also serve as a good case study of mixed culture solid state fermentation, that has rarely been studied. This paper presents the development of a kinetic model for solid-state cocoa beans fermentation using an empirical approach. Series of lab scale cocoa bean fermentations, either natural fermentations without starter addition or fermentations with mixed yeast and lactic acid bacteria starter addition, were used for model parameters estimation. The results showed that cocoa beans fermentation can be modelled mathematically and the best model included substrate utilization, microbial growth, metabolites production and its transport. Although the developed model still can not explain the dynamics in microbial population, this model can sufficiently explained the observed changes in sugar concentration as well as metabolic products in the cocoa bean pulp.
Computational model for Halorhodopsin photocurrent kinetics
Bravo, Jaime; Stefanescu, Roxana; Talathi, Sachin
2013-03-01
Optogenetics is a rapidly developing novel optical stimulation technique that employs light activated ion channels to excite (using channelrhodopsin (ChR)) or suppress (using halorhodopsin (HR)) impulse activity in neurons with high temporal and spatial resolution. This technique holds enormous potential to externally control activity states in neuronal networks. The channel kinetics of ChR and HR are well understood and amenable for mathematical modeling. Significant progress has been made in recent years to develop models for ChR channel kinetics. To date however, there is no model to mimic photocurrents produced by HR. Here, we report the first model developed for HR photocurrents based on a four-state model of the HR photocurrent kinetics. The model provides an excellent fit (root-mean-square error of 3.1862x10-4, to an empirical profile of experimentally measured HR photocurrents. In combination, mathematical models for ChR and HR photocurrents can provide effective means to design test light based control systems to regulate neural activity, which in turn may have implications for the development of novel light based stimulation paradigms for brain disease control. I would like to thank the University of Florida and the Physics Research Experience for Undergraduates (REU) program, funded through NSF DMR-1156737. This research was also supported through start-up funds provided to Dr. Sachin Talathi
Fu, Mingkun; Perlman, Michael; Lu, Qing; Varga, Csanad
2015-03-25
An accelerated stress approach utilizing the moisture-modified Arrhenius equation and JMP statistical software was utilized to quantitatively assess the solid state stability of an investigational oncology drug MLNA under the influence of temperature (1/T) and humidity (%RH). Physical stability of MLNA under stress conditions was evaluated by using XRPD, DSC, TGA, and DVS, while chemical stability was evaluated by using HPLC. The major chemical degradation product was identified as a hydrolysis product of MLNA drug substance, and was subsequently subjected to an investigation of kinetics based on the isoconversion concept. A mathematical model (ln k=-11,991×(1/T)+0.0298×(%RH)+29.8823) based on the initial linear kinetics observed for the formation of this degradant at all seven stress conditions was built by using the moisture-modified Arrhenius equation and JMP statistical software. Comparison of the predicted versus experimental lnk values gave a mean deviation value of 5.8%, an R(2) value of 0.94, a p-value of 0.0038, and a coefficient of variation of the root mean square error CV(RMSE) of 7.9%. These statistics all indicated a good fit to the model for the stress data of MLNA. Both temperature and humidity were shown to have a statistically significant impact on stability by using effect leverage plots (p-valueArrhenius equation modeling theory. The model was found to be of value to aid setting of specifications and retest period, and storage condition selection. A model was also generated using only four conditions, as an example from a resource saving perspective, which was found to provide a good fit to the entire set of data. Copyright © 2015 Elsevier B.V. All rights reserved.
Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation
Ölschläger, M.; Wirth, G.; Smith, C. Morais; Hemmerich, A.
2009-04-01
Approximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas-Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-equation with this property and definite values of the kinetic energy, which suggests the term "kinetic Thomas-Fermi" (KTF) solutions. Despite their formal simplicity, KTF-solutions can possess complex current density fields with unconventional topology. We point out that a large class of light-shift potentials gives rise to KTF-solutions. As elementary examples, we consider one-dimensional and two-dimensional optical lattice scenarios, obtained by means of the superposition of two, three and four laser beams, and discuss the stability properties of the corresponding KTF-solutions. A general method is proposed to excite two-dimensional KTF-solutions in experiments by means of time-modulated light-shift potentials.
Sun, Wenjun; Jiang, Song; Xu, Kun; Li, Shu
2015-12-01
This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP) scheme in all
Reduced Chemical Kinetic Model for Titan Entries
Directory of Open Access Journals (Sweden)
Romain Savajano
2011-01-01
Full Text Available A reduced chemical kinetic model for Titan's atmosphere has been developed. This new model with 18 species and 28 reactions includes the mainfeatures of a more complete scheme, respecting the radiative fluxes. It has been verified against three key elements: a sensitivity analysis, the equilibrium chemical composition using shock tube simulations in CHEMKIN, and the results of computational fluid dynamics (CFDs simulations.
Alkaline Hydrolysis Kinetics Modeling of Bagasse Pentosan Dissolution
Directory of Open Access Journals (Sweden)
Yuxin Liu
2013-11-01
Full Text Available The main pentosan components of sugarcane bagasse, which can be subjected to alkaline hydrolysis, are xylose, arabinose, glucose, and galactose. The pentosan reaction mechanism was considered for alkali-treated bagasse with variation of temperature and time. The kinetics of pentosan degradation were studied concurrently at temperatures of 50 °C, 70 °C, and 90 °C, with a solid-liquid mass ratio of 1:15, a stirring speed of 500 revolutions/min, and different holding times for bagasse alkali pre-extraction. With respect to residual pentosan content and the losses of raw material, the hydrolysis rates of alkali pre-extraction and pentosan degradation reactions of bagasse all followed pseudo-first-order kinetic models. Finally, the main degradation activation energy was determined to be 20.86 KJ/mol, and the residual degradation activation energy was 28.75 KJ/mol according to the Arrhenius equation.
Compartmental modeling and tracer kinetics
Anderson, David H
1983-01-01
This monograph is concerned with mathematical aspects of compartmental an alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a ...
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... that describes the variation between subjects. The ODE setup implies that the variation for a single subject is described by a single parameter (or vector), namely the variance (covariance) of the residuals. Furthermore the prediction of the states is given as the solution to the ODEs and hence assumed...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...
Feng, Xin; Ye, Xingyou; Park, Jun-Bom; Lu, Wenli; Morott, Joe; Beissner, Brad; Lian, Zhuoyang John; Pinto, Elanor; Bi, Vivian; Porter, Stu; Durig, Tom; Majumdar, Soumyajit; Repka, Michael A
2015-01-01
The recrystallization of an amorphous drug in a solid dispersion system could lead to a loss in the drug solubility and bioavailability. The primary objective of the current research was to use an improved kinetic model to evaluate the recrystallization kinetics of amorphous structures and to further understand the factors influencing the physical stability of amorphous solid dispersions. Amorphous solid dispersions of fenofibrate with different molecular weights of hydroxypropylcellulose, HPC (Klucel™ LF, EF, ELF) were prepared utilizing hot-melt extrusion technology. Differential scanning calorimetry was utilized to quantitatively analyze the extent of recrystallization in the samples stored at different temperatures and relative humidity (RH) conditions. The experimental data were fitted into the improved kinetics model of a modified Avrami equation to calculate the recrystallization rate constants. Klucel LF, the largest molecular weight among the HPCs used, demonstrated the greatest inhibition of fenofibrate recrystallization. Additionally, the recrystallization rate (k) decreased with increasing polymer content, however exponentially increased with higher temperature. Also k increased linearly rather than exponentially over the range of RH studied.
Thermodynamic and kinetic modelling: creep resistant materials
DEFF Research Database (Denmark)
Hald, John; Korcakova, L.; Danielsen, Hilmar Kjartansson
2008-01-01
particles and coarsening of MX, M23C6 and Laves phase particles. The modelling provided new insight into the long term stability of new steels. Modelling of the detrimental precipitation of Z phase Cr(V,Nb)N is described, which points to new approaches in alloy development for higher temperatures......The use of thermodynamic and kinetic modelling of microstructure evolution in materials exposed to high temperatures in power plants is demonstrated with two examples. Precipitate stability in martensitic 9–12%Cr steels is modelled including equilibrium phase stability, growth of Laves phase...
Advanced structural equation modeling issues and techniques
Marcoulides, George A
2013-01-01
By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.
Structural Equation Modeling in Rehabilitation Counseling Research
Chan, Fong; Lee, Gloria K.; Lee, Eun-Jeong; Kubota, Coleen; Allen, Chase A.
2007-01-01
Structural equation modeling (SEM) has become increasingly popular in counseling, psychology, and rehabilitation research. The purpose of this article is to provide an overview of the basic concepts and applications of SEM in rehabilitation counseling research using the AMOS statistical software program.
Application of a hybrid kinetic-continuum solver to the near wall modelling
Rovenskaya, O.; Croce, G.
2014-11-01
A hybrid method dynamically coupling the direct numerical solution of the S-model kinetic equation and Navier-Stokes equations is applied to a numerical simulation of the flow through the channel of a finite length due to arbitrarily pressure ratios and for a wide range of Knudsen number. The decomposition of the physical domain into kinetic and hydrodynamic sub-domains is updated at each time step. The solution is advanced in time simultaneously in both kinetic and hydrodynamic domains: the coupling is achieved by matching half fluxes at the interface of the kinetic and Navier-Stokes domains, thus taking care of the conservation of momentum, energy and mass through the interface. Solver efficiency is increased via MPI (Message Passing Interface) parallelization. Accuracy and reliability of the method, for different decomposition criteria, are assessed via comparison with a pure kinetic solution.
Langrangian model of nitrogen kinetics in the Chattahoochee river
Jobson, H.E.
1987-01-01
A Lagrangian reference frame is used to solve the convection-dispersion equation and interpret water-quality obtained from the Chattahoochee River. The model was calibrated using unsteady concentrations of organic nitrogen, ammonia, and nitrite plus nitrate obtained during June 1977 and verified using data obtained during August 1976. Reaction kinetics of the cascade type are shown to provide a reasonable description of the nitrogen-species processes in the Chattahoochee River. The conceptual model is easy to visualize in the physical sense and the output includes information that is not easily determined from an Eulerian approach, but which is very helpful in model calibration and data interpretation. For example, the model output allows one to determine which data are of most value in model calibration or verification.
Simulation of styrene polymerization reactors: kinetic and thermodynamic modeling
Directory of Open Access Journals (Sweden)
A. S. Almeida
2008-06-01
Full Text Available A mathematical model for the free radical polymerization of styrene is developed to predict the steady-state and dynamic behavior of a continuous process. Special emphasis is given for the kinetic and thermodynamic models, where the most sensitive parameters were estimated using data from an industrial plant. The thermodynamic model is based on a cubic equation of state and a mixing rule applied to the low-pressure vapor-liquid equilibrium of polymeric solutions, suitable for modeling the auto-refrigerated polymerization reactors, which use the vaporization rate to remove the reaction heat from the exothermic reactions. The simulation results show the high predictive capability of the proposed model when compared with plant data for conversion, average molecular weights, polydispersity, melt flow index, and thermal properties for different polymer grades.
Kinetic modeling of 3D equilibria in a tokamak
Albert, C. G.; Heyn, M. F.; Kasilov, S. V.; Kernbichler, W.; Martitsch, A. F.; Runov, A. M.
2016-11-01
External resonant magnetic perturbations (RMPs) can modify the magnetic topology in a tokamak. In this case the magnetic field cannot generally be described by ideal MHD equilibrium equations in the vicinity of resonant magnetic surfaces where parallel and perpendicular relaxation timescales are comparable. Usually, resistive MHD models are used to describe these regions. In the present work, a kinetic model is used for this purpose. Within this model, plasma response, current and charge density are computed with help of a Monte Carlo method, where guiding center orbit equations are solved using a semianalytical geometrical integrator. Besides its higher efficiency in comparison to usual integrators this method is not sensitive to noise in field quantities. The computed charges and currents are used to calculate the electromagnetic field with help of a finite element solver. A preconditioned iterative scheme is applied to search for a self-consistent solution. The discussed method is aimed at the nonlinear kinetic description of RMPs in experiments on Edge Localized Mode (ELM) mitigation by external perturbation coil systems without simplification of the device geometry.
Energy Technology Data Exchange (ETDEWEB)
Shtykov, N. M., E-mail: nshtykov@mail.ru; Palto, S. P.; Umanskii, B. A. [Russian Academy of Sciences, Shubnikov Institute of Crystallography (Russian Federation)
2013-08-15
We report on the results of calculating the conditions for light generation in cholesteric liquid crystals doped with fluorescent dyes using kinetic equations. Specific features of spectral properties of the chiral cholesteric medium as a photonic structure and spatially distributed type of the feedback in the active medium are taken into account. The expression is derived for the threshold pump radiation intensity as a function of the dye concentration and sample thickness. The importance of taking into account the distributed loss level in the active medium for calculating the optimal parameters of the medium and for matching the calculated values with the results of experiments is demonstrated.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.
Capolupo, A; Giampaolo, S M; Illuminati, F
2013-10-01
Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly
Capolupo, Antonio; Illuminati, Fabrizio
2013-01-01
Based on accurate Lennard-Jones type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analogue in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed.
MODELING STYRENE HYDROGENATION KINETICS USING PALLADIUM CATALYSTS
Directory of Open Access Journals (Sweden)
G. T. Justino
Full Text Available Abstract The high octane number of pyrolysis gasoline (PYGAS explains its insertion in the gasoline pool. However, its use is troublesome due to the presence of gum-forming chemicals which, in turn, can be removed via hydrogenation. The use of Langmuir-Hinshelwood kinetic models was evaluated for hydrogenation of styrene, a typical gum monomer, using Pd/9%Nb2O5-Al2O3 as catalyst. Kinetic models accounting for hydrogen dissociative and non-dissociative adsorption were considered. The availability of one or two kinds of catalytic sites was analyzed. Experiments were carried out in a semi-batch reactor at constant temperature and pressure in the absence of transport limitations. The conditions used in each experiment varied between 16 - 56 bar and 60 - 100 ºC for pressure and temperature, respectively. The kinetic models were evaluated using MATLAB and EMSO software. Models using adsorption of hydrogen and organic molecules on the same type of site fitted the data best.
Kierkels, A. H. M.; Velázquez, J. J. L.
2016-06-01
We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.
Equation of motion of canonical tensor model and Hamilton-Jacobi equation of general relativity
Chen, Hua; Sato, Yuki
2016-01-01
The canonical tensor model (CTM) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the ADM formalism of general relativity, and is studied as a discretized model for quantum gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the tensor up to the forth order, and show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal s...
Phonon Boltzmann equation-based discrete unified gas kinetic scheme for multiscale heat transfer
Guo, Zhaoli
2016-01-01
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and ballistic regimes, and can present accurate solutions in the whole transition regime as well. The DUGKS is a self-adaptive multiscale method for the capturing of local transport process. Numerical tests for both heat transfers with different Knudsen numbers are presented to validate the current method.
Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation.
Chen, Jiunn-Wei; Pu, Shi; Wang, Qun; Wang, Xin-Nian
2013-06-28
We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a four-dimensional Euclidean Berry monopole which gives an axial anomaly. By integrating out the zeroth component of the 4-momentum p, we reproduce the previous three-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF[over ˜]σρ∼EσBσ). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.
Directory of Open Access Journals (Sweden)
L. Alfonso
2010-03-01
Full Text Available The kinetic collection equation (KCE has been widely used to describe the evolution of the average droplet spectrum due to the collection process that leads to the development of precipitation in warm clouds. This deterministic, integro-differential equation only has analytic solution for very simple kernels. For more realistic kernels, the KCE needs to be integrated numerically. In this study, the validity time of the KCE for the hydrodynamic kernel is estimated by a direct comparison of Monte Carlo simulations with numerical solutions of the KCE. The simulation results show that when the largest droplet becomes separated from the smooth spectrum, the total mass calculated from the numerical solution of the KCE is not conserved and, thus, the KCE is no longer valid. This result confirms the fact that for realistic kernels appropriate for precipitation development within warm clouds, the KCE can only be applied to the continuous portion of the mass distribution.
Kinetic modelling of cytochrome c adsorption on SBA-15.
Yokogawa, Yoshiyuki; Yamauchi, Rie; Saito, Akira; Yamato, Yuta; Toma, Takeshi
2017-01-01
The adsorption capacity of mesoporous silicate (MPS) materials as an adsorbent for protein adsorption from the aqueous phase and the mechanism of the adsorption processes by comparative analyses of the applicability of five kinetic transfer models, pseudo-first-order model, pseudo-second-order model, Elovich kinetic model, Bangham's equation model, and intraparticle diffusion model, were investigated. A mixture of tetraethyl orthosilicate (TEOS) and triblock copolymer as a template was stirred, hydrothermally treated to form the mesoporous SBA-15 structure, and heat-treated at 550°C to form the MPS material, SBA-15. The synthesized SBA-15 was immersed in a phosphate buffered saline (PBS) solution containing cytochrome c for 2, 48, and 120 hours at 4°C. The TEM observations of proteins on/in mesoporous SBA-15 revealed the protein behaviors. The holes of the MPS materials were observed to overlap those of the stained proteins for the first 2 hours of immersion. The stained proteins were observed between primary particles and partly inside the mesoporous channels in the MPS material when it had been immersed for 48 hours. For MPS when it had been immersed for 120 hours, stained proteins were observed in almost all meso-scale channels of MPS. The time profiles for adsorption of proteins can be described well by Bangham's equation model and the intraparticle diffusion model. The Bangham's equation model is based on the assumption that pore diffusion was the only rate controlling step during adsorption, whose contribution to the overall mechanism of cytochrome c adsorption on SBA-15 should not be neglected. The kinetic curves obtained from the experiment for cytochrome c adsorption on SBA-15 could show the three steps: the initial rapid increase of the adsorbed amount of cytochrome c, the second gradual increase, and the final equilibrium stage. These three adsorption steps can be interpreted well by the multi-linearity of the intraparticle diffusion model
Kinetic models of gene expression including non-coding RNAs
Zhdanov, Vladimir P.
2011-03-01
In cells, genes are transcribed into mRNAs, and the latter are translated into proteins. Due to the feedbacks between these processes, the kinetics of gene expression may be complex even in the simplest genetic networks. The corresponding models have already been reviewed in the literature. A new avenue in this field is related to the recognition that the conventional scenario of gene expression is fully applicable only to prokaryotes whose genomes consist of tightly packed protein-coding sequences. In eukaryotic cells, in contrast, such sequences are relatively rare, and the rest of the genome includes numerous transcript units representing non-coding RNAs (ncRNAs). During the past decade, it has become clear that such RNAs play a crucial role in gene expression and accordingly influence a multitude of cellular processes both in the normal state and during diseases. The numerous biological functions of ncRNAs are based primarily on their abilities to silence genes via pairing with a target mRNA and subsequently preventing its translation or facilitating degradation of the mRNA-ncRNA complex. Many other abilities of ncRNAs have been discovered as well. Our review is focused on the available kinetic models describing the mRNA, ncRNA and protein interplay. In particular, we systematically present the simplest models without kinetic feedbacks, models containing feedbacks and predicting bistability and oscillations in simple genetic networks, and models describing the effect of ncRNAs on complex genetic networks. Mathematically, the presentation is based primarily on temporal mean-field kinetic equations. The stochastic and spatio-temporal effects are also briefly discussed.
Quantum kinetics and thermalization in a particle bath model.
Alamoudi, S M; Boyanovsky, D; de Vega, H J
1999-07-01
We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.
Extended master equation models for molecular communication networks.
Chou, Chun Tung
2013-06-01
We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signaling molecules, which are diffused over the medium, to the receiver to realize the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time series of signaling molecule counts, while diffusion in the medium and chemical reactions at the receivers are modeled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance of the receiver output signals, and derive closed-form expressions for the mean receiver output signal of the RDMEX model. These closed-form expressions reveal that the output signal of a receiver can be affected by the presence of other receivers. Numerical examples are provided to demonstrate the properties of the model.
Multiensemble Markov models of molecular thermodynamics and kinetics.
Wu, Hao; Paul, Fabian; Wehmeyer, Christoph; Noé, Frank
2016-06-07
We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models-clustering of high-dimensional spaces and modeling of complex many-state systems-with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein-ligand binding model.
Equation of State of the Two-Dimensional Hubbard Model
Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-01
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.
Bayesian Data-Model Fit Assessment for Structural Equation Modeling
Levy, Roy
2011-01-01
Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…
Micellization kinetics in block copolymer solutions : Scaling model
Dormidontova, EE
1999-01-01
The kinetics of micelle evolution of diblock copolymers from unimers toward the equilibrium state is studied analytically on the basis of consideration of the kinetic equations. The association/dissociation rate constants for unimer insertion/expulsion and micelle fusion/fission are calculated by
Micellization kinetics in block copolymer solutions : Scaling model
Dormidontova, EE
1999-01-01
The kinetics of micelle evolution of diblock copolymers from unimers toward the equilibrium state is studied analytically on the basis of consideration of the kinetic equations. The association/dissociation rate constants for unimer insertion/expulsion and micelle fusion/fission are calculated by ap
Kinetic effects in edge plasma: kinetic modeling for edge plasma and detached divertor
Takizuka, T.
2017-03-01
Detached divertor is considered a solution for the heat control in magnetic-confinement fusion reactors. Numerical simulations using the comprehensive divertor codes based on the plasma fluid modeling are indispensable for the design of the detached divertor in future reactors. Since the agreement in the results between detached-divertor experiments and simulations has been rather fair but not satisfactory, further improvement of the modeling is required. The kinetic effect is one of key issues for improving the modeling. Complete kinetic behaviors are able to be simulated by the kinetic modeling. In this paper at first, major kinetic effects in edge plasma and detached divertor are listed. One of the most powerful kinetic models, particle-in-cell (PIC) model, is described in detail. Several results of PIC simulations of edge-plasma kinetic natures are presented. Future works on PIC modeling and simulation for the deeper understanding of edge plasma and detached divertor are discussed.
Niceno, B.; Dhotre, M.T.; Deen, N.G.
2008-01-01
In this work, we have presented a one-equation model for sub-grid scale (SGS) kinetic energy and applied it for an Euler-Euler large eddy simulation (EELES) of a bubble column reactor. The one-equation model for SGS kinetic energy shows improved predictions over the state-of-the-art dynamic
A kinetic model for the transport of electrons in a graphene layer
Fermanian Kammerer, Clotilde; Méhats, Florian
2016-12-01
In this article, we propose a new numerical scheme for the computation of the transport of electrons in a graphene device. The underlying quantum model for graphene is a massless Dirac equation, whose eigenvalues display a conical singularity responsible for non-adiabatic transitions between the two modes. We first derive a kinetic model which takes the form of two Boltzmann equations coupled by a collision operator modeling the non-adiabatic transitions. This collision term includes a Landau-Zener transfer term and a jump operator whose presence is essential in order to ensure a good energy conservation during the transitions. We propose an algorithmic realization of the semi-group solving the kinetic model, by a particle method. We give analytic justification of the model and propose a series of numerical experiments studying the influences of the various sources of errors between the quantum and the kinetic models.
Klinman, Judith P
2014-01-01
The final arbiter of enzyme mechanism is the ability to establish and test a kinetic mechanism. Isotope effects play a major role in expanding the scope and insight derived from the Michaelis-Menten equation. The integration of isotope effects into the formalism of the Michaelis-Menten equation began in the 1970s and has continued until the present. This review discusses a family of eukaryotic copper proteins, including dopamine β-monooxygenase, tyramine β-monooxygenase and peptidylglycine α-amidating enzyme, which are responsible for the synthesis of neuroactive compounds, norepinephrine, octopamine and C-terminally carboxamidated peptides, respectively. The review highlights the results of studies showing how combining kinetic isotope effects with initial rate parameters permits the evaluation of: (a) the order of substrate binding to multisubstrate enzymes; (b) the magnitude of individual rate constants in complex, multistep reactions; (c) the identification of chemical intermediates; and (d) the role of nonclassical (tunnelling) behaviour in C-H activation. © 2013 FEBS.
Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism.
Fleming, R M T; Thiele, I; Provan, G; Nasheuer, H P
2010-06-07
The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.
Energy Technology Data Exchange (ETDEWEB)
Polo L, M. A.; Espinosa P, G. [Universidad Autonoma Metropolitana, Unidad Iztapalapa, Area de Ingenieria en Recursos Energeticos, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 Mexico D. F. (Mexico)], e-mail: gepe@xanum.uam.mx
2009-10-15
In this work is presented the deduction and solution of punctual equation of neutronic kinetics of second order, which is obtained applying the fundamental principles of nuclear reactor physics. The work hypothesis consisted on considering that the temporary dependence of current vector is not worthless in the constitutive law for the approach of neutronic processes with the diffusion equation. As results of work eight roots of analytical solution of punctual equation of neutronic kinetics of second order are obtained for case of six groups of slowed neutrons, a root more respect the classic pattern of punctual equation of neutronic kinetics. This theory can be used when appear highly heterogeneous configurations in the nuclear reactor. (Author)
Simulation of DME synthesis from coal syngas by kinetics model
Energy Technology Data Exchange (ETDEWEB)
Shim, H.M.; Lee, S.J.; Yoo, Y.D.; Yun, Y.S.; Kim, H.T. [Ajou University, Suwon (Republic of Korea)
2009-05-15
DME (Dimethyl Ether) has emerged as a clean alternative fuel for diesel. In this study it is developed a simulation model through a kinetics model of the ASPEN plus simulator, performed to detect operating characteristics of DME direct synthesis. An overall DME synthesis process is referenced by experimental data of 3 ton/day (TPD) coal gasification pilot plant located at IAE in Korea. Supplying condition of DME synthesis model is equivalently set to 80 N/m{sup 3} of syngas which is derived from a coal gasification plant. In the simulation it is assumed that the overall DME synthesis process proceeds with steady state, vapor-solid reaction with DME catalyst. The physical properties of reactants are governed by Soave-Redlich-Kwong (SRK) EOS in this model. A reaction model of DME synthesis is considered that is applied with the LHHW (Langmuir-Hinshelwood Hougen Watson) equation as an adsorption-desorption model on the surface of the DME catalyst. After adjusting the kinetics of the DME synthesis reaction among reactants with experimental data, the kinetics of the governing reactions inner DME reactor are modified and coupled with the entire DME synthesis reaction. For validating simulation results of the DME synthesis model, the obtained simulation results are compared with experimental results: conversion ratio, DME yield and DME production rate. Then, a sensitivity analysis is performed by effects of operating variables such as pressure, temperature of the reactor, void fraction of catalyst and H{sub 2}/CO ratio of supplied syngas with modified model. According to simulation results, optimum operating conditions of DME reactor are obtained in the range of 265-275{sup o}C and 60 kg/cm{sup 2}. And DME production rate has a maximum value in the range of 1-1.5 of H{sub 2}/CO ratio in the syngas composition.
MATHEMATICAL MODELING OF ORANGE SEED DRYING KINETICS
Directory of Open Access Journals (Sweden)
Daniele Penteado Rosa
2015-06-01
Full Text Available Drying of orange seeds representing waste products from juice processing was studied in the temperatures of 40, 50, 60 and 70 °C and drying velocities of 0.6, 1.0 and 1.4 m/s. Experimental drying kinetics of orange seeds were obtained using a convective air forced dryer. Three thin-layer models: Page model, Lewis model, and the Henderson-Pabis model and the diffusive model were used to predict the drying curves. The Henderson-Pabis and the diffusive models show the best fitting performance and statistical evaluations. Moreover, the temperature dependence on the effective diffusivity followed an Arrhenius relationship, and the activation energies ranging from 16.174 to 16.842 kJ/mol
Indian Academy of Sciences (India)
Jai Prakash
2013-01-01
Ionic thermocurrent (ITC) spectrum is much similar to a thermoluminescence (TL) glow curve involving monomolecular kinetics. It has already been reported that different orders of kinetics are involved in TL processes, which depend specifically on the extent of recombination and simultaneous retrapping. It is found that the involvement of different orders of kinetics in ITC spectrum depends on the experimental conditions of polarization and rate of rapid cooling. Consequently, order of kinetics involved in the ITC spectrum does not represent any specific feature of the system under investigation. An equation is developed which explains the occurrence of ITC spectrum involving any order of kinetics. Dielectric relaxation parameters, order of kinetics and approximate number of dipoles per unit volume are evaluated conveniently and easily following the proposed model.
Self-dual soliton solutions in a Chern-Simons-CP(1) model with a nonstandard kinetic term
Casana, Rodolfo; Sourrouille, Lucas
2014-07-01
A generalization of the Chern-Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomol'nyi equations. The Bogomol'nyi-Prasad-Sommerfield (BPS) energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The self-dual equations are solved analytically and verified numerically.
Manning, Robert M.
2009-01-01
Based on a theoretical model of the propagation of electromagnetic waves through a hypersonically induced plasma, it has been demonstrated that the classical radiofrequency communications blackout that is experienced during atmospheric reentry can be mitigated through the appropriate control of an external magnetic field of nominal magnitude. The model is based on the kinetic equation treatment of Vlasov and involves an analytical solution for the electric and magnetic fields within the plasma allowing for a description of the attendant transmission, reflection and absorption coefficients. The ability to transmit through the magnetized plasma is due to the magnetic windows that are created within the plasma via the well-known whistler modes of propagation. The case of 2 GHz transmission through a re-entry plasma is considered. The coefficients are found to be highly sensitive to the prevailing electron density and will thus require a dynamic control mechanism to vary the magnetic field as the plasma evolves through the re-entry phase.
Is it appropriate to model turbidity currents with the three-equation model?
Hu, Peng; Pähtz, Thomas; He, Zhiguo
2015-07-01
The three-equation model (TEM) was developed in the 1980s to model turbidity currents (TCs) and has been widely used ever since. However, its physical justification was questioned because self-accelerating TCs simulated with the steady TEM seemed to violate the turbulent kinetic energy balance. This violation was considered as a result of very strong sediment erosion that consumes more turbulent kinetic energy than is produced. To confine bed erosion and thus remedy this issue, the four-equation model (FEM) was introduced by assuming a proportionality between the bed shear stress and the turbulent kinetic energy. Here we analytically proof that self-accelerating TCs simulated with the original steady TEM actually never violate the turbulent kinetic energy balance, provided that the bed drag coefficient is not unrealistically low. We find that stronger bed erosion, surprisingly, leads to more production of turbulent kinetic energy due to conversion of potential energy of eroded material into kinetic energy of the current. Furthermore, we analytically show that, for asymptotically supercritical flow conditions, the original steady TEM always produces self-accelerating TCs if the upstream boundary conditions ("ignition" values) are chosen appropriately, while it never does so for asymptotically subcritical flow conditions. We numerically show that our novel method to obtain the ignition values even works for Richardson numbers very near to unity. Our study also includes a comparison of the TEM and FEM closures for the bed shear stress to simulation data of a coupled Large Eddy and Discrete Element Model of sediment transport in water, which suggests that the TEM closure might be more realistic than the FEM closure.
The geometry of a vorticity model equation
Escher, Joachim; Wunsch, Marcus
2010-01-01
We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\\ge 2$.
Functional Difference Equations and an Epidemic Model.
1980-06-09
ADDRESS 12. REPORT DATE AIR FORCE OFFICE OF SCIENTIFIC RESEARC 913 June 9, 1980 BOLLING AIR FORCE BASE , WASHINGTON, D.tI,3. NUMBEROFAGS 14. MONITORING...allowed spatial effects in an S - I model to arrive at the equation t S(t,x) = S(t,x).J B(;x, )S(t+6,0) dAdO in some region f cR. If X is the ordered
Kinetic modeling and exploratory numerical simulation of chloroplastic starch degradation
Directory of Open Access Journals (Sweden)
Nag Ambarish
2011-06-01
Full Text Available Abstract Background Higher plants and algae are able to fix atmospheric carbon dioxide through photosynthesis and store this fixed carbon in large quantities as starch, which can be hydrolyzed into sugars serving as feedstock for fermentation to biofuels and precursors. Rational engineering of carbon flow in plant cells requires a greater understanding of how starch breakdown fluxes respond to variations in enzyme concentrations, kinetic parameters, and metabolite concentrations. We have therefore developed and simulated a detailed kinetic ordinary differential equation model of the degradation pathways for starch synthesized in plants and green algae, which to our knowledge is the most complete such model reported to date. Results Simulation with 9 internal metabolites and 8 external metabolites, the concentrations of the latter fixed at reasonable biochemical values, leads to a single reference solution showing β-amylase activity to be the rate-limiting step in carbon flow from starch degradation. Additionally, the response coefficients for stromal glucose to the glucose transporter kcat and KM are substantial, whereas those for cytosolic glucose are not, consistent with a kinetic bottleneck due to transport. Response coefficient norms show stromal maltopentaose and cytosolic glucosylated arabinogalactan to be the most and least globally sensitive metabolites, respectively, and β-amylase kcat and KM for starch to be the kinetic parameters with the largest aggregate effect on metabolite concentrations as a whole. The latter kinetic parameters, together with those for glucose transport, have the greatest effect on stromal glucose, which is a precursor for biofuel synthetic pathways. Exploration of the steady-state solution space with respect to concentrations of 6 external metabolites and 8 dynamic metabolite concentrations show that stromal metabolism is strongly coupled to starch levels, and that transport between compartments serves to
Modelling dimercaptosuccinic acid (DMSA) plasma kinetics in humans
van Eijkeren, Jan C H; Olie, J Daniël N; Bradberry, Sally M; Vale, J Allister; de Vries, Irma; Meulenbelt, Jan; Hunault, Claudine C
2016-01-01
CONTEXT: No kinetic models presently exist which simulate the effect of chelation therapy on lead blood concentrations in lead poisoning. OBJECTIVE: Our aim was to develop a kinetic model that describes the kinetics of dimercaptosuccinic acid (DMSA; succimer), a commonly used chelating agent, that c
A kinetic model of plasma turbulence
Servidio, S.; Valentini, F.; Perrone, D.; Greco, A.; Califano, F.; Matthaeus, W. H.; Veltri, P.
2015-01-01
A Hybrid Vlasov-Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of the proper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropy T ⊥/T ∥ (where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given by T ⊥/T ∥ and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature
Mathematical Modelling of Thermal Degradation Kinetics of Ascorbic ...
African Journals Online (AJOL)
However, adequate study has not been conducted to exploit the potential of this ... of ascorbic acid in yeabesha gomen fitted first-order reaction kinetic model ... Activation energy for ascorbic degeneration kinetics of yeabesha gomen was ...
Thermodynamic and kinetic modeling of transcriptional pausing.
Tadigotla, Vasisht R; O Maoiléidigh, Dáibhid; Sengupta, Anirvan M; Epshtein, Vitaly; Ebright, Richard H; Nudler, Evgeny; Ruckenstein, Andrei E
2006-03-21
We present a statistical mechanics approach for the prediction of backtracked pauses in bacterial transcription elongation derived from structural models of the transcription elongation complex (EC). Our algorithm is based on the thermodynamic stability of the EC along the DNA template calculated from the sequence-dependent free energy of DNA-DNA, DNA-RNA, and RNA-RNA base pairing associated with (i) the translocational and size fluctuations of the transcription bubble; (ii) changes in the associated DNA-RNA hybrid; and (iii) changes in the cotranscriptional RNA secondary structure upstream of the RNA exit channel. The calculations involve no adjustable parameters except for a cutoff used to discriminate paused from nonpaused complexes. When applied to 100 experimental pauses in transcription elongation by Escherichia coli RNA polymerase on 10 DNA templates, the approach produces statistically significant results. We also present a kinetic model for the rate of recovery of backtracked paused complexes. A crucial ingredient of our model is the incorporation of kinetic barriers to backtracking resulting from steric clashes of EC with the cotranscriptionally generated RNA secondary structure, an aspect not included explicitly in previous attempts at modeling the transcription elongation process.
Principles and practice of structural equation modeling
Kline, Rex B
2015-01-01
Emphasizing concepts and rationale over mathematical minutiae, this is the most widely used, complete, and accessible structural equation modeling (SEM) text. Continuing the tradition of using real data examples from a variety of disciplines, the significantly revised fourth edition incorporates recent developments such as Pearl's graphing theory and the structural causal model (SCM), measurement invariance, and more. Readers gain a comprehensive understanding of all phases of SEM, from data collection and screening to the interpretation and reporting of the results. Learning is enhanced by ex
Vertical spectral representation in primitive equation models of the atmosphere
Energy Technology Data Exchange (ETDEWEB)
Mizzi, A.; Tribbia, J. [National Center for Atmospheric Research, Boulder, CO (United States); Curry, J. [Univ. of Colorado, Boulder, CO (United States)
1995-08-01
Attempts to represent the vertical structure in primitive equation models of the atmosphere with the spectral method have been unsuccessful to date. Linear stability analysis showed that small time steps were required for computational stability near the upper boundary with a vertical spectral representation and found it necessary to use an artificial constraint to force temperature to zero when pressure was zero to control the upper-level horizontal velocities. This ad hoc correction is undesirable, and an analysis that shows such a correction is unnecessary is presented. By formulating the model in terms of velocity and geopotential and then using the hydrostatic equation to calculate temperature from geopotential, temperature is necessarily zero when pressure is zero. The authors applied this technique to the dry-adiabatic primitive equations on the equatorial {beta} and tropical f planes. Vertical and horizontal normal modes were used as the spectral basis functions. The vertical modes are based on vertical normal modes, and the horizontal modes are normal modes for the primitive equations on a {beta} or f plane. The results show that the upper-level velocities do not necessarily increase, total energy is conserved, and kinetic energy is bounded. The authors found an upper-level temporal oscillation in the horizontal domain integral of the horizontal velocity components that is related to mass and velocity field imbalances in the initial conditions or introduced during the integration. Through nonlinear normal-mode initialization, the authors effectively removed the initial condition imbalance and reduced the amplitude of this oscillation. It is hypothesized that the vertical spectral representation makes the model more sensitive to initial condition imbalances, or it introduces imbalance during the integration through vertical spectral truncation. 20 refs., 12 figs.
A limit model for thermoelectric equations
Consiglieri, Luisa
2010-01-01
We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both spatial and temperature dependent transport coefficients under some real boundary conditions in accordance with the Seebeck-Peltier-Thomson cross-effects. Our first purpose is that the existence of a weak solution holds true under minimal assumptions on the data, as in particular convex domains with Lipschitz boundary. The proof is based on a fixed point argument, compactness methods, and existence and regularity theory for elliptic scalar equations. In this process, we prove W^{1,p}-regularity for Neumann problem to an elliptic second order equation in divergence form with discontinuous coefficient by using the potential theory. The second one is to show the existence of a limit model illustrating the asymptotic situation.
Thermodynamically consistent model calibration in chemical kinetics
Directory of Open Access Journals (Sweden)
Goutsias John
2011-05-01
Full Text Available Abstract Background The dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function. Results We introduce a thermodynamically consistent model calibration (TCMC method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from http://www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database. Conclusions TCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new
Kinetic models for the VASIMR thruster helicon plasma source
Batishchev, Oleg; Molvig, Kim
2001-10-01
Helicon gas discharge [1] is widely used by industry because of its remarkable efficiency [2]. High energy and fuel efficiencies make it very attractive for space electrical propulsion applications. For example, helicon plasma source is used in the high specific impulse VASIMR [3] plasma thruster, including experimental prototypes VX-3 and upgraded VX-10 [4] configurations, which operate with hydrogen (deuterium) and helium plasmas. We have developed a set of models for the VASIMR helicon discharge. Firstly, we use zero-dimensional energy and mass balance equations to characterize partially ionized gas condition/composition. Next, we couple it to one-dimensional hybrid model [6] for gas flow in the quartz tube of the helicon. We compare hybrid model results to a purely kinetic simulation of propellant flow in gas feed + helicon source subsystem. Some of the experimental data [3-4] are explained. Lastly, we discuss full-scale kinetic modeling of coupled gas and plasmas [5-6] in the helicon discharge. [1] M.A.Lieberman, A.J.Lihtenberg, 'Principles of ..', Wiley, 1994; [2] F.F.Chen, Plas. Phys. Contr. Fus. 33, 339, 1991; [3] F.Chang-Diaz et al, Bull. APS 45 (7) 129, 2000; [4] J.Squire et al., Bull. APS 45 (7) 130, 2000; [5] O.Batishchev et al, J. Plasma Phys. 61, part II, 347, 1999; [6] O.Batishchev, K.Molvig, AIAA technical paper 2000-3754, -14p, 2001.
Economic inequality and mobility in kinetic models for social sciences
Letizia Bertotti, Maria; Modanese, Giovanni
2016-10-01
Statistical evaluations of the economic mobility of a society are more difficult than measurements of the income distribution, because they require to follow the evolution of the individuals' income for at least one or two generations. In micro-to-macro theoretical models of economic exchanges based on kinetic equations, the income distribution depends only on the asymptotic equilibrium solutions, while mobility estimates also involve the detailed structure of the transition probabilities of the model, and are thus an important tool for assessing its validity. Empirical data show a remarkably general negative correlation between economic inequality and mobility, whose explanation is still unclear. It is therefore particularly interesting to study this correlation in analytical models. In previous work we investigated the behavior of the Gini inequality index in kinetic models in dependence on several parameters which define the binary interactions and the taxation and redistribution processes: saving propensity, taxation rates gap, tax evasion rate, welfare means-testing etc. Here, we check the correlation of mobility with inequality by analyzing the mobility dependence from the same parameters. According to several numerical solutions, the correlation is confirmed to be negative.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Wave equation modelling using Julia programming language
Kim, Ahreum; Ryu, Donghyun; Ha, Wansoo
2016-04-01
Julia is a young high-performance dynamic programming language for scientific computations. It provides an extensive mathematical function library, a clean syntax and its own parallel execution model. We developed 2d wave equation modeling programs using Julia and C programming languages and compared their performance. We used the same modeling algorithm for the two modeling programs. We used Julia version 0.3.9 in this comparison. We declared data type of function arguments and used inbounds macro in the Julia program. Numerical results showed that the C programs compiled with Intel and GNU compilers were faster than Julia program, about 18% and 7%, respectively. Taking the simplicity of dynamic programming language into consideration, Julia can be a novel alternative of existing statically typed programming languages.
Ab initio determination of kinetics for atomic layer deposition modeling
Remmers, Elizabeth M.
A first principles model is developed to describe the kinetics of atomic layer deposition (ALD) systems. This model requires no fitting parameters, as it is based on the reaction pathways, structures, and energetics obtained from quantum-chemical studies. Using transition state theory and partition functions from statistical mechanics, equilibrium constants and reaction rates can be calculated. Several tools were created in Python to aid in the calculation of these quantities, and this procedure was applied to two systems- zinc oxide deposition from diethyl zinc (DEZ) and water, and alumina deposition from trimethyl aluminum (TMA) and water. A Gauss-Jordan factorization is used to decompose the system dynamics, and the resulting systems of equations are solved numerically to obtain the temporal concentration profiles of these two deposition systems.
A spatial kinetic model for simulating VVER-1000 start-up transient
Energy Technology Data Exchange (ETDEWEB)
Kashi, Samira [Department of Nuclear Engineering, Shahid Beheshti University, Tehran (Iran, Islamic Republic of); Moghaddam, Nader Maleki, E-mail: nader.moghaddam@gmail.com [Department of Nuclear Engineering and Physics, Amir Kabir University of Technology, Tehran (Iran, Islamic Republic of); Shahriari, Majid [Department of Nuclear Engineering, Shahid Beheshti University, Tehran (Iran, Islamic Republic of)
2011-06-15
Research highlights: > A spatial kinetic model of a VVER-1000 reactor core is presented. > The reactor power is tracked using the point kinetic equations from 100 W to 612 kW. > The lamped parameter approximation is used for solving the energy balance equations. > The value of reactivity related to feedback effects of core elements is calculated. > The main neutronic parameters during the transient are calculated. - Abstract: An accurate prediction of reactor core behavior in transients depends on how much it could be possible to exactly determine the thermal feedbacks of the core elements such as fuel, clad and coolant. In short time transients, results of these feedbacks directly affect the reactor power and determine the reactor response. Such transients are commonly happened during the start-up process which makes it necessary to carefully evaluate the detail of process. Hence this research evaluates a short time transient occurring during the start up of VVER-1000 reactor. The reactor power was tracked using the point kinetic equations from HZP state (100 W) to 612 kW. Final power (612 kW) was achieved by withdrawing control rods and resultant excess reactivity was set into dynamic equations to calculate the reactor power. Since reactivity is the most important part in the point kinetic equations, using a Lumped Parameter (LP) approximation, energy balance equations were solved in different zones of the core. After determining temperature and total reactivity related to feedbacks in each time step, the exact value of reactivity is obtained and is inserted into point kinetic equations. In reactor core each zone has a specific temperature and its corresponding thermal feedback. To decrease the effects of point kinetic approximations, these partial feedbacks in different zones are superposed to show an accurate model of reactor core dynamics. In this manner the reactor point kinetic can be extended to the whole reactor core which means 'Reactor spatial
Nonlinear kinetic modeling and simulations of Raman scattering in a two-dimensional geometry
Directory of Open Access Journals (Sweden)
Bénisti Didier
2013-11-01
Full Text Available In this paper, we present our nonlinear kinetic modeling of stimulated Raman scattering (SRS by the means of envelope equations, whose coefficients have been derived using a mixture of perturbative and adiabatic calculations. First examples of the numerical resolution of these envelope equations in a two-dimensional homogeneous plasma are given, and the results are compared against those of particle-in-cell (PIC simulations. These preliminary comparisons are encouraging since our envelope code provides threshold intensities consistent with those of PIC simulations while requiring computational resources reduced by 4 to 5 orders of magnitude compared to full-kinetic codes.
A simple model for Brownian motion leading to the Langevin equation
Grooth, de Bart G.
1999-01-01
A simple one-dimensional model is presented for the motion of a Brownian particle. It is shown how the collisions between a Brownian particle and its surrounding molecules lead to the Langevin equation, the power spectrum of the stochastic force, and the equipartition of kinetic energy.
A refined way of solving reactor point kinetics equations for imposed reactivity insertions
Directory of Open Access Journals (Sweden)
Ganapol Barry D.
2009-01-01
Full Text Available We apply the concept of convergence acceleration, also known as extrapolation, to find the solution of the reactor kinetics equations (RKEs. The method features simplicity in that an approximate finite difference formulation is constructed and converged to high accuracy from knowledge of the error term. Through the Romberg extrapolation, we demonstrate its high accuracy for a variety of imposed reactivity insertions found in the literature. The unique feature of the proposed algorithm, called RKE/R(omberg, is that no special attention is given to the stiffness of the RKEs. Finally, because of its simplicity and accuracy, the RKE/R algorithm is arguably the most efficient numerical solution of the RKEs developed to date.
Energy Technology Data Exchange (ETDEWEB)
Tumelero, Fernanda; Petersen, Claudio Zen; Goncalves, Glenio Aguiar [Universidade Federal de Pelotas, Capao do Leao, RS (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcelo [Universidade Federal do Rio Grande do Sul, Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica
2016-12-15
In this work, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. The main idea is to expand the neutron density and delayed neutron precursors as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions and the analytical continuation is used to determine the solutions of the next intervals. A genuine error control is developed based on an analogy with the Rest Theorem. For illustration, we also report simulations for different approaches types (linear, quadratic and cubic). The results obtained by numerical simulations for linear approximation are compared with results in the literature.
On Kinetics Modeling of Vibrational Energy Transfer
Gilmore, John O.; Sharma, Surendra P.; Cavolowsky, John A. (Technical Monitor)
1996-01-01
Two models of vibrational energy exchange are compared at equilibrium to the elementary vibrational exchange reaction for a binary mixture. The first model, non-linear in the species vibrational energies, was derived by Schwartz, Slawsky, and Herzfeld (SSH) by considering the detailed kinetics of vibrational energy levels. This model recovers the result demanded at equilibrium by the elementary reaction. The second model is more recent, and is gaining use in certain areas of computational fluid dynamics. This model, linear in the species vibrational energies, is shown not to recover the required equilibrium result. Further, this more recent model is inconsistent with its suggested rate constants in that those rate constants were inferred from measurements by using the SSH model to reduce the data. The non-linear versus linear nature of these two models can lead to significant differences in vibrational energy coupling. Use of the contemporary model may lead to significant misconceptions, especially when integrated in computer codes considering multiple energy coupling mechanisms.
KINETIC MODELLING AND PERFORMANCE ANALYSIS OF THE FOUR-POST-FRAME LIFTINGMECHANICAL SYSTEM
Institute of Scientific and Technical Information of China (English)
高建华; 杨汝清; 胡洪国
2001-01-01
The kinetic model of the four-post-frame lifting mechanical system was established. The stiffness and damping matrices of differential equations of motion were obtained by using Lagrange's equations. And the dynamic characteristics of system were analyzed by modal analysis method. Based upon this, the modifications of structural parameters which can improve dynamic performance were discussed. The low-level high-speed palletizer MDJ1200L was taken as a real case in the paper.
Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George
2016-05-01
The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.
Liao, Fei; Tian, Kao-Cong; Yang, Xiao; Zhou, Qi-Xin; Zeng, Zhao-Chun; Zuo, Yu-Ping
2003-03-01
The reliability of kinetic substrate quantification by nonlinear fitting of the enzyme reaction curve to the integrated Michaelis-Menten equation was investigated by both simulation and preliminary experimentation. For simulation, product absorptivity epsilon was 3.00 mmol(-1) L cm(-1) and K(m) was 0.10 mmol L(-1), and uniform absorbance error sigma was randomly inserted into the error-free reaction curve of product absorbance A(i) versus reaction time t(i) calculated according to the integrated Michaelis-Menten equation. The experimental reaction curve of arylesterase acting on phenyl acetate was monitored by phenol absorbance at 270 nm. Maximal product absorbance A(m) was predicted by nonlinear fitting of the reaction curve to Eq. (1) with K(m) as constant. There were unique A(m) for best fitting of both the simulated and experimental reaction curves. Neither the error in reaction origin nor the variation of enzyme activity changed the background-corrected value of A(m). But the range of data under analysis, the background absorbance, and absorbance error sigma had an effect. By simulation, A(m) from 0.150 to 3.600 was predicted with reliability and linear response to substrate concentration when there was 80% consumption of substrate at sigma of 0.001. Restriction of absorbance to 0.700 enabled A(m) up to 1.800 to be predicted at sigma of 0.001. Detection limit reached A(m) of 0.090 at sigma of 0.001. By experimentation, the reproducibility was 4.6% at substrate concentration twice the K(m), and A(m) linearly responded to phenyl acetate with consistent absorptivity for phenol, and upper limit about twice the maximum of experimental absorbance. These results supported the reliability of this new kinetic method for enzymatic analysis with enhanced upper limit and precision.
Zhang, Chao; Chen, Yin-Guang
2013-03-01
Based on activated sludge model No. 2 (ASM2), the anaerobic/aerobic kinetic model of phosphorus-accumulating organisms (PAO) was established with mixed short-chain fatty acids (SCFAs) as the base substance in enhanced biological phosphorus removal process. The characteristic of the PAO model was that the anaerobic metabolism rates of glycogen degradation, poly-beta-hydroxyalkanoates synthesis and polyphosphate hydrolysis were expressed by SCFAs uptake equation, and the effects of anaerobic maintenance on kinetics and stoichiometry were considered. The PAO kinetic model was composed of 3 soluble components, 4 particulate components and a pH parameter, which constituted the matrix of stoichiometric coefficients. On the basis of PAO model, the GAO kinetic model was established, which included 7 processes, and phosphorus content influenced the aerobic metabolism only.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Energy Technology Data Exchange (ETDEWEB)
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
2014-12-26
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature – specifically, “jumps” in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique – both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Energy Technology Data Exchange (ETDEWEB)
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
2014-11-25
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature – specifically, “jumps” in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique – both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
Energy Technology Data Exchange (ETDEWEB)
Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com [Institute of Applied Mechanics, National Taiwan University, Taipei 10764, Taiwan (China)
2015-07-20
A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.
Gompertz kinetics model of fast chemical neurotransmission currents.
Easton, Dexter M
2005-10-01
At a chemical synapse, transmitter molecules ejected from presynaptic terminal(s) bind reversibly with postsynaptic receptors and trigger an increase in channel conductance to specific ions. This paper describes a simple but accurate predictive model for the time course of the synaptic conductance transient, based on Gompertz kinetics. In the model, two simple exponential decay terms set the rates of development and decline of transmitter action. The first, r, triggering conductance activation, is surrogate for the decelerated rate of growth of conductance, G. The second, r', responsible for Y, deactivation of the conductance, is surrogate for the decelerated rate of decline of transmitter action. Therefore, the differential equation for the net conductance change, g, triggered by the transmitter is dg/dt=g(r-r'). The solution of that equation yields the product of G(t), representing activation, and Y(t), which defines the proportional decline (deactivation) of the current. The model fits, over their full-time course, published records of macroscopic ionic current associated with fast chemical transmission. The Gompertz model is a convenient and accurate method for routine analysis and comparison of records of synaptic current and putative transmitter time course. A Gompertz fit requiring only three independent rate constants plus initial current appears indistinguishable from a Markov fit using seven rate constants.
Partial differential equation models in macroeconomics.
Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin
2014-11-13
The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
Structural equation modeling for observational studies
Grace, J.B.
2008-01-01
Structural equation modeling (SEM) represents a framework for developing and evaluating complex hypotheses about systems. This method of data analysis differs from conventional univariate and multivariate approaches familiar to most biologists in several ways. First, SEMs are multiequational and capable of representing a wide array of complex hypotheses about how system components interrelate. Second, models are typically developed based on theoretical knowledge and designed to represent competing hypotheses about the processes responsible for data structure. Third, SEM is conceptually based on the analysis of covariance relations. Most commonly, solutions are obtained using maximum-likelihood solution procedures, although a variety of solution procedures are used, including Bayesian estimation. Numerous extensions give SEM a very high degree of flexibility in dealing with nonnormal data, categorical responses, latent variables, hierarchical structure, multigroup comparisons, nonlinearities, and other complicating factors. Structural equation modeling allows researchers to address a variety of questions about systems, such as how different processes work in concert, how the influences of perturbations cascade through systems, and about the relative importance of different influences. I present 2 example applications of SEM, one involving interactions among lynx (Lynx pardinus), mongooses (Herpestes ichneumon), and rabbits (Oryctolagus cuniculus), and the second involving anuran species richness. Many wildlife ecologists may find SEM useful for understanding how populations function within their environments. Along with the capability of the methodology comes a need for care in the proper application of SEM.
Carbone, Francesco; El, Gennady
2015-01-01
We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. We use the KdV soliton gas as a simplest analytically accessible model yielding major insight into the general properties of soliton gases in integrable systems. Two model problems are considered: (i) the propagation of a `trial' soliton through a one-component `cold' soliton gas consisting of randomly distributed solitons of approximately the same amplitude; and (ii) collision of two cold soliton gases of different amplitudes (soliton gas shock tube problem) leading to the formation of an incoherend dispersive shock wave. In both cases excellent agreement is observed between the analytical predictions of the soliton gas kinetics and the direct numerical simulations. Our results confirm relevance of the kinetic equation for solitons as a quantitatively accurate model for macrosco...
Meta-analytic structural equation modelling
Jak, Suzanne
2015-01-01
This book explains how to employ MASEM, the combination of meta-analysis (MA) and structural equation modelling (SEM). It shows how by using MASEM, a single model can be tested to explain the relationships between a set of variables in several studies. This book gives an introduction to MASEM, with a focus on the state of the art approach: the two stage approach of Cheung and Cheung & Chan. Both, the fixed and the random approach to MASEM are illustrated with two applications to real data. All steps that have to be taken to perform the analyses are discussed extensively. All data and syntax files are available online, so that readers can imitate all analyses. By using SEM for meta-analysis, this book shows how to benefit from all available information from all available studies, even if few or none of the studies report about all relationships that feature in the full model of interest.
MODELLING OF KINETICS OF FLUORINE ADSORPTION ONTO MODIFIED DIATOMITE
Directory of Open Access Journals (Sweden)
VEACESLAV ZELENTSOV
2017-03-01
Full Text Available The paper presents kinetics modelling of adsorption of fluorine onto modified diatomite, its fundamental characteristics and mathematical derivations. Three models of defluoridation kinetics were used to fit the experimental results on adsorption fluorine onto diatomite: the pseudo-first order model Lagergren, the pseudo-second order model G. McKay and H.S. Ho and intraparticle diffusion model of W.J. Weber and J.C. Morris. Kinetics studies revealed that the adsorption of fluorine followed second-order rate model, complimented by intraparticle diffusion kinetics. The adsorption mechanism of fluorine involved three stages – external surface adsorption, intraparticle diffusion and the stage of equilibrium.
On the Use of Structural Equation Models in Marketing Modeling
Steenkamp, J.E.B.M.; Baumgartner, H.
2000-01-01
We reflect on the role of structural equation modeling (SEM) in marketing modeling and managerial decision making. We discuss some benefits provided by SEM and alert marketing modelers to several recent developments in SEM in three areas: measurement analysis, analysis of cross-sectional data, and a
Kinetic depletion model for pellet ablation
Energy Technology Data Exchange (ETDEWEB)
Kuteev, Boris V. [State Technical Univ., St. Petersburg (Russian Federation)
2001-11-01
A kinetic model for depletion effect, which determines pellet ablation when the pellet passes a rational magnetic surface, is formulated. The model predicts a moderate decrease of the ablation rate compared with the earlier considered monoenergy versions [1, 2]. For typical T-10 conditions the ablation rate reduces by a reactor of 2.5 when the 1-mm pellet penetrates through the plasma center. A substantial deceleration of pellets -about 15% per centimeter of low shire rational q region; is predicted. Penetration for Low Field Side and High Field Side injections is considered taking into account modification of the electron distribution function by toroidal magnetic field. It is shown that Shafranov shift and toroidal effects yield the penetration length for HFS injection higher by a factor of 1.5. This fact should be taken into account when plasma-shielding effects on penetration are considered. (author)
Holographic kinetic k-essence model
Energy Technology Data Exchange (ETDEWEB)
Cruz, Norman [Departamento de Fisica, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Santiago (Chile)], E-mail: ncruz@lauca.usach.cl; Gonzalez-Diaz, Pedro F.; Rozas-Fernandez, Alberto [Colina de los Chopos, Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 121, 28006 Madrid (Spain)], E-mail: a.rozas@cfmac.csic.es; Sanchez, Guillermo [Departamento de Matematica y Ciencia de la Computacion, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Santiago (Chile)], E-mail: gsanchez@usach.cl
2009-08-31
We consider a connection between the holographic dark energy density and the kinetic k-essence energy density in a flat FRW universe. With the choice c{>=}1, the holographic dark energy can be described by a kinetic k-essence scalar field in a certain way. In this Letter we show this kinetic k-essential description of the holographic dark energy with c{>=}1 and reconstruct the kinetic k-essence function F(X)
Energy Technology Data Exchange (ETDEWEB)
Tumelero, Fernanda, E-mail: fernanda.tumelero@yahoo.com.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Petersen, Claudio Z.; Goncalves, Glenio A.; Lazzari, Luana, E-mail: claudiopeteren@yahoo.com.br, E-mail: gleniogoncalves@yahoo.com.br, E-mail: luana-lazzari@hotmail.com [Universidade Federal de Pelotas (DME/UFPEL), Capao do Leao, RS (Brazil). Instituto de Fisica e Matematica
2015-07-01
In this work, we present a solution of the Neutron Point Kinetics Equations with temperature feedback effects applying the Polynomial Approach Method. For the solution, we consider one and six groups of delayed neutrons precursors with temperature feedback effects and constant reactivity. The main idea is to expand the neutron density, delayed neutron precursors and temperature as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions of the problem and the analytical continuation is used to determine the solutions of the next intervals. With the application of the Polynomial Approximation Method it is possible to overcome the stiffness problem of the equations. In such a way, one varies the time step size of the Polynomial Approach Method and performs an analysis about the precision and computational time. Moreover, we compare the method with different types of approaches (linear, quadratic and cubic) of the power series. The answer of neutron density and temperature obtained by numerical simulations with linear approximation are compared with results in the literature. (author)
A first course in differential equations, modeling, and simulation
Smith, Carlos A
2011-01-01
IntroductionAn Introductory ExampleModelingDifferential EquationsForcing FunctionsBook ObjectivesObjects in a Gravitational FieldAn Example Antidifferentiation: Technique for Solving First-Order Ordinary Differential EquationsBack to Section 2-1Another ExampleSeparation of Variables: Technique for Solving First-Order Ordinary Differential Equations Back to Section 2-5Equations, Unknowns, and Degrees of FreedomClassical Solutions of Ordinary Linear Differential EquationsExamples of Differential EquationsDefinition of a Linear Differential EquationIntegrating Factor MethodCharacteristic Equation
Energy Technology Data Exchange (ETDEWEB)
Zhang, Fan [ORNL; Yeh, Gour-Tsyh [University of Central Florida, Orlando; Parker, Jack C [ORNL; Brooks, Scott C [ORNL; Pace, Molly [ORNL; Kim, Young Jin [ORNL; Jardine, Philip M [ORNL; Watson, David B [ORNL
2007-01-01
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M-NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C.; Brooks, Scott C.; Pace, Molly N.; Kim, Young-Jin; Jardine, Philip M.; Watson, David B.
2007-06-01
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing NE equilibrium reactions and a set of reactive transport equations of M- NE kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
A stochastic differential equation model of diurnal cortisol patterns
Brown, E. N.; Meehan, P. M.; Dempster, A. P.
2001-01-01
Circadian modulation of episodic bursts is recognized as the normal physiological pattern of diurnal variation in plasma cortisol levels. The primary physiological factors underlying these diurnal patterns are the ultradian timing of secretory events, circadian modulation of the amplitude of secretory events, infusion of the hormone from the adrenal gland into the plasma, and clearance of the hormone from the plasma by the liver. Each measured plasma cortisol level has an error arising from the cortisol immunoassay. We demonstrate that all of these three physiological principles can be succinctly summarized in a single stochastic differential equation plus measurement error model and show that physiologically consistent ranges of the model parameters can be determined from published reports. We summarize the model parameters in terms of the multivariate Gaussian probability density and establish the plausibility of the model with a series of simulation studies. Our framework makes possible a sensitivity analysis in which all model parameters are allowed to vary simultaneously. The model offers an approach for simultaneously representing cortisol's ultradian, circadian, and kinetic properties. Our modeling paradigm provides a framework for simulation studies and data analysis that should be readily adaptable to the analysis of other endocrine hormone systems.
Kinetic modelling of nitrogen and organics removal in vertical and horizontal flow wetlands.
Saeed, Tanveer; Sun, Guangzhi
2011-05-01
This paper provides a comparative evaluation of the kinetic models that were developed to describe the biodegradation of nitrogen and organics removal in wetland systems. Reaction kinetics that were considered in the model development included first order kinetics, Monod and multiple Monod kinetics; these kinetics were combined with continuous-stirred tank reactor (CSTR) or plug flow pattern to produce equations to link inlet and outlet concentrations of each key pollutants across a single wetland. Using three statistical parameters, a critical evaluation of five potential models was made for vertical and horizontal flow wetlands. The results recommended the models that were developed based on Monod models, for predicting the removal of nitrogen and organics in a vertical and horizontal flow wetland system. No clear correlation was observed between influent BOD/COD values and kinetic coefficients of BOD(5) in VF and HF wetlands, illustrating that the removal of biodegradable organics was insensitive to the nature of organic matter. Higher effluent COD/TN values coincided with greater denitrification kinetic coefficients, signifying the dependency of denitrification on the availability of COD in VF wetland systems. In contrast, the trend was opposite in HF wetlands, indicating that availability of NO(3)-N was the main limiting step for nitrogen removal. Overall, the results suggested the possible application of the developed alternative predictive models, for understanding the complex biodegradation routes of nitrogen and organics removal in VF and HF wetland systems.
Kinetic modelling of coupled transport across biological membranes.
Korla, Kalyani; Mitra, Chanchal K
2014-04-01
In this report, we have modelled a secondary active co-transporter (symport and antiport), based on the classical kinetics model. Michaelis-Menten model of enzyme kinetics for a single substrate, single intermediate enzyme catalyzed reaction was proposed more than a hundred years ago. However, no single model for the kinetics of co-transport of molecules across a membrane is available in the literature We have made several simplifying assumptions and have followed the basic Michaelis-Menten approach. The results have been simulated using GNU Octave. The results will be useful in general kinetic simulations and modelling.
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
Applying Meta-Analysis to Structural Equation Modeling
Hedges, Larry V.
2016-01-01
Structural equation models play an important role in the social sciences. Consequently, there is an increasing use of meta-analytic methods to combine evidence from studies that estimate the parameters of structural equation models. Two approaches are used to combine evidence from structural equation models: A direct approach that combines…
Parameter Estimation of Partial Differential Equation Models
Xun, Xiaolei
2013-09-01
Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from long-range infrared light detection and ranging data. Supplementary materials for this article are available online. © 2013 American Statistical Association.
Bezerra, Rui M F; Fraga, Irene; Dias, Albino A
2013-01-01
Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Liao, Fei; Zhu, Xiao-Yun; Wang, Yong-Mei; Zuo, Yu-Ping
2005-01-31
The estimation of enzyme kinetic parameters by nonlinear fitting reaction curve to the integrated Michaelis-Menten rate equation ln(S(0)/S)+(S(0)-S)/K(m)=(V(m)/K(m))xt was investigated and compared to that by fitting to (S(0)-S)/t=V(m)-K(m)x[ln(S(0)/S)/t] (Atkins GL, Nimmo IA. The reliability of Michaelis-Menten constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. Biochem J 1973;135:779-84) with uricase as the model. Uricase reaction curve was simulated with random absorbance error of 0.001 at 0.075 mmol/l uric acid. Experimental reaction curve was monitored by absorbance at 293 nm. For both CV and deviation kinetic parameters and applicable for the characterization of enzyme inhibitors.
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Directory of Open Access Journals (Sweden)
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
Kershaw closures for linear transport equations in slab geometry I: Model derivation
Schneider, Florian
2016-10-01
This paper provides a new class of moment models for linear kinetic equations in slab geometry. These models can be evaluated cheaply while preserving the important realizability property, that is the fact that the underlying closure is non-negative. Several comparisons with the (expensive) state-of-the-art minimum-entropy models are made, showing the similarity in approximation quality of the two classes.
Measurement of the Equation of State of the Two-Dimensional Hubbard Model
Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael
2016-05-01
The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 constitute benchmarks for state-of-the-art theoretical approaches.
Voter Model Perturbations and Reaction Diffusion Equations
Cox, J Theodore; Perkins, Edwin
2011-01-01
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins and the second confirms a conjecture of Ohtsuki et al in the ...
Electrothermal Model of Kinetic Inductance Detectors
Thomas, Christopher N; Goldie, David J
2014-01-01
An electrothermal model of Kinetic Inductance Detectors (KIDs) is described. The non-equilibrium state of the resonator's quasiparticle system is characterized by an effective temperature, which because of readout-power heating is higher than that of the bath. By balancing the flow of energy into the quasiparticle system, it is possible to calculate the steady-state large-signal, small-signal and noise behaviour. Resonance-curve distortion and hysteretic switching appear naturally within the framework. It is shown that an electrothermal feedback process exists, which affects all aspects of behaviour. It is also shown that generation-recombination noise can be interpreted in terms of the thermal fluctuation noise in the effective thermal conductance that links the quasiparticle and phonon systems of the resonator. Because the scheme is based on electrothermal considerations, multiple elements can be added to simulate the behaviour of complex devices, such as resonators on membranes, again taking into account r...
The General Linear Model as Structural Equation Modeling
Graham, James M.
2008-01-01
Statistical procedures based on the general linear model (GLM) share much in common with one another, both conceptually and practically. The use of structural equation modeling path diagrams as tools for teaching the GLM as a body of connected statistical procedures is presented. A heuristic data set is used to demonstrate a variety of univariate…
Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S
2013-10-18
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).
Transition study of 3D aerodynamic configures using improved transport equations modeling
Directory of Open Access Journals (Sweden)
Xu Jiakuan
2016-08-01
Full Text Available As boundary layer transition plays an important role in aerodynamic drag prediction, the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport (SST eddy-viscosity model, a new method, the SST-NTS-NCF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the NTS equation proposed by Coder, which simulates Tollmien–Schlichting wave transition. The turbulent kinetic energy equation is modified by introducing a new source term that simulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2A015, NLF(2-0415 and ONERA-D infinite swept wing and ONERA-M6 swept wing validate the predictive quality of the new SST-NTS-NCF model.
Transition study of 3D aerodynamic configures using improved transport equations modeling
Institute of Scientific and Technical Information of China (English)
Xu Jiakuan; Bai Junqiang; Zhang Yang; Qiao Lei
2016-01-01
As boundary layer transition plays an important role in aerodynamic drag prediction, the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport (SST) eddy-viscosity model, a new method, the SST-NTS-NCF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the NTS equation proposed by Coder, which simulates Tollmien–Schlichting wave tran-sition. The turbulent kinetic energy equation is modified by introducing a new source term that sim-ulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2)A015, NLF(2)-0415 and ONERA-D infinite swept wing and ONERA-M6 swept wing validate the predictive quality of the new SST-NTS-NCF model.
Modeling neck linker of kinesin motor movement with MRSR stochastic differential equation
Razali, Wan Qashishah Akmal Wan; Ramli, Siti Norafidah Mohd; Radiman, Shahidan
2016-11-01
Stochastic differential equation has a significant role in a range of biological areas including molecular motor like kinesin motor. Mean-reverting square root (MRSR) stochastic differential equation is commonly used in economics and finance areas. In this study, we use the MRSR stochastic differential equation to model neck linker motion of kinesin motor by considering the possibilities of rightward direction and occasionally in the leftward direction of kinesin movements. This neck linker docking model of kinesin motor incorporates the conformational change in the chemical kinetics and the tethered diffusion of the free head of kinesin motor. Here, we demonstrate this model by using Hookean spring method which referred to the stiffness model of neck linker. The motion of kinesin motor seems to be well described to move in unidirectional way with volatile behavior based on MRSR rather than common stochastic differential equation [DOI 10.1007/s11538-011-9697-6].
Laplace transform in tracer kinetic modeling
Energy Technology Data Exchange (ETDEWEB)
Hauser, Eliete B., E-mail: eliete@pucrs.br [Instituto do Cerebro (InsCer/FAMAT/PUC-RS), Porto Alegre, RS, (Brazil). Faculdade de Matematica
2013-07-01
The main objective this paper is to quantify the pharmacokinetic processes: absorption, distribution and elimination of radiopharmaceutical(tracer), using Laplace transform method. When the drug is administered intravenously absorption is complete and is available in the bloodstream to be distributed throughout the whole body in all tissues and fluids, and to be eliminated. Mathematical modeling seeks to describe the processes of distribution and elimination through compartments, where distinct pools of tracer (spatial location or chemical state) are assigned to different compartments. A compartment model is described by a system of differential equations, where each equation represents the sum of all the transfer rates to and from a specific compartment. In this work a two-tissue irreversible compartment model is used for description of tracer, [{sup 18}F]2-fluor-2deoxy-D-glucose. In order to determine the parameters of the model, it is necessary to have information about the tracer delivery in the form of an input function representing the time-course of tracer concentration in arterial blood or plasma. We estimate the arterial input function in two stages and apply the Levenberg-Marquardt Method to solve nonlinear regressions. The transport of FDG across de arterial blood is very fast in the first ten minutes and then decreases slowly. We use de Heaviside function to represent this situation and this is the main contribution of this study. We apply the Laplace transform and the analytical solution for two-tissue irreversible compartment model is obtained. The only approach is to determinate de arterial input function. (author)
A review on solar wind modeling: kinetic and fluid aspects
Echim, Marius; Lie-Svendsen, Oystein
2013-01-01
We review the main advantages and limitations of the kinetic exospheric and fluid models of the solar wind (SW). We discuss the hydrostatic model imagined by Chapman, the first supersonic hydrodynamic models published by Parker and the first generation subsonic kinetic model proposed by Chamberlain. It is shown that a correct estimation of the electric field as in the second generation kinetic exospheric models developed by Lemaire and Scherer, provides a supersonic expansion of the corona, reconciling the hydrodynamic and the kinetic approach. The third generation kinetic exospheric models considers kappa velocity distribution function (VDF) instead of a Maxwellian at the exobase and in addition they treat a non-monotonic variation of the electric potential with the radial distance; the fourth generation exospheric models include Coulomb collisions based on the Fokker--Planck collision term. Multi-fluid models of the solar wind provide a coarse grained description and reproduce with success the spatio-tempor...
Energy Technology Data Exchange (ETDEWEB)
Kim, Song Hyun; Woo, Myeong Hyun; Shin, Chang Ho [Hanyang University, Seoul (Korea, Republic of); Pyeon, Cheol Ho [Kyoto University, Osaka (Japan)
2015-10-15
In this study, a new balance equation to overcome the problems generated by the previous methods is proposed using source-based balance equation. And then, a simple problem is analyzed with the proposed method. In this study, a source-based balance equation with the time dependent fission kernel was derived to simplify the kinetics equation. To analyze the partial variations of reactor characteristics, two representative methods were introduced in previous studies; (1) quasi-statics method and (2) multipoint technique. The main idea of quasistatics method is to use a low-order approximation for large integration times. To realize the quasi-statics method, first, time dependent flux is separated into the shape and amplitude functions, and shape function is calculated. It is noted that the method has a good accuracy; however, it can be expensive as a calculation cost aspect because the shape function should be fully recalculated to obtain accurate results. To improve the calculation efficiency, multipoint method was proposed. The multipoint method is based on the classic kinetics equation with using Green's function to analyze the flight probability from region r' to r. Those previous methods have been used to analyze the reactor kinetics analysis; however, the previous methods can have some limitations. First, three group variables (r{sub g}, E{sub g}, t{sub g}) should be considered to solve the time dependent balance equation. This leads a big limitation to apply large system problem with good accuracy. Second, the energy group neutrons should be used to analyze reactor kinetics problems. In time dependent problem, neutron energy distribution can be changed at different time. It can affect the change of the group cross section; therefore, it can lead the accuracy problem. Third, the neutrons in a space-time region continually affect the other space-time regions; however, it is not properly considered in the previous method. Using birth history of the
Structural equation models from paths to networks
Westland, J Christopher
2015-01-01
This compact reference surveys the full range of available structural equation modeling (SEM) methodologies. It reviews applications in a broad range of disciplines, particularly in the social sciences where many key concepts are not directly observable. This is the first book to present SEM’s development in its proper historical context–essential to understanding the application, strengths and weaknesses of each particular method. This book also surveys the emerging path and network approaches that complement and enhance SEM, and that will grow in importance in the near future. SEM’s ability to accommodate unobservable theory constructs through latent variables is of significant importance to social scientists. Latent variable theory and application are comprehensively explained, and methods are presented for extending their power, including guidelines for data preparation, sample size calculation, and the special treatment of Likert scale data. Tables of software, methodologies and fit st...
Berim, Gersh O.; Ruckenstein, Eli
2003-11-01
A generalized kinetic Ising model is applied to the description of phase transformations in lattice systems. A procedure, based on the conjecture that the probability distribution function of the states of the system is similar to the equilibrium one, is used for closing the infinite chain of kinetic equations. The method is illustrated by treating as an example the one-dimensional Ising model. The predicted rate of phase transformation (RPT) demonstrates various time behaviors dependent upon the details of the interactions between spins and a heat bath. If the parameters W0 and W the reciprocals of which characterize, respectively, the time scales of growth (decay) and splitting (coagulation) of clusters have the same order of magnitude, then the RPT is constant during almost the entire transformation process. For the case W=0, which corresponds to the absence of splitting and coagulation of clusters, the phase transformation follows an exponential law in the final stage and is linear with respect to time during the initial one. It has a similar behavior for W0≫W≠0; however, the RPT in the final stage is much smaller in the last case than for W=0. In the absence of supersaturation, RPT decreases to zero as T→Tc, where Tc(=0 K) is the phase transition temperature for a one-dimensional model. The time-dependent size distribution of clusters is for all times exponential with respect to the cluster size. The average size of the cluster far from both equilibrium and initial state grows linearly in time. Both the above quantities behave in a manner similar to those obtained by Monte Carlo simulations for systems of higher dimension.
Chemical Kinetic Modeling of Biofuel Combustion
Sarathy, Subram Maniam
Bioalcohols, such as bioethanol and biobutanol, are suitable replacements for gasoline, while biodiesel can replace petroleum diesel. Improving biofuel engine performance requires understanding its fundamental combustion properties and the pathways of combustion. This study's contribution is experimentally validated chemical kinetic combustion mechanisms for biobutanol and biodiesel. Fundamental combustion data and chemical kinetic mechanisms are presented and discussed to improve our understanding of biofuel combustion. The net environmental impact of biobutanol (i.e., n-butanol) has not been studied extensively, so this study first assesses the sustainability of n-butanol derived from corn. The results indicate that technical advances in fuel production are required before commercializing biobutanol. The primary contribution of this research is new experimental data and a novel chemical kinetic mechanism for n-butanol combustion. The results indicate that under the given experimental conditions, n-butanol is consumed primarily via abstraction of hydrogen atoms to produce fuel radical molecules, which subsequently decompose to smaller hydrocarbon and oxygenated species. The hydroxyl moiety in n-butanol results in the direct production of the oxygenated species such as butanal, acetaldehyde, and formaldehyde. The formation of these compounds sequesters carbon from forming soot precursors, but they may introduce other adverse environmental and health effects. Biodiesel is a mixture of long chain fatty acid methyl esters derived from fats and oils. This research study presents high quality experimental data for one large fatty acid methyl ester, methyl decanoate, and models its combustion using an improved skeletal mechanism. The results indicate that methyl decanoate is consumed via abstraction of hydrogen atoms to produce fuel radicals, which ultimately lead to the production of alkenes. The ester moiety in methyl decanoate leads to the formation of low molecular
A note on solutions of an equation modelling arterial deformation
Energy Technology Data Exchange (ETDEWEB)
Gordoa, P.R. [Area de Matematica Aplicada, ESCET, Universidad Rey Juan Carlos, C/ Tulipan s/n, 28933 Mostoles, Madrid (Spain)]. E-mail: pilar.gordoa@urjc.es
2007-08-15
The derivation of exact solutions for a partial differential equation modelling arterial deformation in large arteries is considered. Amongst other results, we show that, for any values of the parameters appearing in the equation, solutions in terms of the first Painleve transcendent can be obtained. This is in spite of the non-integrability of the equation. We also establish a connection, via an approximation of the equation under study by the Korteweg-de Vries equation, with the second Painleve equation. Our results thus serve to further demonstrate the wide applicability and importance of the Painleve equations.
Kinetic model of water vapour adsorption by gluten-free starch
Ocieczek, Aneta; Kostek, Robert; Ruszkowska, Millena
2015-01-01
This study evaluated the kinetics of water vapour adsorption on the surface of starch molecules derived from wheat. The aim of the study was to determine an equation that would allow estimation of water content in tested material in any timepoint of the adsorption process aimed at settling a balance with the environment. An adsorption isotherm of water vapour on starch granules was drawn. The parameters of the Guggenheim, Anderson, and De Boer equation were determined by characterizing the tested product and adsorption process. The equation of kinetics of water vapour adsorption on the surface of starch was determined based on the Guggenheim, Anderson, and De Boer model describing the state of equilibrium and on the model of a first-order linear inert element describing the changes in water content over time.
Pyrolysis Kinetic Modelling of Wheat Straw from the Pannonian Region
Directory of Open Access Journals (Sweden)
Ivan Pešenjanski
2016-01-01
Full Text Available The pyrolysis/devolatilization is a basic step of thermochemical processes and requires fundamental characterization. In this paper, the kinetic model of pyrolysis is specified as a one-step global reaction. This type of reaction is used to describe the thermal degradation of wheat straw samples by measuring rates of mass loss of solid matter at a linear increase in temperature. The mentioned experiments were carried out using a derivatograph in an open-air environment. The influence of different factors was investigated, such as particle size, humidity levels, and the heating rate in the kinetics of devolatilization. As the measured values of mass loss and temperature functions transform in Arrhenius coordinates, the results are shown in the form of saddle curves. Such characteristics cannot be approximated with one equation in the form of Arrhenius law. For use in numerical applications, transformed functions can be approximated by linear regression for three separate intervals. Analysis of measurement resulting in granulation and moisture content variations shows that these factors have no significant influence. Tests of heating rate variations confirm the significance of this impact, especially in warmer regions. The influence of this factor should be more precisely investigated as a general variable, which should be the topic of further experiments.
Integration Strategies for Efficient Multizone Chemical Kinetics Models
Energy Technology Data Exchange (ETDEWEB)
McNenly, M J; Havstad, M A; Aceves, S M; Pitz, W J
2009-10-15
Three integration strategies are developed and tested for the stiff, ordinary differential equation (ODE) integrators used to solve the fully coupled multizone chemical kinetics model. Two of the strategies tested are found to provide more than an order of magnitude of improvement over the original, basic level of usage for the stiff ODE solver. One of the faster strategies uses a decoupled, or segregated, multizone model to generate an approximate Jacobian. This approach yields a 35-fold reduction in the computational cost for a 20 zone model. Using the same approximate Jacobian as a preconditioner for an iterative Krylov-type linear system solver, the second improved strategy achieves a 75-fold reduction in the computational cost for a 20 zone model. The faster strategies achieve their cost savings with no significant loss of accuracy. The pressure, temperature and major species mass fractions agree with the solution from the original integration approach to within six significant digits; and the radical mass fractions agree with the original solution to within four significant digits. The faster strategies effectively change the cost scaling of the multizone model from cubic to quadratic, with respect to the number of zones. As a consequence of the improved scaling, the 40 zone model offers more than a 250-fold cost savings over the basic calculation.
Thermoluminescence of zircon: a kinetic model
Turkin, A A; Vainshtein, D I; Hartog, H W D
2003-01-01
The mineral zircon, ZrSiO sub 4 , belongs to a class of promising materials for geochronometry by means of thermoluminescence (TL) dating. The development of a reliable and reproducible method for TL dating with zircon requires detailed knowledge of the processes taking place during exposure to ionizing radiation, long-term storage, annealing at moderate temperatures and heating at a constant rate (TL measurements). To understand these processes one needs a kinetic model of TL. This paper is devoted to the construction of such a model. The goal is to study the qualitative behaviour of the system and to determine the parameters and processes controlling TL phenomena of zircon. The model considers the following processes: (i) Filling of electron and hole traps at the excitation stage as a function of the dose rate and the dose for both (low dose rate) natural and (high dose rate) laboratory irradiation. (ii) Time dependence of TL fading in samples irradiated under laboratory conditions. (iii) Short time anneali...
Shear-Driven Reconnection in Kinetic Models
Black, C.; Antiochos, S. K.; Germaschewski, K.; Karpen, J. T.; DeVore, C. R.; Bessho, N.
2015-12-01
The explosive energy release in solar eruptive phenomena is believed to be due to magnetic reconnection. In the standard model for coronal mass ejections (CME) and/or solar flares, the free energy for the event resides in the strongly sheared magnetic field of a filament channel. The pre-eruption force balance consists of an upward force due to the magnetic pressure of the sheared field countered by a downward tension due to overlying unsheared field. Magnetic reconnection disrupts this force balance; therefore, it is critical for understanding CME/flare initiation, to model the onset of reconnection driven by the build-up of magnetic shear. In MHD simulations, the application of a magnetic-field shear is a trivial matter. However, kinetic effects are dominant in the diffusion region and thus, it is important to examine this process with PIC simulations as well. The implementation of such a driver in PIC methods is challenging, however, and indicates the necessity of a true multiscale model for such processes in the solar environment. The field must be sheared self-consistently and indirectly to prevent the generation of waves that destroy the desired system. Plasma instabilities can arise nonetheless. In the work presented here, we show that we can control this instability and generate a predicted out-of-plane magnetic flux. This material is based upon work supported by the National Science Foundation under Award No. AGS-1331356.
Multiple-relaxation-time lattice Boltzmann kinetic model for combustion.
Xu, Aiguo; Lin, Chuandong; Zhang, Guangcai; Li, Yingjun
2015-04-01
To probe both the hydrodynamic nonequilibrium (HNE) and thermodynamic nonequilibrium (TNE) in the combustion process, a two-dimensional multiple-relaxation-time (MRT) version of lattice Boltzmann kinetic model (LBKM) for combustion phenomena is presented. The chemical energy released in the progress of combustion is dynamically coupled into the system by adding a chemical term to the LB kinetic equation. Aside from describing the evolutions of the conserved quantities, the density, momentum, and energy, which are what the Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained description on the evolutions of some nonconserved quantities. The current model works for both subsonic and supersonic flows with or without chemical reaction. In this model, both the specific-heat ratio and the Prandtl number are flexible, the TNE effects are naturally presented in each simulation step. The model is verified and validated via well-known benchmark tests. As an initial application, various nonequilibrium behaviors, including the complex interplays between various HNEs, between various TNEs, and between the HNE and TNE, around the detonation wave in the unsteady and steady one-dimensional detonation processes are preliminarily probed. It is found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave, that even locally, the system viscosity (or heat conductivity) results in two kinds of competing trends, to increase and to decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses.
Kiernan, D; Malone, A; O'Brien, T; Simms, C K
2015-01-01
Regression equations based on pelvic anatomy are routinely used to estimate the hip joint centre during gait analysis. While the associated errors have been well documented, the clinical significance of these errors has not been reported. This study investigated the clinical agreement of three commonly used regression equation sets (Bell et al., Davis et al. and Orthotrak software) against the equations of Harrington et al. Full 3-dimensional gait analysis was performed on 18 healthy paediatric subjects. Kinematic and kinetic data were calculated using each set of regression equations and compared to Harrington et al. In addition, the Gait Profile Score and GDI-Kinetic were used to assess clinical significance. Bell et al. was the best performing set with differences in Gait Profile Score (0.13°) and GDI-Kinetic (0.84 points) falling below the clinical significance threshold. Small deviations were present for the Orthotrak set for hip abduction moment (0.1 Nm/kg), however differences in Gait Profile Score (0.27°) and GDI-Kinetic (2.26 points) remained below the clinical threshold. Davis et al. showed least agreement with a clinically significant difference in GDI-Kinetic score (4.36 points). It is proposed that Harrington et al. or Bell et al. regression equation sets are used during gait analysis especially where inverse dynamic data are calculated. Orthotrak is a clinically acceptable alternative however clinicians must be aware of the effects of error on hip abduction moment. The Davis et al. set should be used with caution for inverse dynamic analysis as error could be considered clinically meaningful.
Energy Technology Data Exchange (ETDEWEB)
Pradhan, Santosh K., E-mail: santosh@aerb.gov.in [Nuclear Safety Analysis Division, Atomic Energy Regulatory Board, Mumbai 400094 (India); Obaidurrahman, K. [Nuclear Safety Analysis Division, Atomic Energy Regulatory Board, Mumbai 400094 (India); Iyer, Kannan N. [Department of Mechanical Engineering, IIT Bombay, Mumbai 400076 (India); Gaikwad, Avinash J. [Nuclear Safety Analysis Division, Atomic Energy Regulatory Board, Mumbai 400094 (India)
2016-04-15
Highlights: • A multi-point kinetics model is developed for RELAP5 system thermal hydraulics code. • Model is validated against extensive 3D kinetics code. • RELAP5 multi-point kinetics formulation is used to investigate critical break for LOCA in PHWR. - Abstract: Point kinetics approach in system code RELAP5 limits its use for many of the reactivity induced transients, which involve asymmetric core behaviour. Development of fully coupled 3D core kinetics code with system thermal-hydraulics is the ultimate requirement in this regard; however coupling and validation of 3D kinetics module with system code is cumbersome and it also requires access to source code. An intermediate approach with multi-point kinetics is appropriate and relatively easy to implement for analysis of several asymmetric transients for large cores. Multi-point kinetics formulation is based on dividing the entire core into several regions and solving ODEs describing kinetics in each region. These regions are interconnected by spatial coupling coefficients which are estimated from diffusion theory approximation. This model offers an advantage that associated ordinary differential equations (ODEs) governing multi-point kinetics formulation can be solved using numerical methods to the desired level of accuracy and thus allows formulation based on user defined control variables, i.e., without disturbing the source code and hence also avoiding associated coupling issues. Euler's method has been used in the present formulation to solve several coupled ODEs internally at each time step. The results have been verified against inbuilt point-kinetics models of RELAP5 and validated against 3D kinetics code TRIKIN. The model was used to identify the critical break in RIH of a typical large PHWR core. The neutronic asymmetry produced in the core due to the system induced transient was effectively handled by the multi-point kinetics model overcoming the limitation of in-built point kinetics model
Reflected kinetics model for nuclear space reactor kinetics and control scoping calculations
Energy Technology Data Exchange (ETDEWEB)
Washington, K.E.
1986-05-01
The objective of this research is to develop a model that offers an alternative to the point kinetics (PK) modelling approach in the analysis of space reactor kinetics and control studies. Modelling effort will focus on the explicit treatment of control drums as reactivity input devices so that the transition to automatic control can be smoothly done. The proposed model is developed for the specific integration of automatic control and the solution of the servo mechanism problem. The integration of the kinetics model with an automatic controller will provide a useful tool for performing space reactor scoping studies for different designs and configurations. Such a tool should prove to be invaluable in the design phase of a space nuclear system from the point of view of kinetics and control limitations.
Adaptive change of basis in entropy-based moment closures for linear kinetic equations
Alldredge, Graham W; O'Leary, Dianne P; Tits, André L
2013-01-01
Entropy-based (M_N) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and efficiently. We present a complete and practical numerical algorithm for solving the dual problem in one-dimensional, slab geometries. The closure is only well-defined on the set of moments that are realizable from a positive underlying distribution, and as the boundary of the realizable set is approached, the dual problem becomes increasingly difficult to solve due to ill-conditioning of the Hessian matrix. To improve the condition number of the Hessian, we advocate the use of a change of polynomial basis, defined using a Cholesky factorization of the Hessian, that permits solution of problems nearer to the boundary of the realizable set. We also advocate a fixed quadrature scheme, rather than adaptive quadrature, since the latter introduces unnecessary expense and changes th...
Parameter estimation for models of ligninolytic and cellulolytic enzyme kinetics
Energy Technology Data Exchange (ETDEWEB)
Wang, Gangsheng [ORNL; Post, Wilfred M [ORNL; Mayes, Melanie [ORNL; Frerichs, Joshua T [ORNL; Jagadamma, Sindhu [ORNL
2012-01-01
While soil enzymes have been explicitly included in the soil organic carbon (SOC) decomposition models, there is a serious lack of suitable data for model parameterization. This study provides well-documented enzymatic parameters for application in enzyme-driven SOC decomposition models from a compilation and analysis of published measurements. In particular, we developed appropriate kinetic parameters for five typical ligninolytic and cellulolytic enzymes ( -glucosidase, cellobiohydrolase, endo-glucanase, peroxidase, and phenol oxidase). The kinetic parameters included the maximum specific enzyme activity (Vmax) and half-saturation constant (Km) in the Michaelis-Menten equation. The activation energy (Ea) and the pH optimum and sensitivity (pHopt and pHsen) were also analyzed. pHsen was estimated by fitting an exponential-quadratic function. The Vmax values, often presented in different units under various measurement conditions, were converted into the same units at a reference temperature (20 C) and pHopt. Major conclusions are: (i) Both Vmax and Km were log-normal distributed, with no significant difference in Vmax exhibited between enzymes originating from bacteria or fungi. (ii) No significant difference in Vmax was found between cellulases and ligninases; however, there was significant difference in Km between them. (iii) Ligninases had higher Ea values and lower pHopt than cellulases; average ratio of pHsen to pHopt ranged 0.3 0.4 for the five enzymes, which means that an increase or decrease of 1.1 1.7 pH units from pHopt would reduce Vmax by 50%. (iv) Our analysis indicated that the Vmax values from lab measurements with purified enzymes were 1 2 orders of magnitude higher than those for use in SOC decomposition models under field conditions.
Kinetic Model of Optical Characteristics of Banknote Paper During Artificial Aging
Kulak, M. I.; Kyrychok, T. Yu.; Miadziak, D. M.; Kyrychok, P. O.
2016-09-01
A phenomenological kinetic equation is obtained for the change in color difference and brightness of banknote paper during aging. A solution is obtained for the kinetic equation. The coefficients of the kinetic function are determined from experimental data. Kinetic functions are constructed for three samples of the banknote paper. By analysis of the coefficients of the kinetic function it is possible to compare the paper according to its resistance towards the aging process.
Kinetic modeling in pre-clinical positron emission tomography
Energy Technology Data Exchange (ETDEWEB)
Kuntner, Claudia [AIT Austrian Institute of Technology GmbH, Seibersdorf (Austria). Biomedical Systems, Health and Environment Dept.
2014-07-01
Pre-clinical positron emission tomography (PET) has evolved in the last few years from pure visualization of radiotracer uptake and distribution towards quantification of the physiological parameters. For reliable and reproducible quantification the kinetic modeling methods used to obtain relevant parameters of radiotracer tissue interaction are important. Here we present different kinetic modeling techniques with a focus on compartmental models including plasma input models and reference tissue input models. The experimental challenges of deriving the plasma input function in rodents and the effect of anesthesia are discussed. Finally, in vivo application of kinetic modeling in various areas of pre-clinical research is presented and compared to human data.
Serdenko, T. V.; Barabash, Y. M.; Knox, P. P.; Seifullina, N. Kh.
2016-06-01
The present work is related to the investigation of slow kinetics of electron transport in the reaction centers (RCs) of Rhodobacter sphaeroides. Experimental data on the absorption kinetics of aqueous solutions of reaction centers at different modes of photoexcitation are given. It is shown that the kinetics of oxidation and reduction of RCs are well described by the sum of three exponential functions. This allows to suggest a two-level kinetic model for electron transport in the RC as a system of four electron-conformational states which correspond to three balance differential equations combined with state equation. The solution of inverse problem made it possible to obtain the rate constant values in kinetic equations for different times and intensities of exciting light. Analysis of rate constant values in different modes of RC excitation allowed to suggest that two mechanisms of structural changes are involved in RC photo-oxidation. One mechanism leads to the increment of the rate of electron return, another one—to its drop. Structural changes were found out to occur in the RCs under incident light. After light was turned off, the reduction of RCs was determined by the second mechanism.
Stydy on the Model of Ion Exchange Kinetics
Institute of Scientific and Technical Information of China (English)
ChenFengrong; JiangZhixin
1994-01-01
In this paper, a macrokinetics model equation describing the characteristics of the solid-liquid mass transfer has been proposed.The qualitative analysis and experimental verification have been done for this mode equation.The model equation can explain the ion exchange process considerably well.
Zakharov, A Yu
2016-01-01
The exact closed equation of motion for microscopic distribution function of classical many-body system with account of interactions retardation between particles is derived. It is shown that interactions retardation leads to irreversible behaviour of many-body systems.
Matsui, Yoshihiko; Ando, Naoya; Yoshida, Tomoaki; Kurotobi, Ryuji; Matsushita, Taku; Ohno, Koichi
2011-02-01
The capacity to adsorb natural organic matter (NOM) and polystyrene sulfonates (PSSs) on small particle-size activated carbon (super-powdered activated carbon, SPAC) is higher than that on larger particle-size activated carbon (powdered-activated carbon, PAC). Increased adsorption capacity is likely attributable to the larger external surface area because the NOM and PSS molecules do not completely penetrate the adsorbent particle; they preferentially adsorb near the outer surface of the particle. In this study, we propose a new isotherm equation, the Shell Adsorption Model (SAM), to explain the higher adsorption capacity on smaller adsorbent particles and to describe quantitatively adsorption isotherms of activated carbons of different particle sizes: PAC and SPAC. The SAM was verified with the experimental data of PSS adsorption kinetics as well as equilibrium. SAM successfully characterized PSS adsorption isotherm data for SPACs and PAC simultaneously with the same model parameters. When SAM was incorporated into an adsorption kinetic model, kinetic decay curves for PSSs adsorbing onto activated carbons of different particle sizes could be simultaneously described with a single kinetics parameter value. On the other hand, when SAM was not incorporated into such an adsorption kinetic model and instead isotherms were described by the Freundlich model, the kinetic decay curves were not well described. The success of the SAM further supports the adsorption mechanism of PSSs preferentially adsorbing near the outer surface of activated carbon particles.
Kinetic models of cell growth, substrate utilization and bio ...
African Journals Online (AJOL)
STORAGESEVER
2008-05-02
May 2, 2008 ... A simple model was proposed using the Logistic Equation for the growth,. Leudeking-Piret ... (melanoidin) which may create many problems and also .... Where, the constant µ is defined as the specific growth rate. Equation 1 ...
Fitting ARMA Time Series by Structural Equation Models.
van Buuren, Stef
1997-01-01
This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)
Kinetic theories for spin models for cooperative relaxation dynamics
Pitts, Steven Jerome
The facilitated kinetic Ising models with asymmetric spin flip constraints introduced by Jackle and co-workers [J. Jackle, S. Eisinger, Z. Phys. B 84, 115 (1991); J. Reiter, F. Mauch, J. Jackle, Physica A 184, 458 (1992)] exhibit complex relaxation behavior in their associated spin density time correlation functions. This includes the growth of relaxation times over many orders of magnitude when the thermodynamic control parameter is varied, and, in some cases, ergodic-nonergodic transitions. Relaxation equations for the time dependence of the spin density autocorrelation function for a set of these models are developed that relate this autocorrelation function to the irreducible memory function of Kawasaki [K. Kawasaki, Physica A 215, 61 (1995)] using a novel diagrammatic series approach. It is shown that the irreducible memory function in a theory of the relaxation of an autocorrelation function in a Markov model with detailed balance plays the same role as the part of the memory function approximated by a polynomial function of the autocorrelation function with positive coefficients in schematic simple mode coupling theories for supercooled liquids [W. Gotze, in Liquids, Freezing and the Glass Transition, D. Levesque, J. P. Hansen, J. Zinn-Justin eds., 287 (North Holland, New York, 1991)]. Sets of diagrams in the series for the irreducible memory function are summed which lead to approximations of this type. The behavior of these approximations is compared with known results from previous analytical calculations and from numerical simulations. For the simplest one dimensional model, relaxation equations that are closely related to schematic extended mode coupling theories [W. Gotze, ibid] are also derived using the diagrammatic series. Comparison of the results of these approximate theories with simulation data shows that these theories improve significantly on the results of the theories of the simple schematic mode coupling theory type. The potential
Directory of Open Access Journals (Sweden)
José Gilson Louzada Regadas Filho
2011-09-01
Full Text Available This study aimed at estimating the kinetic parameters of ruminal degradation of neutral detergent fiber from agroindustrial byproducts of cashew (pulp and cashew nut, passion fruit, melon, pineapple, West Indian cherry, grape, annatto and coconut through the gravimetric technique of nylon bag, and to evaluate the prediction equation of indigestible fraction of neutral detergent fiber suggested by the Cornell Net Carbohydrate and Protein System. Samples of feed crushed to 2 mm were placed in 7 × 14 cm nylon bags with porosity of 50 µm in a ratio of 20 g DM/cm² and incubated in duplicate in the rumen of a heifer at 0, 3, 6, 9, 12, 16, 24, 36, 48, 72, 96 and 144 hours. The incubation residues were analyzed for NDF content and evaluated by a non-linear logistic model. The evaluation process of predicting the indigestible fraction of NDF was carried out through adjustment of linear regression models between predicted and observed values. There was a wide variation in the degradation parameters of NDF among byproducts. The degradation rate of NDF ranged from 0.0267 h-1 to 0.0971 h-1 for grape and West Indian cherry, respectively. The potentially digestible fraction of NDF ranged from 4.17 to 90.67%, respectively, for melon and coconut byproducts. The CNCPS equation was sensitive to predict the indigestible fraction of neutral detergent fiber of the byproducts. However, due to the high value of the mean squared error of prediction, such estimates are very variable; hence the most suitable would be estimation by biological methods.
Mogilevskaya, Ekaterina; Demin, Oleg; Goryanin, Igor
2006-01-01
This paper studies the effect of salicylate on the energy metabolism of mitochondria using in silico simulations. A kinetic model of the mitochondrial Krebs cycle is constructed using information on the individual enzymes. Model parameters for the rate equations are estimated using in vitro experimental data from the literature. Enzyme concentrations are determined from data on respiration in mitochondrial suspensions containing glutamate and malate. It is shown that inhibition in succinate d...
Mogilevskaya, Ekaterina; Demin, Oleg; Goryanin, Igor
2006-01-01
This paper studies the effect of salicylate on the energy metabolism of mitochondria using in silico simulations. A kinetic model of the mitochondrial Krebs cycle is constructed using information on the individual enzymes. Model parameters for the rate equations are estimated using in vitro experimental data from the literature. Enzyme concentrations are determined from data on respiration in mitochondrial suspensions containing glutamate and malate. It is shown that inhibition in succinate d...
Virtuous organization: A structural equation modeling approach
Directory of Open Access Journals (Sweden)
Majid Zamahani
2013-02-01
Full Text Available For years, the idea of virtue was unfavorable among researchers and virtues were traditionally considered as culture-specific, relativistic and they were supposed to be associated with social conservatism, religious or moral dogmatism, and scientific irrelevance. Virtue and virtuousness have been recently considered seriously among organizational researchers. The proposed study of this paper examines the relationships between leadership, organizational culture, human resource, structure and processes, care for community and virtuous organization. Structural equation modeling is employed to investigate the effects of each variable on other components. The data used in this study consists of questionnaire responses from employees in Payam e Noor University in Yazd province. A total of 250 questionnaires were sent out and a total of 211 valid responses were received. Our results have revealed that all the five variables have positive and significant impacts on virtuous organization. Among the five variables, organizational culture has the most direct impact (0.80 and human resource has the most total impact (0.844 on virtuous organization.
SATL MODEL LESSON IN CHEMICAL KINETICS
African Journals Online (AJOL)
Preferred Customer
Department of Chemistry, The Federal Urdu University of Arts, Science and ... are several strategies, through which teaching and learning of scientific subjects in ... the linear relationships among various factors involved in chemical kinetics.
QE+QSS for Derivation of Kinetic Equations and Stiffness Removing
Gorban, A N
2010-01-01
We present the general formalism of the Quasiequilibrium approximation (QE) with the proof of the persistence of entropy production in the QE approximation. We demonstrate, how to apply this formalism to chemical kinetics and describe the difference between QE and Quasi--Steady--State (QSS) approximations. The celebrated QSS "Michaelis--Menten" kinetics is, as a matter of fact, the "Briggs-Haldane" kinetics. Michaelis and Menten used the QE assumption that all intermediate complexes are in fast equilibrium with free substrates and enzyme. Similar approach was developed by Stuekelberg (1952) for the Boltzmann kinetics. Following them, we combine the QE (fast equilibria) and the QSS (small amounts) approaches and study the general kinetics with fast intermediates present in small amount. We prove the representation of the rate of an elementary reaction as a product of the Boltzmann factor (purely thermodynamic) and the kinetic factor, and found the basic relations between kinetic factors. In the practice of mod...
Adiabatic limit in Abelian Higgs model with application to Seiberg-Witten equations
Sergeev, A.
2017-03-01
In this paper we deal with the (2 + 1)-dimensional Higgs model governed by the Ginzburg-Landau Lagrangian. The static solutions of this model, called otherwise vortices, are described by the theorem of Taubes. This theorem gives, in particular, an explicit description of the moduli space of vortices (with respect to gauge transforms). However, much less is known about the moduli space of dynamical solutions. A description of slowly moving solutions may be given in terms of the adiabatic limit. In this limit the dynamical Ginzburg-Landau equations reduce to the adiabatic equation coinciding with the Euler equation for geodesics on the moduli space of vortices with respect to the Riemannian metric (called T-metric) determined by the kinetic energy of the model. A similar adiabatic limit procedure can be used to describe approximately solutions of the Seiberg-Witten equations on 4-dimensional symplectic manifolds. In this case the geodesics of T-metric are replaced by the pseudoholomorphic curves while the solutions of Seiberg-Witten equations reduce to the families of vortices defined in the normal planes to the limiting pseudoholomorphic curve. Such families should satisfy a nonlinear ∂-equation which can be considered as a complex analogue of the adiabatic equation. Respectively, the arising pseudoholomorphic curves may be considered as complex analogues of adiabatic geodesics in (2 + 1)-dimensional case. In this sense the Seiberg-Witten model may be treated as a (2 + 1)-dimensional analogue of the (2 + 1)-dimensional Abelian Higgs model2.
Innovative first order elimination kinetics working model for easy learning
Directory of Open Access Journals (Sweden)
Navin Budania
2016-06-01
Conclusions: First order elimination kinetics is easily understood with the help of above working model. More and more working models could be developed for teaching difficult topics. [Int J Basic Clin Pharmacol 2016; 5(3.000: 862-864
MODELLING OF BACTERIAL SULPHATE REDUCTION IN ANAEROBIC PONDS : KINETIC INVESTIGATIONS
Harerimana, Casimir; Vasel, Jean-Luc; Jupsin, Hugues; Ouali, Amira
2011-01-01
The aim of the study was first to develop a simple and practical model of anaerobic digestion including sulphate-reduction in anaerobic ponds. The basic microbiology of our model consists of three steps, namely, acidogenesis, methanogenesis, and sulphate reduction. This model includes multiple reaction stoichiometry and substrate utilization kinetics. The second aim was to determine some kinetic parameters associated with this model. The values of these parameters for sulfidogenic bacteria ar...
A kinetic model for the penicillin biosynthetic pathway in
DEFF Research Database (Denmark)
Nielsen, Jens; Jørgensen, Henrik
1996-01-01
A kinetic model for the first two steps in the penicillin biosynthetic pathway, i.e. the ACV synthetase (ACVS) and the isopenicillin N synthetase (IPNS) is proposed. The model is based on Michaelis-Menten type kinetics with non-competitive inhibition of the ACVS by ACV, and competitive inhibition...... of the IPNS by glutathione. The model predicted flux through the pathway corresponds well with the measured rate of penicillin biosynthesis. From the kinetic model the elasticity coefficients and the flux control coefficients are calculated throughout a fed-batch cultivation, and it is found...
The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Technical Institute ``G. Cardano,`` Piazza della Resistenza 1, 00015 Monterotondo Rome (Italy)
1996-12-01
A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}
Introduction to computation and modeling for differential equations
Edsberg, Lennart
2008-01-01
An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h
Microscopic models of traveling wave equations
Brunet, Eric; Derrida, Bernard
1999-09-01
Reaction-diffusion problems are often described at a macroscopic scale by partial derivative equations of the type of the Fisher or Kolmogorov-Petrovsky-Piscounov equation. These equations have a continuous family of front solutions, each of them corresponding to a different velocity of the front. By simulating systems of size up to N=1016 particles at the microscopic scale, where particles react and diffuse according to some stochastic rules, we show that a single velocity is selected for the front. This velocity converges logarithmically to the solution of the F-KPP equation with minimal velocity when the number N of particles increases. A simple calculation of the effect introduced by the cutoff due to the microscopic scale allows one to understand the origin of the logarithmic correction.
Institute of Scientific and Technical Information of China (English)
Ping Ao; Lik Wee Lee; Mary E. Lidstrom; Lan Yin; Xiaomei Zhu
2008-01-01
Here we report a systematic method for constructing a large scale kinetic metabolic model and its initial application to the modeling of central metabolism of Methylobacterium extorquens AM1, a methylotrophic and environmental important bacterium. Its central metabolic network includes formaldehyde metabolism, serine cycle, citric acid cycle, pentose phosphate pathway, ghiconeogensis, PHB synthesis and acetyl-CoA conversion pathway, respiration and energy metabolism. Through a systematic and consistent procedure of finding a set of parameters in the physiological range we overcome an outstanding difficulty in large scale kinetic modeling: the requirement for a massive number of enzymatic reaction parameters. We are able to construct the kinetic model based on general biological considerations and incomplete experimental kinetic parameters. Our method consists of the following major steps: 1) using a generic enzymatic rate equation to reduce the number of enzymatic parameters to a minimum set while still preserving their characteristics; 2) using a set of steady state fluxes and metabolite concenwations in the physiological range as the expected output steady state fluxes and metabolite concentrations for the kinetic model to restrict the parametric space of enzymatic reactions; 3) choosing enzyme constants K's and K'eqs optimized for reactions under physiological concentrations, if their experimental values are unknown; 4) for models which do not cover the entire metabolic network of the organisms, designing a dynamical exchange for the coupling between the metabolism represented in the model and the rest not included.
Yang, S T; Tang, I C; Okos, M R
1988-09-05
Fermentation kinetics of Clostridium formicoaceticum grown on lactate at pH 7.0 and 35 degrees C was studied. Acetate was the only fermentation product and its production was growth associated. The growth of this bacterium was insensitive to the lactate concentrations studied, but was inhibited by acetic acid. A Monod-type expression with product inhibition similar to the noncompetitive inhibition of enzyme kinetics was used to model the batch fermentation. An integrated equation was developed and used to help estimating the kinetic parameters in the model. This mathematical model can be used to simulate the homoacetic fermentation of lactate by C. formicoaceticum at pH 7.0 and 35 degrees C.
Rate equation modelling and investigation of quantum cascade detector characteristics
Saha, Sumit; Kumar, Jitendra
2016-10-01
A simple precise transport model has been proposed using rate equation approach for the characterization of a quantum cascade detector. The resonant tunneling transport is incorporated in the rate equation model through a resonant tunneling current density term. All the major scattering processes are included in the rate equation model. The effect of temperature on the quantum cascade detector characteristics has been examined considering the temperature dependent band parameters and the carrier scattering processes. Incorporation of the resonant tunneling process in the rate equation model improves the detector performance appreciably and reproduces the detector characteristics within experimental accuracy.
Kinetic modeling and fitting software for interconnected reaction schemes: VisKin.
Zhang, Xuan; Andrews, Jared N; Pedersen, Steen E
2007-02-15
Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.
Directory of Open Access Journals (Sweden)
S. Yamoah
2012-04-01
Full Text Available The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. In this study two analytical methods have been presented to solve the point kinetic equations of average one-group of delayed neutrons. These methods which are both approximate solution of the point reactor kinetic equations are compared with a numerical solution using the Euler’s first order method. To obtain accurate solution for the Euler method, a relatively small time step was chosen for the numerical solution. These methods are applied to different types of reactivity to check the validity of the analytical method by comparing the analytical results with the numerical results. From the results, it is observed that the analytical solution agrees well with the numerical solution.
Kinetic models in spin chemistry. 1. The hyperfine interaction
DEFF Research Database (Denmark)
Mojaza, M.; Pedersen, J. B.
2012-01-01
Kinetic models for quantum systems are quite popular due to their simplicity, although they are difficult to justify. We show that the transformation from quantum to kinetic description can be done exactly for the hyperfine interaction of one nuclei with arbitrary spin; more spins are described w...
Directory of Open Access Journals (Sweden)
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
Modeling the kinetics of essential oil hydrodistillation from plant materials
Directory of Open Access Journals (Sweden)
Milojević Svetomir Ž.
2013-01-01
Full Text Available The present work deals with modeling the kinetics of essential oils extraction from plant materials by water and steam distillation. The experimental data were obtained by studying the hydrodistillation kinetics of essential oil from juniper berries. The literature data on the kinetics of essential oils hydrodistillation from different plant materials were also included into the modeling. A physical model based on simultaneous washing and diffusion of essential oil from plant materials were developed to describe the kinetics of essential oils hydrodistillation, and two other simpler models were derived from this physical model assuming either instantaneous washing followed by diffusion or diffusion with no washing (i.e. the first-order kinetics. The main goal was to compare these models and suggest the optimum ones for water and steam distillation and for different plant materials. All three models described well the experimental kinetic data on water distillation irrespective of the type of distillation equipment and its scale, the type of plant materials and the operational conditions. The most applicable one is the model involving simultaneous washing and diffusion of the essential oil. However, this model was generally inapplicable for steam distillation of essential oils, except for juniper berries. For this hydrodistillation technique, the pseudo first-order model was shown to be the best one. In a few cases, a variation of the essential oil yield with time was observed to be sigmoidal and was modeled by the Boltzmann sigmoid function.
USING STRUCTURAL EQUATION MODELING TO INVESTIGATE RELATIONSHIPS AMONG ECOLOGICAL VARIABLES
This paper gives an introductory account of Structural Equation Modeling (SEM) and demonstrates its application using LISRELmodel utilizing environmental data. Using nine EMAP data variables, we analyzed their correlation matrix with an SEM model. The model characterized...
A Global Modeling Framework for Plasma Kinetics: Development and Applications
Parsey, Guy Morland
The modern study of plasmas, and applications thereof, has developed synchronously with com- puter capabilities since the mid-1950s. Complexities inherent to these charged-particle, many- body, systems have resulted in the development of multiple simulation methods (particle-in-cell, fluid, global modeling, etc.) in order to both explain observed phenomena and predict outcomes of plasma applications. Recognizing that different algorithms are chosen to best address specific topics of interest, this thesis centers around the development of an open-source global model frame- work for the focused study of non-equilibrium plasma kinetics. After verification and validation of the framework, it was used to study two physical phenomena: plasma-assisted combustion and the recently proposed optically-pumped rare gas metastable laser. Global models permeate chemistry and plasma science, relying on spatial averaging to focus attention on the dynamics of reaction networks. Defined by a set of species continuity and energy conservation equations, the required data and constructed systems are conceptually similar across most applications, providing a light platform for exploratory and result-search parameter scan- ning. Unfortunately, it is common practice for custom code to be developed for each application-- an enormous duplication of effort which negatively affects the quality of the software produced. Presented herein, the Python-based Kinetic Global Modeling framework (KGMf) was designed to support all modeling phases: collection and analysis of reaction data, construction of an exportable system of model ODEs, and a platform for interactive evaluation and post-processing analysis. A symbolic ODE system is constructed for interactive manipulation and generation of a Jacobian, both of which are compiled as operation-optimized C-code. Plasma-assisted combustion and ignition (PAC/PAI) embody the modernization of burning fuel by opening up new avenues of control and optimization
The Whitham Equation as a Model for Surface Water Waves
Moldabayev, Daulet; Dutykh, Denys
2014-01-01
The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of the water wave problem, it is thought to provide a more faithful description of shorter waves of small amplitude than traditional long wave models such as the KdV equation. In this work, we identify a scaling regime in which the Whitham equation can be derived from the Hamiltonian theory of surface water waves. The Whitham equation is integrated numerically, and it is shown that the equation gives a close approximation of inviscid free surface dynamics as described by the Euler equations. The performance of the Whitham equation as a model for free surface dynamics is also compared to two standard free surface models: the KdV and the BBM equation. It is found that in a wide parameter range of amplitudes and wavelengths, the Whitham equation performs on par with or better tha...
Evaluation of model fit in nonlinear multilevel structural equation modeling
Directory of Open Access Journals (Sweden)
Karin eSchermelleh-Engel
2014-03-01
Full Text Available Evaluating model fit in nonlinear multilevel structural equation models (MSEM presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are nonnormally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of nonnormality, they were not yet investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
Evaluation of model fit in nonlinear multilevel structural equation modeling.
Schermelleh-Engel, Karin; Kerwer, Martin; Klein, Andreas G
2014-01-01
Evaluating model fit in nonlinear multilevel structural equation models (MSEM) presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are non-normally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of non-normality, they have not yet been investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Tomaschewski, Fernanda K.; Segatto, Cynthia F., E-mail: fernandasls_89@hotmail.com, E-mail: cynthia.segatto@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Matematica Aplicada; Barros, Ricardo C., E-mail: rcbarros@pq.cnpq.br [Universidade do Estado do Rio de Janeiro (UERJ), Nova Friburgo, RJ (Brazil). Departamento de Modelagem Computacional
2015-07-01
Presented here is a decomposition method based on series representation of the group angular fluxes and delayed neutron precursors in smoothly continuous functions for energy multigroups, slab-geometry discrete ordinates kinetics equations supplemented with a prescribed number of delayed neutron precursors. Numerical results to a non-reflected sub-critical slab stabilized by steady-state sources are given to illustrate the accuracy and efficiency of the o offered method. (author)
Aromatization of light naphtha fractions on zeolites 1: Kinetic model
Directory of Open Access Journals (Sweden)
Rovenskaja Svetlana A.
2003-01-01
Full Text Available On the basis of analyzing kinetic experimental data performed in laboratory integral reactors a lumping kinetic model of the "Zeoforming" process was developed. A reaction scheme of the lumped components was proposed, that was adapted to the technological requirements. The reaction rate constants and activation energies were estimated, that are valid for certain feed compositions. The model is intended for further modeling and optimization of the process.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Assessment of the kinetic-frictional model for dense granular flow
Institute of Scientific and Technical Information of China (English)
Boon Ho Ng; Yulong Ding; Mojtaba Ghadiri
2008-01-01
This paper aims to quantitatively assess the application of kinetic-frictional model to simulate the motion of dry granular materials in dense condition, in particular, the annular shearing in Couette configuration. The weight of frictional stress was varied to study the contribution of the frictional stress in dense granular flows. The results show that the pure kinetic-theory-based computational fluid dynamics (CFD) model (without frictional stress) over-predicts the dominant solids motion of dense granular flow while adding frictional stress [Schaeffer, D. G. (1987). Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 66(1), 19-50] with the solids pressure of [Lun, C. KTK., Savage, S. B., Jeffrey, D. J., & Chepurniy, N. (1984). Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 140, 223-256] in the CFD model improves the simulation to better conform available experimental results. The results also suggest that frictional stress transmission plays an important role in dense granular flow and should not be neglected in granular flow simulations. Compatible simulation results to the experimental data are seen by increasing the weight of frictional stress to a factor of 1.25-1.5. These improved simulation results suggest the current constitutive relations (kinetic-frictional model) need to be improved in order to better reflect the real dense granular flow.
Lumping procedure for a kinetic model of catalytic naphtha reforming
Directory of Open Access Journals (Sweden)
H. M. Arani
2009-12-01
Full Text Available A lumping procedure is developed for obtaining kinetic and thermodynamic parameters of catalytic naphtha reforming. All kinetic and deactivation parameters are estimated from industrial data and thermodynamic parameters are calculated from derived mathematical expressions. The proposed model contains 17 lumps that include the C6 to C8+ hydrocarbon range and 15 reaction pathways. Hougen-Watson Langmuir-Hinshelwood type reaction rate expressions are used for kinetic simulation of catalytic reactions. The kinetic parameters are benchmarked with several sets of plant data and estimated by the SQP optimization method. After calculation of deactivation and kinetic parameters, plant data are compared with model predictions and only minor deviations between experimental and calculated data are generally observed.
A Bayesian modeling approach for generalized semiparametric structural equation models.
Song, Xin-Yuan; Lu, Zhao-Hua; Cai, Jing-Heng; Ip, Edward Hak-Sing
2013-10-01
In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types-continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.
Gnoffo, Peter A.; Gupta, Roop N.; Shinn, Judy L.
1989-01-01
The conservation equations for simulating hypersonic flows in thermal and chemical nonequilibrium and details of the associated physical models are presented. These details include the curve fits used for defining thermodynamic properties of the 11 species air model, curve fits for collision cross sections, expressions for transport properties, the chemical kinetics models, and the vibrational and electronic energy relaxation models. The expressions are formulated in the context of either a two or three temperature model. Greater emphasis is placed on the two temperature model in which it is assumed that the translational and rotational energy models are in equilibrium at the translational temperature, T, and the vibrational, electronic, and electron translational energy modes are in equilibrium at the vibrational temperature, T sub v. The eigenvalues and eigenvectors associated with the Jacobian of the flux vector are also presented in order to accommodate the upwind based numerical solutions of the complete equation set.
Model equations for simulating flows in multistage turbomachinery
Adamczyk, John J.
1996-01-01
A steady, three dimensional average-passage equation system was derived. The purpose was to simulate multistage turbomachinery flows. These equations describe a steady, viscous flow that is periodic from blade passage to blade passage. Moreover, these equations have a closure problem that is similar to that of the Reynolds-average Navier-Stokes equations. A scaled form of the average-passage equation system could provide an improved mathematical model for simulating the flow in the design and in the off-design conditions of a multistage machine.
Kinetic model for polyhydroxybutyrate (PHB) production by ...
African Journals Online (AJOL)
USER
2010-05-24
May 24, 2010 ... fitted with the logistic equation that can provide adequate description for PHA ... The Lineweaver-Burk plot defined biokinetic coefficients which were described by a simplified ... solving problems encountered in fermentations.
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants
Bezerra, Rui M. F.; Dias, Albino A.
2007-01-01
Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…
A kinetic model for the sedimentation of rod-like particles
Helzel, Christiane
2015-10-12
We consider a coupled system consisting of a kinetic equation coupled to a macroscopic Stokes (or Navier-Stokes) equation and describing the motion of a suspension of rigid rods in gravity. A reciprocal coupling leads to the formation of clusters: The buoyancy force creates a macroscopic velocity gradient that causes the microscopic particles to align so that their sedimentation reinforces the formation of clusters of higher particle density. We provide a quantitative analysis of cluster formation. We derive a nonlinear moment closure model, which consists of evolution equations for the density and second order moments and that uses the structure of spherical harmonics to suggest a closure strategy. For a rectilinear flow we employ the moment closure together with a quasi-dynamic approximation to derive an effective equation, The effective equation is an advection-diffusion equation with nonisotropic diffusion coupled to a Poisson equation, and belongs to the class of the so-called flux-limited Keller-Segel models. For shear flows, we provide an argument for the validity of the effective equation and perform numerical comparisons that indicate good agreement between the original system and the effective theory. Finally, a linear stability analysis on the moment system shows that linear theory predicts a wavelength selection mechanism for the cluster width, provided that the Reynolds number is larger than zero.
Self-dual soliton solutions in a Chern-Simons-CP(1) model with a nonstandard kinetic term
Casana, Rodolfo
2013-01-01
A generalization of the Chern-Simons-CP(1) model is considered by introducing a nonstandard kinetic term. For a particular case, of this nonstandard kinetic term, we show that the model support self-dual Bogomol'nyi equations. The BPS energy has a bound proportional to the sum of the magnetic flux and the CP(1) topological charge. The magnetic flux is a finite quantity proportional to the potential coupling constant and to the effective radius of the topological defect. The self-dual equations are solved analytically and verified numerically.
Equations and their physical interpretation in numerical modeling of heavy metals in fluvial rivers
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the previous work on the transport-transformation of heavy metal pollutants in fluvial rivers, this paper presented the formulation of a two-dimensional model to describe heavy metal transport-transformation in fluvial rivers by considering basic principles of environmental chemistry, hydraulics, mechanics of sediment transport and recent developments along with three very simplified test cases. The model consists of water flow governing equations, sediment transport governing equations, transport-transformation equation of heavy metal pollutants, and convection-diffusion equations of adsorption-desorption kinetics of particulate heavy metal concentrations on suspended load, bed load and bed sediment. The heavy metal transport-transformation equation is basically a mass balance equation, which demonstrates how sediment transport affects transport-transformation of heavy metals in fluvial rivers. The convection-diffusion equations of adsorption-desorption kinetics of heavy metals, being an extension of batch reactor experimental results and a major advancement of the previous work, take both physical transport, i.e. convection and diffusion and chemical reactions, i.e. adsorption-desorption into account. Effects of sediment transport on heavy metal transport-transformation were clarified through three examples. Specifically, the transport-transformation of heavy metals in a steady, uniform and equilibrium sediment-laden flow was calculated by applying this model, and results were shown to be rational. Both theoretical analysis and numerical simulation indicated that the transport-transformation of heavy metals in sediment-laden flows with clay-enriched riverbed possesses not only the generality of common tracer pollutants, but also characteristics of transport-transformation induced by sediment motion. Future work will be conducted to present validation/application of the model with available data.
Dynamic hysteresis modeling including skin effect using diffusion equation model
Hamada, Souad; Louai, Fatima Zohra; Nait-Said, Nasreddine; Benabou, Abdelkader
2016-07-01
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Dynamic hysteresis modeling including skin effect using diffusion equation model
Energy Technology Data Exchange (ETDEWEB)
Hamada, Souad, E-mail: souadhamada@yahoo.fr [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Louai, Fatima Zohra, E-mail: fz_louai@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Nait-Said, Nasreddine, E-mail: n_naitsaid@yahoo.com [LSP-IE: Research Laboratory, Electrical Engineering Department, University of Batna, 05000 Batna (Algeria); Benabou, Abdelkader, E-mail: Abdelkader.Benabou@univ-lille1.fr [L2EP, Université de Lille1, 59655 Villeneuve d’Ascq (France)
2016-07-15
An improved dynamic hysteresis model is proposed for the prediction of hysteresis loop of electrical steel up to mean frequencies, taking into account the skin effect. In previous works, the analytical solution of the diffusion equation for low frequency (DELF) was coupled with the inverse static Jiles-Atherton (JA) model in order to represent the hysteresis behavior for a lamination. In the present paper, this approach is improved to ensure the reproducibility of measured hysteresis loops at mean frequency. The results of simulation are compared with the experimental ones. The selected results for frequencies 50 Hz, 100 Hz, 200 Hz and 400 Hz are presented and discussed.
Structural equation modeling: building and evaluating causal models: Chapter 8
Grace, James B.; Scheiner, Samuel M.; Schoolmaster, Donald R.
2015-01-01
Scientists frequently wish to study hypotheses about causal relationships, rather than just statistical associations. This chapter addresses the question of how scientists might approach this ambitious task. Here we describe structural equation modeling (SEM), a general modeling framework for the study of causal hypotheses. Our goals are to (a) concisely describe the methodology, (b) illustrate its utility for investigating ecological systems, and (c) provide guidance for its application. Throughout our presentation, we rely on a study of the effects of human activities on wetland ecosystems to make our description of methodology more tangible. We begin by presenting the fundamental principles of SEM, including both its distinguishing characteristics and the requirements for modeling hypotheses about causal networks. We then illustrate SEM procedures and offer guidelines for conducting SEM analyses. Our focus in this presentation is on basic modeling objectives and core techniques. Pointers to additional modeling options are also given.
Institute of Scientific and Technical Information of China (English)
Meng-ge Liu; Wei Yu; Chi-xing Zhou
2006-01-01
The kinetic model for diffusion-controlled intermolecular reaction of homogenous polymer under steady shear was theoretically studied. The classic formalism and the concept of conformation ellipsoids were integrated to get a new equation, which directly correlates the rate constant with shear rate. It was found that the rate constant is not monotonic with shear rate. The scale of rate constant is N-1.5 (N is the length of chains), which is in consistent with de Gennes's result.
Modeling Biodegradation Kinetics on Benzene and Toluene and Their Mixture
Directory of Open Access Journals (Sweden)
Aparecido N. Módenes
2007-10-01
Full Text Available The objective of this work was to model the biodegradation kinetics of toxic compounds toluene and benzene as pure substrates and in a mixture. As a control, Monod and Andrews models were used. To predict substrates interactions, more sophisticated models of inhibition and competition, and SKIP (sum kinetics interactions parameters model were applied. The models evaluation was performed based on the experimental data from Pseudomonas putida F1 activities published in the literature. In parameter identification procedure, the global method of particle swarm optimization (PSO was applied. The simulation results show that the better description of the biodegradation process of pure toxic substrate can be achieved by Andrews' model. The biodegradation process of a mixture of toxic substrates is modeled the best when modified competitive inhibition and SKIP models are used. The developed software can be used as a toolbox of a kinetics model catalogue of industrial wastewater treatment for process design and optimization.
Directory of Open Access Journals (Sweden)
L. Alfonso
2012-01-01
Full Text Available In a coagulating system, a sol-gel transition occurs when a single giant particle (a gel arises under certain conditions and begins to consume the mass of smaller but higher populated fraction (the sol. This single giant particle (also known as a runaway particle is detached from the continuous spectrum. Since the kinetic collection equation (KCE only models the evolution of the continuous size of the spectrum, as the largest particle continue to grow by accretion of smaller ones, the liquid water content predicted by the KCE will decrease.
In this paper, the sol-gel transition is proposed as the mechanism that forms the large droplets that are needed to trigger warm rain development in cumulus clouds. By using a collection kernel enhanced by turbulence and a stochastic simulation method, the formation of a runaway droplet is modeled through the turbulent collection process. The model results show that the sol-gel transition (also called gelation leads to the formation of a droplet with mass comparable to the mass of the initial system. The time when the sol-gel transition occurs is estimated with a Monte Carlo method when the parameter ρ (the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value reaches its maximum value. Moreover, we show that without turbulence, the sol-gel transition will not occur. In the context of theoretical cloud microphysics, gelation can be interpreted as the formation of the "lucky droplet" that grows at a much faster rate than the rest of the droplet population and subsequently becomes the embryo for raindrops.
A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency
Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake
2014-01-01
This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…
Reporting Monte Carlo Studies in Structural Equation Modeling
Boomsma, Anne
2013-01-01
In structural equation modeling, Monte Carlo simulations have been used increasingly over the last two decades, as an inventory from the journal Structural Equation Modeling illustrates. Reaching out to a broad audience, this article provides guidelines for reporting Monte Carlo studies in that fiel
DEFF Research Database (Denmark)
Hereu, A.; Dalgaard, Paw; Garriga, M.;
2012-01-01
provided the best fit to the HP-inactivation kinetics. The relationships between the primary kinetic parameters (log kmax and log Nres) and pressure treatments were described by a polynomial secondary model. To estimate HP-inactivation of L. monocytogenes in log (N/N0) over time, a one-step global fitting...... procedure was applied. The secondary model was integrated into the primary model and the combined equation was fitted to the entire data-set to readjust parameter values. Validation of the developed models both under dynamic conditions and using external independent data supported their suitability...... for predictive purposes, e.g., to set the process criteria required to meet food safety objectives. Industrial relevanceQuantitative mathematical models for predicting inactivation of pathogens by HPP provide useful tools for a process optimization and real time control of a unit operation. The developed models...
Biomass torrefaction: modeling of volatile and solid product evolution kinetics.
Bates, Richard B; Ghoniem, Ahmed F
2012-11-01
The aim of this work is the development of a kinetics model for the evolution of the volatile and solid product composition during torrefaction conditions between 200 and 300°C. Coupled to an existing two step solid mass loss kinetics mechanism, this model describes the volatile release kinetics in terms of a set of identifiable chemical components, permitting the solid product composition to be estimated by mass conservation. Results show that most of the volatiles released during the first stage include highly oxygenated species such as water, acetic acid, and carbon dioxide, while volatiles released during the second step are composed primarily of lactic acid, methanol, and acetic acid. This kinetics model will be used in the development of a model to describe reaction energy balance and heat release dynamics.
Kinetic, equilibrium and thermodynamic modelling of the sorption of ...
African Journals Online (AJOL)
Kinetic, equilibrium and thermodynamic modelling of the sorption of metals ... Batch sorption studies were conducted to assess the potential of a ... negative Ea values, indicating their preference to bind to low-energy sites. ... Article Metrics.
Jellium-with-gap model applied to semilocal kinetic functionals
Constantin, Lucian A.; Fabiano, Eduardo; Śmiga, Szymon; Della Sala, Fabio
2017-03-01
We investigate a highly nonlocal generalization of the Lindhard function, given by the jellium-with-gap model. We find a band-gap-dependent gradient expansion of the kinetic energy, which performs noticeably well for large atoms. Using the static linear response theory and the simplest semilocal model for the local band gap, we derive a nonempirical generalized gradient approximation (GGA) of the kinetic energy. This GGA kinetic-energy functional is remarkably accurate for the description of weakly interacting molecular systems within the subsystem formulation of density functional theory.
Energy Technology Data Exchange (ETDEWEB)
Rial, Diego; Vazquez, Jose Antonio; Murado, Miguel Anxo [Instituto de Investigacions Marinas (CSIC), Vigo (ES). Grupo de Reciclado y Valorizacion de Materiales Residuales (REVAL)
2011-05-15
The effects of three heavy metals (Co, Ni and Cd) on the growth kinetics of five bacterial strains with different characteristics (Pseudomonas sp., Phaeobacter sp. strain 27-4, Listonella anguillarum, Carnobacterium piscicola and Leuconostoc mesenteroides subsp. lysis) were studied in a batch system. A bivariate model, function of time and dose, is proposed to describe simultaneously all the kinetic profiles obtained by incubating a microorganism at increasing concentrations of individual metals. This model combines the logistic equation for describing growth, with a modification of the cumulative Weibull's function for describing the dose-dependent variations of growth parameters. The comprehensive model thus obtained - which minimizes the effects of the experimental error - was statistically significant in all the studied cases, and it raises doubts about toxicological evaluations that are based on a single growth parameter, especially if it is not obtained from a kinetic equation. In lactic acid bacteria cultures (C. piscicola and L. mesenteroides), Cd induced remarkable differences in yield and time course of characteristic metabolites. A global parameter is defined (ED{sub 50,{tau}}: dose of toxic chemical that reduces the biomass of a culture by 50% compared to that produced by the control at the time corresponding to its semi maximum biomass) that allows comparing toxic effects on growth kinetics using a single value. (orig.)
Kinetic models in industrial biotechnology - Improving cell factory performance.
Almquist, Joachim; Cvijovic, Marija; Hatzimanikatis, Vassily; Nielsen, Jens; Jirstrand, Mats
2014-07-01
An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed.
Directory of Open Access Journals (Sweden)
Philippe G. LeFloch
2000-12-01
Full Text Available This paper deals with the so-called p-system describing the dynamics of isothermal and compressible fluids. The constitutive equation is assumed to have the typical convexity/concavity properties of the van der Waals equation. We search for discontinuous solutions constrained by the associated mathematical entropy inequality. First, following a strategy proposed by Abeyaratne and Knowles and by Hayes and LeFloch, we describe here the whole family of nonclassical Riemann solutions for this model. Second, we supplement the set of equations with a kinetic relation for the propagation of nonclassical undercompressive shocks, and we arrive at a uniquely defined solution of the Riemann problem. We also prove that the solutions depend $L^1$-continuously upon their data. The main novelty of the present paper is the presence of two inflection points in the constitutive equation. The Riemann solver constructed here is relevant for fluids in which viscosity and capillarity effects are kept in balance.
Kinetic Modelling of Pesticidal Degradation and Microbial Growth in Soil
Institute of Scientific and Technical Information of China (English)
LIUDUO－SEN; WANGZONG－SHENG; 等
1994-01-01
This paper discusses such models for the degradation kinetics of pesticides in soil as the model expressing the degradation rate as a function of two varables:the pesticide concentration and the number of pesticide degrading microorganisms,the model expressing the pesticide concentration as explicit or implicit function of time ,and the model exprssing the pesticide loss rate constants as functions of temperature,These models may interpret the degradation curves with an inflection point.A Kinetic model describing the growth processes of microbial populations in a closed system is reported as well.
New mass loss kinetic model for thermal decomposition of biomass
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Based on non-isothermal experimental results for eight Chinese biomass species, a new kinetic model,named as the "pseudo bi-component separate-stage model (PBSM)", is developed in this note to describe the mass loss behavior of biomass thermal decomposition. This model gains an advantage over the commonly used "pseudo single-component overall model (PSOM)" and "pseudo multi-component overall model (PMOM)". By means of integral analysis it is indicated that the new model is suitable to describe the mass loss kinetics of wood and leaf samples under relatively low heating rates (e.g. 10°C/rin, used in this work).``
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
The evaluation of benzene and phenol biodegradation kinetics by applying non-structured models.
Trigueros, D E G; Módenes, A N; Espinoza-Quiñones, F R; Kroumov, A D
2010-01-01
The biodegradation kinetics of the aromatic hydrocarbons benzene and phenol as single substrates and as a mixture were investigated through non-structured model analysis. The material balance equations involving the models of Monod and Andrews and representing the biodegradation kinetics of individual substrates in batch mode were numerically solved. Further, utilization of a benzene-phenol mixture was described by applying more sophisticated mathematical forms of competitive, noncompetitive and uncompetitive inhibition models as well as the sum kinetic interactions parameters (SKIP) model. In order to improve the performance of the studied models, some modifications were also proposed. The Particle Swarm Global Optimization method, coded in Maple, was applied to the parameter identification procedure of each model, where the least square method was used as a search statistical criterion. The description of the biodegradation kinetics of a benzene-phenol mixture by the competitive inhibition model was based on the information that the compounds could be catabolized via one metabolic pathway of Pseudomonas putida F1. Simulation results were in good agreement with the experimental data and proved the robustness of the applied methods and models. The developed knowledge database could be very useful in the optimization of the biodegradation processes of different bioreactor types and operational conditions.
Kinetic modeling for chemiluminescent radicals in acetylene combustion
Directory of Open Access Journals (Sweden)
Marques Carla S. T.
2006-01-01
Full Text Available Kinetic modeling to reproduce the experimental chemiluminescence of OH*, CHO*, CH* and C2* excited radicals formed in C2H2/O2 combustion in a closed chamber was evaluated. A reaction mechanism with 37 species and 106 elementary reactions for C2H2/O2 combustion at phi=1.00 and phi=1.62 was validated through chemiluminescence measurements, where formation and decay reactions of excited radicals are included. KINAL package was used for simulations. Ordinary differential equations were solved by the DIFF program and production rate analysis were acquired by the ROPA program. There was good agreement between experimental and simulated chemiluminescence profiles of all radicals for both combustions. The results showed CH has a meaningful role in the production of excited radicals. Reactions: H + O2 = OH* + O; CH + O = CHO*; C2H + O2 = CH* + CO2 and CH2 + C = C2* + H2 were the main reactions paths used to reproduce the experimental profiles.
Kinetic model of the bichromatic dark trap for atoms
Krasnov, I. V.
2017-08-01
A kinetic model of atom confinement in a bichromatic dark trap (BDT) is developed with the goal of describing its dissipative properties. The operating principle of the deep BDT is based on using the combination of multiple bichromatic cosine-Gaussian optical beams (CGBs) for creating high-potential barriers, which is described in our previous work (Krasnov 2016 Laser Phys. 26 105501). In the indicated work, particle motion in the BDT is described in terms of classical trajectories. In the present study, particle motion is analyzed by means of the Wigner function (phase-space distribution function (DF)), which allows one to properly take into account the quantum fluctuations of optical forces. Besides, we consider an improved scheme of the BDT, where CGBs create, apart from plane potential barriers, a narrow cooling layer. We find an asymptotic solution of the Fokker-Planck equation for the DF and show that the DF of particles deeply trapped in a BDT with a cooling layer is the Tsallis distribution with the effective temperature, which can be considerably lower than in a BDT without a cooling layer. Moreover, it can be adjusted by slightly changing the CGBs’ radii. We also study the effect of particle escape from the trap due to the scattering of resonant photons and show that the particle lifetime in a BDT can exceed several tens of hours when it is limited by photon scattering.
Modeling circadian clocks: From equations to oscillations
National Research Council Canada - National Science Library
Gonze, Didier
2011-01-01
... (such as light and temperature) is greatly helped by mathematical modeling. In the present paper we review some mathematical models for circadian clocks, ranging from abstract, phenomenological models to the most detailed molecular models...
Juliano, Pablo; Knoerzer, Kai; Fryer, Peter J; Versteeg, Cornelis
2009-01-01
High-pressure, high-temperature (HPHT) processing is effective for microbial spore inactivation using mild preheating, followed by rapid volumetric compression heating and cooling on pressure release, enabling much shorter processing times than conventional thermal processing for many food products. A computational thermal fluid dynamic (CTFD) model has been developed to model all processing steps, including the vertical pressure vessel, an internal polymeric carrier, and food packages in an axis-symmetric geometry. Heat transfer and fluid dynamic equations were coupled to four selected kinetic models for the inactivation of C. botulinum; the traditional first-order kinetic model, the Weibull model, an nth-order model, and a combined discrete log-linear nth-order model. The models were solved to compare the resulting microbial inactivation distributions. The initial temperature of the system was set to 90 degrees C and pressure was selected at 600 MPa, holding for 220 s, with a target temperature of 121 degrees C. A representation of the extent of microbial inactivation throughout all processing steps was obtained for each microbial model. Comparison of the models showed that the conventional thermal processing kinetics (not accounting for pressure) required shorter holding times to achieve a 12D reduction of C. botulinum spores than the other models. The temperature distribution inside the vessel resulted in a more uniform inactivation distribution when using a Weibull or an nth-order kinetics model than when using log-linear kinetics. The CTFD platform could illustrate the inactivation extent and uniformity provided by the microbial models. The platform is expected to be useful to evaluate models fitted into new C. botulinum inactivation data at varying conditions of pressure and temperature, as an aid for regulatory filing of the technology as well as in process and equipment design.
Detailed Chemical Kinetic Modeling of Cyclohexane Oxidation
Energy Technology Data Exchange (ETDEWEB)
Silke, E J; Pitz, W J; Westbrook, C K; Ribaucour, M
2006-11-10
A detailed chemical kinetic mechanism has been developed and used to study the oxidation of cyclohexane at both low and high temperatures. Reaction rate constant rules are developed for the low temperature combustion of cyclohexane. These rules can be used for in chemical kinetic mechanisms for other cycloalkanes. Since cyclohexane produces only one type of cyclohexyl radical, much of the low temperature chemistry of cyclohexane is described in terms of one potential energy diagram showing the reaction of cyclohexyl radical + O{sub 2} through five, six and seven membered ring transition states. The direct elimination of cyclohexene and HO{sub 2} from RO{sub 2} is included in the treatment using a modified rate constant of Cavallotti et al. Published and unpublished data from the Lille rapid compression machine, as well as jet-stirred reactor data are used to validate the mechanism. The effect of heat loss is included in the simulations, an improvement on previous studies on cyclohexane. Calculations indicated that the production of 1,2-epoxycyclohexane observed in the experiments can not be simulated based on the current understanding of low temperature chemistry. Possible 'alternative' H-atom isomerizations leading to different products from the parent O{sub 2}QOOH radical were included in the low temperature chemical kinetic mechanism and were found to play a significant role.
Kinetic modelling of the Fischer-Tropsch synthesis
Energy Technology Data Exchange (ETDEWEB)
Gambaro, C.; Pollesel, P.; Zennaro, R. [Eni S.p.A., San Donato Milanese (Italy); Lietti, L.; Tronconi, E. [Politecnico di Milano (Italy)
2006-07-01
In this work the development of a CO conversion kinetic model of the Fischer-Tropsch process will be presented. Kinetic data were produced testing a Co-based catalyst on two lab units, equipped with a slurry autoclave and a fixed bed reactor respectively. Accordingly, information on the catalytic performances of the same catalyst in two reactor configurations were also obtained. The experimental results were then analyzed with different kinetic models, available in the literature: two mechanistic models, derived by Sarup-Wojciechowski and Yates-Satterfield, and a simple power law rate expression were compared. The parameters of the different rate expressions were estimated by non-linear regression of the kinetic data collected on the two lab units. (orig.)
Directory of Open Access Journals (Sweden)
D. Baumgardner
2013-01-01
Full Text Available Warm rain in real clouds is produced by the collision and coalescence of an initial population of small droplets. The production of rain in warm cumulus clouds is still one of the open problems in cloud physics, and although several mechanisms have been proposed in the past, at present there is no complete explanation for the rapid growth of cloud droplets within the size range of diameters from 10 to 50 μm. By using a collection kernel enhanced by turbulence and a fully stochastic simulation method, the formation of a runaway droplet is modeled through the turbulent collection process. When the runaway droplet forms, the traditional calculation using the kinetic collection equation is no longer valid, since the assumption of a continuous distribution breaks down. There is in essence a phase transition in the system from a continuous distribution to a continuous distribution plus a runaway droplet. This transition can be associated to gelation (also called sol–gel transition and is proposed here as a mechanism for the formation of large droplets required to trigger warm rain development in cumulus clouds. The fully stochastic turbulent model reveals gelation and the formation of a droplet with mass comparable to the mass of the initial system. The time when the sol–gel transition occurs is estimated with a Monte Carlo method when the parameter ρ (the ratio of the standard deviation for the largest droplet mass over all the realizations to the averaged value reaches its maximum value. Moreover, we show that the non-turbulent case does not exhibit the sol–gel transition that can account for the impossibility of producing raindrop embryos in such a system. In the context of cloud physics theory, gelation can be interpreted as the formation of the "lucky droplet" that grows at a much faster rate than the rest of the population and becomes the embryo for runaway raindrops.
Modelling of nonlinear shoaling based on stochastic evolution equations
DEFF Research Database (Denmark)
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics...... are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum...... and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared...
Bayesian structural equation modeling method for hierarchical model validation
Energy Technology Data Exchange (ETDEWEB)
Jiang Xiaomo [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: xiaomo.jiang@vanderbilt.edu; Mahadevan, Sankaran [Department of Civil and Environmental Engineering, Vanderbilt University, Box 1831-B, Nashville, TN 37235 (United States)], E-mail: sankaran.mahadevan@vanderbilt.edu
2009-04-15
A building block approach to model validation may proceed through various levels, such as material to component to subsystem to system, comparing model predictions with experimental observations at each level. Usually, experimental data becomes scarce as one proceeds from lower to higher levels. This paper presents a structural equation modeling approach to make use of the lower-level data for higher-level model validation under uncertainty, integrating several components: lower-level data, higher-level data, computational model, and latent variables. The method proposed in this paper uses latent variables to model two sets of relationships, namely, the computational model to system-level data, and lower-level data to system-level data. A Bayesian network with Markov chain Monte Carlo simulation is applied to represent the two relationships and to estimate the influencing factors between them. Bayesian hypothesis testing is employed to quantify the confidence in the predictive model at the system level, and the role of lower-level data in the model validation assessment at the system level. The proposed methodology is implemented for hierarchical assessment of three validation problems, using discrete observations and time-series data.
Alvaro, M; Bonilla, L L; Carretero, M; Melnik, R V N; Prabhakar, S
2013-08-21
In this paper we develop a kinetic model for the analysis of semiconductor superlattices, accounting for quantum effects. The model consists of a Boltzmann-Poisson type system of equations with simplified Bhatnagar-Gross-Krook collisions, obtained from the general time-dependent Schrödinger-Poisson model using Wigner functions. This system for superlattice transport is supplemented by the quantum mechanical part of the model based on the Ben-Daniel-Duke form of the Schrödinger equation for a cylindrical superlattice of finite radius. The resulting energy spectrum is used to characterize the Fermi-Dirac distribution that appears in the Bhatnagar-Gross-Krook collision, thereby coupling the quantum mechanical and kinetic parts of the model. The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments. It also allows us to determine more accurately the time-dependent characteristics of superlattices, in particular their current density. Results, for several experimentally grown superlattices, are discussed in the context of self-sustained coherent oscillations of the current density which are important in an increasing range of current and potential applications.
Steady-state benchmarks of DK4D: A time-dependent, axisymmetric drift-kinetic equation solver
Energy Technology Data Exchange (ETDEWEB)
Lyons, B. C. [Princeton University, Princeton, New Jersey 08544 (United States); Jardin, S. C. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543-0451 (United States); Ramos, J. J. [Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 (United States)
2015-05-15
The DK4D code has been written to solve a set of time-dependent, axisymmetric, finite-Larmor-radius drift-kinetic equations (DKEs) for the non-Maxwellian part of the electron and ion distribution functions using the full, linearized Fokker–Planck–Landau collision operator. The plasma is assumed to be in the low- to finite-collisionality regime, as is found in the cores of modern and future magnetic confinement fusion experiments. Each DKE is formulated such that the perturbed distribution function carries no net density, parallel momentum, or kinetic energy. Rather, these quantities are contained within the background Maxwellians and would be evolved by an appropriate set of extended magnetohydrodynamic (MHD) equations. This formulation allows for straight-forward coupling of DK4D to existing extended MHD time evolution codes. DK4D uses a mix of implicit and explicit temporal representations and finite element and spectral spatial representations. These, along with other computational methods used, are discussed extensively. Steady-state benchmarks are then presented comparing the results of DK4D to expected analytic results at low collisionality, qualitatively, and to the Sauter analytic fits for the neoclassical conductivity and bootstrap current, quantitatively. These benchmarks confirm that DK4D is capable of solving for the correct, gyroaveraged distribution function in stationary magnetic equilibria. Furthermore, the results presented demonstrate how the exact drift-kinetic solution varies with collisionality as a function of the magnetic moment and the poloidal angle.
Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
Directory of Open Access Journals (Sweden)
Nowak Tomasz Karol
2014-06-01
Full Text Available This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Landscape evolution models: A review of their fundamental equations
Chen, Alex; Darbon, Jérôme; Morel, Jean-Michel
2014-08-01
This paper reviews the main physical laws proposed in landscape evolution models (LEMs). It discusses first the main partial differential equations involved in these models and their variants. These equations govern water runoff, stream incision, regolith-bedrock interaction, hillslope evolution, and sedimentation. A synthesis of existing LEMs is proposed. It proposes three models with growing complexity and with a growing number of components: two-equation models with only two components, governing water and bedrock evolution; three-equation models with three components where water, bedrock, and sediment interact; and finally models with four equations and four interacting components, namely water, bedrock, suspended sediment, and regolith. This analysis is not a mere compilation of existing LEMs. It attempts at giving the simplest and most general physically consistent set of equations, coping with all requirements stated in LEMs and LEM software. Three issues are in particular addressed and hopefully resolved. The first one is a correct formulation of the water transport equation down slopes. A general formulation for this equation is proposed, coping not only with the simplest form computing the drainage area but also with a sound energy dissipation argument associated with the Saint-Venant shallow water equations. The second issue arises from the coexistence of two competing modes, namely the detachment-limited erosion mode on hillslopes, and the transport-limited sediment transport on river beds. The third issue (linked to the second) is the fact that no conservation law is available for material in these two modes. A simple solution proposed to resolve these issues is the introduction, as suggested by several authors, of an additional variable for suspended sediment load in water. With only three variables and three equations, the above-mentioned contradictions seem to be eliminated. Several numerical experiments on real digital elevation models (DEMs
大庆常渣催化裂解反应动力学模型%Establishment of Kinetic Model for Catalytic Pyrolysis of Daqing Atmospheric Residue
Institute of Scientific and Technical Information of China (English)
刘熠斌; 陈小博; 赵辉; 杨朝合
2009-01-01
An 8-lump kinetic model was proposed to predict the yields of propylene, ethylene and gasoline in the catalytic pyrolysis process of Daqing atmospheric residue. The model contains 21 kinetic parameters and one for catalyst deactivation. A series of experiments were carried out in a riser reactor over catalyst named LTB-2. The ki-netic parameters were estimated by using sub-model method, and apparent activation energies were calculated ac-cording to the Arrhenius equation. The predicted yields coincided well with the experimental values. It shows that the kinetic parameters estimated by using the sub-model method were reliable.
Directory of Open Access Journals (Sweden)
Krivtcova Nadezhda
2016-01-01
Full Text Available Modelling of sulfur compounds kinetics was performed, including kinetics of benzothiophene and dibenzothiophene homologues. Modelling is based on experimental data obtained from monitoring of industrial hydrotreating set. Obtained results include kinetic parameters of reactions.
A near-wall two-equation model for compressible turbulent flows
Zhang, H. S.; So, R. M. C.; Speziale, C. G.; Lai, Y. G.
1992-01-01
A near-wall two-equation turbulence model of the k-epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K-omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.
Chemical Kinetic Models for HCCI and Diesel Combustion
Energy Technology Data Exchange (ETDEWEB)
Pitz, W J; Westbrook, C K; Mehl, M; Sarathy, S M
2010-11-15
Predictive engine simulation models are needed to make rapid progress towards DOE's goals of increasing combustion engine efficiency and reducing pollutant emissions. These engine simulation models require chemical kinetic submodels to allow the prediction of the effect of fuel composition on engine performance and emissions. Chemical kinetic models for conventional and next-generation transportation fuels need to be developed so that engine simulation tools can predict fuel effects. The objectives are to: (1) Develop detailed chemical kinetic models for fuel components used in surrogate fuels for diesel and HCCI engines; (2) Develop surrogate fuel models to represent real fuels and model low temperature combustion strategies in HCCI and diesel engines that lead to low emissions and high efficiency; and (3) Characterize the role of fuel composition on low temperature combustion modes of advanced combustion engines.
Acoustic Logging Modeling by Refined Biot's Equations
Plyushchenkov, Boris D.; Turchaninov, Victor I.
An explicit uniform completely conservative finite difference scheme for the refined Biot's equations is proposed. This system is modified according to the modern theory of dynamic permeability and tortuosity in a fluid-saturated elastic porous media. The approximate local boundary transparency conditions are constructed. The acoustic logging device is simulated by the choice of appropriate boundary conditions on its external surface. This scheme and these conditions are satisfactory for exploring borehole acoustic problems in permeable formations in a real axial-symmetrical situation. The developed approach can be adapted for a nonsymmetric case also.
A kinetic model for runaway electrons in the ionosphere
Directory of Open Access Journals (Sweden)
G. Garcia
2006-09-01
Full Text Available Electrodynamic models and measurements with satellites and incoherent scatter radars predict large field aligned current densities on one side of the auroral arcs. Different authors and different kinds of studies (experimental or modeling agree that the current density can reach up to hundreds of µA/m^{2}. This large current density could be the cause of many phenomena such as tall red rays or triggering of unstable ion acoustic waves. In the present paper, we consider the issue of electrons moving through an ionospheric gas of positive ions and neutrals under the influence of a static electric field. We develop a kinetic model of collisions including electrons/electrons, electrons/ions and electrons/neutrals collisions. We use a Fokker-Planck approach to describe binary collisions between charged particles with a long-range interaction. We present the essential elements of this collision operator: the Langevin equation for electrons/ions and electrons/electrons collisions and the Monte-Carlo and null collision methods for electrons/neutrals collisions. A computational example is given illustrating the approach to equilibrium and the impact of the different terms (electrons/electrons and electrons/ions collisions on the one hand and electrons/neutrals collisions on the other hand. Then, a parallel electric field is applied in a new sample run. In this run, the electrons move in the z direction parallel to the electric field. The first results show that all the electron distribution functions are non-Maxwellian. Furthermore, runaway electrons can carry a significant part of the total current density, up to 20% of the total current density.
Energy Technology Data Exchange (ETDEWEB)
Li, Yulan; Hu, Shenyang Y.; Sun, Xin; Khaleel, Mohammad A.
2011-06-15
Microstructure evolution kinetics in irradiated materials has strongly spatial correlation. For example, void and second phases prefer to nucleate and grow at pre-existing defects such as dislocations, grain boundaries, and cracks. Inhomogeneous microstructure evolution results in inhomogeneity of microstructure and thermo-mechanical properties. Therefore, the simulation capability for predicting three dimensional (3-D) microstructure evolution kinetics and its subsequent impact on material properties and performance is crucial for scientific design of advanced nuclear materials and optimal operation conditions in order to reduce uncertainty in operational and safety margins. Very recently the meso-scale phase-field (PF) method has been used to predict gas bubble evolution, void swelling, void lattice formation and void migration in irradiated materials,. Although most results of phase-field simulations are qualitative due to the lake of accurate thermodynamic and kinetic properties of defects, possible missing of important kinetic properties and processes, and the capability of current codes and computers for large time and length scale modeling, the simulations demonstrate that PF method is a promising simulation tool for predicting 3-D heterogeneous microstructure and property evolution, and providing microstructure evolution kinetics for higher scale level simulations of microstructure and property evolution such as mean field methods. This report consists of two parts. In part I, we will present a new phase-field model for predicting interstitial loop growth kinetics in irradiated materials. The effect of defect (vacancy/interstitial) generation, diffusion and recombination, sink strength, long-range elastic interaction, inhomogeneous and anisotropic mobility on microstructure evolution kinetics is taken into account in the model. The model is used to study the effect of elastic interaction on interstitial loop growth kinetics, the interstitial flux, and sink
Excitability in a stochastic differential equation model for calcium puffs.
Rüdiger, S
2014-06-01
Calcium dynamics are essential to a multitude of cellular processes. For many cell types, localized discharges of calcium through small clusters of intracellular channels are building blocks for all spatially extended calcium signals. Because of the large noise amplitude, the validity of noise-approximating model equations for this system has been questioned. Here we revisit the master equations for local calcium release, examine the multiple scales of calcium concentrations in the cluster domain, and derive adapted stochastic differential equations. We show by comparison of discrete and continuous trajectories that the Langevin equations can be made consistent with the master equations even for very small channel numbers. In its deterministic limit, the model reveals that excitability, a dynamical phenomenon observed in many natural systems, is at the core of calcium puffs. The model also predicts a bifurcation from transient to sustained release which may link local and global calcium signals in cells.
Reinisch, Guillaume; Leyssale, Jean-Marc; Vignoles, Gérard L.
2010-10-01
We present an extension of some popular hindered rotor (HR) models, namely, the one-dimensional HR (1DHR) and the degenerated two-dimensional HR (d2DHR) models, allowing for a simple and accurate treatment of internal rotations. This extension, based on the use of a variable kinetic function in the Hamiltonian instead of a constant reduced moment of inertia, is extremely suitable in the case of rocking/wagging motions involved in dissociation or atom transfer reactions. The variable kinetic function is first introduced in the framework of a classical 1DHR model. Then, an effective temperature and potential dependent constant is proposed in the cases of quantum 1DHR and classical d2DHR models. These methods are finally applied to the atom transfer reaction SiCl3+BCl3→SiCl4+BCl2. We show, for this particular case, that a proper accounting of internal rotations greatly improves the accuracy of thermodynamic and kinetic predictions. Moreover, our results confirm (i) that using a suitably defined kinetic function appears to be very adapted to such problems; (ii) that the separability assumption of independent rotations seems justified; and (iii) that a quantum mechanical treatment is not a substantial improvement with respect to a classical one.
Kinetic Modelling of Macroscopic Properties Changes during Crosslinked Polybutadiene Oxidation
Audouin, Ludmila; Coquillat, Marie; Colin, Xavier; Verdu, Jacques; Nevière, Robert
2008-08-01
The thermal oxidation of additive free hydroxyl-terminated polybutadiene (HTPB) isocyanate crosslinked rubber bulk samples has been studied at 80, 100 and 120 °C in air. The oxidation kinetics has been monitored by gravimetry and thickness distribution of oxidation products was determined by FTIR mapping. Changes of elastic shear modulus G' during oxidation were followed during oxidation at the same temperatures. The kinetic model established previously for HTPB has been adapted for bulk sample oxidation using previously determined set of kinetic parameters. Oxygen diffusion control of oxidation has been introduced into the model. The mass changes kinetic curves and oxidation products profiles were simulated and adequate fit was obtained. Using the rubber elasticity theory the elastic modulus changes were simulated taking into account the elastically active chains concentration changes due to chain scission and crosslinking reactions. The reasonable fit of G' as a function of oxidation time experimental curves was obtained.
A Kinetic Model of Chromium in a Flame
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Chromium has been identified as a carcinogenic metal.Incineration is the useful method for disposal of toxic chromium hazard waste and a chromium kinetic model in a flame is very important to study chromium oxidation.Chromium chemical kinetics over a range of temperatures of a hydrogen/air flame is proposed.Nine chromium compounds and fifty-eight reversible chemical reactions were considered The forward reaction rates are calculated based on the molecular collision approach for unknown ones and Arrhenius's Law for known ones.The backward reaction rates were calculated according to forward reaction rates, the equilibrium constants and chemical thermodynamics.It is verified by several equilibrium cases and is tested by a hydrogen/air diffusion flame.The results show that the kinetic model could be used in cases in which the chromium kinetics play an important role in a flame
A simple model for complex dissolution kinetics: a case study of norfloxacin.
Skrdla, Peter J
2007-10-18
A new semi-empirical model, particularly useful for studying complex dissolution kinetics, is presented here. It uses only two 'fit parameters', each possessing physically relevant units (in the time domain). The model is based on the idea that dispersion (variation) in the activation energy barrier may arise in certain cases, as a result of (quantized) molecular kinetic energies affecting the speed of the rate-determining step (r.d.s.) of the dissolution event. For such 'dispersive dissolutions', the r.d.s. is assumed to involve 2D denucleation. The author's dispersive kinetic model is shown to be applicable to the dissolution of various formulations of norfloxacin which produce very asymmetric, sigmoidal concentration versus time (C-t) profiles. It is derived by assuming an activation energy distribution having the functional form of the Maxwell-Boltzmann (M-B) distribution, coupled with a first-order rate expression. However, this model can also be reduced to give the same functional form as the classical Noyes-Whitney equation, in order to accurately fit/describe dissolution profiles which appear logarithmic (such profiles are due to dissolution phenomena that are not dispersive; i.e. for cases where the activation energy is essentially single-valued). Thus, the kinetic model presented in this work may potentially find broad applicability to the modeling of various dissolution trends observed in the literature.
Øien, Alf H
2004-01-01
Attempts are presented of an analogue modelling of Daphnia responses to various influences and stimuli, as distribution of food and of predators. An aim of the study is to examine to what extent a statistical-mechanical approach may be useful as a tool in modelling of Daphnia swarms behaviour. In the modelling we follow a line close to test particle studies in physical sciences. A generalized kinetic equation of what we shall call daphnicles is derived. The modelling incorporates individual characteristics of daphnicles, as position, velocity, degree of food saturation and responses daphnicles have to outside influences. Each daphnicle we assume responds to some stimuli in ordered ways and to others in stochastic ways, and the degree or strength of reactions depends on the density of all daphnicles, the density of food available, the saturation level of daphnicles and the threat level in the environment, or background, the daphnicles are living on. Some fluid equations of daphnicle swarms are subsequently derived from the basic equation, and solutions are given of the model-equations, including a food distribution equation, in some particular cases that show peculiarities in reactions of daphnicles to food, degree of saturation and to threat, when these are acting alone, and in combination. The modelling results may be compared to results of laboratory experiments of Daphnia behaviour that soon will be performed.
Energy Technology Data Exchange (ETDEWEB)
Carman, R.J. [Department of Physics, Division of Information and Communications Sciences, Macquarie University, Sydney, NSW (Australia)). E-mail: rcarman@physics.mq.edu.au; Mildren, R.P. [Centre for Lasers and Applications, Division of Information and Communications Sciences, Macquarie University, Sydney, NSW (Australia)
2000-10-07
In modelling the plasma kinetics in dielectric barrier discharges (DBDs), the electron energy conservation equation is often included in the rate equation analysis (rather than utilizing the local-field approximation) with the assumption that the electron energy distribution function (EEDF) has a Maxwellian profile. We show that adopting a Maxwellian EEDF leads to a serious overestimate of the calculated ionization/excitation rate coefficients and the electron mobility for typical plasma conditions in a xenon DBD. Alternative EEDF profiles are trialed (Druyvesteyn, bi-Maxwellian and bi-Druyvesteyn) and benchmarked against EEDFs obtained from solving the steady-state Boltzmann equation. A bi-Druyvesteyn EEDF is shown to be more inherently accurate for modelling simulations of xenon DBDs. (author)
Soluble Boltzmann equations for internal state and Maxwell models
Futcher, E.; Hoare, M.R.; Hendriks, E.M.; Ernst, M.H.
1980-01-01
We consider a class of scalar nonlinear Boltzmann equations describing the evolution of a microcanonical ensemble in which sub-systems exchange internal energy ‘randomly’ in binary interactions. In the continuous variable version these models can equally be interpreted as Boltzmann equations for Ma
Modeling systems containing alkanolamines with the CPA equation of state
DEFF Research Database (Denmark)
Avlund, Ane Søgaard; Kontogeorgis, Georgios; Michelsen, Michael Locht
2008-01-01
An association model, the cubic-plus-association (CPA) equation of state (EoS), is applied for the first time to a class of multifunctional compounds (alkanolamines). Three alkanolamines of practical and scientific significance are considered; monoethanolamine (MEA), diethanolamine (DEA...... studied using the CPA equation of state (alcohols, amines, and glycols)....
Model equation for simulating flows in multistage turbomachinery
Adamczyk, J. J.
1985-01-01
A steady, three-dimensional average-passage equation system is derived for use in simulating multistage turbomachinery flows. These equations describe a steady, viscous flow that is periodic from blade passage to blade passage. From this system of equations, various reduced forms can be derived for use in simulating the three-dimensional flow field within multistage machinery. It is suggested that a properly scaled form of the averaged-passage equation system would provide an improved mathematical model for simulating the flow in multistage machines at design and, in particular, at off-design conditions.
Transformation of equations in analysis of proportionality through referent models
Romay, E O
2006-01-01
In proportionality of objects, samples or populations, usually we work with Z score of proportionality calculated through referent models, instead directly with the variables of the objects in itself. In these studies we have the necessity to transform, the equations that use the variables of the object, in equations that directly use like variables Z score. In the present work a method is developed to transform the parametric equations, in equations in variables Z using like example the studies of human proportionality from the Phantom stratagem of Ross and Wilson.
Kinetic exchange models: From molecular physics to social science
Patriarca, Marco; Chakraborti, Anirban
2013-08-01
We discuss several multi-agent models that have their origin in the kinetic exchange theory of statistical mechanics and have been recently applied to a variety of problems in the social sciences. This class of models can be easily adapted for simulations in areas other than physics, such as the modeling of income and wealth distributions in economics and opinion dynamics in sociology.
Kinetic exchange models: From molecular physics to social science
Patriarca, Marco
2013-01-01
We discuss several multi-agent models that have their origin in the kinetic exchange theory of statistical mechanics and have been recently applied to a variety of problems in the social sciences. This class of models can be easily adapted for simulations in areas other than physics, such as the modeling of income and wealth distributions in economics and opinion dynamics in sociology.
Physiologically based kinetic modeling of the bioactivation of myristicin
Al-Malahmeh, Amer J.; Al-Ajlouni, Abdelmajeed; Wesseling, Sebastiaan; Soffers, Ans E.M.F.; Al-Subeihi, A.; Kiwamoto, Reiko; Vervoort, Jacques; Rietjens, Ivonne M.C.M.
2016-01-01
The present study describes physiologically based kinetic (PBK) models for the alkenylbenzene myristicin that were developed by extension of the PBK models for the structurally related alkenylbenzene safrole in rat and human. The newly developed myristicin models revealed that the formation of th
Meta-analysis a structural equation modeling approach
Cheung, Mike W-L
2015-01-01
Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the impo
Introduction to Structural Equation Modelling Using SPSS and Amos
Blunch, Niels J
2008-01-01
. Introduction to Structural Equation Modelling using SPSS and AMOS is a complete guide to carrying out your own structural equation modelling project. Assuming no previous experience of the subject, and a minimum of mathematical knowledge, this is the ideal guide for those new to structural equation modelling (SEM). Each chapter begins with learning objectives, and ends with a list of the new concepts introduced and questions to open up further discussion. Exercises for each chapter, incuding the necessary data, can be downloaded from the book's website. Helpful real life examples are include
Chemical kinetic modeling of H{sub 2} applications
Energy Technology Data Exchange (ETDEWEB)
Marinov, N.M.; Westbrook, C.K.; Cloutman, L.D. [Lawrence Livermore National Lab., CA (United States)] [and others
1995-09-01
Work being carried out at LLNL has concentrated on studies of the role of chemical kinetics in a variety of problems related to hydrogen combustion in practical combustion systems, with an emphasis on vehicle propulsion. Use of hydrogen offers significant advantages over fossil fuels, and computer modeling provides advantages when used in concert with experimental studies. Many numerical {open_quotes}experiments{close_quotes} can be carried out quickly and efficiently, reducing the cost and time of system development, and many new and speculative concepts can be screened to identify those with sufficient promise to pursue experimentally. This project uses chemical kinetic and fluid dynamic computational modeling to examine the combustion characteristics of systems burning hydrogen, either as the only fuel or mixed with natural gas. Oxidation kinetics are combined with pollutant formation kinetics, including formation of oxides of nitrogen but also including air toxics in natural gas combustion. We have refined many of the elementary kinetic reaction steps in the detailed reaction mechanism for hydrogen oxidation. To extend the model to pressures characteristic of internal combustion engines, it was necessary to apply theoretical pressure falloff formalisms for several key steps in the reaction mechanism. We have continued development of simplified reaction mechanisms for hydrogen oxidation, we have implemented those mechanisms into multidimensional computational fluid dynamics models, and we have used models of chemistry and fluid dynamics to address selected application problems. At the present time, we are using computed high pressure flame, and auto-ignition data to further refine the simplified kinetics models that are then to be used in multidimensional fluid mechanics models. Detailed kinetics studies have investigated hydrogen flames and ignition of hydrogen behind shock waves, intended to refine the detailed reactions mechanisms.
A unifying kinetic framework for modeling oxidoreductase-catalyzed reactions
Chang, Ivan; Baldi, Pierre
2013-01-01
Motivation: Oxidoreductases are a fundamental class of enzymes responsible for the catalysis of oxidation–reduction reactions, crucial in most bioenergetic metabolic pathways. From their common root in the ancient prebiotic environment, oxidoreductases have evolved into diverse and elaborate protein structures with specific kinetic properties and mechanisms adapted to their individual functional roles and environmental conditions. While accurate kinetic modeling of oxidoreductases is thus imp...
Application of Detailed Chemical Kinetics to Combustion Instability Modeling
2016-01-04
under two different conditions corresponding to marginally stable and unstable operation in order to evaluate the performance of the chemical kinetics...instability is a complex interaction between acoustics and the heat release due to combustion.In rocket engines, which are acoustically compact, there is...and amplitudes remains a challenge. The present article is an attempt towards addressing such discrepancies by enhancing the chemical kinetics model
Wang, Zhandong
2015-07-01
Ethylcyclohexane (ECH) is a model compound for cycloalkanes with long alkyl side-chains. A preliminary investigation on ECH (Wang et al., Proc. Combust. Inst., 35, 2015, 367-375) revealed that an accurate ECH kinetic model with detailed fuel consumption mechanism and aromatic growth pathways, as well as additional ECH pyrolysis and oxidation data with detailed species concentration covering a wide pressure and temperature range are required to understand the ECH combustion kinetics. In this work, the flow reactor pyrolysis of ECH at various pressures (30, 150 and 760Torr) was studied using synchrotron vacuum ultraviolet (VUV) photoionization mass spectrometry (PIMS) and gas chromatography (GC). The mole fraction profiles of numerous major and minor species were evaluated, and good agreement was observed between the PIMS and GC data sets. Furthermore, a fuel-rich burner-stabilized laminar premixed ECH/O
Wang, Jia X; Uribe, Francisco A; Springer, Thomas E; Zhang, Junliang; Adzic, Radoslav R
2008-01-01
According to Sergio Trasatti, "A true theory of electrocatalysis will not be available until activity can be calculated a priori from some known properties of the materials." Toward this goal, we developed intrinsic kinetic equations for the hydrogen oxidation reaction (HOR) and the oxygen reduction reaction (ORR) using as the kinetic parameters the free energies of adsorption and activation for elementary reactions. Rigorous derivation retained the intrinsic connection between the intermediates' adsorption isotherms and the kinetic equations, affording us an integrated approach for establishing the reaction mechanisms based upon various experimental and theoretical results. Using experimentally deduced free energy diagrams and activity-and-barriers plot for the ORR on Pt(111), we explained why the Tafel slope in the large overpotential region is double that in the small overpotential region. For carbon-supported Pt nanoparticles (Pt/C), the polarization curves measured with thin-film rotating disk electrodes also exhibit the double Tafel slope, albeit Pt(111) is several times more active than the Pt nanoparticles when the current is normalized by real surface area. An analytic method was presented for the polarization curves measured with H2 in proton exchange membrane fuel cells (PEMFCs). The fit to a typical iR-free polarization curve at 80 degrees C revealed that the change of the Tafel slope occurs at about 0.77 V that is the reversible potential for the transition between adsorbed O and OH on Pt/C. This is significant because it predicts that the Butler-Volmer equation can only fit the data above this potential, regardless the current density. We also predicted a decrease of the Tafel slope from 70 to 65 mV dec(-1) at 80 degrees C with increasing oxygen partial pressure, which is consistent with the observation reported in literature.
An Overview on R Packages for Structural Equation Modeling
Directory of Open Access Journals (Sweden)
Haibin Qiu
2014-05-01
Full Text Available The aim of this study is to present overview on R packages for structural equation modeling. Structural equation modeling, a statistical technique for testing and estimating causal relations using an amalgamation of statistical data and qualitative causal hypotheses, allow both confirmatory and exploratory modeling, meaning they are matched to both hypothesis testing and theory development. R project or R language, a free and popular programming language and computer software surroundings for statistical computing and graphics, is popularly used among statisticians for developing statistical computer software and data analysis. The major finding is that it is necessary to build excellent and enough structural equation modeling packages for R users to do research. Numerous packages for structural equation modeling of R project are introduced in this study and most of them are enclosed in the Comprehensive R Archive Network task view Psychometrics.
A stochastic particle system modeling the Carleman equation
Energy Technology Data Exchange (ETDEWEB)
Caprino, S.; De Masi, A.; Presutti, E.; Pulvirenti, M. (Universita dell' Aquila (Italy))
1989-05-01
Two species of Brownian particles on the unit circle are considered; both have diffusion coefficient {sigma} > 0 but different velocities (drift), 1 for one species and {minus}1 for the other. During the evolution the particles randomly change their velocity: if two particles have the same velocity and are at distance {<=} {var epsilon} ({var epsilon} being a positive parameter), they both may simultaneously flip their velocity according to a poisson process of a given intensity. The analogue of the Boltzmann-Grad limit is studied when {var epsilon} goes to zero and the total number of particles increases like {var epsilon}{sup {minus}1}. In such a limit propagation of chaos and convergence to a limiting kinetic equation are proven globally in time, under suitable assumptions on the initial state. If, furthermore, {sigma} depends on {var epsilon} and suitably vanishes when {var epsilon} goes to zero, then the limiting kinetic equation (for the density of the two species of particles) is the Carleman equation.
Numerical prediction of kinetic model for enzymatic hydrolysis of cellulose using DAE-QMOM approach
Jamil, N. M.; Wang, Q.
2016-06-01
Bioethanol production from lignocellulosic biomass consists of three fundamental processes; pre-treatment, enzymatic hydrolysis, and fermentation. In enzymatic hydrolysis phase, the enzymes break the cellulose chains into sugar in the form of cellobiose or glucose. A currently proposed kinetic model for enzymatic hydrolysis of cellulose that uses population balance equation (PBE) mechanism was studied. The complexity of the model due to integrodifferential equations makes it difficult to find the analytical solution. Therefore, we solved the full model of PBE numerically by using DAE-QMOM approach. The computation was carried out using MATLAB software. The numerical results were compared to the asymptotic solution developed in the author's previous paper and the results of Griggs et al. Besides confirming the findings were consistent with those references, some significant characteristics were also captured. The PBE model for enzymatic hydrolysis process can be solved using DAE-QMOM method. Also, an improved understanding of the physical insights of the model was achieved.
Vosika, Z.; Mitić, V. V.; Vasić, A.; Lazović, G.; Matija, L.; Kocić, Lj. M.
2017-03-01
In this paper, Caputo based Michaelis-Menten kinetic model based on Time Scale Calculus (TSC) is proposed. The main reason for its consideration is a study of tumor cells population growth dynamics. In the particular case discrete-continuous time kinetics, Michaelis-Menten model is numerically treated, using a new algorithm proposed by authors, called multistep generalized difference transformation method (MSGDETM). In addition numerical simulations are performed and is shown that it represents the upgrade of the multi-step variant of generalized differential transformation method (MSGDTM). A possible conditions for its further development are discussed and possible experimental verification is described.
Fillion-Gourdeau, F; Bandrauk, A D
2015-01-01
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.
Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
Energy Technology Data Exchange (ETDEWEB)
Fillion-Gourdeau, F., E-mail: filliong@CRM.UMontreal.ca [Université du Québec, INRS – Énergie, Matériaux et Télécommunications, Varennes, J3X 1S2 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Lorin, E., E-mail: elorin@math.carleton.ca [School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada); Bandrauk, A.D., E-mail: andre.bandrauk@usherbrooke.ca [Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, Sherbrooke, J1K 2R1 (Canada); Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4 (Canada)
2016-02-15
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The apparent activation energies and frequency factors of the double reversible transformations occurring in heating CuZnAlMnNi shape memory alloy (SMA) were deduced as AEx .M = 62.597 8 kJ/mol, AEm.A 153.92 kJ'mol,Ax-m = 5.223 2 × 109s 1, and AM-A = 2.325 1 × l023 s 1, respectively. The kinetic equations of the two transfornations during heating were established simultaneously.
Partial Least Squares Structural Equation Modeling with R
Ravand, Hamdollah; Baghaei, Purya
2016-01-01
Structural equation modeling (SEM) has become widespread in educational and psychological research. Its flexibility in addressing complex theoretical models and the proper treatment of measurement error has made it the model of choice for many researchers in the social sciences. Nevertheless, the model imposes some daunting assumptions and…
ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES
Directory of Open Access Journals (Sweden)
Josip Arnerić
2010-12-01
Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.