Computer models for kinetic equations of magnetically confined plasmas
International Nuclear Information System (INIS)
Killeen, J.; Kerbel, G.D.; McCoy, M.G.; Mirin, A.A.; Horowitz, E.J.; Shumaker, D.E.
1987-01-01
This paper presents four working computer models developed by the computational physics group of the National Magnetic Fusion Energy Computer Center. All of the models employ a kinetic description of plasma species. Three of the models are collisional, i.e., they include the solution of the Fokker-Planck equation in velocity space. The fourth model is collisionless and treats the plasma ions by a fully three-dimensional particle-in-cell method
Empiric model for mean generation time adjustment factor for classic point kinetics equations
International Nuclear Information System (INIS)
Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C.
2017-01-01
Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)
Empiric model for mean generation time adjustment factor for classic point kinetics equations
Energy Technology Data Exchange (ETDEWEB)
Goes, David A.B.V. de; Martinez, Aquilino S.; Goncalves, Alessandro da C., E-mail: david.goes@poli.ufrj.br, E-mail: aquilino@lmp.ufrj.br, E-mail: alessandro@con.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Departamento de Engenharia Nuclear
2017-11-01
Point reactor kinetics equations are the easiest way to observe the neutron production time behavior in a nuclear reactor. These equations are derived from the neutron transport equation using an approximation called Fick's law leading to a set of first order differential equations. The main objective of this study is to review classic point kinetics equation in order to approximate its results to the case when it is considered the time variation of the neutron currents. The computational modeling used for the calculations is based on the finite difference method. The results obtained with this model are compared with the reference model and then it is determined an empirical adjustment factor that modifies the point reactor kinetics equation to the real scenario. (author)
Al-Musawi, Tariq J; Brouers, Francois; Zarrabi, Mansur
2017-02-01
In this study, the kinetic data of the adsorption of two antibiotics onto three nanoadsorbents was modeled using the Brouers-Sotolongo fractal model. The model parameters were calculated at different initial antibiotic concentrations using various approximations of the kinetic equation for two quantities of practical relevance: the sorption power and the half-time characteristic of the sorption. The merits of the nanomaterial were then compared in terms of their application in the elimination of dangerous antibiotic wastes. We also developed a formula to calculate the effective rate of the best adsorbent. This study presents the modeling method in detail and has a pedagogical value for similar researches.
Watkins, N W; Credgington, D; Sanchez, R; Rosenberg, S J; Chapman, S C
2009-04-01
Lévy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm) is a model process of this type, combining alpha-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk (CTRW), with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst "sizes" and "durations" in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.
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.
Equations for the kinetic modeling of supersonically flowing electrically excited lasers
International Nuclear Information System (INIS)
Lind, R.C.
1973-01-01
The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration--vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is discussed
Kinetic equation solution by inverse kinetic method
International Nuclear Information System (INIS)
Salas, G.
1983-01-01
We propose a computer program (CAMU) which permits to solve the inverse kinetic equation. The CAMU code is written in HPL language for a HP 982 A microcomputer with a peripheral interface HP 9876 A ''thermal graphic printer''. The CAMU code solves the inverse kinetic equation by taking as data entry the output of the ionization chambers and integrating the equation with the help of the Simpson method. With this program we calculate the evolution of the reactivity in time for a given disturbance
International Nuclear Information System (INIS)
Parisot, M.
2011-01-01
This work is dedicated study of a problem resulting from plasma physics: the thermal transfer of electrons in a plasma close to equilibrium Maxwellian. Firstly, a dimensional study of the Vlasov-Fokker-Planck-Maxwell system is performed, allowing one hand to identify a physically relevant parameter of scale and also to define mathematically the contours of validity domain. The asymptotic regime called Spitzer-Harm is studied for a relatively general class of collision operator. The following part of this work is devoted to the derivation and study of the hydrodynamic limit of the system of Vlasov-Maxwell-Landau outside the strictly asymptotic. A model proposed by Schurtz and Nicolais located in this context and analyzed. The particularity of this model lies in the application of a delocalization operation in the heat flux. The link with non-local models of Luciani and Mora is established as well as mathematics properties as the principle of maximum and entropy dissipation. Then a formal derivation from the Vlasov equations with a simplified collision operator, is proposed. The derivation, inspired by the recent work of D. Levermore, involves decomposition methods according to the spherical harmonics and methods of closing called diffusion methods. A hierarchy of intermediate models between the kinetic equations and the hydrodynamic limit is described. In particular a new hydrodynamic system integro-differential by nature, is proposed. The Schurtz and Nicolai model appears as a simplification of the system resulting from the derivation, assuming a steady flow of heat. The above results are then generalized to account for the internal energy dependence which appears naturally in the equation establishment. The existence and uniqueness of the solution of the nonstationary system are established in a simplified framework. The last part is devoted was the implementation of a specific numerical scheme to solve these models. We propose a finite volume approach can be
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.
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
International Nuclear Information System (INIS)
Li, Zhihui; Ma, Qiang; Wu, Junlin; Jiang, Xinyu; Zhang, Hanxin
2014-01-01
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
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
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 kinetic equation for irreversible aggregation
International Nuclear Information System (INIS)
Zanette, D.H.
1990-09-01
We introduce a kinetic equation for describing irreversible aggregation in the ballistic regime, including velocity distributions. The associated evolution for the macroscopic quantities is studied, and the general solution for Maxwell interaction models is obtained in the Fourier representation. (author). 23 refs
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. Copyright © 2012 Elsevier B.V. All rights reserved.
Epstein, Irving R.; Luo, Yin
1991-07-01
Delayed feedback plays a key role in most, if not all chemical oscillators. We derive general results useful in the linear stability analysis of models that explicitly incorporate delay by using differential delay equations. Two models of nonlinear chemical oscillators, the cross-shaped phase diagram model of Boissonade and De Kepper and the Oregonator, are modified by deleting a feedback species and mimicking its effect by a delay in the kinetics of another variable. With an appropriate choice of the delay time, the reduced models behave very much like the full systems. It should be possible to carry out similar reductions on more complex mechanisms of oscillating reactions, thereby providing insight into the role of delayed feedback in these systems.
Receptor binding kinetics equations: Derivation using the Laplace transform method.
Hoare, Sam R J
Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time
International Nuclear Information System (INIS)
Vlahostergios, Z.; Yakinthos, K.; Goulas, A.
2009-01-01
We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.
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.
Fractional Bhatnagar-Gross-Krook kinetic equation
Goychuk, Igor
2017-11-01
The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.
International Nuclear Information System (INIS)
Kimpland, R.H.
1996-01-01
A normalized form of the point kinetics equations, a prompt jump approximation, and the Nordheim-Fuchs model are used to model nuclear systems. Reactivity feedback mechanisms considered include volumetric expansion, thermal neutron temperature effect, Doppler effect and void formation. A sample problem of an excursion occurring in a plutonium solution accidentally formed in a glovebox is presented
Saylor, Rick D.; Ford, Gregory D.
The integration of systems of ordinary differential equations (ODEs) that arise in atmospheric photochemistry is of significant concern to tropospheric and stratospheric chemistry modelers. As a consequence of the stiff nature of these ODE systems, their solution requires a large fraction of the total computational effort in three-dimensional chemical model simulations. Several integration techniques have been proposed and utilized over the years in an attempt to provide computationally efficient, yet accurate, solutions to chemical kinetics ODES. In this work, we present a comparison of some of these techniques and argue that valid comparisons of ODE solvers must take into account the trade-off between solution accuracy and computational efficiency. Misleading comparison results can be obtained by neglecting the fact that any ODE solution method can be made faster or slower by manipulation of the appropriate error tolerances or time steps. Comparisons among ODE solution techniques should therefore attempt to identify which technique can provide the most accurate solution with the least computational effort over the entire range of behavior of each technique. We present here a procedure by which ODE solver comparisons can achieve this goal. Using this methodology, we compare a variety of integration techniques, including methods proposed by Hesstvedt et al. (1978, Int. J. Chem. Kinet.10, 971-994), Gong and Cho (1993, Atmospheric Environment27A, 2147-2160), Young and Boris (1977, J. phys. Chem.81, 2424-2427) and Hindmarsh (1983, In Scientific Computing (edited by Stepleman R. S. et al.), pp. 55-64. North-Holland, Amsterdam). We find that Gear-type solvers such as the Livermore Solver for ordinary differential equations (LSODE) and the sparse-matrix version of LSODE (LSODES) provide the most accurate solution of our test problems with the least computational effort.
International Nuclear Information System (INIS)
Ravetto, P.; Sumini, M.; Ganapol, B.D.
1988-01-01
In an attempt to better understand the influence of prompt and delayed neutrons on nuclear reactor dynamics, a continuous slowing down model based on Fermi age theory was developed several years ago. This model was easily incorporated into the one-group diffusion equation and provided a realistic physical picture of how delayed and prompt neutrons slow down and simultaneously diffuse throughout a medium. The model allows for different slowing down times for each delayed neutron group as well as for prompt neutrons and for spectral differences between the two typed of neutrons. Because of its generality, this model serves not only a a useful predictive tool to anticipate reactor transients, but also as an excellent educational tool to demonstrate the effect of delayed neutrons in reactor kinetics. However, because of numerical complications, the slowing down model could not be developed to its full potential. In particular, the major limitation was the inversion of the Laplace transform, which relied on a knowledge of the poles associated with the resulting transformed flux. For this reason, only one group of delayed neutrons and times longer than the slowing down times could be considered. As is shown, the new inversion procedure removes the short time limitation as well as allows for any number of delayed neutron groups. The inversion technique is versatile and is useful in teaching numerical methods in nuclear science
Kinetic equations for longitudinal stochastic cooling
International Nuclear Information System (INIS)
Bisognano, J.J.
1980-07-01
A kinetic equation approach to stochastic cooling is presented. Equations for one and two particle distribution functions are derived from the principle of conservation of the number of ensemble systems. The violation of Liouville's theorem is expressed by certain self-interaction terms. The two-particle distribution describes Schottky noise and feedback effects and is analyzed by techniques of the Lenard-Balescu equation for plasmas. The resulting expression for the one particle distribution is of the form of a Fokker-Planck equation. The suppression of Schottky signals for arbitrary machine impedance is discussed in terms of particle correlations
The Balescu kinetic equation with exchange interaction
International Nuclear Information System (INIS)
Belyi, V V; Kukharenko, Yu A
2009-01-01
Starting with the quantum BBGKY hierarchy for the distribution functions, we have obtained the quantum kinetic equation including the dynamical screening of the interaction potential, which exactly takes into account the exchange scattering in the plasma. The collision integral is expressed in terms of the Green function of the linearized Hartree–Fock equation. The potential energy takes into account the polarization and exchange interaction too
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.
DEFF Research Database (Denmark)
Costa, Rafael S.; Machado, Daniel; Rocha, Isabel
2010-01-01
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...
Schmitz, Guy; Kolar-Anić, Ljiljana Z; Anić, Slobodan R; Cupić, Zeljko D
2008-12-25
The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.
Iterative Approximate Solutions of Kinetic Equations for Reversible Enzyme Reactions
Khoshnaw, S.
2012-01-01
We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are included in appendices.
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.
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.
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...
GENERAL EQUATIONS OF CARBONIZATION OF EUCALYPTUS SPP KINETIC MECHANISMS
Directory of Open Access Journals (Sweden)
Túlio Jardim Raad
2006-06-01
Full Text Available In the present work, a set of general equations related to kinetic mechanism of wood compound carbonization: hemicelluloses, cellulose and lignin was obtained by Avrami-Eroffev and Arrhenius equations and Thermogravimetry of Eucalyptus cloeziana, Eucalyptus camaldulensis, Corymbia citriodora, Eucalyptus urophylla and Eucalyptus grandis samples, TG-Isothermal and TG-Dynamic. The different thermal stabilities and decomposition temperature bands of those species compounds were applied as strategy to obtain the kinetic parameters: activation energy, exponential factor and reaction order. The kinetic model developed was validated by thermogravimetric curves from carbonization of others biomass such as coconut. The kinetic parameters found were - Hemicelluloses: E=98,6 kJmol, A=3,5x106s-1 n=1,0; - Cellulose: E=182,2 kJmol, A=1,2x1013s-1 n=1,5; - Lignin: E=46,6 kJmol, A=2,01s-1 n=0,41. The set of equations can be implemented in a mathematical model of wood carbonization simulation (with heat and mass transfer equations with the aim of optimizing the control and charcoal process used to produce pig iron.
Modified mean generation time parameter in the neutron point kinetics equations
Energy Technology Data Exchange (ETDEWEB)
Diniz, Rodrigo C.; Gonçalves, Alessandro C.; Rosa, Felipe S.S., E-mail: alessandro@nuclear.ufrj.br, E-mail: frosa@if.ufrj.br [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil)
2017-07-01
This paper proposes an approximation for the modified point kinetics equations proposed by NUNES et. al, 2015, through the adjustment of a kinetic parameter. This approximation consists of analyzing the terms of the modified point kinetics equations in order to identify the least important ones for the solution, resulting in a modification of the mean generation time parameter that incorporates all influences of the additional terms of the modified kinetics. This approximation is applied on the inverse kinetics, to compare the results with the inverse kinetics from the modified kinetics in order to validate the proposed model. (author)
Modified mean generation time parameter in the neutron point kinetics equations
International Nuclear Information System (INIS)
Diniz, Rodrigo C.; Gonçalves, Alessandro C.; Rosa, Felipe S.S.
2017-01-01
This paper proposes an approximation for the modified point kinetics equations proposed by NUNES et. al, 2015, through the adjustment of a kinetic parameter. This approximation consists of analyzing the terms of the modified point kinetics equations in order to identify the least important ones for the solution, resulting in a modification of the mean generation time parameter that incorporates all influences of the additional terms of the modified kinetics. This approximation is applied on the inverse kinetics, to compare the results with the inverse kinetics from the modified kinetics in order to validate the proposed model. (author)
One dimensional code to solve multigroup kinetic equations
International Nuclear Information System (INIS)
Alcantara, H.G. de; Prati, A.; Rosa, M.A.P.; Nair, R.P.K.
1985-01-01
It is described a computer program for the numerical solution of neutron kinetic equations in the multigroup theory for one dimensional medium. The spatial dependence is discretized by finite differences. The time integration is obtained by the method of ponderated residuals and iterative solution. It is examined one method of convergence acceleration. The program studies the reactivity feedback by the variation of temperature or density. It is simulated the simplified model of heat extraction. (M.C.K.) [pt
Kinetic theory of flocking: derivation of hydrodynamic equations.
Ihle, Thomas
2011-03-01
It is shown how to explicitly coarse-grain the microscopic dynamics of the rule-based Vicsek model for self-propelled agents. The hydrodynamic equations are derived by means of an Enskog-type kinetic theory. Expressions for all transport coefficients are given. The transition from a disordered to a flocking state, which at large particle speeds appears to be a fluctuation-induced first-order phase transition, is studied numerically and analytically.
Studies of the solution method for reactor Kinetics equations
International Nuclear Information System (INIS)
Andrade Oliveira, E. de.
1982-10-01
An analysis of the performance of some numerical methods which are employed in order to reduce the computing time in the process of obtaining solutions to nuclear reactor kinetics equations, are made. The methods which have been studied are: Pade schemes, Frequency Transformation and Temporal Synthesis. The investigation on the performance of the above mentioned methods is made based on models of point Kinetics and spacial Kinetics in 1 dimension. The applications and numerical examples presented try to simulate a PWR-type reactor by use of material parameters characteristical of this type of reactor. Several tests were made with each method, employing two types of transients: whithout material parameter variation during the transient, and with material parameter variation at a constant rate. (Author) [pt
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.
Electromagnetic banana kinetic equation and its applications in tokamaks
Shaing, K. C.; Chu, M. S.; Sabbagh, S. A.; Seol, J.
2018-03-01
A banana kinetic equation in tokamaks that includes effects of the finite banana width is derived for the electromagnetic waves with frequencies lower than the gyro-frequency and the bounce frequency of the trapped particles. The radial wavelengths are assumed to be either comparable to or shorter than the banana width, but much wider than the gyro-radius. One of the consequences of the banana kinetics is that the parallel component of the vector potential is not annihilated by the orbit averaging process and appears in the banana kinetic equation. The equation is solved to calculate the neoclassical quasilinear transport fluxes in the superbanana plateau regime caused by electromagnetic waves. The transport fluxes can be used to model electromagnetic wave and the chaotic magnetic field induced thermal particle or energetic alpha particle losses in tokamaks. It is shown that the parallel component of the vector potential enhances losses when it is the sole transport mechanism. In particular, the fact that the drift resonance can cause significant transport losses in the chaotic magnetic field in the hitherto unknown low collisionality regimes is emphasized.
Regularized Structural Equation Modeling
Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.
2016-01-01
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. PMID:27398019
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.
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.
Pöschl, U.; Rudich, Y.; Ammann, M.
2007-12-01
Aerosols and clouds play central roles in atmospheric chemistry and physics, climate, air pollution, and public health. The mechanistic understanding and predictability of aerosol and cloud properties, interactions, transformations, and effects are, however, still very limited. This is due not only to the limited availability of measurement data, but also to the limited applicability and compatibility of model formalisms used for the analysis, interpretation, and description of heterogeneous and multiphase processes. To support the investigation and elucidation of atmospheric aerosol and cloud surface chemistry and gas-particle interactions, we present a comprehensive kinetic model framework with consistent and unambiguous terminology and universally applicable rate equations and parameters. It enables a detailed description of mass transport and chemical reactions at the gas-particle interface, and it allows linking aerosol and cloud surface processes with gas phase and particle bulk processes in systems with multiple chemical components and competing physicochemical processes. The key elements and essential aspects of the presented framework are: a simple and descriptive double-layer surface model (sorption layer and quasi-static layer); straightforward flux-based mass balance and rate equations; clear separation of mass transport and chemical reactions; well-defined and consistent rate parameters (uptake and accommodation coefficients, reaction and transport rate coefficients); clear distinction between gas phase, gas-surface, and surface-bulk transport (gas phase diffusion, surface and bulk accommodation); clear distinction between gas-surface, surface layer, and surface-bulk reactions (Langmuir-Hinshelwood and Eley-Rideal mechanisms); mechanistic description of concentration and time dependences (transient and steady-state conditions); flexible addition of unlimited numbers of chemical species and physicochemical processes; optional aggregation or resolution
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…
Uncertainty quantification for hyperbolic and kinetic equations
Pareschi, Lorenzo
2017-01-01
This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.
African Journals Online (AJOL)
Petrophysical, Decompaction and Linear Regression techniques were used to investigate overpressure, degree of compaction and to derive a model compaction equation for. -1. -1 hydrostatic sandstones. Compaction coefficients obtained range from 0.0003 - 0.0005 m (averaging 0.0004 m ) and percentage compaction ...
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
International Nuclear Information System (INIS)
Petersen, Claudio Z.; Vilhena, Marco Tullio; Bodmann, Bardo; Dulla, Sandra; Ravetto, Piero
2011-01-01
The three-dimensions multigroup neutron kinetics diffusion equations is considered to predict the behavior of neutrons in a nuclear reactor. In this work we develop a method that allows to construct an analytical solution to the equations of kinetic space. The spatial kinetic model has a crucial problem for a quasi real-time prediction of reactor power, especially at start-up, shut-down or change in power, by virtue of the stiff character of the equations. In order to circumvent problems that typically occur in numerical approaches, we solve the neutron kinetics diffusion equation in a homogeneous parallelepiped analytically, considering two energy groups and six group of delayed neutrons. Applying the GITT (generalized integral transform technique) in the vertical direction, we cast the original problem into a two-dimensional one with known solution. We report on numerical results, and comparisons against the ones of the literature. (author)
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.
Modeling chemical kinetics graphically
Heck, A.
2012-01-01
In literature on chemistry education it has often been suggested that students, at high school level and beyond, can benefit in their studies of chemical kinetics from computer supported activities. Use of system dynamics modeling software is one of the suggested quantitative approaches that could
A nondissipative simulation method for the drift kinetic equation
International Nuclear Information System (INIS)
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)
A nonlinear bounce kinetic equation for trapped electrons
International Nuclear Information System (INIS)
Gang, F.Y.
1990-03-01
A nonlinear bounce averaged drift kinetic equation for trapped electrons is derived. This equation enables one to compute the nonlinear response of the trapped electron distribution function in terms of the field-line projection of a potential fluctuation left-angle e -inqθ φ n right-angle b . It is useful for both analytical and computational studies of the nonlinear evolution of short wavelength (n much-gt 1) trapped electron mode-driven turbulence. 7 refs
Review of Kaganove's solution for the reactor point kinetics equations
International Nuclear Information System (INIS)
Couto, R.T.; Santo, A.C.F. de.
1993-09-01
A review of Kaganove's method for the reactor point kinetics equations solution is performed. This was method chosen to calculate the power in ATR, a computer program for the analysis of reactivity transients. The reasons for this choice and the adaptation of the method to the purposes of ATR are presented. (author)
A stochastic model of enzyme kinetics
Stefanini, Marianne; Newman, Timothy; McKane, Alan
2003-10-01
Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2015-01-01
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 structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789
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...
A Nonlinear Evolution Equation in an Ordered Space, Arising from Kinetic Theory
Grünfeld, C P
2005-01-01
We investigate the Cauchy problem for a nonlinear evolution equation, formulated in an abstract Lebesgue space, as a generalization of various Boltzmann kinetic models. Our main result provides sufficient conditions for the existence, uniqueness, and positivity of global in time solutions. The proof is based on ideas behind a well-known monotonicity method, originally developed within the existence theory of the classical Boltzmann equation in $L^1$. Our application examples concern Smoluchowski's coagulation equation, a Povzner-like equation with dissipative collisions, and a Boltzmann model with chemical reactions.
International Nuclear Information System (INIS)
Silva, Milena Wollmann da; Vilhena, Marco Tullio M.B.; Bodmann, Bardo Ernst J.; Vasques, Richard
2015-01-01
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)
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)
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.
Comparative analysis of solution methods of the punctual kinetic equations
International Nuclear Information System (INIS)
Hernandez S, A.
2003-01-01
The following one written it presents a comparative analysis among different analytical solutions for the punctual kinetics equation, which present two variables of interest: a) the temporary behavior of the neutronic population, and b) The temporary behavior of the different groups of precursors of delayed neutrons. The first solution is based on a method that solves the transfer function of the differential equation for the neutronic population, in which intends to obtain the different poles that give the stability of this transfer function. In this section it is demonstrated that the temporary variation of the reactivity of the system can be managed as it is required, since the integration time for this method doesn't affect the result. However, the second solution is based on an iterative method like that of Runge-Kutta or the Euler method where the algorithm was only used to solve first order differential equations giving this way solution to each differential equation that conforms the equations of punctual kinetics. In this section it is demonstrated that only it can obtain a correct temporary behavior of the neutronic population when it is integrated on an interval of very short time, forcing to the temporary variation of the reactivity to change very quick way without one has some control about the time. In both methods the same change is used so much in the reactivity of the system like in the integration times, giving validity to the results graph the one the temporary behavior of the neutronic population vs. time. (Author)
Different seeds to solve the equations of stochastic point kinetics using the Euler-Maruyama method
International Nuclear Information System (INIS)
Suescun D, D.; Oviedo T, M.
2017-09-01
In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and
Verification of continuum drift kinetic equation solvers in NIMROD
Energy Technology Data Exchange (ETDEWEB)
Held, E. D.; Ji, J.-Y. [Utah State University, Logan, Utah 84322-4415 (United States); Kruger, S. E. [Tech-X Corporation, Boulder, Colorado 80303 (United States); Belli, E. A. [General Atomics, San Diego, California 92186-5608 (United States); Lyons, B. C. [Program in Plasma Physics, Princeton University, Princeton, New Jersey 08543-0451 (United States)
2015-03-15
Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speed coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.
Numerical simulation of stochastic point kinetic equation in the dynamical system of nuclear reactor
International Nuclear Information System (INIS)
Saha Ray, S.
2012-01-01
Highlights: ► In this paper stochastic neutron point kinetic equations have been analyzed. ► Euler–Maruyama method and Strong Taylor 1.5 order method have been discussed. ► These methods are applied for the solution of stochastic point kinetic equations. ► Comparison between the results of these methods and others are presented in tables. ► Graphs for neutron and precursor sample paths are also presented. -- Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors.
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.
Shannon, Robin; Glowacki, David R
2018-02-15
The chemical master equation is a powerful theoretical tool for analyzing the kinetics of complex multiwell potential energy surfaces in a wide range of different domains of chemical kinetics spanning combustion, atmospheric chemistry, gas-surface chemistry, solution phase chemistry, and biochemistry. There are two well-established methodologies for solving the chemical master equation: a stochastic "kinetic Monte Carlo" approach and a matrix-based approach. In principle, the results yielded by both approaches are identical; the decision of which approach is better suited to a particular study depends on the details of the specific system under investigation. In this Article, we present a rigorous method for accelerating stochastic approaches by several orders of magnitude, along with a method for unbiasing the accelerated results to recover the "true" value. The approach we take in this paper is inspired by the so-called "boxed molecular dynamics" (BXD) method, which has previously only been applied to accelerate rare events in molecular dynamics simulations. Here we extend BXD to design a simple algorithmic strategy for accelerating rare events in stochastic kinetic simulations. Tests on a number of systems show that the results obtained using the BXD rare event strategy are in good agreement with unbiased results. To carry out these tests, we have implemented a kinetic Monte Carlo approach in MESMER, which is a cross-platform, open-source, and freely available master equation solver.
Asymptotic Completeness for Relativistic Kinetic Equations with Short-range Interaction Forces
Ha, Seung-Yeal; Kim, Yong Duck; Lee, Ho; Noh, Se Eun
2007-01-01
We present an $L^1$-asymptotic completeness results for relativistic kinetic equations with short range interaction forces. We show that the uniform phase space-time bound for nonlinear terms to the relativistic nonlinear kinetic equations yields the asymptotic completeness of the relativistic kinetic equations. For this space-time bound, we employ dispersive estimates and explicit construction of a Lyapunov functional.
A Universal Integrated Rate Equation for Chemical Kinetics.
Allen, Wesley D
2018-04-13
The overarching analytic integrated rate equation for the chemical kinetics of any reversible or irreversible reaction involving an arbitrary number of species and any integral orders is shown to be Π i=1 r [1 - f i -1 ξ( t)] γ i = e (-1) r F 0 t , where ξ( t) is the extent of reaction variable, the f i are roots of a polynomial of order r, the exponents are determined by γ i = Π k(≠ i) r ( f i - f k ) -1 , and F 0 is a factor involving the stoichiometric coefficients and rate constants ( k ± ). All integrated rate equations of elementary reactions appearing in chemical kinetics are special cases of this universal solution. Not only does the solution provide insight into the analytical form of the exponents γ i and F 0 that govern the time evolution of the system, but it also provides an elegant framework for the pedagogy and application of kinetics in physical chemistry.
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.
International Nuclear Information System (INIS)
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
Violon, D
2012-12-01
To develop a multicompartment model of only essential human body components that predicts the contrast medium concentration vs time curve in a chosen compartment after an intravenous injection. Also to show that the model can be used to time adequately contrast-enhanced CT series. A system of linked time delay instead of ordinary differential equations described the model and was solved with a Matlab program (Matlab v. 6.5; The Mathworks, Inc., Natick, MA). All the injection and physiological parameters were modified to cope with normal or pathological situations. In vivo time-concentration curves from the literature were recalculated to validate the model. The recalculated contrast medium time-concentration curves and parameters are given. The results of the statistical analysis of the study findings are expressed as the median prediction error and the median absolute prediction error values for both the time delay and ordinary differential equation systems; these are situated well below the generally accepted maximum 20% limit. The presented program correctly predicts the time-concentration curve of an intravenous contrast medium injection and, consequently, allows an individually tailored approach of CT examinations with optimised use of the injected contrast medium volume, as long as time delay instead of ordinary differential equations are used. The presented program offers good preliminary knowledge of the time-contrast medium concentration curve after any intravenous injection, allowing adequate timing of a CT examination, required by the short scan time of present-day scanners. The injected volume of contrast medium can be tailored to the individual patient with no more contrast medium than is strictly needed.
Conditional Hyperbolic Quadrature Method of Moments for Kinetic Equations
Fox, Rodney,; Laurent, Frédérique; Vié, Aymeric
2017-01-01
The conditional quadrature method of moments (CQMOM) was introduced by Yuan and Fox [J. Comput. Phys. 230 (22), 8216–8246 (2011)] to reconstruct a velocity distribution function (VDF) from a finite set of its integer moments. The reconstructed VDF takes the form of a sum of weighted Dirac delta functions in velocity phase space, and provides a closure for the spatial flux term in the corresponding kinetic equation. The CQMOM closure for the flux leads to a weakly hyperbolic system of moment e...
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
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...... 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...... by the algorithm can be influenced in order to assign the desired type of rate law to each reaction. This algorithm is implemented in the software package SBMLsqueezer 2. In addition, this program contains an integrated connection to the kinetics database SABIO-RK to obtain experimentally-derived rate laws when...
Nonequilibrium Statistical Operator Method and Generalized Kinetic Equations
Kuzemsky, A. L.
2018-01-01
We consider some principal problems of nonequilibrium statistical thermodynamics in the framework of the Zubarev nonequilibrium statistical operator approach. We present a brief comparative analysis of some approaches to describing irreversible processes based on the concept of nonequilibrium Gibbs ensembles and their applicability to describing nonequilibrium processes. We discuss the derivation of generalized kinetic equations for a system in a heat bath. We obtain and analyze a damped Schrödinger-type equation for a dynamical system in a heat bath. We study the dynamical behavior of a particle in a medium taking the dissipation effects into account. We consider the scattering problem for neutrons in a nonequilibrium medium and derive a generalized Van Hove formula. We show that the nonequilibrium statistical operator method is an effective, convenient tool for describing irreversible processes in condensed matter.
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 models and parameters estimation study of biomass and ...
African Journals Online (AJOL)
The growth kinetics and modeling of ethanol production from inulin by Pichia caribbica (KC977491) were studied in a batch system. Unstructured models were proposed using the logistic equation for growth, the Luedeking-Piret equation for ethanol production and modified Leudeking-Piret model for substrate consumption.
Kinetic models and parameters estimation study of biomass and ...
African Journals Online (AJOL)
compaq
2017-01-11
Jan 11, 2017 ... The growth kinetics and modeling of ethanol production from inulin by Pichia caribbica (KC977491) were studied in a batch system. Unstructured models were proposed using the logistic equation for growth, the Luedeking-Piret equation for ethanol production and modified Leudeking-Piret model for.
Kinetic models of cell growth, substrate utilization and bio ...
African Journals Online (AJOL)
Bio-decolorization kinetic studies of distillery effluent in a batch culture were conducted using Aspergillus fumigatus. A simple model was proposed using the Logistic Equation for the growth, Leudeking-Piret kinetics for bio-decolorization, and also for substrate utilization. The proposed models appeared to provide a suitable ...
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.)
Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach
International Nuclear Information System (INIS)
Shushin, A I
2005-01-01
Anomalous specific features of the kinetics of subdiffusion-assisted bimolecular reactions (time-dependence, dependence on parameters of systems, etc) are analysed in detail with the use of the non-Markovian stochastic Liouville equation (SLE), which has been recently derived within the continuous-time random-walk (CTRW) approach. In the CTRW approach, subdiffusive motion of particles is modelled by jumps whose onset probability distribution function is of a long-tailed form. The non-Markovian SLE allows for rigorous describing of some peculiarities of these reactions; for example, very slow long-time behaviour of the kinetics, non-analytical dependence of the reaction rate on the reactivity of particles, strong manifestation of fluctuation kinetics showing itself in very slowly decreasing behaviour of the kinetics at very long times, etc
Kinetics of subdiffusion-assisted reactions: non-Markovian stochastic Liouville equation approach
Energy Technology Data Exchange (ETDEWEB)
Shushin, A I [Institute of Chemical Physics, Russian Academy of Sciences, 117977, GSP-1, Kosygin str. 4, Moscow (Russian Federation)
2005-01-01
Anomalous specific features of the kinetics of subdiffusion-assisted bimolecular reactions (time-dependence, dependence on parameters of systems, etc) are analysed in detail with the use of the non-Markovian stochastic Liouville equation (SLE), which has been recently derived within the continuous-time random-walk (CTRW) approach. In the CTRW approach, subdiffusive motion of particles is modelled by jumps whose onset probability distribution function is of a long-tailed form. The non-Markovian SLE allows for rigorous describing of some peculiarities of these reactions; for example, very slow long-time behaviour of the kinetics, non-analytical dependence of the reaction rate on the reactivity of particles, strong manifestation of fluctuation kinetics showing itself in very slowly decreasing behaviour of the kinetics at very long times, etc.
Balance of liquid-phase turbulence kinetic energy equation for bubble-train flow
International Nuclear Information System (INIS)
Ilic, Milica; Woerner, Martin; Cacuci, Dan Gabriel
2004-01-01
In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k-ε and the two-phase k-l model is evaluated. (author)
Non-relativistic and relativistic quantum kinetic equations in nuclear physics.
Botermans, Wilhelmus Martinus Maria
1989-01-01
In this thesis, we discussed the derivation of quantum kinetic equations appropriate for applications in nuclear physics, both in a non-relativistic and in a relativistic context. In each case we obtained a kinetic equation together with an equation for the effective interaction. The latter serves
Cabrales, Luis E Bergues; Nava, Juan J Godina; Aguilera, Andrés Ramírez; Joa, Javier A González; Ciria, Héctor M Camué; González, Maraelys Morales; Salas, Miriam Fariñas; Jarque, Manuel Verdecia; González, Tamara Rubio; Mateus, Miguel A O'Farril; Brooks, Soraida C Acosta; Palencia, Fabiola Suárez; Zamora, Lisset Ortiz; Quevedo, María C Céspedes; Seringe, Sarah Edward; Cuitié, Vladimir Crombet; Cabrales, Idelisa Bergues; González, Gustavo Sierra
2010-10-28
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. 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. 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. 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.
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
Directory of Open Access Journals (Sweden)
S. I. Badulin
2017-06-01
Full Text Available 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.
Differential equation methods for simulation of GFP kinetics in non-steady state experiments.
Phair, Robert D
2018-03-15
Genetically encoded fluorescent proteins, combined with fluorescence microscopy, are widely used in cell biology to collect kinetic data on intracellular trafficking. Methods for extraction of quantitative information from these data are based on the mathematics of diffusion and tracer kinetics. Current methods, although useful and powerful, depend on the assumption that the cellular system being studied is in a steady state, that is, the assumption that all the molecular concentrations and fluxes are constant for the duration of the experiment. Here, we derive new tracer kinetic analytical methods for non-steady state biological systems by constructing mechanistic nonlinear differential equation models of the underlying cell biological processes and linking them to a separate set of differential equations governing the kinetics of the fluorescent tracer. Linking the two sets of equations is based on a new application of the fundamental tracer principle of indistinguishability and, unlike current methods, supports correct dependence of tracer kinetics on cellular dynamics. This approach thus provides a general mathematical framework for applications of GFP fluorescence microscopy (including photobleaching [FRAP, FLIP] and photoactivation to frequently encountered experimental protocols involving physiological or pharmacological perturbations (e.g., growth factors, neurotransmitters, acute knockouts, inhibitors, hormones, cytokines, and metabolites) that initiate mechanistically informative intracellular transients. When a new steady state is achieved, these methods automatically reduce to classical steady state tracer kinetic analysis. © 2018 Phair. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).
International Nuclear Information System (INIS)
Kantorovich, L.N.; Fogel, G.M.; Gotlib, V.I.
1990-01-01
Thermoluminescence kinetics is discussed within the framework of a band model containing an arbitrary number of types of recombination and trapping centres at an arbitrary correlation of all centre parameters. It is shown that the initial system of kinetic equations is reduced to an equivalent system consisting of two integro-differential equations which permit one to perform an accurate generalisation, in the case of a continuous centre distribution, to their parameters for the description of irradiation and thermoluminescence, taking into account charge carrier redistribution to both types of centre. In addition, if only one electron (hole) channel is taken into account, only one integro-differential equation is obtained. On the basis of this equation a precise algebraic equation is obtained for calculation of the area of an arbitrary part of the thermoluminescence curve (TLC), consisting of one or several peaks, which slightly overlap with other peaks. It is shown that at doses which are less than the saturation dose, when the centres are not completely filled by the charge carriers, the dose dependences of such a part of the TLC may have a non-linear character at a simultaneous linear dependence of the area of the whole TLC. At doses which are greater than the saturation dose, the dose dependences of the area of the whole TLC, as well as of its separate parts, undergo breaks at the saturation doses. (author)
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.
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
A Numerical Method for Kinetic Semiconductor Equations in the Drift Diffusion limit
Klar, Axel
1997-01-01
An asymptotic-induced scheme for kinetic semiconductor equations with the diffusion scaling is developed. The scheme is based on the asymptotic analysis of the kinetic semiconductor equation. It works uniformly for all ranges of mean free paths. The velocity discretization is done using quadrature points equivalent to a moment expansion method. Numerical results for different physical situations are presented.
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
Solution of initial value problem of gyro-kinetic equation
International Nuclear Information System (INIS)
Yamagishi, Tomejiro
1996-03-01
Applying the Laplace transform technique, the initial value problem of gyro-kinetic equation is solved for the electrostatic ion temperature gradient instability situation in slab and toroidal systems. The transformed perturbed scalar potential, when evaluated on the real frequency axis, tends to small as the growth rate increases, and shows a singularity only at the marginal stability state. The time dependent solution for perturbed scalar potential is expressed in terms of the discrete mode and the continuum contribution. At the marginal stability state, the discrete eigenvalue attains the continuous eigenvalue spectrum. For the subcritical state the discrete eigenvalue moves into the next Riemann surface and tends to a damping mode, which has been numerically examined making use of the analytically continued dispersion relation. The time-dependent perturbed distribution is expressed in terms of the discrete mode, the velocity dependent beam mode, and the continuum contribution. Some characteristics of the discrete and continuum contribution are examined, and application to anomalous transport theory is suggested. (author)
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
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.
On a closed form solution of the point kinetics equations with reactivity feedback of temperature
International Nuclear Information System (INIS)
Silva, Jeronimo J.A.; Vilhena, Marco T.M.B.; Petersen, Claudio Z.; Bodmann, Bardo E.J.; Alvim, Antonio C.M.
2011-01-01
An analytical solution of the point kinetics equations to calculate reactivity as a function of time by the Decomposition method has recently appeared in the literature. In this paper, we go one step forward, by considering the neutron point kinetics equations together with temperature feedback effects. To accomplish that, we extended the point kinetics by a temperature perturbation, obtaining a second order nonlinear ordinary differential equation. This equation is then solved by the Decomposition Method, that is, by expanding the neutron density in a series and the nonlinear terms into Adomian Polynomials. Substituting these expansions into the nonlinear ordinary equation, we construct a recursive set of linear problems that can be solved by the methodology previously mentioned for the point kinetics equation. We also report on numerical simulations and comparisons against literature results. (author)
Comment on the Berkeley kinetic network model
Doeksen, D.K.; Jongschaap, R.J.J.; Kamphuis, H.
1985-01-01
A kinetic model for the rheological behavior of polymeric systems, i.e. the Berkeley kinetic network model, is compared with a generalized transient-network model. It turns out that the Berkeley kinetic network model fits quite well in the framework of the transient-network model. From the point of
Development of simple kinetic models and parameter estimation for ...
African Journals Online (AJOL)
PANCHIGA
2016-09-28
Sep 28, 2016 ... by methanol. In this study, the unstructured models based on growth kinetic equation, fed-batch mass balance and constancy of cell and protein yields were developed and constructed following the substrates, glycerol and methanol. The growth model on glycerol is mostly published while the growth model ...
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
Quantum kinetic Heisenberg models: a unique dynamics
International Nuclear Information System (INIS)
Timonen, J.; Pilling, D.J.; Bullough, R.K.
1986-01-01
We suggest that the dynamics Glauber embodied in his kinetic Ising model can be introduced similarly and in an apparently unique way, into the quantum statistical mechanics of the quantum-integrable models like the Heisenberg, sine-Gordon and Massive Thirring models. The latter may suggest an extension of the theory to unique kinetic Ising models in two dimensions. The kinetic repulsive bose gas which is studied in detail in the steady state seems to be a solvable kinetic model. (author)
Accelerated procedure to solve kinetic equation for neutral atoms in a hot plasma
Tokar, Mikhail Z.
2017-12-01
The recombination of plasma charged components, electrons and ions of hydrogen isotopes, on the wall of a fusion reactor is a source of neutral molecules and atoms, recycling back into the plasma volume. Here neutral species participate, in particular, in charge-exchange (c-x) collisions with the plasma ions and, as a result, atoms of high energies with chaotically directed velocities are generated. Some fraction of these hot atoms hit the wall. Statistical Monte Carlo methods normally used to model c-x atoms are too time consuming for reasonably small level of accident errors and extensive parameter studies are problematic. By applying pass method to evaluate integrals from functions, including the ion velocity distribution, an iteration approach to solve one-dimensional kinetic equation [1], being alternative to Monte Carlo procedure, has been tremendously accelerated, at least by a factor of 30-50 [2]. Here this approach is developed further to solve the 2-D kinetic equation, applied to model the transport of c-x atoms in the vicinity of an opening in the wall, e.g., the entrance of the duct guiding to a diagnostic installation. This is necessary to determine firmly the energy spectrum of c-x atoms penetrating into the duct and to assess the erosion of the installation there. The results of kinetic modeling are compared with those obtained with the diffusion description for c-x atoms, being strictly relevant under plasma conditions of low temperature and high density, where the mean free path length between c-x collisions is much smaller than that till the atom ionization by electrons. It is demonstrated that the previous calculations [3], done with the diffusion approximation for c-x atoms, overestimate the erosion rate of Mo mirrors in a reactor by a factor of 3 compared to the result of the present kinetic study.
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.
Solving many-body Schrödinger equations with kinetic energy partition method
Chen, Yu-Hsin; Chao, Sheng D.
2018-01-01
We present a general formulation of our previously developed kinetic energy partition (KEP) method for solving many-bodySchrödinger equations. In atomic physics, as well as in general molecular and solid state physics, solving many-electronSchrödinger equations is a very challenging task, often called Dirac's challenge. The central problem is how to properly handle the electron-electron Coulomb repulsion interactions. Using the KEP solution scheme, in addition to dividing the kinetic energy into partial terms, the electron-electron Coulomb interaction is also separated into parts to be associated with a "negative mass" kinetic energy term. Therefore, the full Hamiltonian can be expressed as a simple sum of subsystem Hamiltonians, each representing an effective one-body problem. Using a Hartree-like product in constructing the wave-function, we achieve fast convergence in the calculations of the ground state energies. First, the model Moshinsky atoms are used to illustrate the solution procedure. We then apply this new KEP method to harmonium atoms and obtain precise energies with an error less than 5% using only two basis functions from each subsystem. It is thus very promising that this methodology, when further extended, can be useful for general many-body systems.
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.
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
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.
A kinetic equation for linear stable fractional motion with applications to space plasma physics
Energy Technology Data Exchange (ETDEWEB)
Watkins, Nicholas W [British Antarctic Survey, Cambridge, UK; Credgington, Daniel [British Antarctic Survey, Cambridge, UK; Sanchez, Raul [ORNL; Rosenberg, SJ [British Antarctic Survey, Cambridge, UK; Chapman, Sandra C [University of Warwick, UK
2009-01-01
Levy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm) is a model process of this type, combining {alpha}-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk (CTRW), with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst 'sizes' and 'durations' in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Bodmann, Bardo E.J.; Alvim, Antonio Carlos Marques
2011-01-01
The authors solved analytically the neutron kinetic equations in a homogeneous slab, assuming the multi group energy model and six delayed neutron precursor groups by the Generalized Integral Laplace Transform Technique (GILTT) for a multi-layered slab. To this end, averaged values for the nuclear parameters in the multi-layered slab are used and the solution is constructed following the idea of Adomian's decomposition method upon reducing the heterogeneous problem to a set of recursive problems with constant parameters in the multi-layered slab. More specifically, the corrections that render the initially homogeneous problem into a heterogeneous one are plugged into the equation as successive source terms. To the best of our knowledge this sort of solution is novel and not found in literature. We further present some numerical simulations. (author)
Ising models and soliton equations
International Nuclear Information System (INIS)
Perk, J.H.H.; Au-Yang, H.
1985-01-01
Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained
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.
Fluid models for kinetic effects in toroidal plasmas
International Nuclear Information System (INIS)
Smolyakov, A.I.; Hirose, A.; Yagi, M.; Callen, J.D.
1995-01-01
Fluid models for toroidal plasma are considered paying particular attention to the effects of particle motion along the equilibrium magnetic field. It is shown that the basic fluid equations can be obtained either as moments of the drift-kinetic equation, or from the standard fluid equations by expanding them in 1/B small parameter. It is shown that the collisionless gyroviscosity accounts for the effects of the particle magnetic drift in the parallel component of the momentum balance equation. Simple truncated model of the plasma response for arbitrary ω D (magnetic drift frequency) and k parallel V t (parallel transit frequency) is proposed. In the absence of resonances, which can be inhibited by the particle magnetic drift, this model recovers the exact kinetic results with satisfactory accuracy. In general case, the kinetic closure for the effects of the particle motion along the magnetic field is suggested in terms of the parallel viscosity and the heat flux. They are directly calculated from the linear drift-kinetic equation. Simplified expressions in the different asymptotic limits are derived
Fully implicit kinetic modelling of collisional plasmas
International Nuclear Information System (INIS)
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
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...
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.
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....
International Nuclear Information System (INIS)
Nahla, Abdallah A.
2011-01-01
Highlights: → An efficient technique for the nonlinear reactor kinetics equations is presented. → This method is based on Backward Euler or Crank Nicholson and fundamental matrix. → Stability of efficient technique is defined and discussed. → This method is applied to point kinetics equations of six-groups of delayed neutrons. → Step, ramp, sinusoidal and temperature feedback reactivities are discussed. - Abstract: The point reactor kinetics equations of multi-group of delayed neutrons in the presence Newtonian temperature feedback effects are a system of stiff nonlinear ordinary differential equations which have not any exact analytical solution. The efficient technique for this nonlinear system is based on changing this nonlinear system to a linear system by the predicted value of reactivity and solving this linear system using the fundamental matrix of the homogenous linear differential equations. The nonlinear point reactor kinetics equations are rewritten in the matrix form. The solution of this matrix form is introduced. This solution contains the exponential function of a variable coefficient matrix. This coefficient matrix contains the unknown variable, reactivity. The predicted values of reactivity in the explicit form are determined replacing the exponential function of the coefficient matrix by two kinds, Backward Euler and Crank Nicholson, of the rational approximations. The nonlinear point kinetics equations changed to a linear system of the homogenous differential equations. The fundamental matrix of this linear system is calculated using the eigenvalues and the corresponding eigenvectors of the coefficient matrix. Stability of the efficient technique is defined and discussed. The efficient technique is applied to the point kinetics equations of six-groups of delayed neutrons with step, ramp, sinusoidal and the temperature feedback reactivities. The results of these efficient techniques are compared with the traditional methods.
Development of simple kinetic models and parameter estimation for ...
African Journals Online (AJOL)
In order to describe and predict the growth and expression of recombinant proteins by using a genetically modified Pichia pastoris, we developed a number of unstructured models based on growth kinetic equation, fed-batch mass balance and the assumptions of constant cell and protein yields. The growth of P. pastoris on ...
Interactive differential equations modeling program
International Nuclear Information System (INIS)
Rust, B.W.; Mankin, J.B.
1976-01-01
Due to the recent emphasis on mathematical modeling, many ecologists are using mathematics and computers more than ever, and engineers, mathematicians and physical scientists are now included in ecological projects. However, the individual ecologist, with intuitive knowledge of the system, still requires the means to critically examine and adjust system models. An interactive program was developed with the primary goal of allowing an ecologist with minimal experience in either mathematics or computers to develop a system model. It has also been used successfully by systems ecologists, engineers, and mathematicians. This program was written in FORTRAN for the DEC PDP-10, a remote terminal system at Oak Ridge National Laboratory. However, with relatively minor modifications, it can be implemented on any remote terminal system with a FORTRAN IV compiler, or equivalent. This program may be used to simulate any phenomenon which can be described as a system of ordinary differential equations. The program allows the user to interactively change system parameters and/or initial conditions, to interactively select a set of variables to be plotted, and to model discontinuities in the state variables and/or their derivatives. One of the most useful features to the non-computer specialist is the ability to interactively address the system parameters by name and to interactively adjust their values between simulations. These and other features are described in greater detail
International Nuclear Information System (INIS)
Carver, M.B.; Baudouin, A.P.
1976-01-01
The algorithm due to Gear is recognized as one of the best available integration routines, permitting large time steps while maintaining acceptable error tolerance and stability. The method is implicit, requiring a matrix solution involving the Jacobian. This has hitherto required excessive storage for large equation systems (>100 equations). The algorithm has been used for the solution of small systems involving neutron kinetics, and encouraging results motivated an investigation of the application of sparse matrix techniques to the matrix manipulation within the algorithm. The resulting routines handle large systems of equations very efficiently. Part 1 of this paper describes these new routines, and Part 2 discusses their application to neutron kinetics. (author)
International Nuclear Information System (INIS)
Tashakor, S.; Jahanfarnia, G.; Hashemi-Tilehnoee, M.
2010-01-01
Point reactor kinetics equations are solved numerically using one group of delayed neutrons and with fuel burn-up and temperature feedback included. To calculate the fraction of one-group delayed neutrons, a group of differential equations are solved by an implicit time method. Using point reactor kinetics equations, changes in mean neutrons density, temperature, and reactivity are calculated in different times during the reactor operation. The variation of reactivity, temperature, and maximum power with time are compared with the predictions by other methods.
Punshon-Smith, Samuel; Smith, Scott
2018-02-01
This article studies the Cauchy problem for the Boltzmann equation with stochastic kinetic transport. Under a cut-off assumption on the collision kernel and a coloring hypothesis for the noise coefficients, we prove the global existence of renormalized (in the sense of DiPerna/Lions) martingale solutions to the Boltzmann equation for large initial data with finite mass, energy, and entropy. Our analysis includes a detailed study of weak martingale solutions to a class of linear stochastic kinetic equations. This study includes a criterion for renormalization, the weak closedness of the solution set, and tightness of velocity averages in {{L}1}.
Derivation of a new kinetic equation. Application to the determination of viscosity coefficients
International Nuclear Information System (INIS)
Frey, Jean-Jacques
1970-01-01
By introducing a new hypothesis concerning the closure in the B.B.G.K.Y. equation system, an approximate expression for f 12 is obtained. By inserting this expression in the first B.B.G.K.Y. equation, a new kinetic equation results. It is verified that this equation does in fact give the fluid mechanics equations, and new expressions for the shear and expansion viscosity coefficients are obtained. The numerical calculations which have been carried out show that very satisfactory agreement exists with experimental results. (author) [fr
Comparison of kinetic model for biogas production from corn cob
Shitophyta, L. M.; Maryudi
2018-04-01
Energy demand increases every day, while the energy source especially fossil energy depletes increasingly. One of the solutions to overcome the energy depletion is to provide renewable energies such as biogas. Biogas can be generated by corn cob and food waste. In this study, biogas production was carried out by solid-state anaerobic digestion. The steps of biogas production were the preparation of feedstock, the solid-state anaerobic digestion, and the measurement of biogas volume. This study was conducted on TS content of 20%, 22%, and 24%. The aim of this research was to compare kinetic models of biogas production from corn cob and food waste as a co-digestion using the linear, exponential equation, and first-kinetic models. The result showed that the exponential equation had a better correlation than the linear equation on the ascending graph of biogas production. On the contrary, the linear equation had a better correlation than the exponential equation on the descending graph of biogas production. The correlation values on the first-kinetic model had the smallest value compared to the linear and exponential models.
Kinetics and hybrid kinetic-fluid models for nonequilibrium gas and plasmas
International Nuclear Information System (INIS)
Crouseilles, N.
2004-12-01
For a few decades, the application of the physics of plasmas has appeared in different fields like laser-matter interaction, astrophysics or thermonuclear fusion. In this thesis, we are interested in the modeling and the numerical study of nonequilibrium gas and plasmas. To describe such systems, two ways are usually used: the fluid description and the kinetic description. When we study a nonequilibrium system, fluid models are not sufficient and a kinetic description have to be used. However, solving a kinetic model requires the discretization of a large number of variables, which is quite expensive from a numerical point of view. The aim of this work is to propose a hybrid kinetic-fluid model thanks to a domain decomposition method in the velocity space. The derivation of the hybrid model is done in two different contexts: the rarefied gas context and the more complicated plasmas context. The derivation partly relies on Levermore's entropy minimization approach. The so-obtained model is then discretized and validated on various numerical test cases. In a second stage, a numerical study of a fully kinetic model is presented. A collisional plasma constituted of electrons and ions is considered through the Vlasov-Poisson-Fokker-Planck-Landau equation. Then, a numerical scheme which preserves total mass and total energy is presented. This discretization permits in particular a numerical study of the Landau damping. (author)
Kinetics model for lutate dosimetry
International Nuclear Information System (INIS)
Lima, M.F.; Mesquita, C.H.
2013-01-01
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®. 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
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......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...... 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 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...
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 V max and K m 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 V max , K m and K s 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].
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].
Stability of generalized Runge-Kutta methods for stiff kinetics coupled differential equations
International Nuclear Information System (INIS)
Aboanber, A E
2006-01-01
A stability and efficiency improved class of generalized Runge-Kutta methods of order 4 are developed for the numerical solution of stiff system kinetics equations for linear and/or nonlinear coupled differential equations. The determination of the coefficients required by the method is precisely obtained from the so-called equations of condition which in turn are derived by an approach based on Butcher series. Since the equations of condition are fewer in number, free parameters can be chosen for optimizing any desired feature of the process. A further related coefficient set with different values of these parameters and the region of absolute stability of the method have been introduced. In addition, the A(α) stability properties of the method are investigated. Implementing the method in a personal computer estimated the accuracy and speed of calculations and verified the good performances of the proposed new schemes for several sample problems of the stiff system point kinetics equations with reactivity feedback
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.
An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons
International Nuclear Information System (INIS)
Yamoah, S.; Akaho, E.H.K.; Nyarko, B.J.B.
2013-01-01
Highlights: ► Analytical solution is proposed to solve the point reactor kinetics equations (PRKE). ► The method is based on formulating a coefficient matrix of the PRKE. ► The method was applied to solve the PRKE for six groups of delayed neutrons. ► Results shows good agreement with other traditional methods in literature. ► The method is accurate and efficient for solving the point reactor kinetics equations. - Abstract: 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, an accurate analytical solution of point reactor kinetics equations with multi-group of delayed neutrons for specified reactivity changes is proposed to calculate the change in neutron density. The method is based on formulating a coefficient matrix of the homogenous differential equations of the point reactor kinetics equations and calculating the eigenvalues and the corresponding eigenvectors of the coefficient matrix. A small time interval is chosen within which reactivity relatively stays constant. The analytical method was applied to solve the point reactor kinetics equations with six-groups delayed neutrons for a representative thermal reactor. The problems of step, ramp and temperature feedback reactivities are computed and the results compared with other traditional methods. The comparison shows that the method presented in this study is accurate and efficient for solving the point reactor kinetics equations of multi-group of delayed neutrons
Wen Zhu; Junsheng Liu; Meng Li
2014-01-01
A series of zwitterionic hybrid membranes were prepared via the ring opening of 1,3-propanesultone with the amine groups in the chains of TMSPEDA and a subsequent sol-gel process. Their kinetic models for strontium removal were investigated using three two-parameter kinetic equations (i.e., Lagergren pseudo-first order, pseudo-second order, and Elovich models). Adsorption mechanism was evaluated using intraparticle diffusion model, diffusion-chemisorption model, and Boyd equation. It was foun...
A Gas-kinetic Discontinuous Galerkin Method for Viscous Flow Equations
International Nuclear Information System (INIS)
Liu, Hongwei; Xu, Kun
2007-01-01
This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for viscous flow computation. The construction of the RKDG method is based on a gas-kinetic formulation, which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at the cell interface through a simple hybrid gas distribution function. Due to the intrinsic connection between the gaskinetic BGK model and the Navier-Stokes equations, the Navier-Stokes flux is automatically obtained by the present method. Numerical examples for both one dimensional (10) and two dimensional(20) compressible viscous flows are presented to demonstrate the accuracy and shock capturing capability of the current RKDG method
Modelling conjugation with stochastic differential equations
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik
2010-01-01
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......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...
Comparative analysis among several methods used to solve the point kinetic equations
International Nuclear Information System (INIS)
Nunes, Anderson L.; Goncalves, Alessandro da C.; Martinez, Aquilino S.; Silva, Fernando Carvalho da
2007-01-01
The main objective of this work consists on the methodology development for comparison of several methods for the kinetics equations points solution. The evaluated methods are: the finite differences method, the stiffness confinement method, improved stiffness confinement method and the piecewise constant approximations method. These methods were implemented and compared through a systematic analysis that consists basically of confronting which one of the methods consume smaller computational time with higher precision. It was calculated the relative which function is to combine both criteria in order to reach the goal. Through the analyses of the performance factor it is possible to choose the best method for the solution of point kinetics equations. (author)
Comparative analysis among several methods used to solve the point kinetic equations
Energy Technology Data Exchange (ETDEWEB)
Nunes, Anderson L.; Goncalves, Alessandro da C.; Martinez, Aquilino S.; Silva, Fernando Carvalho da [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear; E-mails: alupo@if.ufrj.br; agoncalves@con.ufrj.br; aquilino@lmp.ufrj.br; fernando@con.ufrj.br
2007-07-01
The main objective of this work consists on the methodology development for comparison of several methods for the kinetics equations points solution. The evaluated methods are: the finite differences method, the stiffness confinement method, improved stiffness confinement method and the piecewise constant approximations method. These methods were implemented and compared through a systematic analysis that consists basically of confronting which one of the methods consume smaller computational time with higher precision. It was calculated the relative which function is to combine both criteria in order to reach the goal. Through the analyses of the performance factor it is possible to choose the best method for the solution of point kinetics equations. (author)
Kinetic computer modeling of microwave surface-wave plasma production
International Nuclear Information System (INIS)
Ganachev, Ivan P.
2004-01-01
Kinetic computer plasma modeling occupies an intermediate position between the time consuming rigorous particle dynamic simulation and the fast but rather rough cold- or warm-plasma fluid models. The present paper reviews the kinetic modeling of microwave surface-wave discharges with accent on recent kinetic self-consistent models, where the external input parameters are reduced to the necessary minimum (frequency and intensity of the applied microwave field and pressure and geometry of the discharge vessel). The presentation is limited to low pressures, so that Boltzmann equation is solved in non-local approximation and collisional electron heating is neglected. The numerical results reproduce correctly the bi-Maxwellian electron energy distribution functions observed experimentally. (author)
Application of flexible model in neutron dynamics equations
International Nuclear Information System (INIS)
Liu Cheng; Zhao Fuyu; Fu Xiangang
2009-01-01
Big errors will occur in the modeling by multimode methodology when the available core physical parameter sets are insufficient. In this paper, the fuzzy logic membership function is introduced to figure out the values of these parameters on any point of lifetime through limited several sets of values, and thus to obtain the neutron dynamics equations on any point of lifetime. In order to overcome the effect of subjectivity in the membership function selection on the parameter calculation, quadratic optimization is carried out to the membership function by genetic algorithm, to result in a more accurate neutron kinetics equation on any point of lifetime. (authors)
Numerical solution of multi groups point kinetic equations by simulink toolbox of Matlab software
International Nuclear Information System (INIS)
Hadad, K.; Mohamadi, A.; Sabet, H.; Ayobian, N.; Khani, M.
2004-01-01
The simulink toolbox of Matlab Software was employed to solve the point kinetics equation with six group delayed neutrons. The method of Adams-Bash ford showed a good convergence in solving the system of simultaneous equations and the obtained results showed good agreements with other numerical schemes. The flexibility of the package in changing the system parameters and the user friendly interface makes this approach a reliable educational package in revealing the affects of reactivity changes on power incursions
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.
Second-order accurate kinetic schemes for the ultra-relativistic Euler equations
International Nuclear Information System (INIS)
Kunik, Matthias; Qamar, Shamsul; Warnecke, Gerald
2003-01-01
A second-order accurate kinetic scheme for the numerical solution of the relativistic Euler equations is presented. These equations describe the flow of a perfect fluid in terms of the particle density n, the spatial part of the four-velocity u and the pressure p. The kinetic scheme, is based on the well-known fact that the relativistic Euler equations are the moments of the relativistic Boltzmann equation of the kinetic theory of gases when the distribution function is a relativistic Maxwellian. The kinetic scheme consists of two phases, the convection phase (free-flight) and collision phase. The velocity distribution function at the end of the free-flight is the solution of the collisionless transport equation. The collision phase instantaneously relaxes the distribution to the local Maxwellian distribution. The fluid dynamic variables of density, velocity, and internal energy are obtained as moments of the velocity distribution function at the end of the free-flight phase. The scheme presented here is an explicit method and unconditionally stable. The conservation laws of mass, momentum and energy as well as the entropy inequality are everywhere exactly satisfied by the solution of the kinetic scheme. The scheme also satisfies positivity and L 1 -stability. The scheme can be easily made into a total variation diminishing method for the distribution function through a suitable choice of the interpolation strategy. In the numerical case studies the results obtained from the first- and second-order kinetic schemes are compared with the first- and second-order upwind and central schemes. We also calculate the experimental order of convergence and numerical L 1 -stability of the scheme for smooth initial data
Zhang, Chuang; Guo, Zhaoli; Chen, Songze
2017-12-01
An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.
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. 2009 Elsevier Ltd. All rights reserved.
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.
A mathematical model for iodine kinetics
International Nuclear Information System (INIS)
Silva, E.A.T. da.
1976-01-01
A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt
Kinetic model for polyhydroxybutyrate (PHB) production by ...
African Journals Online (AJOL)
USER
2010-05-24
May 24, 2010 ... Key words: Kinetic model, polyhydroxyalkanoates, Hydrogenophaga pseudoflava, logistic model, Monod, biopolymer. INTRODUCTION. Polyhydroxybutyrate (PHB) is a biopolymer that can be used as a biodegradable thermoplastic material for waste management strategies and biocompatibility in medical.
Matrix solution of point kinetic equation in a fluidized bed nuclear reactor
International Nuclear Information System (INIS)
Vilhena, M.T. de; Claeyssen, J.R.
1990-01-01
The purpose of this work is to solve the point kinetic equation for a Fluidized Bed Nuclear Reactor by matrix series formulation, showing it is a simple and accurate method, observing this is a scale problem of Stiff type for small time. (author)
Cohen, J.S.; Suttorp, L.G.
1982-01-01
The generating functions for the collision brackets associated with two alternative convergent kinetic equations are derived for small values of the plasma parameter. It is shown that the first few terms in the asymptotic expansions of these generating functions are identical. Consequently, both
Sivasamy, Pavithra; Ganapathy, Jansi Rani Palaniyandi; Thinakaran, Iswarya; Lakshmanan, Rajendran
2016-01-01
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 expression...
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.
Study of crystallization kinetics of peek thermoplastics using Nakamura equation
Chalid, Mochamad; Muhammad Joshua Y., B.; Fikri, Arbi Irsyad; Gregory, Noel; Priadi, Dedi; Fatriansyah, Jaka Fajar
2018-04-01
We have simulated the time evolution of relative crystallization of PEEK at various cooling rates (10, 15, 20 °C/min) and made comparison with the experiments. The simulation was conducted using Nakamura model which is a modified Avrami model. The model is a 1 cm radius of circle with the cooling plate which was placed in the upper part of the circle. The cooling plate temperature was varied in order to obtain particular cooling rates. The measurement point is located near upper boundary in order to minimize the heat transfer effect. The general trend of time evolution of crystallization was well captured although some discrepancies occured. These discrepancies may be attributed to the heat transfer effect and secondary crystallization.
Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena
International Nuclear Information System (INIS)
Lin Chuan-Dong; Li Ying-Jun; Xu Ai-Guo; Zhang Guang-Cai
2014-01-01
A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier—Stokes equations, including contribution of chemical reaction, via the Chapman—Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
On the exact solution for the multi-group kinetic neutron diffusion equation in a rectangle
International Nuclear Information System (INIS)
Petersen, C.Z.; Vilhena, M.T.M.B. de; Bodmann, B.E.J.
2011-01-01
In this work we consider the two-group bi-dimensional kinetic neutron diffusion equation. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursor yields are expanded in a truncated double series in terms of eigenfunctions that, upon insertion into the kinetic equation and upon taking moments, results in a first order linear differential matrix equation with source terms. We split the matrix appearing in the transformed problem into a sum of a diagonal matrix plus the matrix containing the remaining terms and recast the transformed problem into a form that can be solved in the spirit of Adomian's recursive decomposition formalism. Convergence of the solution is guaranteed by the Cardinal Interpolation Theorem. We give numerical simulations and comparisons with available results in the literature. (author)
Differential Equations Models to Study Quorum Sensing.
Pérez-Velázquez, Judith; Hense, Burkhard A
2018-01-01
Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.
Thermodynamically Feasible Kinetic Models of Reaction Networks
Ederer, Michael; Gilles, Ernst Dieter
2007-01-01
The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts th...
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...
Modeling animal movements using stochastic differential equations
Haiganoush K. Preisler; Alan A. Ager; Bruce K. Johnson; John G. Kie
2004-01-01
We describe the use of bivariate stochastic differential equations (SDE) for modeling movements of 216 radiocollared female Rocky Mountain elk at the Starkey Experimental Forest and Range in northeastern Oregon. Spatially and temporally explicit vector fields were estimated using approximating difference equations and nonparametric regression techniques. Estimated...
Stochastic differential equation model to Prendiville processes
International Nuclear Information System (INIS)
Granita; Bahar, Arifah
2015-01-01
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
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.
Kinetics interpretation model of isothermal martensite reactions
International Nuclear Information System (INIS)
Guimaraes, J.R.C.
1976-01-01
It was discussed details associated to the interpretation of kinetics of martencite heterogeneous nucleation in isothermal reactions. It was proposed a model which allows compute the variation of concentration of preferencial sites nucleation with a volumetric martencite fraction [pt
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...
Janssen, A.E.M.; Sjursnes, B.J.; Vakunov, A.V.; Halling, P.J.
1999-01-01
The Ping-Pong model (incl. alcohol inhibition) is not the correct model to describe the kinetics of a lipase-catalyzed esterification reaction. The first product, water, is always present at the start of the reaction. This leads to an equation with one extra parameter. This new equation fits our
Fully Kinetic Ion Models for Magnetized Plasma Simulations
Sturdevant, Benjamin J.
This thesis focuses on the development of simulation models, based on fully resolving the gyro-motion of ions with the Lorentz force equations of motion, for studying low-frequency phenomena in well-magnetized plasma systems. Such models, known as fully kinetic ion models, offer formal simplicity over higher order gyrokinetic ion models and may provide an important validation tool or replacement for gyrokinetic ion models in applications where the gyrokinetic ordering assumptions are in question. Methods for dealing with the added difficulty of resolving the short time scales associated with the ion gyro-motion in fully kinetic ion models are explored with the use of graphics processing units (GPUs) and advanced time integration algorithms, including sub-cycling, orbit averaging and variational integrators. Theoretical work is performed to analyze the effects of the ion Bernstein modes, which are known to cause difficulties in simulations based on fully kinetic ion models. In addition, the first simulation results for the ion temperature gradient driven instability in toroidal geometry using a fully kinetic ion model are presented. Finally, during the course of this work, a method for analyzing the effects of a finite time step size and spatial grid in the delta-f approach to the particle-in-cell method was developed for the first time. This method was applied to an implicit time integration scheme and has revealed some unusual numerical properties related to the delta-f method.
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
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.
Kinetic models for irreversible processes on a lattice
International Nuclear Information System (INIS)
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
Generalized latent variable modeling multilevel, longitudinal, and structural equation models
Skrondal, Anders; Rabe-Hesketh, Sophia
2004-01-01
This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models.
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
Derivation of a reduced kinetic equation using Lie-transform techniques
International Nuclear Information System (INIS)
Brizard, A.
1991-01-01
The asymptotic elimination of fast time scales from a general kinetic equation, of the form: ∂ t f+z·∂ x f = C[f], facilitates the study of the long time behavior of its solution f(z,t). Here z describe the single-particle Hamiltonian dynamics and the operator C, which may possess nonlinear functional dependence on f, describes processes (such as discrete-particle effects, resonant wave-particle effects, or effects due to external sources) which cause changes in f as it is convectively transported along a Hamiltonian phase-space trajectory. When a fast time scale is associated with z through the dependence on a fast angle θ (whose frequency θ = Ω satisfies ε ≡ 1/Ωτ much-lt 1, where τ is a slow time scale of interest), a near-identity phase-space transformation T ε :z→Z (carried out with Lie-transform techniques) yields reduced Hamiltonian dynamical equations Z ε which are θ-independent. The corresponding transformed kinetic equation is derived. Averaging this equation over the fast angle θ yields a kinetic equation for left-angle F right-angle, the θ-averaged part of F. In general, the θ-dependence of C ε couples the kinetic equations for left-angle F right-angle and F, the θ-dependent part of F. One solves for the Fourier coefficient F l (associated with e ilθ ) as a functional of left-angle F right-angle. One obtains a reduced kinetic equation for left-angle F right-angle: d R left-angle F right-angle/dt = C R [left-angle F right-angle]. General expressions for C R are given, as well as expressions for the guiding-center and oscillation-center phase-space transformations of a linear Fokker-Planck operator. A discussion of the relationship with Mynick's work is presented
A general hybrid kinetic-fluid model for collisionless magnetic reconnection
International Nuclear Information System (INIS)
Martinell, Julio J.
2006-01-01
A general set of equations appropriate for the description of the plasma dynamics within a collisionless magnetized plasma during the process of magnetic reconnection is derived. The particular geometry considered is that of a Harris pinch with a guide field and full kinetic equations for the perturbations are found, valid within the singular layer around the reconnecting region. Ion equations take into account finite Larmor radius effects while electron dynamics is based on the gyro-averaged drift kinetic equation. A more manageable model is obtained by resorting to fluid equations for the ions and retaining electron kinetic effects. It is shown that these equations give the same results obtained from the two-fluid theory in the limit of the collisionless tearing mode for different regimes
A self-consistent kinetic modeling of a 1-D, bounded, plasma in ...
Indian Academy of Sciences (India)
Abstract. A self-consistent kinetic treatment is presented here, where the Boltzmann equation is solved for a particle ... This paper reports on the findings of a kinetic code that retains col- lisions and sources, models ..... was used in the runs reported in this paper, the source of particles is modified from the explicit source Л(Ъ).
Classical Antiferromagnetism in Kinetically Frustrated Electronic Models
Sposetti, C. N.; Bravo, B.; Trumper, A. E.; Gazza, C. J.; Manuel, L. O.
2014-05-01
We study, by means of the density matrix renormalization group, the infinite U Hubbard model—with one hole doped away from half filling—in triangular and square lattices with frustrated hoppings, which invalidate Nagaoka's theorem. We find that these kinetically frustrated models have antiferromagnetic ground states with classical local magnetization in the thermodynamic limit. We identify the mechanism of this kinetic antiferromagnetism with the release of the kinetic energy frustration, as the hole moves in the established antiferromagnetic background. This release can occur in two different ways: by a nontrivial spin Berry phase acquired by the hole, or by the effective vanishing of the hopping amplitude along the frustrating loops.
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…
A model unified field equation
International Nuclear Information System (INIS)
Perring, J.K.; Skyrme, T.H.R.
1994-01-01
The classical solutions of a unified field theory in a two-dimensional space-time are considered. This system, a model of a interacting mesons and baryons, illustrates how the particle can be built from a wave-packet of mesons and how reciprocally the meson appears as a tightly bound combination of particle and antiparticle. (author). 6 refs
Application of the fractional neutron point kinetic equation: Start-up of a nuclear reactor
International Nuclear Information System (INIS)
Polo-Labarrios, M.-A.; Espinosa-Paredes, G.
2012-01-01
Highlights: ► Neutron density behavior at reactor start up with fractional neutron point kinetics. ► There is a relaxation time associated with a rapid variation in the neutron flux. ► Physical interpretation of the fractional order is related with non-Fickian effects. ► Effect of the anomalous diffusion coefficient and the relaxation time is analyzed. ► Neutron density is related with speed and duration of the control rods lifting. - Abstract: In this paper we present the behavior of the variation of neutron density when the nuclear reactor power is increased using the fractional neutron point kinetic (FNPK) equation with a single-group of delayed neutron precursor. It is considered that there is a relaxation time associated with a rapid variation in the neutron flux and its physical interpretation of the fractional order is related with non-Fickian effects from the neutron diffusion equation point of view. We analyzed the case of increase the nuclear reactor power when reactor is cold start-up which is a process of inserting reactivity by lifting control rods discontinuously. The results show that for short time scales of the start-up the neutronic density behavior with FNPK shows sub-diffusive effects whose absorption are government by control rods velocity. For large times scale, the results shows that the classical equation of the neutron point kinetics over predicted the neutron density regarding to FNPK.
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.
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
Radhadrishnan, Krishnan
1993-01-01
A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.
Gyrofluid turbulence models with kinetic effects
Energy Technology Data Exchange (ETDEWEB)
Dorland, W.; Hammett, G.W.
1992-12-01
Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u[parallel], T[parallel], and T[perpendicular] along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived which may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau-damping model which is equivalent to a multi-pole approximation to the plasma dispersion function, extended to include finite Larmor radius effects. In particular, new dissipative, nonlinear terms are found which model the perpendicular phase-mixing of the distribution function along contours of constant electrostatic potential. These FLR phase-mixing'' terms introduce a hyperviscosity-like damping [proportional to] k[sub [perpendicular
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.
Study and discretization of kinetic models and fluid models at low Mach number
International Nuclear Information System (INIS)
Dellacherie, Stephane
2011-01-01
This thesis summarizes our work between 1995 and 2010. It concerns the analysis and the discretization of Fokker-Planck or semi-classical Boltzmann kinetic models and of Euler or Navier-Stokes fluid models at low Mach number. The studied Fokker-Planck equation models the collisions between ions and electrons in a hot plasma, and is here applied to the inertial confinement fusion. The studied semi-classical Boltzmann equations are of two types. The first one models the thermonuclear reaction between a deuterium ion and a tritium ion producing an α particle and a neutron particle, and is also in our case used to describe inertial confinement fusion. The second one (known as the Wang-Chang and Uhlenbeck equations) models the transitions between electronic quantified energy levels of uranium and iron atoms in the AVLIS isotopic separation process. The basic properties of these two Boltzmann equations are studied, and, for the Wang-Chang and Uhlenbeck equations, a kinetic-fluid coupling algorithm is proposed. This kinetic-fluid coupling algorithm incited us to study the relaxation concept for gas and immiscible fluids mixtures, and to underline connections with classical kinetic theory. Then, a diphasic low Mach number model without acoustic waves is proposed to model the deformation of the interface between two immiscible fluids induced by high heat transfers at low Mach number. In order to increase the accuracy of the results without increasing computational cost, an AMR algorithm is studied on a simplified interface deformation model. These low Mach number studies also incited us to analyse on cartesian meshes the inaccuracy at low Mach number of Godunov schemes. Finally, the LBM algorithm applied to the heat equation is justified
Non-relativistic and relativistic quantum kinetic equations in nuclear physics
International Nuclear Information System (INIS)
Botermans, W.M.M.
1989-01-01
In this thesis an attempt is made to draw up a quantummechanical tranport equation for the explicit calculation oof collision processes between two (heavy) ions, by making proper approaches of the exact equations (non-rel.: N-particles Schroedinger equation; rel.: Euler-Lagrange field equations.). An important starting point in the drag-up of the theory is the behaviour of nuclear matter in equilibrium which is determined by individual as well as collective effects. The central point in this theory is the effective interaction between two nucleons both surrounded by other nucleons. In the derivation of the tranport equations use is made of the green's function formalism as developed by Schwinger and Keldys. For the Green's function kinematic equations are drawn up and are solved by choosing a proper factorization of three- and four-particle Green's functions in terms of one- and two-particle Green's functions. The necessary boundary condition is obtained by explicitly making use of Boltzmann's assumption that colliding particles are statistically uncorrelated. Finally a transport equation is obtained in which the mean field as well as the nucleon-nucleon collisions are given by the same (medium dependent) interaction. This interaction is the non-equilibrium extension of the interaction as given in the Brueckner theory of nuclear matter. Together, kinetic equation and interaction, form a self-consistent set of equations for the case of a non-relativistic as well as for the case of a relativistic starting point. (H.W.) 148 refs.; 6 figs.; 411 schemes
Shumilin, A. V.; Kabanov, V. V.; Dediu, V. I.
2018-03-01
We derive kinetic equations for polaron hopping in organic materials that explicitly take into account the double occupation possibility and pair intersite correlations. The equations include simplified phenomenological spin dynamics and provide a self-consistent framework for the description of the bipolaron mechanism of the organic magnetoresistance. At low applied voltages, the equations can be reduced to those for an effective resistor network that generalizes the Miller-Abrahams network and includes the effect of spin relaxation on the system resistivity. Our theory discloses the close relationship between the organic magnetoresistance and the intersite correlations. Moreover, in the absence of correlations, as in an ordered system with zero Hubbard energy, the magnetoresistance vanishes.
International Nuclear Information System (INIS)
Oliveira, F.R.; Bodmann, B.E.J.; Vilhena, M.T.; Carvalho, F.
2017-01-01
Highlights: • The present work presents an exact solution to neutron spatial kinetic equation. • It is an exact solution in a heterogeneous cylinder with temporal dependence. • The solution was constructed through the separation of variables method. - Abstract: In the present work we discuss a system of partial differential equations that model neutron space-kinetics in cylindrical geometry and are defined by two sectionally homogeneous cylinder cells, mono-energetic neutrons and one group of delayed neutron precursors. The solution is determined using the technique of variable separation. The associated complete spectra with respect to each variable separation are analysed and truncated such as to allow a parameterized global solution. For the obtained solution we present some numerical results for the scalar neutron flux and its time dependence and projection on the cylinder axis z and the radial and cylinder axis projection. As a case study we consider an insertion of an absorbing medium in the upper cylinder cell. Continuity of the scalar flux at the interface between the two cylinder elements and conserved current density is explained and related to scale invariance of the partial differential equation system together with the initial and boundary conditions. Some numerical results for the scalar angular neutron flux and associated current densities are shown.
Thermodynamic and kinetic modelling: creep resistant materials
DEFF Research Database (Denmark)
Hald, John; Korcakova, L.; Danielsen, Hilmar Kjartansson
2008-01-01
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...
Transfer equations for modeling interrill erosion
Nouhou bako, Amina; Darboux, Frédéric; James, François; Lucas, Carine
2016-01-01
Numerous models are available for matter transfer along an hillslope. They are usually process-specific, requiring to use several models to simulate transfers along an hillslope. To overcome this issue, we develop a new model valid for chemical (nutrients, pollutants, dissolved carbon) and particle transfers by water. It is able to simulate both interrill and rill erosion. This new equation encompasses the previous models of Gao et al. (2004), Hairsine and Rose (1992, 1991) and Lajeunesse et ...
Langevin equations for competitive growth models.
Silveira, F A; Aarão Reis, F D A
2012-01-01
Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension ν and the nonlinear coefficient λ of the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with p according to the divergence of local height differences when p→0. The superposition of those scaling factors gives ν~p(2) for random deposition with surface relaxation (RDSR) as the CD, and ν~p, λ~p(3/2) for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability p for the latter, is also constructed. It shows linear p dependence of λ, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some p-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients. © 2012 American Physical Society
PET kinetic analysis. Compartmental model
International Nuclear Information System (INIS)
Watabe, Hiroshi; Ikoma, Yoko; Shidahara, Miho; Kimura, Yuichi; Naganawa, Mika
2006-01-01
Positron emission tomography (PET) enables not only visualization of the distribution of radiotracer, but also has ability to quantify several biomedical functions. Compartmental model is a basic idea to analyze dynamic PET data. This review describes the principle of the compartmental model and categorizes the techniques and approaches for the compartmental model according to various aspects: model design, experimental design, invasiveness, and mathematical solution. We also discussed advanced applications of the compartmental analysis with PET. (author)
Directory of Open Access Journals (Sweden)
Gladush M.G.
2015-01-01
Full Text Available We obtained the system of Maxwell-Bloch equations (MB that describe the interaction of cw laser with optically active impurity centers (particles embedded in a dielectric material. The dielectric material is considered as a continuous medium with sufficient laser detuning from its absorption lines. The model takes into account the effects associated with both the real and the imaginary part of the dielectric constant of the material. MB equations were derived within a many-particle quantum-kinetic formalism, which is based on Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY hierarchy for reduced density matrices and correlation operators of material particles and the quantized radiation field modes. It is shown that this method is beneficial to describe the effects of individual and collective behavior of the light emitters and requires no phenomenological procedures. It automatically takes into account the characteristics associated with the presence of non-resonant and resonant particles filling the space between the optical centers.
Phosphate Kinetic Models in Hemodialysis: A Systematic Review.
Laursen, Sisse H; Vestergaard, Peter; Hejlesen, Ole K
2018-01-01
Understanding phosphate kinetics in dialysis patients is important for the prevention of hyperphosphatemia and related complications. One approach to gain new insights into phosphate behavior is physiologic modeling. Various models that describe and quantify intra- and/or interdialytic phosphate kinetics have been proposed, but there is a dearth of comprehensive comparisons of the available models. The objective of this analysis was to provide a systematic review of existing published models of phosphate metabolism in the setting of maintenance hemodialysis therapy. Systematic review. Hemodialysis patients. Studies published in peer-reviewed journals in English about phosphate kinetic modeling in the setting of hemodialysis therapy. Modeling equations from specific reviewed studies. Changes in plasma phosphate or serum phosphate concentrations. Of 1,964 nonduplicate studies evaluated, 11 were included, comprising 9 different phosphate models with 1-, 2-, 3-, or 4-compartment assumptions. Between 2 and 11 model parameters were included in the models studied. Quality scores of the studies using the Newcastle-Ottawa Scale ranged from 2 to 11 (scale, 0-14). 2 studies were considered low quality, 6 were considered medium quality, and 3 were considered high quality. Only English-language studies were included. Many parameters known to influence phosphate balance are not included in existing phosphate models that do not fully reflect the physiology of phosphate metabolism in the setting of hemodialysis. Moreover, models have not been sufficiently validated for their use as a tool to simulate phosphate kinetics in hemodialysis therapy. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.
Modeling capsid kinetics assembly from the steady state distribution of multi-sizes aggregates
Energy Technology Data Exchange (ETDEWEB)
Hozé, Nathanaël; Holcman, David
2014-01-24
The kinetics of aggregation for particles of various sizes depends on their diffusive arrival and fusion at a specific nucleation site. We present here a mean-field approximation and a stochastic jump model for aggregates at equilibrium. This approach is an alternative to the classical Smoluchowski equations that do not have a close form and are not solvable in general. We analyze these mean-field equations and obtain the kinetics of a cluster formation. Our approach provides a simplified theoretical framework to study the kinetics of viral capsid formation, such as HIV from the self-assembly of the structural proteins Gag.
A MATLAB toolbox for structural kinetic modeling.
Girbig, Dorothee; Selbig, Joachim; Grimbs, Sergio
2012-10-01
Structural kinetic modeling (SKM) enables the analysis of dynamical properties of metabolic networks solely based on topological information and experimental data. Current SKM-based experiments are hampered by the time-intensive process of assigning model parameters and choosing appropriate sampling intervals for Monte-Carlo experiments. We introduce a toolbox for the automatic and efficient construction and evaluation of structural kinetic models (SK models). Quantitative and qualitative analyses of network stability properties are performed in an automated manner. We illustrate the model building and analysis process in detailed example scripts that provide toolbox implementations of previously published literature models. The source code is freely available for download at http://bioinformatics.uni-potsdam.de/projects/skm. girbig@mpimp-golm.mpg.de.
AIREK-MOD, Time Dependent Reactor Kinetics with Feedback Differential Equation
International Nuclear Information System (INIS)
Tamagnini, C.
1984-01-01
1 - Nature of physical problem solved: Solves the reactor kinetic equations with respect to time. A standard form for the reactivity behaviour has been introduced in which the reactivity is given by the sum of a polynomial, sine, cosine and exponential expansion. Tabular form is also included. The presence of feedback differential equations in which the dependence on variables different from the considered one is considered enables many heat-exchange problems to be dealt with. 2 - Method of solution: The method employed for the solution of the differential equations is the one developed by E.R. Cohen (Geneva Conference, 1958). 3 - Restrictions on the complexity of the problem: The maximum number of differential equations that can be solved simultaneously is 50. Within this limitation there may be n delayed neutron groups (n less than or equal to 25), on m other linear feedback equations (n+m less than or equal to 49). CDC 1604 version was offered by EIR (Institut Federal de Recherches en matiere de reacteurs, Switzerland)
Joint modelling rationale for chained equations
2014-01-01
Background Chained equations imputation is widely used in medical research. It uses a set of conditional models, so is more flexible than joint modelling imputation for the imputation of different types of variables (e.g. binary, ordinal or unordered categorical). However, chained equations imputation does not correspond to drawing from a joint distribution when the conditional models are incompatible. Concurrently with our work, other authors have shown the equivalence of the two imputation methods in finite samples. Methods Taking a different approach, we prove, in finite samples, sufficient conditions for chained equations and joint modelling to yield imputations from the same predictive distribution. Further, we apply this proof in four specific cases and conduct a simulation study which explores the consequences when the conditional models are compatible but the conditions otherwise are not satisfied. Results We provide an additional “non-informative margins” condition which, together with compatibility, is sufficient. We show that the non-informative margins condition is not satisfied, despite compatible conditional models, in a situation as simple as two continuous variables and one binary variable. Our simulation study demonstrates that as a consequence of this violation order effects can occur; that is, systematic differences depending upon the ordering of the variables in the chained equations algorithm. However, the order effects appear to be small, especially when associations between variables are weak. Conclusions Since chained equations is typically used in medical research for datasets with different types of variables, researchers must be aware that order effects are likely to be ubiquitous, but our results suggest they may be small enough to be negligible. PMID:24559129
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.
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
A MODEL FOR POSTRADIATION STEM CELL KINETICS,
In polycythemic rats observed for 17 days postradiation (300 R, 250 KVP X-rays) it was noted that stem cell release diminished to 8 percent of the...correlate these findings with a kinetic model of erythropoiesis. It was suggested that the initial depression in stem cell release might be due to cellular
Kinetic model for polyhydroxybutyrate (PHB) production by ...
African Journals Online (AJOL)
A kinetic model that describes microbial growth, biopolymer production and substrate consumption is used to predict the performance of batch fermentation of Hydrogenophaga pseudoflava. H. pseudoflava DSMZ 1034 is useful in synthesizing polyhydroxyalkanoates (PHAs).The experimental data was also fitted with the ...
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.
An equilibrium and kinetic modeling
African Journals Online (AJOL)
SERVER
2007-06-18
Jun 18, 2007 ... The Langmuir and Freundlich adsorption models fitted well with the equilibrium data of the process studied. .... dosages. For the determination of adsorption isotherms, 4 g of bio- sorbent was used at five different .... The basic assumption of the Langmuir theory is that ad- sorption takes place at specific sites ...
International Nuclear Information System (INIS)
Dudarev, S.L.
1988-01-01
A quantum kinetic equation for the particle density matrix in a crystal is formulated. It describes inelastic collisions without recourse to the Born approximation in the problem of scattering by an atom or nucleus. A solution is found of the problem of spin incoherent scattering and depolarization of neutrons in a thick crystal. Analytic expressions are obtained for the intensity distribution in Kossel patterns arising on diffraction of the particles emitted from the crystal. Resonance singularities in the backscattering angular spectrum are observed which are similar to those encountered in the problem of weak localization of waves in a randomly inhomogeneous medium
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.
Gyrofluid turbulence models with kinetic effects
International Nuclear Information System (INIS)
Dorland, W.; Hammett, G.W.
1992-12-01
Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u parallel, T parallel, and T perpendicular along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived which may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau-damping model which is equivalent to a multi-pole approximation to the plasma dispersion function, extended to include finite Larmor radius effects. In particular, new dissipative, nonlinear terms are found which model the perpendicular phase-mixing of the distribution function along contours of constant electrostatic potential. These ''FLR phase-mixing'' terms introduce a hyperviscosity-like damping ∝ k perpendicular 2 |Φ rvec k rvec k x rvec k'| which should provide a physics-based damping mechanism at high k perpendicular ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory
Gyrofluid turbulence models with kinetic effects
Energy Technology Data Exchange (ETDEWEB)
Dorland, W.; Hammett, G.W.
1992-12-01
Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u{parallel}, T{parallel}, and T{perpendicular} along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived which may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau-damping model which is equivalent to a multi-pole approximation to the plasma dispersion function, extended to include finite Larmor radius effects. In particular, new dissipative, nonlinear terms are found which model the perpendicular phase-mixing of the distribution function along contours of constant electrostatic potential. These ``FLR phase-mixing`` terms introduce a hyperviscosity-like damping {proportional_to} k{sub {perpendicular}}{sup 2}{vert_bar}{Phi}{sub {rvec k}}{rvec k} {times}{rvec k}{prime}{vert_bar} which should provide a physics-based damping mechanism at high k{perpendicular}{rho} which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.
Kinetic Ising model for desorption from a chain
Geldart, D. J. W.; Kreuzer, H. J.; Rys, Franz S.
1986-10-01
Adsorption along a linear chain of adsorption sites is considered in an Ising model with nearest neighbor interactions. The kinetics are studied in a master equation approach with transition probabilities describing single spin flips to mimic adsorption-desorption processes. Exchange of two spins to account for diffusion can be included as well. Numerical results show that desorption is frequently of fractional (including zero) order. Only at low coverage and high temperature is desorption a first order process. Finite size effects and readsorption are also studied.
Modeling gas kinetic effects in drop collision and impact
Chubynsky, Mykyta V.; Belousov, Kirill I.; Lockerby, Duncan A.; Sprittles, James E.
2017-11-01
When liquid drops collide with each other (collision) or with a solid surface (impact), the thickness of the intervening gas film (which, in particular, gives rise to bouncing off wettable surfaces) is often comparable to the mean free path of the gas molecules and thus gas kinetic effects are significant. We study drop collision and impact computationally using an interface-tracking finite element approach. The gas film is treated in the lubrication approximation. Gas kinetic effects are taken into account by introducing factors (functions of the Knudsen number) modifying the gas flow rate and shear stress. Our results for drop collision are in excellent agreement with those of Li who modeled the gas using the full Navier-Stokes equations with an effective viscosity. For impact, where Li's approach cannot be used, we obtain good agreement with drop bouncing experiments. We acknowledge the support of the Leverhulme Trust and the EPSRC (EP/N016602/1).
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.
Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion
Sánchez-Vizuet, Tonatiuh; Cerfon, Antoine J.
2018-02-01
We study the approximation and stability properties of a recently popularized discretization strategy for the speed variable in kinetic equations, based on pseudo-spectral collocation on a grid defined by the zeros of a non-standard family of orthogonal polynomials called Maxwell polynomials. Taking a one-dimensional equation describing energy diffusion due to Fokker–Planck collisions with a Maxwell–Boltzmann background distribution as the test bench for the performance of the scheme, we find that Maxwell based discretizations outperform other commonly used schemes in most situations, often by orders of magnitude. This provides a strong motivation for their use in high-dimensional gyrokinetic simulations. However, we also show that Maxwell based schemes are subject to a non-modal time stepping instability in their most straightforward implementation, so that special care must be given to the discrete representation of the linear operators in order to benefit from the advantages provided by Maxwell polynomials.
Nonlinear integral equations for the sausage model
Ahn, Changrim; Balog, Janos; Ravanini, Francesco
2017-08-01
The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.
Uncertainty quantification for kinetic models in socio-economic and life sciences
Dimarco, Giacomo; Pareschi, Lorenzo; Zanella, Mattia
2017-01-01
Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronizati...
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 ...
Stochastic differential equations used to model conjugation
DEFF Research Database (Denmark)
Philipsen, Kirsten Riber; Christiansen, Lasse Engbo
be split into measurement noise and system noise. The system noise is used to compensate for those biological processes not explicitly described by the model. Many authors model conjugation by a simple mass action model first proposed by Levin et al. (1979). Also Michaelis-Menten dependence...... by an experiment conducted with E. faecium. In addition, we suggest that a 3rd order time-delay must be included in the model to account for the delay before a newly conjugated plasmid is expressed. A ML estimate of the parameters based on experimental data is found using the software CTSM. The conjugation rate......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...
Modeling and Prediction Using Stochastic Differential Equations
DEFF Research Database (Denmark)
Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp
2016-01-01
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......) for modeling and forecasting. It is argued that this gives models and predictions which better reflect reality. The SDE approach also offers a more adequate framework for modeling and a number of efficient tools for model building. A software package (CTSM-R) for SDE-based modeling is briefly described....... 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...
Coupled kinetic equations for fermions and bosons in the relaxation-time approximation
Florkowski, Wojciech; Maksymiuk, Ewa; Ryblewski, Radoslaw
2018-02-01
Kinetic equations for fermions and bosons are solved numerically in the relaxation-time approximation for the case of one-dimensional boost-invariant geometry. Fermions are massive and carry baryon number, while bosons are massless. The conservation laws for the baryon number, energy, and momentum lead to two Landau matching conditions, which specify the coupling between the fermionic and bosonic sectors and determine the proper-time dependence of the effective temperature and baryon chemical potential of the system. The numerical results illustrate how a nonequilibrium mixture of fermions and bosons approaches hydrodynamic regime described by the Navier-Stokes equations with appropriate forms of the kinetic coefficients. The shear viscosity of a mixture is the sum of the shear viscosities of fermion and boson components, while the bulk viscosity is given by the formula known for a gas of fermions, however, with the thermodynamic variables characterising the mixture. Thus, we find that massless bosons contribute in a nontrivial way to the bulk viscosity of a mixture, provided fermions are massive. We further observe the hydrodynamization effect, which takes place earlier in the shear sector than in the bulk one. The numerical studies of the ratio of the longitudinal and transverse pressures show, to a good approximation, that it depends on the ratio of the relaxation and proper times only. This behavior is connected with the existence of an attractor solution for conformal systems.
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 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.
International Nuclear Information System (INIS)
Hatlee, M.D.; Kozak, J.J.
1981-01-01
In this paper we focus on a particular class of intramicellar kinetic processes: reversible reactions of molecularity two taking place in the interior (or perhaps the immediate vicinity) of a micellar assembly. We formulate a stochastic master equation to describe an ensemble of compartmentalized, distributed systems wherein the (only) microscopic chemical event is a photoinduced, reversible, bimolecular reaction. Then, for an initial distribution of reactants assumed to be Poissonian, we calculate and characterize the overall (macroscopic) dynamics displayed by such a system. The resulting kinetic description is compared with the behavior found previously for the simpler case of irreversible, intramicellar kinetic processes. Finally, we introduce and then investigate the notion of an ''apparent'' equilibrium constant Q for a reversible reaction taking place in a compartmentalized, distributed system and compare this quantity with the ''canonical'' equilibrium constant K obtained for the (same) reversible reaction carried out in bulk, homogeneous solution. The full behavior of Q=Q(K) is explored numerically, and we prove analytically that Qapprox.K 2 in the small K limit and that Q is independent of K in the limit of large K. The experimental consequences of the theory are dicussed in some detail
Large-time behavior of discrete kinetic equations with non-symmetric interactions
Arnold, Anton; Carrillo, Jose A.; Tidriri, Moulay D.
2002-01-01
We consieder the initial-boundary value problem for general linear discrete velocity models appearing in kinetic theory. With time independent inflow boundary data we prove the existence of a unique steady state and the exponential convergence in time towards the steady state. The proof is based on the construction of suitable multiplyers used in a weighted L^{2}-norm.
Green, David L.; Berry, Lee A.; Simpson, Adam B.; Younkin, Timothy R.
2018-04-01
We present the KINETIC-J code, a computational kernel for evaluating the linearized Vlasov equation with application to calculating the kinetic plasma response (current) to an applied time harmonic wave electric field. This code addresses the need for a configuration space evaluation of the plasma current to enable kinetic full-wave solvers for waves in hot plasmas to move beyond the limitations of the traditional Fourier spectral methods. We benchmark the kernel via comparison with the standard k →-space forms of the hot plasma conductivity tensor.
Structural Equation Modeling with the Smartpls
Directory of Open Access Journals (Sweden)
Christian M. Ringle
2014-05-01
Full Text Available The objective of this article is to present a didactic example of Structural Equation Modeling using the software SmartPLS 2.0 M3. The program mentioned uses the method of Partial Least Squares and seeks to address the following situations frequently observed in marketing research: Absence of symmetric distributions of variables measured by a theory still in its beginning phase or with little “consolidation”, formative models, and/or a limited amount of data. The growing use of SmartPLS has demonstrated its robustness and the applicability of the model in the areas that are being studied.
Directory of Open Access Journals (Sweden)
Emmanuel Frenod
2002-01-01
Full Text Available We study the qualitative behavior of solutions to the Vlasov equation with strong external magnetic field and oscillating electric field. This model is relevant to the understanding of isotop resonant separation. We show that the effective equation is a kinetic equation with a memory term. This memory term involves a pseudo-differential operator whose kernel is characterized by an integral equation involving Bessel functions. The kernel is explicitly given in some particular cases.
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.
International Nuclear Information System (INIS)
Sathiyasheela, T.
2009-01-01
Point kinetics equations (P. K. E) are system of differential equations, which is solved simultaneously to get the neutron density as a function of time for a given reactivity input. P. K. E are stiff differential equations, computational solution through the conventional explicit method will give a stable consistent result only for smaller time steps. Analytical solutions are available either with step or ramp reactivity insertion without considering the source power contribution. When a reactor operates at low power, the neutron source gives a considerable contribution to the net reactor power. Similarly, when the reactor is brought to delayed critical with the presence of external source, the sub critical reactor kinetics studies with source power are important to understand the power behavior as a function of reactivity insertion rate with respect to the initial reactivity. In the present work, P.K.E with one group delayed neutron are solved analytically to determine the reactor power as a function of reactivity insertion rate in the presence of neutron source. The analytical solution is a combination of converging two infinite series. Truncated infinite series is the analytical solution of P.K E. A general formulation is made by Combining both the ramp reactivity and step reactivity solution. So that the analytical solution could be useful in analyzing either step and ramp reactivity insertion exclusively or the combination of both. This general formulation could be useful in analyzing many reactor operations, like the air bubble passing through the core, stuck rod conditions, uncontrolled withdrawal of controlled rod, discontinuous lifting of control rod, lowering of rod and etc. Results of analytical solutions are compared against the results of numerical solution which is developed based on Cohen's method. The comparisons are found to be good for all kind of positive and negative ramp reactivity insertions, with or without the combination of step reactivity
Numerical solution of the 1D kinetics equations using a cubic reduced nodal scheme
International Nuclear Information System (INIS)
Gomez T, A.M.; Valle G, E. del; Delfin L, A.; Alonso V, G.
2003-01-01
In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as Θ scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)
A mathematical model on germinal center kinetics andtermination
DEFF Research Database (Denmark)
Kesmir, Can; De Boer, R.J.
1999-01-01
We devise a mathematical model to study germinal center (GC) kinetics. Earlier models for GC kinetics areextended by explicitly modeling 1) the cell division history of centroblasts, 2) the Ag uptake by centrocytes,and 3) T cell dynamics. Allowing for T cell kinetics and T-B cell interactions, we...
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
Graphical Tools for Linear Structural Equation Modeling
2014-06-01
regression coefficient βS A.CQ1 van- ishes, which can be used to test whether the specification of Model 2 is compatible with the data. Most...because they are all compatible with the graph in Figure 19a, which displays the skeleton and v-structures. Note that we cannot reverse the edge from...im- plications of linear structual equation models. R-428, <http://ftp.cs.ucla.edu/pub/stat_ser/r428.pdf>, CA. To ap- pear in Proceedings of AAAI-2014
Growth Kinetics and Modeling of Direct Oxynitride Growth with NO-O2 Gas Mixtures
Energy Technology Data Exchange (ETDEWEB)
Everist, Sarah; Nelson, Jerry; Sharangpani, Rahul; Smith, Paul Martin; Tay, Sing-Pin; Thakur, Randhir
1999-05-03
We have modeled growth kinetics of oxynitrides grown in NO-O_{2} gas mixtures from first principles using modified Deal-Grove equations. Retardation of oxygen diffusion through the nitrided dielectric was assumed to be the dominant growth-limiting step. The model was validated against experimentally obtained curves with good agreement. Excellent uniformity, which exceeded expected walues, was observed.
Chen, Xiangjun; Xiao, Namin; Cai, Minghui; Li, Dianzhong; Li, Guangyao; Sun, Guangyong; Rolfe, Bernard F.
2016-09-01
An inverse model is proposed to construct the mathematical relationship between continuous cooling transformation (CCT) kinetics with constant rates and the isothermal one. The kinetic parameters in JMAK equations of isothermal kinetics can be deduced from the experimental CCT kinetics. Furthermore, a generalized model with a new additive rule is developed for predicting the kinetics of nucleation and growth during diffusional phase transformation with arbitrary cooling paths based only on CCT curve. A generalized contribution coefficient is introduced into the new additivity rule to describe the influences of current temperature and cooling rate on the incubation time of nuclei. Finally, then the reliability of the proposed model is validated using dilatometry experiments of a microalloy steel with fully bainitic microstructure based on various cooling routes.
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
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 Evolutionary Algorithms with Stochastic Differential Equations.
Heredia, Jorge Pérez
2017-11-20
There has been renewed interest in modelling the behaviour of evolutionary algorithms (EAs) by more traditional mathematical objects, such as ordinary differential equations or Markov chains. The advantage is that the analysis becomes greatly facilitated due to the existence of well established methods. However, this typically comes at the cost of disregarding information about the process. Here, we introduce the use of stochastic differential equations (SDEs) for the study of EAs. SDEs can produce simple analytical results for the dynamics of stochastic processes, unlike Markov chains which can produce rigorous but unwieldy expressions about the dynamics. On the other hand, unlike ordinary differential equations (ODEs), they do not discard information about the stochasticity of the process. We show that these are especially suitable for the analysis of fixed budget scenarios and present analogues of the additive and multiplicative drift theorems from runtime analysis. In addition, we derive a new more general multiplicative drift theorem that also covers non-elitist EAs. This theorem simultaneously allows for positive and negative results, providing information on the algorithm's progress even when the problem cannot be optimised efficiently. Finally, we provide results for some well-known heuristics namely Random Walk (RW), Random Local Search (RLS), the (1+1) EA, the Metropolis Algorithm (MA), and the Strong Selection Weak Mutation (SSWM) algorithm.
Exploratory structural equation modeling of personality data.
Booth, Tom; Hughes, David J
2014-06-01
The current article compares the use of exploratory structural equation modeling (ESEM) as an alternative to confirmatory factor analytic (CFA) models in personality research. We compare model fit, factor distinctiveness, and criterion associations of factors derived from ESEM and CFA models. In Sample 1 (n = 336) participants completed the NEO-FFI, the Trait Emotional Intelligence Questionnaire-Short Form, and the Creative Domains Questionnaire. In Sample 2 (n = 425) participants completed the Big Five Inventory and the depression and anxiety scales of the General Health Questionnaire. ESEM models provided better fit than CFA models, but ESEM solutions did not uniformly meet cutoff criteria for model fit. Factor scores derived from ESEM and CFA models correlated highly (.91 to .99), suggesting the additional factor loadings within the ESEM model add little in defining latent factor content. Lastly, criterion associations of each personality factor in CFA and ESEM models were near identical in both inventories. We provide an example of how ESEM and CFA might be used together in improving personality assessment. © The Author(s) 2014.
International Nuclear Information System (INIS)
Tumelero, Fernanda; Petersen, Claudio Zen; Goncalves, Glenio Aguiar; Schramm, Marcelo
2016-01-01
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.
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.
Chu, Khim Hoong
2017-11-09
Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6 cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.
International Nuclear Information System (INIS)
Nakahara, Yasuaki; Ise, Takeharu; Kobayashi, Kensuke; Itoh, Yasuyuki
1975-12-01
A new method has been developed for numerical solution of a class of nonlinear Volterra integro-differential equations with quadratic nonlinearity. After dividing the domain of the variable into subintervals, piecewise approximations are applied in the subintervals. The equation is first integrated over a subinterval to obtain the piecewise equation, to which six approximate treatments are applied, i.e. fully explicit, fully implicit, Crank-Nicolson, linear interpolation, quadratic and cubic spline. The numerical solution at each time step is obtained directly as a positive root of the resulting algebraic quadratic equation. The point reactor kinetics with a ramp reactivity insertion, linear temperature feedback and delayed neutrons can be described by one of this type of nonlinear Volterra integro-differential equations. The algorithm is applied to the Argonne benchmark problem and a model problem for a fast reactor without delayed neutrons. The fully implicit method has been found to be unconditionally stable in the sense that it always gives the positive real roots. The cubic spline method is divergent, and the other four methods are intermediate in between. From the estimation of the stability, convergency, accuracy and CPU time, it is concluded that the Crank-Nicolson method is best, then the linear interpolation method comes closely next to it. Discussions are also made on the possibility of applying the algorithm to the fusion reactor kinetics in the form of a nonlinear partial differential equation. (auth.)
Electron kinetics modeling in a weakly ionized gas
International Nuclear Information System (INIS)
Boeuf, Jean-Pierre
1985-01-01
This work presents some features of electron kinetics in a weakly ionized gas. After a summary of the basis and recent developments of the kinetic theory, and a review of the most efficient numerical techniques for solving the Boltzmann equation, several aspects of electron motion in gases are analysed. Relaxation phenomena toward equilibrium under a uniform electric field, and the question of the existence of the hydrodynamic regime are first studied. The coupling between electron kinetics and chemical kinetics due to second kind collisions in Nitrogen is then analysed; a quantitative description of the evolution of the energy balance, accounting for electron-molecule as well as molecule-molecule energy transfer is also given. Finally, electron kinetics in space charge distorted, highly non uniform electric fields (glow discharges, streamers propagation) is investigated with microscopic numerical methods based on Boltzmann and Poisson equations. (author) [fr
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
Rout, Bapin Kumar; Brooks, Geoff; Rhamdhani, M. Akbar; Li, Zushu; Schrama, Frank N. H.; Sun, Jianjun
2018-04-01
A multi-zone kinetic model coupled with a dynamic slag generation model was developed for the simulation of hot metal and slag composition during the basic oxygen furnace (BOF) operation. The three reaction zones (i) jet impact zone, (ii) slag-bulk metal zone, (iii) slag-metal-gas emulsion zone were considered for the calculation of overall refining kinetics. In the rate equations, the transient rate parameters were mathematically described as a function of process variables. A micro and macroscopic rate calculation methodology (micro-kinetics and macro-kinetics) were developed to estimate the total refining contributed by the recirculating metal droplets through the slag-metal emulsion zone. The micro-kinetics involves developing the rate equation for individual droplets in the emulsion. The mathematical models for the size distribution of initial droplets, kinetics of simultaneous refining of elements, the residence time in the emulsion, and dynamic interfacial area change were established in the micro-kinetic model. In the macro-kinetics calculation, a droplet generation model was employed and the total amount of refining by emulsion was calculated by summing the refining from the entire population of returning droplets. A dynamic FetO generation model based on oxygen mass balance was developed and coupled with the multi-zone kinetic model. The effect of post-combustion on the evolution of slag and metal composition was investigated. The model was applied to a 200-ton top blowing converter and the simulated value of metal and slag was found to be in good agreement with the measured data. The post-combustion ratio was found to be an important factor in controlling FetO content in the slag and the kinetics of Mn and P in a BOF process.
Rout, Bapin Kumar; Brooks, Geoff; Rhamdhani, M. Akbar; Li, Zushu; Schrama, Frank N. H.; Sun, Jianjun
2018-01-01
A multi-zone kinetic model coupled with a dynamic slag generation model was developed for the simulation of hot metal and slag composition during the basic oxygen furnace (BOF) operation. The three reaction zones (i) jet impact zone, (ii) slag-bulk metal zone, (iii) slag-metal-gas emulsion zone were considered for the calculation of overall refining kinetics. In the rate equations, the transient rate parameters were mathematically described as a function of process variables. A micro and macroscopic rate calculation methodology (micro-kinetics and macro-kinetics) were developed to estimate the total refining contributed by the recirculating metal droplets through the slag-metal emulsion zone. The micro-kinetics involves developing the rate equation for individual droplets in the emulsion. The mathematical models for the size distribution of initial droplets, kinetics of simultaneous refining of elements, the residence time in the emulsion, and dynamic interfacial area change were established in the micro-kinetic model. In the macro-kinetics calculation, a droplet generation model was employed and the total amount of refining by emulsion was calculated by summing the refining from the entire population of returning droplets. A dynamic FetO generation model based on oxygen mass balance was developed and coupled with the multi-zone kinetic model. The effect of post-combustion on the evolution of slag and metal composition was investigated. The model was applied to a 200-ton top blowing converter and the simulated value of metal and slag was found to be in good agreement with the measured data. The post-combustion ratio was found to be an important factor in controlling FetO content in the slag and the kinetics of Mn and P in a BOF process.
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.
Chemical kinetics and modeling of planetary atmospheres
Yung, Yuk L.
1990-01-01
A unified overview is presented for chemical kinetics and chemical modeling in planetary atmospheres. The recent major advances in the understanding of the chemistry of the terrestrial atmosphere make the study of planets more interesting and relevant. A deeper understanding suggests that the important chemical cycles have a universal character that connects the different planets and ultimately link together the origin and evolution of the solar system. The completeness (or incompleteness) of the data base for chemical kinetics in planetary atmospheres will always be judged by comparison with that for the terrestrial atmosphere. In the latter case, the chemistry of H, O, N, and Cl species is well understood. S chemistry is poorly understood. In the atmospheres of Jovian planets and Titan, the C-H chemistry of simple species (containing 2 or less C atoms) is fairly well understood. The chemistry of higher hydrocarbons and the C-N, P-N chemistry is much less understood. In the atmosphere of Venus, the dominant chemistry is that of chlorine and sulfur, and very little is known about C1-S coupled chemistry. A new frontier for chemical kinetics both in the Earth and planetary atmospheres is the study of heterogeneous reactions. The formation of the ozone hole on Earth, the ubiquitous photochemical haze on Venus and in the Jovian planets and Titan all testify to the importance of heterogeneous reactions. It remains a challenge to connect the gas phase chemistry to the production of aerosols.
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.
Zhu, Wen; Liu, Junsheng; Li, Meng
2014-01-01
A series of zwitterionic hybrid membranes were prepared via the ring opening of 1,3-propanesultone with the amine groups in the chains of TMSPEDA and a subsequent sol-gel process. Their kinetic models for strontium removal were investigated using three two-parameter kinetic equations (i.e., Lagergren pseudo-first order, pseudo-second order, and Elovich models). Adsorption mechanism was evaluated using intraparticle diffusion model, diffusion-chemisorption model, and Boyd equation. It was found that the adsorption of strontium ions on these zwitterionic hybrid membranes fitted well with the Lagergren pseudo-second order model. Mechanism insights suggested that diffusion-chemisorption was one of the main adsorption mechanisms. Boyd equation exhibited that film-diffusion mechanism might be the control process during the starting period. These findings are very useful in strontium removal from the stimulated radioactive wastewater.
Directory of Open Access Journals (Sweden)
Wen Zhu
2014-01-01
Full Text Available A series of zwitterionic hybrid membranes were prepared via the ring opening of 1,3-propanesultone with the amine groups in the chains of TMSPEDA and a subsequent sol-gel process. Their kinetic models for strontium removal were investigated using three two-parameter kinetic equations (i.e., Lagergren pseudo-first order, pseudo-second order, and Elovich models. Adsorption mechanism was evaluated using intraparticle diffusion model, diffusion-chemisorption model, and Boyd equation. It was found that the adsorption of strontium ions on these zwitterionic hybrid membranes fitted well with the Lagergren pseudo-second order model. Mechanism insights suggested that diffusion-chemisorption was one of the main adsorption mechanisms. Boyd equation exhibited that film-diffusion mechanism might be the control process during the starting period. These findings are very useful in strontium removal from the stimulated radioactive wastewater.
Mathematical modeling and the two-phase constitutive equations
International Nuclear Information System (INIS)
Boure, J.A.
1975-01-01
The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr
Solubility of the transport equation in the kinetics of coagulation and fragmentation
International Nuclear Information System (INIS)
Dubovskii, P B
2001-01-01
We prove a local existence theorem for a continuous solution of the spatially inhomogeneous kinetic coagulation-fragmentation model of Smoluchowski. Then we prove the solubility of the problem in the large in the class of continuous functions. It is important to emphasize that we admit unbounded integral kernels in both cases. The uniqueness of the solution and its continuous dependence on the input data are also demonstrated
International Nuclear Information System (INIS)
Carvalho Gonçalves, Wemerson de; Martinez, Aquilino Senra; Carvalho da Silva, Fernando
2015-01-01
Highlights: • We define the new function importance. • We calculate the kinetic parameters Λ, β, Γ and Q to: 0.95, 0.96, 0.97, 0.98 and 0.99. • We compared the results with those obtained by the main important functions. • We found that the calculated kinetic parameters are physically consistent. - Abstract: This paper aims to determine the parameters for a new set of equations of point kinetic subcritical systems, based on the concept of importance of Heuristic Generalized Perturbation Theory (HGPT). The importance function defined here is related to both the subcriticality and the external neutron source worth (which keeps the system at steady state). The kinetic parameters defined in this work are compared with the corresponding parameters when adopting the importance functions proposed by Gandini and Salvatores (2002), Dulla et al. (2006) and Nishihara et al. (2003). Furthermore, the point kinetics equations developed here are solved for two different transients, considering the parameters obtained with different importance functions. The results collected show that there is a similar behavior of the solution of the point kinetics equations, when used with the parameters obtained by the importance functions proposed by Gandini and Salvatores (2002) and Dulla et al. (2006), specially near the criticality. However, this is not verified as the system gets farther from criticality
Kinetic modelling of the Maillard reaction between proteins and sugars
Brands, C.M.J.
2002-01-01
Keywords: Maillard reaction, sugar isomerisation, kinetics, multiresponse modelling, brown colour formation, lysine damage, mutagenicity, casein, monosaccharides, disaccharides, aldoses, ketoses
The aim of this thesis was to determine the kinetics of the Maillard reaction between
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.
Radio wave propagation and parabolic equation modeling
Apaydin, Gokhan
2018-01-01
A thorough understanding of electromagnetic wave propagation is fundamental to the development of sophisticated communication and detection technologies. The powerful numerical methods described in this book represent a major step forward in our ability to accurately model electromagnetic wave propagation in order to establish and maintain reliable communication links, to detect targets in radar systems, and to maintain robust mobile phone and broadcasting networks. The first new book on guided wave propagation modeling and simulation to appear in nearly two decades, Radio Wave Propagation and Parabolic Equation Modeling addresses the fundamentals of electromagnetic wave propagation generally, with a specific focus on radio wave propagation through various media. The authors explore an array of new applications, and detail various v rtual electromagnetic tools for solving several frequent electromagnetic propagation problems. All of the methods described are presented within the context of real-world scenari...
Rout, Bapin Kumar; Brooks, Geoffrey; Akbar Rhamdhani, M.; Li, Zushu; Schrama, Frank N. H.; Overbosch, Aart
2018-03-01
In a previous study by the authors (Rout et al. in Metall Mater Trans B 49:537-557, 2018), a dynamic model for the BOF, employing the concept of multizone kinetics was developed. In the current study, the kinetics of decarburization reaction is investigated. The jet impact and slag-metal emulsion zones were identified to be primary zones for carbon oxidation. The dynamic parameters in the rate equation of decarburization such as residence time of metal drops in the emulsion, interfacial area evolution, initial size, and the effects of surface-active oxides have been included in the kinetic rate equation of the metal droplet. A modified mass-transfer coefficient based on the ideal Langmuir adsorption equilibrium has been proposed to take into account the surface blockage effects of SiO2 and P2O5 in slag on the decarburization kinetics of a metal droplet in the emulsion. Further, a size distribution function has been included in the rate equation to evaluate the effect of droplet size on reaction kinetics. The mathematical simulation indicates that decarburization of the droplet in the emulsion is a strong function of the initial size and residence time. A modified droplet generation rate proposed previously by the authors has been used to estimate the total decarburization rate by slag-metal emulsion. The model's prediction shows that about 76 pct of total carbon is removed by reactions in the emulsion, and the remaining is removed by reactions at the jet impact zone. The predicted bath carbon by the model has been found to be in good agreement with the industrially measured data.
Semi-continuous and multigroup models in extended kinetic theory
Koller, W
2000-01-01
The aim of this thesis is to study energy discretization of the Boltzmann equation in the framework of extended kinetic theory. In case that external fields can be neglected, the semi- continuous Boltzmann equation yields a sound basis for various generalizations. Semi-continuous kinetic equations describing a three component gas mixture interacting with monochromatic photons as well as a four component gas mixture undergoing chemical reactions are established and investigated. These equations reflect all major aspects (conservation laws, equilibria, H-theorem) of the full continuous kinetic description. For the treatment of the spatial dependence, an expansion of the distribution function in terms of Legendre polynomials is carried out. An implicit finite differencing scheme is combined with the operator splitting method. The obtained numerical schemes are applied to the space homogeneous study of binary chemical reactions and to spatially one-dimensional laser-induced acoustic waves. In the presence of exte...
International Nuclear Information System (INIS)
Damiano, B.; March-Leuba, J.A.; Euler, J.A.
1990-01-01
This paper describes a technique for calculating boiling water reactor (BWR) behavior during steady-state limit-cycle oscillations. An approximate solution is obtained from the application of Galerkin's method to a BWR dynamic model consisting of the point-kinetics equations and the LAPUR-calculated power-to-reactivity feedback-transfer function. The approximate-solution technique is described, and comparisons of approximate solutions with numerical results and measured data are given. 7 refs., 5 figs
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
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.
Comparison of the kinetics of different Markov models for ligand binding under varying conditions
Martini, Johannes W. R.; Habeck, Michael
2015-03-01
We recently derived a Markov model for macromolecular ligand binding dynamics from few physical assumptions and showed that its stationary distribution is the grand canonical ensemble [J. W. R. Martini, M. Habeck, and M. Schlather, J. Math. Chem. 52, 665 (2014)]. The transition probabilities of the proposed Markov process define a particular Glauber dynamics and have some similarity to the Metropolis-Hastings algorithm. Here, we illustrate that this model is the stochastic analog of (pseudo) rate equations and the corresponding system of differential equations. Moreover, it can be viewed as a limiting case of general stochastic simulations of chemical kinetics. Thus, the model links stochastic and deterministic approaches as well as kinetics and equilibrium described by the grand canonical ensemble. We demonstrate that the family of transition matrices of our model, parameterized by temperature and ligand activity, generates ligand binding kinetics that respond to changes in these parameters in a qualitatively similar way as experimentally observed kinetics. In contrast, neither the Metropolis-Hastings algorithm nor the Glauber heat bath reflects changes in the external conditions correctly. Both converge rapidly to the stationary distribution, which is advantageous when the major interest is in the equilibrium state, but fail to describe the kinetics of ligand binding realistically. To simulate cellular processes that involve the reversible stochastic binding of multiple factors, our pseudo rate equation model should therefore be preferred to the Metropolis-Hastings algorithm and the Glauber heat bath, if the stationary distribution is not of only interest.
Comparison of the kinetics of different Markov models for ligand binding under varying conditions
International Nuclear Information System (INIS)
Martini, Johannes W. R.; Habeck, Michael
2015-01-01
We recently derived a Markov model for macromolecular ligand binding dynamics from few physical assumptions and showed that its stationary distribution is the grand canonical ensemble [J. W. R. Martini, M. Habeck, and M. Schlather, J. Math. Chem. 52, 665 (2014)]. The transition probabilities of the proposed Markov process define a particular Glauber dynamics and have some similarity to the Metropolis-Hastings algorithm. Here, we illustrate that this model is the stochastic analog of (pseudo) rate equations and the corresponding system of differential equations. Moreover, it can be viewed as a limiting case of general stochastic simulations of chemical kinetics. Thus, the model links stochastic and deterministic approaches as well as kinetics and equilibrium described by the grand canonical ensemble. We demonstrate that the family of transition matrices of our model, parameterized by temperature and ligand activity, generates ligand binding kinetics that respond to changes in these parameters in a qualitatively similar way as experimentally observed kinetics. In contrast, neither the Metropolis-Hastings algorithm nor the Glauber heat bath reflects changes in the external conditions correctly. Both converge rapidly to the stationary distribution, which is advantageous when the major interest is in the equilibrium state, but fail to describe the kinetics of ligand binding realistically. To simulate cellular processes that involve the reversible stochastic binding of multiple factors, our pseudo rate equation model should therefore be preferred to the Metropolis-Hastings algorithm and the Glauber heat bath, if the stationary distribution is not of only interest
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 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.
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.
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…
The Cauchy problem for the Bogolyubov hierarchy of equations. The BCS model
International Nuclear Information System (INIS)
Vidybida, A.K.
1975-01-01
A chain of Bogolyubov's kinetic equations for an infinite quantum system of particles distributed in space with the mean density 1/V and interacting with the BCS model operator is considered as a single abstract equation in some countable normalized space bsup(v) of sequences of integral operators. In this case an unique solution of the Cauchy problem has been obtained at arbitrary initial conditions from bsup(v), stationary solutions of the equation have been derived, and the class of the initial conditions which approach to stationary ones is indicated
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.
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.
Microscopic kinetic model for polymer crystal growth
Hu, Wenbing
2011-03-01
Linear crystal growth rates characterize the net result of competition between growth and melting at the liquid-solid interfaces. The rate equation for polymer crystal growth can be derived with a barrier term for crystal growth and with a driving force term of excess lamellar thickness, provided that growth and melting share the same rate-determining steps at the growth front. Such an ansatz can be verified by the kinetic symmetry between growth and melting around the melting point of lamellar crystals, as made in our recent dynamic Monte Carlo simulations. The profile of the growth/melting front appears as wedge-shaped, with the free energy barrier for intramolecular secondary crystal nucleation at its top, and with the driving force gained via instant thickening at its bottom. Such a scenario explains unique phenomena on polymer crystal growth, such as chain folding, regime transitions, molecular segregation of polydisperse polymers, self-poisoning with integer-number chain-folding of short chains, and colligative growth rates of binary mixtures of two chain lengths. Financial support from NNSFC No. 20825415 and NBRPC No. 2011CB606100 is acknowledged.
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
Dunkel, Jörn; Hänggi, Peter (Prof. Dr. Dr. h.c. mult.)
2006-01-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, non-relativistic LE is deduced from this model, by taking into account the non-relativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativi...
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. Copyright © 2013 Elsevier Ltd. All rights reserved.
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)
A physiologically based model for denitrogenation kinetics
Directory of Open Access Journals (Sweden)
Ira Katz
2017-01-01
Full Text Available Under normal conditions we continuously breathe 78% nitrogen (N2 such that the body tissues and fluids are saturated with dissolved N2. For normobaric medical gas administration at high concentrations, the N2 concentration must be less than that in the ambient atmosphere; therefore, nitrogen will begin to be released by the body tissues. There is a need to estimate the time needed for denitrogenation in the planning of surgical procedures. In this paper we will describe the application of a physiologically based pharmacokinetic model to denitrogenation kinetics. The results are compared to the data resulting from experiments in the literature that measured the end tidal N2 concentration while breathing 100% oxygen in the form of moderately rapid and slow compartment time constants. It is shown that the model is in general agreement with published experimental data. Correlations for denitrogenation as a function of subject weight are provided.
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)
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...
International Nuclear Information System (INIS)
Si, S.
2012-01-01
The Universal Algorithm of Stiffness Confinement Method (UASCM) for neutron kinetics model of multi-dimensional and multi-group transport equations or diffusion equations has been developed. The numerical experiments based on transport theory code MGSNM and diffusion theory code MGNEM have demonstrated that the algorithm has sufficient accuracy and stability. (authors)
Modelling and parallel calculation of a kinetic boundary layer
International Nuclear Information System (INIS)
Perlat, Jean Philippe
1998-01-01
This research thesis aims at addressing reliability and cost issues in the calculation by numeric simulation of flows in transition regime. The first step has been to reduce calculation cost and memory space for the Monte Carlo method which is known to provide performance and reliability for rarefied regimes. Vector and parallel computers allow this objective to be reached. Here, a MIMD (multiple instructions, multiple data) machine has been used which implements parallel calculation at different levels of parallelization. Parallelization procedures have been adapted, and results showed that parallelization by calculation domain decomposition was far more efficient. Due to reliability issue related to the statistic feature of Monte Carlo methods, a new deterministic model was necessary to simulate gas molecules in transition regime. New models and hyperbolic systems have therefore been studied. One is chosen which allows thermodynamic values (density, average velocity, temperature, deformation tensor, heat flow) present in Navier-Stokes equations to be determined, and the equations of evolution of thermodynamic values are described for the mono-atomic case. Numerical resolution of is reported. A kinetic scheme is developed which complies with the structure of all systems, and which naturally expresses boundary conditions. The validation of the obtained 14 moment-based model is performed on shock problems and on Couette flows [fr
Effective-field theory on the kinetic Ising model
International Nuclear Information System (INIS)
Shi Xiaoling; Wei Guozhu; Li Lin
2008-01-01
As an analytical method, the effective-field theory (EFT) is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the square lattice (Z=4) and the simple cubic lattice (Z=6), respectively. The dynamic order parameter, the hysteresis loop area and the dynamic correlation are calculated. In the field amplitude h 0 /ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn, and the dynamical tricritical point has been observed. We also make the compare results of EFT with that given by using the mean field theory (MFT)
Monochloramination of resorcinol: mechanism and kinetic modeling.
Cimetiere, Nicolas; Dossier-Berne, Florence; De Laat, Joseph
2009-12-15
The kinetics of monochloramination of resorcinol, 4-chlororesorcinol, and 4,6-dichlororesorcinol have been investigated over the pH range of 5-12, at 23 +/- 2 degrees C. Monochloramine solutions were prepared with ammonia-to-chlorine ratios (N/Cl) ranging from 1.08 to 31 mol/mol. Under conditions that minimize free chlorine reactions (N/Cl > 2 mol/mol), the apparent second-order rate constants of monochloramination of resorcinol compounds show a maximum at pH values between 8.6 and 10.2. The intrinsic second-order rate constants for the reaction of monochloramine with the acid-base forms of the dihydroxybenzenes (Ar(OH)(2), Ar(OH)O(-), and Ar(O(-))(2)) were calculated from the apparent second-order rate constants. The stoichiometric coefficients for the formation of 4-chlororesorcinol by monochloramination of resorcinol and 4,6-dichlororesorcinol by monochloramination of 4-chlororesorcinol were found to be equal to 0.66 +/- 0.05 and 0.25 +/- 0.02 mol/mol, respectively at pH 8.6. A kinetic model that incorporates reactions of free chlorine and monochloramine with the different acid-base forms of resorcinol compounds simulated well the initial rates of degradation of resorcinol compounds and was useful to evaluate the contribution of free chlorine reactions to the overall rates of degradation of resorcinol at low N/Cl ratios.
Lavrova, Anastasia I; Postnikov, Eugene B; Zyubin, Andrey Yu; Babak, Svetlana V
2017-04-01
We consider two approaches to modelling the cell metabolism of 6-mercaptopurine, one of the important chemotherapy drugs used for treating acute lymphocytic leukaemia: kinetic ordinary differential equations, and Boolean networks supplied with one controlling node, which takes continual values. We analyse their interplay with respect to taking into account ATP concentration as a key parameter of switching between different pathways. It is shown that the Boolean networks, which allow avoiding the complexity of general kinetic modelling, preserve the possibility of reproducing the principal switching mechanism.
Climate models with delay differential equations
Keane, Andrew; Krauskopf, Bernd; Postlethwaite, Claire M.
2017-11-01
A fundamental challenge in mathematical modelling is to find a model that embodies the essential underlying physics of a system, while at the same time being simple enough to allow for mathematical analysis. Delay differential equations (DDEs) can often assist in this goal because, in some cases, only the delayed effects of complex processes need to be described and not the processes themselves. This is true for some climate systems, whose dynamics are driven in part by delayed feedback loops associated with transport times of mass or energy from one location of the globe to another. The infinite-dimensional nature of DDEs allows them to be sufficiently complex to reproduce realistic dynamics accurately with a small number of variables and parameters. In this paper, we review how DDEs have been used to model climate systems at a conceptual level. Most studies of DDE climate models have focused on gaining insights into either the global energy balance or the fundamental workings of the El Niño Southern Oscillation (ENSO) system. For example, studies of DDEs have led to proposed mechanisms for the interannual oscillations in sea-surface temperature that is characteristic of ENSO, the irregular behaviour that makes ENSO difficult to forecast and the tendency of El Niño events to occur near Christmas. We also discuss the tools used to analyse such DDE models. In particular, the recent development of continuation software for DDEs makes it possible to explore large regions of parameter space in an efficient manner in order to provide a "global picture" of the possible dynamics. We also point out some directions for future research, including the incorporation of non-constant delays, which we believe could improve the descriptive power of DDE climate models.
A discontinuous Galerkin method on kinetic flocking models
Tan, Changhui
2014-01-01
We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale and Motsch-Tadmor models. We prove flocking behavior for the kinetic descriptions of flocking systems, which indicates a concentration in velocity variable in infinite time. We propose a discontinuous Galerkin method to treat the asymptotic $\\delta$-singularity, and construct high order positive preserving scheme to solve kinetic flocking systems.
Kinetic theory model for the flow of a simple gas from a two-dimensional nozzle
Riley, B. R.; Scheller, K. W.
1989-01-01
A system of nonlinear integral equations equivalent to the Krook kinetic equation for the steady state is the mathematical basis used to develop a computer code to model the flowfields for low-thrust two-dimensional nozzles. The method of characteristics was used to solve numerically by an iteration process the approximated Boltzmann equation for the number density, temperature, and velocity profiles of a simple gas as it exhausts into a vacuum. Results predict backscatter and show the effect of the inside wall boundary layer on the flowfields external to the nozzle.
Challenges for the kinetic unified dark matter model
International Nuclear Information System (INIS)
Giannakis, Dimitrios; Hu, Wayne
2005-01-01
Given that the dark matter and dark energy in the Universe affect cosmological observables only gravitationally, their phenomenology may be described by a single stress-energy tensor. True unification however requires a theory that reproduces the successful phenomenology of ΛCDM and that requirement places specific constraints on the stress structure of the matter. We show that a recently proposed unification through an offset quadratic kinetic term for a scalar field is exactly equivalent to a fluid with a closed-form barotropic equation of state plus cosmological constant. The finite pressure at high densities introduces a cutoff in the linear power spectrum, which may alleviate the dark matter substructure problem; we provide a convenient fitting function for such studies. Given that sufficient power must remain to reionize the Universe, the equation of state today is nonrelativistic with p∝ρ 2 and a Jeans scale in the parsec regime for all relevant densities. Structure may then be evolved into the nonlinear regime with standard hydrodynamic techniques. In fact, the model is equivalent to the well-studied collisional dark matter with negligible mean free path. If recent observations of the triaxiality of dark matter halos and ram pressure stripping in galaxy clusters are confirmed, this model will be ruled out
Incremental parameter estimation of kinetic metabolic network models
Directory of Open Access Journals (Sweden)
Jia Gengjie
2012-11-01
Full Text Available Abstract Background An efficient and reliable parameter estimation method is essential for the creation of biological models using ordinary differential equation (ODE. Most of the existing estimation methods involve finding the global minimum of data fitting residuals over the entire parameter space simultaneously. Unfortunately, the associated computational requirement often becomes prohibitively high due to the large number of parameters and the lack of complete parameter identifiability (i.e. not all parameters can be uniquely identified. Results In this work, an incremental approach was applied to the parameter estimation of ODE models from concentration time profiles. Particularly, the method was developed to address a commonly encountered circumstance in the modeling of metabolic networks, where the number of metabolic fluxes (reaction rates exceeds that of metabolites (chemical species. Here, the minimization of model residuals was performed over a subset of the parameter space that is associated with the degrees of freedom in the dynamic flux estimation from the concentration time-slopes. The efficacy of this method was demonstrated using two generalized mass action (GMA models, where the method significantly outperformed single-step estimations. In addition, an extension of the estimation method to handle missing data is also presented. Conclusions The proposed incremental estimation method is able to tackle the issue on the lack of complete parameter identifiability and to significantly reduce the computational efforts in estimating model parameters, which will facilitate kinetic modeling of genome-scale cellular metabolism in the future.
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.
Yessayan, Lenar; Yee, Jerry; Frinak, Stan; Kwon, David; Szamosfalvi, Balazs
2015-01-01
Concomitant severe metabolic alkalosis, hypernatremia, and kidney failure pose a therapeutic challenge. Hemodialysis to correct azotemia and abnormal electrolytes results in rapid correction of serum sodium, bicarbonate, and urea but presents a risk for dialysis disequilibrium and brain edema. We describe a patient with Zollinger-Ellison syndrome with persistent encephalopathy, severe metabolic alkalosis (highest bicarbonate 81 mEq/L), hypernatremia (sodium 157 mEq/L), and kidney failure despite 30 hours of intravenous crystalloids and proton pump inhibitor. We used continuous renal replacement therapy (RRT) with delivered hourly urea clearance of ~3 L/hour (24 hour sustained low efficiency dialysis with regional citrate anticoagulation protocol at blood flow rate 60 ml/min and dialysate flow rate 400 ml/min). To mitigate a pronounced decrease in plasma osmolality while removing urea from this hypernatremic patient, dialysate sodium was set to start at 155 mEq/L then at 150 mEq/L after 6 hours. Serum bicarbonate, urea, and sodium were slowly corrected over 26 hours. This case demonstrates how to regulate and predict the systemic bicarbonate level using single pool kinetic modeling during convective or diffusive RRT. Kinetic modeling provides a valuable tool for systemic blood pH control in future combined use of extracorporeal CO2 removal and continuous RRT systems.
Laplace transform in tracer kinetic modeling
International Nuclear Information System (INIS)
Hauser, Eliete B.
2013-01-01
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, [ 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)
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)
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
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.
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
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)
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.
Reflected kinetics model for nuclear space reactor kinetics and control scoping calculations
International Nuclear Information System (INIS)
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
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...
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.
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.
Kinetic models of cell growth, substrate utilization and bio ...
African Journals Online (AJOL)
STORAGESEVER
2008-05-02
May 2, 2008 ... Bio-decolorization kinetic studies of distillery effluent in a batch culture were conducted using. Aspergillus .... (2). Where X0 is inoculum's concentration and S0 is initial substrate concentration in g/l, respectively. Rearranging equation 2 gives: sx sx. Y. X. SY. X. S .... generation and biodecolorization.
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
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
In this report we continue with the description of a newly developed numerical method to solve the drift kinetic equation for ions and electrons in toroidal plasmas. Several numerical aspects, already outlined in a previous report [Informes Tecnicos Ciemat 1165, mayo 2009], will be treated now in more detail. Aside from discussing the method in the context of other existing codes, various aspects will be now explained from the viewpoint of numerical methods: the way to solve convection equations, the adopted boundary conditions, the real-space meshing procedures along with a new software developed to build them, and some additional questions related with the parallelization and the numerical integration. (Author) 16 refs
International Nuclear Information System (INIS)
Barros, R.C. de.
1992-05-01
Presented here is a new numerical nodal method for the simulation of the axial power distribution within nuclear reactors using the one-dimensional one speed kinetics diffusion model with one group of delayed neutron precursors. Our method is based on a spectral analysis of the nodal kinetics equations. These equations are obtained by integrating the original kinetics equations separately over a time step and over a spatial node, and then considering flat approximations for the forward difference terms. These flat approximations are the only approximations that are considered in the method. As a result, the spectral nodal method for space - time reactor kinetics generates numerical solutions for space independent problems or for time independent problems that are completely free from truncation errors. We show numerical results to illustrate the method's accuracy for coarse mesh calculations. (author)
Energy Technology Data Exchange (ETDEWEB)
Palma, Daniel A.P. [CEFET QUIMICA de Nilopolis/RJ, 21941-914 Rio de Janeiro (Brazil)], E-mail: agoncalves@con.ufrj.br; Martinez, Aquilino S.; Goncalves, Alessandro C. [COPPE/UFRJ - Programa de Engenharia Nuclear, Rio de Janeiro (Brazil)
2009-09-15
The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.
International Nuclear Information System (INIS)
Palma, Daniel A.P.; Martinez, Aquilino S.; Goncalves, Alessandro C.
2009-01-01
The analytical solution of point kinetics equations with a group of delayed neutrons is useful in predicting the variation of neutron density during the start-up of a nuclear reactor. In the practical case of an increase of nuclear reactor power resulting from the linear insertion of reactivity, the exact analytical solution cannot be obtained. Approximate solutions have been obtained in previous articles, based on considerations that need to be verifiable in practice. In the present article, an alternative analytic solution is presented for point kinetics equations in which the only approximation consists of disregarding the term of the second derivative for neutron density in relation to time. The results proved satisfactory when applied to practical situations in the start-up of a nuclear reactor through the control rods withdraw.
Energy Technology Data Exchange (ETDEWEB)
Grioui, Najla; Halouani, Kamel [Micro-Electro-Thermal Systems - Industrial Energy Systems Group METS-IESG, Institut Preparatoire aux Etudes d' Ingenieurs de Sfax IPEIS, B.P. 805, 3000 Sfax (Tunisia); Zoulalian, Andre [Laboratoire d' Etudes et de Recherches sur le Materiau Bois LERMAB, Universite Henri Point Carre Nancy 1 UHP, B.P. 239, 54506 Vandoeuvre les Nancy Cedex (France); Halouani, Foued [Ecole Nationale d' Ingenieurs de Sfax ENIS, B.P. 3038, Sfax (Tunisia)
2006-01-01
The kinetics of olive wood carbonization is investigated by means of isothermal thermogravimetric analysis method. Measurements were carried out in a thermobalance for different fixed temperatures between 498 and 648K. A two-stage semi-global kinetic model consisting of four sequential steps was proposed to derive kinetic parameters. The olive wood is classified in three pseudo-components. For the first two, similar thermal degradation mechanisms take place in a single reaction step. For the third, the thermal degradation takes place in two consecutive steps. The isothermal conditions allow the kinetic constants (activation energy and pre-exponential factors) to be estimated by means of the analytical solution of the mass conservation equations. An overall good agreement was obtained with activation energy values available in the literature.
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...
Energy Technology Data Exchange (ETDEWEB)
Suescun D, D.; Oviedo T, M., E-mail: daniel.suescun@usco.edu.co [Universidad Surcolombiana, Av. Pastrana Borrero - Carrera 1, Neiva, Huila (Colombia)
2017-09-15
In this paper, a numerical study of stochastic differential equations that describe the kinetics in a nuclear reactor is presented. These equations, known as the stochastic equations of punctual kinetics they model temporal variations in neutron population density and concentrations of deferred neutron precursors. Because these equations are probabilistic in nature (since random oscillations in the neutrons and population of precursors were considered to be approximately normally distributed, and these equations also possess strong coupling and stiffness properties) the proposed method for the numerical simulations is the Euler-Maruyama scheme that provides very good approximations for calculating the neutron population and concentrations of deferred neutron precursors. The method proposed for this work was computationally tested for different seeds, initial conditions, experimental data and forms of reactivity for a group of precursors and then for six groups of deferred neutron precursors at each time step with 5000 Brownian movements per seed. In a paper reported in the literature, the Euler-Maruyama method was proposed, but there are many doubts about the reported values, in addition to not reporting the seed used, so in this work is expected to rectify the reported values. After taking the average of the different seeds used to generate the pseudo-random numbers the results provided by the Euler-Maruyama scheme will be compared in mean and standard deviation with other methods reported in the literature and results of the deterministic model of the equations of the punctual kinetics. This comparison confirms in particular that the Euler-Maruyama scheme is an efficient method to solve the equations of stochastic point kinetics but different from the values found and reported by another author. The Euler-Maruyama method is simple and easy to implement, provides acceptable results for neutron population density and concentration of deferred neutron precursors and
Stepwise kinetic equilibrium models of quantitative polymerase chain reaction
Cobbs, Gary
2012-01-01
Abstract Background Numerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most pote...
International Nuclear Information System (INIS)
Mirzaei, M.; Shahverdi, M.
2004-01-01
This paper is proposed to compare the performances of deferent inviscid flux approximation methods in solution of two-dimensional Euler equations. The methods belong to two different group of flux splitting methods: flux difference splitting (FDS) methods and kinetic flux vector splitting (KFVS) method. Here Roe method and Osher method belonging to flux difference splitting (FDS) group have been employed and their performances are compared with that of kinetic flux vector splitting method (KFVS). Roe and Osher methods are based on approximate solution of Riemann problem over computational cell surfaces while the KFVS has a quit different base. In KFVS inviscid fluxes are approximated based on the kinetic theory and correlation between Boltzmann equation and Euler equations. For comparison the performances of the above mentioned methods three different problems have been solved. The first problem is flow over a 10 degree compression-expansion ramp with Mach number of 2.0, the second one is a transonic flow with Mach number of 0.85 over a 4.2% circular bump in a duct and the third is supersonic flow with Mach number of 3.0 over a circular blunt slab. (author)
Kinetic theory model predictions compared with low-thrust axisymmetric nozzle plume data
Riley, B. R.; Fuhrman, S. J.; Penko, P. F.
1993-01-01
A system of nonlinear integral equations equivalent to the steady-state Krook kinetic equation was used to model the flow from a low-thrust axisymmetric nozzle. The mathematical model was used to numerically calculate the number density, temperature, and velocity of a simple gas as it expands into a near vacuum. With these quantities the gas pressure and flow directions of the gas near the exit plane were calculated and compared with experimental values for a low-thrust nozzle of the same geometry and mass flow rate.
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.
Performance of neutron kinetics models for ADS transient analyses
International Nuclear Information System (INIS)
Rineiski, A.; Maschek, W.; Rimpault, G.
2002-01-01
Within the framework of the SIMMER code development, neutron kinetics models for simulating transients and hypothetical accidents in advanced reactor systems, in particular in Accelerator Driven Systems (ADSs), have been developed at FZK/IKET in cooperation with CE Cadarache. SIMMER is a fluid-dynamics/thermal-hydraulics code, coupled with a structure model and a space-, time- and energy-dependent neutronics module for analyzing transients and accidents. The advanced kinetics models have also been implemented into KIN3D, a module of the VARIANT/TGV code (stand-alone neutron kinetics) for broadening application and for testing and benchmarking. In the paper, a short review of the SIMMER and KIN3D neutron kinetics models is given. Some typical transients related to ADS perturbations are analyzed. The general models of SIMMER and KIN3D are compared with more simple techniques developed in the context of this work to get a better understanding of the specifics of transients in subcritical systems and to estimate the performance of different kinetics options. These comparisons may also help in elaborating new kinetics models and extending existing computation tools for ADS transient analyses. The traditional point-kinetics model may give rather inaccurate transient reaction rate distributions in an ADS even if the material configuration does not change significantly. This inaccuracy is not related to the problem of choosing a 'right' weighting function: the point-kinetics model with any weighting function cannot take into account pronounced flux shape variations related to possible significant changes in the criticality level or to fast beam trips. To improve the accuracy of the point-kinetics option for slow transients, we have introduced a correction factor technique. The related analyses give a better understanding of 'long-timescale' kinetics phenomena in the subcritical domain and help to evaluate the performance of the quasi-static scheme in a particular case. One
Role of secondary instability theory and parabolized stability equations in transition modeling
El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.
1993-01-01
In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.
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...
Hierarchical regression analysis in structural Equation Modeling
de Jong, P.F.
1999-01-01
In a hierarchical or fixed-order regression analysis, the independent variables are entered into the regression equation in a prespecified order. Such an analysis is often performed when the extra amount of variance accounted for in a dependent variable by a specific independent variable is the main
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.
International Nuclear Information System (INIS)
Ol'khovskij, I.I.; Sadykov, N.M.
1980-01-01
The paper deals with the development of classical-statistical approach to the orientational effect theory with account of the influence of the two-particle correlation function of a crystal on diffusion processes. Peculiarities of fast particle movement in the crystal moving at small angles to crystallographic axes and planes are caused by a great number of correlated collisions of the beam particle with the crystal atoms during which the particle slightly deviates in each collision from the direction of its movement before the collision. Obtained is the kinetic equation for the distribution function over coordinates and velocities describing the movement of these particles in the crystal. Lacking the particle deceleration the equation describing movement of the beam particles in the averaged potential and their diffusion by velocities is also obtained. The main peculiarity of these equations is the fact that they take into account strong spatial non-uniformity in the crystal atom distribution [ru
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
Superfluid kinetic equation approach to the dynamics of the 3He A-B phase boundary
International Nuclear Information System (INIS)
Palmeri, J.
1990-01-01
The dynamics of the A-B phase boundary is studied using a nonequilibrium theory inspired by the microscopic approach to flux flow in type-II superconductors, namely a generalized two-fluid model consisting of coupled dynamical equations for the superfluid order parameter and the quasiparticle fluid. The interface mobility is obtained to lowest order in the front velocity in three different dynamical regimes: the gapless, hydrodynamic, and ballistic. Experiments have so far only been performed in the ballistic regime, and in this regime we find that, if only Andreev scattering processes are accounted for in the interface mobility, then the theoretical predictions for the terminal velocity of the planar interface are too big by a factor ∼2. From this we conclude that there may be other important contributions to the interface mobility in the ballistic regime, and we discuss a few possibilities
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.
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
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 advectiondiffusion 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. For rectilinear flow we show numerical results which indicate that the quasi-dynamic provides accurate approximations. 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.
Prior sensitivity analysis in default Bayesian structural equation modeling
van Erp, S.J.; Mulder, J.; Oberski, Daniel L.
2018-01-01
Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models while solving some of the issues often encountered in classical maximum likelihood (ML) estimation, such as nonconvergence and inadmissible solutions. An important
Modeling High Frequency Semiconductor Devices Using Maxwell's Equations
National Research Council Canada - National Science Library
El-Ghazaly, Samier
1999-01-01
.... In this research, we first replaced the conventional semiconductor device models, which are based on Poisson's Equation as a semiconductor model, with a new one that uses the full-wave electro...
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.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the third of a series [Informes Tecnicos Ciemat 1165 y 1172] devoted to the development of a new numerical code to solve the guiding center equation for electrons and ions in toroidal plasmas. Two calculation meshes corresponding to axisymmetric tokamaks are now prepared and the kinetic equation is expanded so the standard terms of neoclassical theory --fi rst order terms in the Larmor radius expansion-- can be identified, restricting the calculations correspondingly. Using model density and temperature profiles for the plasma, several convergence test are performed depending on the calculation meshes and the expansions of the distribution function; then the results are compared with the theory [Hinton and Hazeltine, Rev. Mod. Phys. (1976)]. (Author) 18 refs
COMPARATIVE ANALYSIS OF SOME EXISTING KINETIC MODELS ...
African Journals Online (AJOL)
The biosorption of three heavy metal ions namely; Zn2+, Cu2+ and Mn2+ using five microorganisms namely; Bacillus circulans, Pseudomonas aeruginosa, Staphylococcus xylosus, Streptomyces rimosus and Yeast (Saccharomyces sp.) were studied. In this paper, the effectiveness of six existing and two proposed kinetic ...
Reverberation Modelling Using a Parabolic Equation Method
2012-10-01
results obtained by other authors and methods. Résumé …..... RDDC Atlantique a élaboré un modèle de fouillis d’échos acoustiques fondé sur les modes...PE pour parabolic equation), pour déterminer la faisabilité du calcul du champ acoustique et de la réverbération des échos de cibles dans différents...2012. Introduction ou contexte : RDDC Atlantique a élaboré un modèle de fouillis d’échos acoustiques fondé sur les modes normaux adiabatiques pour
Nodal kinetics model upgrade in the Penn State coupled TRAC/NEM codes
International Nuclear Information System (INIS)
Beam, Tara M.; Ivanov, Kostadin N.; Baratta, Anthony J.; Finnemann, Herbert
1999-01-01
The Pennsylvania State University currently maintains and does development and verification work for its own versions of the coupled three-dimensional kinetics/thermal-hydraulics codes TRAC-PF1/NEM and TRAC-BF1/NEM. The subject of this paper is nodal model enhancements in the above mentioned codes. Because of the numerous validation studies that have been performed on almost every aspect of these codes, this upgrade is done without a major code rewrite. The upgrade consists of four steps. The first two steps are designed to improve the accuracy of the kinetics model, based on the nodal expansion method. The polynomial expansion solution of 1D transverse integrated diffusion equation is replaced with a solution, which uses a semi-analytic expansion. Further the standard parabolic polynomial representation of the transverse leakage in the above 1D equations is replaced with an improved approximation. The last two steps of the upgrade address the code efficiency by improving the solution of the time-dependent NEM equations and implementing a multi-grid solver. These four improvements are implemented into the standalone NEM kinetics code. Verification of this code was accomplished based on the original verification studies. The results show that the new methods improve the accuracy and efficiency of the code. The verification of the upgraded NEM model in the TRAC-PF1/NEM and TRAC-BF1/NEM coupled codes is underway
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.
International Nuclear Information System (INIS)
Reynolds, J. M.; Lopez-Bruna, D.
2009-01-01
This report is the first of a series dedicated to the numerical calculation of the evolution of fusion plasmas in general toroidal geometry, including TJ-II plasmas. A kinetic treatment has been chosen: the evolution equation of the distribution function of one or several plasma species is solved in guiding center coordinates. The distribution function is written as a Maxwellian one modulated by polynomial series in the kinetic coordinates with no other approximations than those of the guiding center itself and the computation capabilities. The code allows also for the inclusion of the three-dimensional electrostatic potential in a self-consistent manner, but the initial objective has been set to solving only the neoclassical transport. A high order conservative method (Spectral Difference Method) has been chosen in order to discretized the equation for its numerical solution. In this first report, in addition to justifying the work, the evolution equation and its approximations are described, as well as the baseline of the numerical procedures. (Author) 28 refs
Improved Kinetic Models for High-Speed Combustion Simulation
National Research Council Canada - National Science Library
Montgomery, C. J; Tang, Q; Sarofim, A. F; Bockelie, M. J; Gritton, J. K; Bozzelli, J. W; Gouldin, F. C; Fisher, E. M; Chakravarthy, S
2008-01-01
Report developed under an STTR contract. The overall goal of this STTR project has been to improve the realism of chemical kinetics in computational fluid dynamics modeling of hydrocarbon-fueled scramjet combustors...
Mathematical modelling of water radiolysis kinetics under reactor conditions
International Nuclear Information System (INIS)
Khodulev, L.B.; Shapova, E.A.
1989-01-01
Experimental data on coolant radiolysis (RBMK-1000 reactor) were used to construct mathematical model of water radiolysis kinetics under reactor conditions. Good agreement of calculation results with the experiment is noted
On coupling fluid plasma and kinetic neutral physics models
Joseph, I.; Rensink, M.E.; Stotler, D.P.; Dimits, A.M.; LoDestro, L.L.; Porter, G.D.; Rognlien, T.D.; Sjogreen, B.; Umansky, M.V.
2017-01-01
The coupled fluid plasma and kinetic neutral physics equations are analyzed through theory and simulation of benchmark cases. It is shown that coupling methods that do not treat the coupling rates implicitly are restricted to short time steps for stability. Fast charge exchange, ionization and recombination coupling rates exist, even after constraining the solution by requiring that the neutrals are at equilibrium. For explicit coupling, the present implementation of Monte Carlo correlated sa...
Error Propagation in Equations for Geochemical Modeling of ...
Indian Academy of Sciences (India)
This paper presents error propagation equations for modeling of radiogenic isotopes during mixing of two components or end-members. These equations can be used to estimate errors on an isotopic ratio in the mixture of two components, as a function of the analytical errors or the total errors of geological field sampling ...
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)....
Soluble Boltzmann equations for internal state and Maxwell models
Futcher, E.; Hoare, M.R.; Hendriks, E.M.; Ernst, M.H.
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
Modelling equation of knee force during instep kicking using ...
African Journals Online (AJOL)
This paper presents the biomechanics analysis of the football players, to obtain the equation that relates with the variables and to get the force model equation when the kicking was made. The subjects delivered instep kicking by using the dominant's leg where one subjects using right and left leg. 2 Dimensional analysis ...
Analysis of a kinetic multi-segment foot model part II: kinetics and clinical implications.
Bruening, Dustin A; Cooney, Kevin M; Buczek, Frank L
2012-04-01
Kinematic multi-segment foot models have seen increased use in clinical and research settings, but the addition of kinetics has been limited and hampered by measurement limitations and modeling assumptions. In this second of two companion papers, we complete the presentation and analysis of a three segment kinetic foot model by incorporating kinetic parameters and calculating joint moments and powers. The model was tested on 17 pediatric subjects (ages 7-18 years) during normal gait. Ground reaction forces were measured using two adjacent force platforms, requiring targeted walking and the creation of two sub-models to analyze ankle, midtarsal, and 1st metatarsophalangeal joints. Targeted walking resulted in only minimal kinematic and kinetic differences compared with walking at self selected speeds. Joint moments and powers were calculated and ensemble averages are presented as a normative database for comparison purposes. Ankle joint powers are shown to be overestimated when using a traditional single-segment foot model, as substantial angular velocities are attributed to the mid-tarsal joint. Power transfer is apparent between the 1st metatarsophalangeal and mid-tarsal joints in terminal stance/pre-swing. While the measurement approach presented here is limited to clinical populations with only minimal impairments, some elements of the model can also be incorporated into routine clinical gait analysis. Copyright © 2011 Elsevier B.V. All rights reserved.
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
Kinetic modeling of formic acid pulping of bagasse.
Tu, Qiliang; Fu, Shiyu; Zhan, Huaiyu; Chai, Xinsheng; Lucia, Lucian A
2008-05-14
Organic solvent or organosolv pulping processes are alternatives to soda or kraft pulping to delignify lignocellulosic materials for the production of paper pulp. Formic acid, a typical organosolv system, has been presently examined under atmospheric pressure to pulp bagasse fibers. It was shown that efficient bagasse pulping was achieved when the formic acid concentration was limited to 90% (v/v). A statistical kinetic model based on the experimental results for the delignification of bagasse during formic acid pulping was developed that can be described as follows: D (delignification) = 0.747 x C(formicacid) (1.688) x (1 - e(-0.05171t)), an equation that can be used to predict the lignin content in formic acid during the pulping process. The delignification of bagasse by 90% formic acid was almost completed after approximately 80 min, while extended pulping did not improve the delignification but tended to degrade the carbohydrates in bagasse, especially the hemicelluloses, which were rapidly hydrolyzed at the onset of pulping.
Kinetic modelization of water-rock interaction processes
International Nuclear Information System (INIS)
Pena, J.; Gimeno, M.J.
1994-01-01
A review of basic concepts in kinetics of low temperature natural systems is given: elementary and overall reactions, steady state and reaction mechanism, sequential reactions, parallel reactions and rate-determining step, temperature dependence of rate constant and principle of detailed balancing. The current status of kinetics modeling of water/rock interaction is treated. The comparison of the mean life of the processes with the residence time of the water in the system is very useful to decide the application or not of the kinetics treatment to the water/rock interaction processes. The right application of the kinetics treatment to the water/rock interaction needs the knowledge of the magnitude of the surface through which the water/rock reaction take place and its variation with time. Two ways to treat kinetically the water/rock interaction are the Mass Transfer method and the quasi-stationary state method
DEFF Research Database (Denmark)
Saa, Pedro A.; Nielsen, Lars K.
2017-01-01
Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive...... capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction...
Turbulence modeling methods for the compressible Navier-Stokes equations
Coakley, T. J.
1983-01-01
Turbulence modeling methods for the compressible Navier-Stokes equations, including several zero- and two-equation eddy-viscosity models, are described and applied. Advantages and disadvantages of the models are discussed with respect to mathematical simplicity, conformity with physical theory, and numerical compatibility with methods. A new two-equation model is introduced which shows advantages over other two-equation models with regard to numerical compatibility and the ability to predict low-Reynolds-number transitional phenomena. Calculations of various transonic airfoil flows are compared with experimental results. A new implicit upwind-differencing method is used which enhances numerical stability and accuracy, and leads to rapidly convergent steady-state solutions.
Yang-Mills equation for the collective model
Sparks, Nick; Rosensteel, George
2015-10-01
To determine the collective model connection, an equation is needed that relates the connection to the nuclear current. The correct equation is the Yang-Mills equation for the collective model bundle. The essential mathematical structure of both Yang-Mills and the collective model is a bundle with a differential geometric connection, but the particulars are quite different. In particular, the base manifold for Yang-Mills is Minkowski space, whereas the base manifold for the collective model is the space of all nuclear orientations and quadrupole deformations. The Lie structure groups are both non-abelian: Yang-Mills electroweak is U(2) and the collective model is SO(3). The YM equation is derived from the YM Lagrangian which depends on the bundle curvature. Solutions are found for rotation about one principal axis. These solutions range continuously from the irrotational flow to the rigid body connections as the current ranges from irrotational to rigid.
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.
International Nuclear Information System (INIS)
Hamada, Yasser Mohamed
2013-01-01
Highlights: ► Generalized power series method has extended to solve the point kinetics equations with temperature feedback. ► Convergence of both the power series and the partial sums are discussed. ► The method helps reduction the number of iterations and computational times. ► The accuracy of the method is confirmed by testing five different cases of temperature reactivity feedback. - Abstract: In this paper, generalized power series method (GPWS) is developed to obtain approximate solutions to point kinetics equations with feedback. The stiffness of the kinetics equations restricts the time interval to a small increment, which in turn restricts the traditional power series method (PWS) within a very small constant step size especially when the generation times are very small. The GPWS method has introduced time intervals that are much longer than time intervals used in the conventional numerical integrations like Generalized Runge–Kutta or power series methods, and it is thus useful in reducing computing time. Convergence of both the power series and the partial sums are discussed and the time step has been restricted within a circle of convergence by using the convergence conditions. Local truncation errors and some other constraints are used to produce the largest step size allowable at each step while keeping the error within a specific tolerance. The accuracy of the method is examined using five different cases of temperature reactivity feedback for step and ramp impressive reactivities with one and six groups of delayed neutrons. Supercritical (prompt and delayed) processes of a nuclear reactor with temperature feedback are discussed while inserting large and small reactivities. Results obtained by GPWS method attest the effectiveness the theoretical analysis, they demonstrate that the convergence of the iteration scheme can be controllable. The proposed method is accurate when compared to the analytical and numerical methods
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......High pressure (HP) inactivation curves of Listeria monocytogenes CTC1034 (ca. 107CFU/g) on sliced RTE cooked meat products (ham and mortadella) were obtained at pressures from 300 to 800MPa. A clear tail shape was observed at pressures above 450MPa and the log-linear with tail primary model...... 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...
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.
Development of a kinetic model for biological sulphate reduction ...
African Journals Online (AJOL)
Further, in the BSR model the end-product sulphide has a gaseous equilibrium not in the UCTADM1 model, and hence the physical gas exchange for sulphide is included. The BSR biological, chemical and physical processes are integrated with those of the UCTADM1 model, to give a complete kinetic model for competitive ...
Detailed chemical kinetic modeling of cyclohexane oxidation.
Silke, Emma J; Pitz, William J; Westbrook, Charles K; Ribaucour, Marc
2007-05-17
A detailed chemical kinetic mechanism has been developed and used to study the oxidation of cyclohexane at both low and high temperatures. Rules for reaction rate constants are developed for the low-temperature combustion of cyclohexane. These rules can be used for in chemical kinetic mechanisms for other cycloalkanes. Because 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 with O2 through five-, six-, and seven-membered-ring transition states. The direct elimination of cyclohexene and HO2 from RO2 is included in the treatment using a modified rate constant of Cavallotti et al. (Proc. Combust. Inst. 2007, 31, 201). 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 cannot be simulated according to the current understanding of low-temperature chemistry. Possible "alternative" H-atom isomerizations leading to different products from the parent O2QOOH radical were included in the low-temperature chemical kinetic mechanism and were found to play a significant role.
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.
Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis
International Nuclear Information System (INIS)
Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A.D.
2016-01-01
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.
Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing
International Nuclear Information System (INIS)
Kokkinakis, I.W.; Drikakis, D.; Youngs, D.L.; Williams, R.J.R.
2015-01-01
Highlights: • We present a new improved version of the K–L model. • The improved K–L is found in good agreement with the multi-fluid model and ILES. • The study concerns Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. - Abstract: This paper presents a new, improved version of the K–L model, as well as a detailed investigation of K–L and multi-fluid models with reference to high-resolution implicit large eddy simulations of compressible Rayleigh–Taylor mixing. The accuracy of the models is examined for different interface pressures and specific heat ratios for Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. It is shown that the original version of the K–L model requires modifications in order to provide comparable results to the multi-fluid model. The modifications concern the addition of an enthalpy diffusion term to the energy equation; the formulation of the turbulent kinetic energy (source) term in the K equation; and the calculation of the local Atwood number. The proposed modifications significantly improve the results of the K–L model, which are found in good agreement with the multi-fluid model and implicit large eddy simulations with respect to the self-similar mixing width; peak turbulent kinetic energy growth rate, as well as volume fraction and turbulent kinetic energy profiles. However, a key advantage of the two-fluid model is that it can represent the degree of molecular mixing in a direct way, by transferring mass between the two phases. The limitations of the single-fluid K–L model as well as the merits of more advanced Reynolds-averaged Navier–Stokes models are also discussed throughout the paper.
A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow
Xu, Kun
1999-01-01
A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.
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.
Continuous time structural equation modeling with R package ctsem
Driver, C.C.; Oud, J.H.L.; Völkle, M.C.
2017-01-01
We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1) and time series (N = 1) data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models) in the social and behavioural sciences are discrete time models. An
A simultaneous equations model of fiscal policy interactions
Allers, Maarten A.; Elhorst, J. Paul
Existing studies of fiscal policy interactions are based on single equation (SE) models of either taxation or expenditures, without specifying the underlying social welfare function, without taking account of budget constraints and without allowing for cost differences between jurisdictions. Taking
The use of Structural Equation Modelling (SEM) in Capital Structure ...
African Journals Online (AJOL)
analytic structural equation modelling (SEM) methodology. The SEM Methodology allows the use of more than one indicator for a latent variable. It also estimates the latent variables and accommodates reciprocal causation and interdependences ...
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Dynamic data analysis modeling data with differential equations
Ramsay, James
2017-01-01
This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...
Modelling of nonlinear shoaling based on stochastic evolution equations
DEFF Research Database (Denmark)
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
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...... with experimental data in four different cases as well as with the underlying deterministic model. In general, the agreement is found to be acceptable, even far beyond the region where Gaussianity (Gaussian sea state) may be justified. (C) 1998 Elsevier Science B.V....
Euler and Navier endash Stokes limits of the Uehling endash Uhlenbeck quantum kinetic equations
International Nuclear Information System (INIS)
Arlotti, L.; Lachowicz, M.
1997-01-01
The Uehling endash Uhlenbeck evolution equations for gases of identical quantum particles either fermions or bosons, in the case in which the collision kernel does not depend on the distribution function, are considered. The existence of solutions and their asymptotic relations with solutions of the hydrodynamic equations both at the level of the Euler system and at the level of the Navier endash Stokes system are proved. copyright 1997 American Institute of Physics
Illness-death model: statistical perspective and differential equations.
Brinks, Ralph; Hoyer, Annika
2018-01-27
The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.
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/m2. 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.
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.
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...... with a very good approximation. The crucial points are: to represents the quantum coherent oscillations by first order rate constants, and to determine the number of kinetic channels corresponding to a given interaction. We consider a radical pair system with spin selective reactions and calculate the spin...
International Nuclear Information System (INIS)
Paixao, S.B.
1987-01-01
In order to find out the numerical solutions of point reactor kinetic, the exponential approximation method is used. The basic assumption is: the neutron populations and delayed precursors behave exponentially with an asymptotic characteristic frequency corresponding to the reactivity. The CIPOR (Point Kinetc with Feedback) computer code was elaborated, and several cases were implemented. (M.C.K.) [pt
International Nuclear Information System (INIS)
Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T.
2017-01-01
In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)
Energy Technology Data Exchange (ETDEWEB)
Tumelero, Fernanda; Bodmann, Bardo E. J.; Vilhena, Marco T. [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos Graduacao em Engenharia Mecanica; Lapa, Celso M.F., E-mail: fernanda.tumelero@yahoo.com.br, E-mail: bardo.bodmann@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: lapa@ien.gov.br [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)
2017-07-01
In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the rst recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution. (author)
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
Finite Feedback Cycling in Structural Equation Models
Hayduk, Leslie A.
2009-01-01
In models containing reciprocal effects, or longer causal loops, the usual effect estimates assume that any effect touching a loop initiates an infinite cycling of effects around that loop. The real world, in contrast, might permit only finite feedback cycles. I use a simple hypothetical model to demonstrate that if the world permits only a few…
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.
Computer kinetic modelling of radionuclide accumulation in Marine organisms
International Nuclear Information System (INIS)
Quintella, H.M.; Santimateo, D.; Paschoa, A.S.
1977-01-01
Continuous System Modelling Program (CSMP) is used to simulate the first step of the kinetic of a radionuclide in a food chain by using the exponential model of accumulation from water-to-algae based on data found in the literature. The use of computer modelling as a tool for environmental studies is discussed as far as economical advantages and future applications are concerned
Reaction Kinetics Model of Polymerization in the Absence of ...
African Journals Online (AJOL)
This paper is on reaction kinetics models for approximating diffuse propagation reaction fronts in one-dimensional gasless combustion type models. This study is carried out in the context of free-radical frontal polymerization (FP) via a propagating, self sustaining reacting front in the absence of material diffusion. The model ...
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.
Probabilistic Model Checking of Biological Systems with Uncertain Kinetic Rates
Barbuti, Roberto; Levi, Francesca; Milazzo, Paolo; Scatena, Guido
We present an abstraction of the probabilistic semantics of Multiset Rewriting to formally express systems of reactions with uncertain kinetic rates. This allows biological systems modelling when the exact rates are not known, but are supposed to lie in some intervals. On these (abstract) models we perform probabilistic model checking obtaining lower and upper bounds for the probabilities of reaching states satisfying given properties. These bounds are under- and over-approximations, respectively, of the probabilities one would obtain by verifying the models with exact kinetic rates belonging to the intervals.
Constitutive equation of concrete: Mesomechanical isotropic model
Czech Academy of Sciences Publication Activity Database
Kafka, Vratislav; Vokoun, David
2005-01-01
Roč. 1, č. 2 (2005), s. 183-193 ISSN 1573-6105 Institutional research plan: CEZ:AV0Z20710524 Keywords : plasticity * constitutive modeling * concrete * mesomechanics Subject RIV: JI - Composite Materials
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/O2/Ar flame at 30Torr was studied using synchrotron VUV PIMS. A detailed kinetic model for ECH high temperature pyrolysis and oxidation was developed and validated against the pyrolysis and flame data performed in this work. Further validation of the kinetic model is presented against literature data including species concentrations in jet-stirred reactor oxidation, ignition delay times in a shock tube, and laminar flame speeds at various pressures and equivalence ratios. The model well predicts the consumption of ECH, the growth of aromatics, and the global combustion properties. Reaction flux and sensitivity analysis were utilized to elucidate chemical kinetic features of ECH combustion under various reaction conditions. © 2015 The Combustion Institute.
Detailed Chemical Kinetic Modeling of Hydrazine Decomposition
Meagher, Nancy E.; Bates, Kami R.
2000-01-01
The purpose of this research project is to develop and validate a detailed chemical kinetic mechanism for gas-phase hydrazine decomposition. Hydrazine is used extensively in aerospace propulsion, and although liquid hydrazine is not considered detonable, many fuel handling systems create multiphase mixtures of fuels and fuel vapors during their operation. Therefore, a thorough knowledge of the decomposition chemistry of hydrazine under a variety of conditions can be of value in assessing potential operational hazards in hydrazine fuel systems. To gain such knowledge, a reasonable starting point is the development and validation of a detailed chemical kinetic mechanism for gas-phase hydrazine decomposition. A reasonably complete mechanism was published in 1996, however, many of the elementary steps included had outdated rate expressions and a thorough investigation of the behavior of the mechanism under a variety of conditions was not presented. The current work has included substantial revision of the previously published mechanism, along with a more extensive examination of the decomposition behavior of hydrazine. An attempt to validate the mechanism against the limited experimental data available has been made and was moderately successful. Further computational and experimental research into the chemistry of this fuel needs to be completed.
Chen, Jie; Zhao, Bin; An, Qiang; Wang, Xia; Zhang, Yi Xin
2016-04-01
Alcaligenes faecalis strain NR has the capability of simultaneous ammonium and organic carbon removal under sole aerobic conditions. The growth and substrate removal characteristics of A. faecalis strain NR were studied and appropriate kinetic models were developed. The maximum substrate removal rate of NH4 (+)-N and TOC were determined as 2.27 mg NH4 (+)-N/L/h and 30.00 mg TOC/L/h, respectively with initial NH4 (+)-N = 80 mg/L and TOC = 800 mg/L. Single-substrate models and double-substrate models based on Monod, Contois, Moser and Teissier were employed to describe the bioprocess kinetic coefficients. As a result, two double-substrate models, Teissier-Contois and Contois-Contois, were considered to be appropriate to model growth kinetics with both NH4 (+)-N and TOC as limiting substrates. The kinetic constants of maximum growth rate (μ max) and half-saturation constant (K S and B S) were obtained by solving multiple equations with regression. This work can be used to further understand and predict the performance of heterotrophic nitrifiers, and thus provides specific guidance of these functional strains in practical wastewater treatment process.
Shapiro, Adam B
2014-05-09
DNA ligase seals the nicks in the phosphodiester backbone between Okazaki fragments during DNA replication. DNA ligase has an unusual Bi Ter Ping Pong kinetic mechanism. Its substrates in eubacteria are NAD+ and nicked DNA (nDNA). Its products are nicotinamide mononucleotide (NMN), adenosine 5'-monophosphate (AMP), and sealed DNA. Investigation of the kinetic mechanism and measurement of the kinetic constants of DNA ligase using steady-state kinetics would benefit from the availability of the complete steady-state rate equation, including terms for product concentrations and product-related kinetic constants, which has not previously been published. The rate equations for two possible Bi Ter kinetic mechanisms for DNA ligase, including products, are reported. The mechanisms differ according to whether the last two products, AMP and sealed DNA, are released in an ordered or rapid-equilibrium random (RER) manner. Steady-state kinetic studies of product inhibition by NMN and AMP were performed with Haemophilus influenzae NAD+-dependent DNA ligase. The complete rate equation enabled measurement of dissociation constants for NAD+, NMN, and AMP and eliminated one of 3 possible product release mechanisms. Steady-state kinetic product inhibition experiments and complete steady-state kinetic rate equations were used to measure dissociation constants of NAD+, NMN, and AMP and eliminate the possibility that AMP is the second product released in an ordered mechanism. Determining by steady-state kinetics whether the release of sealed DNA and AMP products goes by an ordered (AMP last off) or RER mechanism was shown to require a product inhibition study using sealed DNA.
Transport modelling in coastal waters using stochastic differential equations
Charles, W.M.
2007-01-01
In this thesis, the particle model that takes into account the short term correlation behaviour of pollutants dispersion has been developed. An efficient particle model for sediment transport has been developed. We have modified the existing particle model by adding extra equations for the
[Precision of data from models of sodium kinetics in hemodialysis].
Ahrenholz, P; Falkenhagen, D; Hähling, D; Klinkmann, H
1990-08-01
The 1-pool-model of sodium kinetics during hemodialysis is based upon the assumption of an immediate compensation of osmotic shifts. This assumption is not supported by measurements of plasma sodium, total protein concentration and colloid osmotic pressure kinetics. When a high dialysate sodium concentration is applied, an inflow of sodium into the plasma space occurs, which results in an osmotic suction and thus a plasma dilution. These conditions can be represented by a 2-pool-model taking into consideration capillary filtration. The results indicate that following the first treatment period the sodium kinetics are sufficiently explained by a 1-pool-model with the total body water as distribution volume. Both the plasma sodium concentration and the eliminated sodium at the end of a hemodialysis treatment can be described to an acceptable level by the 1-pool-model. The input of the measured in-vivo sodium dialysance value (or alternatively the urea clearance) is necessary.
On the Schroedinger equation for the minisuperspace models
International Nuclear Information System (INIS)
Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.
2000-01-01
We obtain a time-dependent Schroedinger equation for the Friedmann-Robertson-Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necessary to include an additional action invariant under the reparametrization of time. The last one does not change the equations of motion of the system, but changes only the constraint which at the quantum level becomes time-dependent Schroedinger equation. The same procedure is applied to the supersymmetric case and the supersymmetric quantum constraints are obtained, one of them is a square root of the Schroedinger operator
Kinetics models describing degradation-relaxation effects in nanoinhomogeneous substances
Shpotyuk, O.; Balitska, V.; Brunner, M.
2017-12-01
The mathematical models of degradation-relaxation kinetics are considered for jammed systems composed of screen-printed spinel Cu0.1Ni0.1Co1.6Mn1.2O4 and conductive Ag or Ag-Pd alloys. Structurally-intrinsic nanoinhomogeneities due to Ag and Ag-Pd diffusants embedded in spinel phase environment are shown to define governing kinetics of thermally-induced degradation obeying an obvious non-exponential behaviour in the resistance drift. The stretched-to-compressed exponential crossover is detected for degradation-relaxation kinetics in these systems with conductive contacts made of Ag-Pd and Ag alloys. Under essential migration of conductive phase, the resulting kinetics is though to be considerable two-step diffusing process originated from Ag penetration deep into spinel ceramics.
Generalized heat-transport equations: parabolic and hyperbolic models
Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio
2018-03-01
We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.
Multigroup perturbation model for kinetic analysis of nuclear reactors
International Nuclear Information System (INIS)
Souza, G.M.
1989-01-01
The scope of this work is the development of a multigroup perturbation theory for the purpose of Kinetic and dynamic analysis of nuclear reactors. The equations that describe the reactor behavior were presented in all generality and written in the shorthand notation of matrices and vectors. In the derivation of those equations indetermined operators and discretizing factors were introduced and then determined by comparision with conventional equations. Fick's Law was developed in higher orders for neutron and importance current density. The solution of the direct and adjoint fields were represented by combination of the eigenfunctions of the B and B* operators and the eigenvalue modulus equality was established mathematically. In the derivation of the reactivity expression the B operator perturbation was split in two non coupled to the flux form and level. The prompt neutrons effective mean life was derived from reactor equations and importance conservation. The establishment of the Nordheim's equation, although modified, was based on Gandini. Finally, a mathematical interpretation of the flux-trap region was avented. (author)
Javad Azarhoosh, Mohammad; Halladj, Rouein; Askari, Sima
2017-10-01
In this study, a new kinetic model for methanol to light olefins (MTO) reactions over a hierarchical SAPO-34 catalyst using the Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism was presented and the kinetic parameters was obtained using a genetic algorithm (GA) and genetic programming (GP). Several kinetic models for the MTO reactions have been presented. However, due to the complexity of the reactions, most reactions are considered lumped and elementary, which cannot be deemed a completely accurate kinetic model of the process. Therefore, in this study, the LHHW mechanism is presented as kinetic models of MTO reactions. Because of the non-linearity of the kinetic models and existence of many local optimal points, evolutionary algorithms (GA and GP) are used in this study to estimate the kinetic parameters in the rate equations. Via the simultaneous connection of the code related to modelling the reactor and the GA and GP codes in the MATLAB R2013a software, optimization of the kinetic models parameters was performed such that the least difference between the results from the kinetic models and experiential results was obtained and the best kinetic parameters of MTO process reactions were achieved. A comparison of the results from the model with experiential results showed that the present model possesses good accuracy.
Circumnutation modeled by reaction-diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Lubkin, S.R.
1992-01-01
In studies of biological oscillators, plants are only rarely examined. The authors study a common sub-diurnal oscillation of plants, called circumnutation. Based on experimental evidence that the oscillations consist of a turgor wave traveling around a growing plant part, circumnutation is modeled by a nonlinear reaction-diffusion system with cylindrical geometry. Because of its simplicity, and because biological oscillations are so common, an oscillatory [lambda]-[omega] reaction-diffusion system is chosen for the model. The authors study behavior of traveling waves in [lambda]-[omega] systems. The authors show the existence of Hopf bifurcations and the stability of the limit cycles born at the Hopf bifurcation for some parameter values. Using a Lindstedt-type perturbation scheme, the authors construct periodic solutions of the [lambda]-[omega] system near a Hopf bifurcation and show that the periodic solutions superimposed on the original traveling wave have the effect of altering its overall frequency and amplitude. Circumnutating plants generally display a strong directional preference to their oscillations, which is species-dependent. Circumnutation is modeled by a [lambda]-[omega] system on an annulus of variable width, which does not possess reflection symmetry about any axis. The annulus represents a region of high potassium concentration in the cross-section of the stem. The asymmetry of the annulus represents the anatomical asymmetry of the plant. Traveling waves are constructed on this variable-width annulus by a perturbation scheme, and perturbing the width of the annulus alters the amplitude and frequency of traveling waves on the domain by a small (order [epsilon][sup 2]) amount. The speed, frequency, and stability are unaffected by the direction of travel of the wave on the annulus. This indicates that the [lambda]-[omega] system on a variable-width domain cannot account for directional preferences of traveling waves in biological systems.
Model Equations of Shape Memory Effect - Nitinol
Directory of Open Access Journals (Sweden)
Ion Vela
2010-01-01
Full Text Available Even it has been already confirmed that SMA’s have high potential for robotic actuators, actuators included in space robotics, underwater robotics, robotics for logistics, safety, as well as “green robotics” (robotics for the environment, energy conservation, sustainable development or agriculture, the number of applications of SMA-based actuators is still quite small, especially in applications in which their large strains, high specific work output and structural integration potential are useful,. The paper presents a formulated mathematical model calculated for binary SMA (Ni-Ti, helpful to estimate the stress distribution along with the transformation ratio of a SMA active element.
Padrino, Juan C.; Sprittles, James; Lockerby, Duncan
2017-11-01
Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).
Cáceres, Lizethly; Escudey, Mauricio; Fuentes, Edwar; Báez, María E
2010-07-15
Metsulfuron-methyl sorption kinetic was studied in Andisol and Ultisol soils in view of their distinctive physical and chemical properties: acidic pH and variable surface charge. Different kinetic models were applied to the experimental results. The pseudo-second-order model fitted sorption kinetics data better than the pseudo-first-order model. The rate constant and the initial rate constant values obtained through this model demonstrated the different behavior of metsulfuron-methyl in both kinds of soils, both parameters being the highest for Andisol. The application of Elovich equation, intraparticle diffusion model and a two-site nonequilibrium model (TSNE) allowed to conclude that: (i) the high organic matter content is the governing factor for Andisols where mass transfer across the boundary layer, and in a lesser degree, intraparticle diffusion were the two processes controlling sorption kinetic and (ii) the mineral composition was more relevant in Ultisols where rate was controlled almost exclusively by intraparticle diffusion into macropores and micropores. The slower sorption rate on Ultisols, the mechanism involved and the lower sorption capacity of this kind of soils must be taken into account to assess leaching behavior of this herbicide. 2010 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Mallet, J.
2012-01-01
This research thesis stands at the crossroad of plasma physics, numerical analysis and applied mathematics. After an introduction presenting the problematic and previous works, the author recalls some basis of classical kinetic models for plasma physics (collisionless kinetic theory and Vlasov equation, collisional kinetic theory with the non-relativistic Maxwell-Fokker-Plansk system) and describes the fundamental properties of the collision operators such as conservation laws, entropy dissipation, and so on. He reports the improvement of a deterministic numerical method to solve the non-relativistic Vlasov-Maxwell system coupled with Fokker-Planck-Landau type operators. The efficiency of each high order scheme is compared. The evolution of the hot spot is studied in the case of thermonuclear reactions in the centre of the pellet in a weakly collisional regime. The author focuses on the simulation of the kinetic electron collisional transport in inertial confinement fusion (ICF) between the laser absorption zone and the ablation front. A new approach is then introduced to reduce the huge computation time obtained with kinetic models. In a last chapter, the kinetic continuous equation in spherical domain is described and a new model is chosen for collisions in order to preserve collision properties
Computer-Aided Construction of Chemical Kinetic Models
Energy Technology Data Exchange (ETDEWEB)
Green, William H. [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2014-12-31
The combustion chemistry of even simple fuels can be extremely complex, involving hundreds or thousands of kinetically significant species. The most reasonable way to deal with this complexity is to use a computer not only to numerically solve the kinetic model, but also to construct the kinetic model in the first place. Because these large models contain so many numerical parameters (e.g. rate coefficients, thermochemistry) one never has sufficient data to uniquely determine them all experimentally. Instead one must work in “predictive” mode, using theoretical rather than experimental values for many of the numbers in the model, and as appropriate refining the most sensitive numbers through experiments. Predictive chemical kinetics is exactly what is needed for computer-aided design of combustion systems based on proposed alternative fuels, particularly for early assessment of the value and viability of proposed new fuels before those fuels are commercially available. This project was aimed at making accurate predictive chemical kinetics practical; this is a challenging goal which requires a range of science advances. The project spanned a wide range from quantum chemical calculations on individual molecules and elementary-step reactions, through the development of improved rate/thermo calculation procedures, the creation of algorithms and software for constructing and solving kinetic simulations, the invention of methods for model-reduction while maintaining error control, and finally comparisons with experiment. Many of the parameters in the models were derived from quantum chemistry calculations, and the models were compared with experimental data measured in our lab or in collaboration with others.
A mathematical model of combustion kinetics of municipal solid ...
African Journals Online (AJOL)
Municipal Solid Waste has become a serious environmental problem troubling many cities. In this paper, a mathematical model of combustion kinetics of municipal solid waste with focus on plastic waste was studied. An analytical solution is obtained for the model. From the numerical simulation, it is observed that the ...
Simplified kinetic models of methanol oxidation on silver
DEFF Research Database (Denmark)
Andreasen, A.; Lynggaard, H.; Stegelmann, C.
2005-01-01
Recently the authors developed a microkinetic model of methanol oxidation on silver [A. Andreasen, H. Lynggaard, C. Stegelmann, P. Stoltze, Surf. Sci. 544 (2003) 5-23]. The model successfully explains both surface science experiments and kinetic experiments at industrial conditions applying...
Simplified kinetic models of methanol oxidation on silver
DEFF Research Database (Denmark)
Andreasen, Anders; Lynggaard, Hasse Harloff; Stegelmann, Carsten
2005-01-01
Recently the authors developed a microkinetic model of methanol oxidation on silver [A. Andreasen, H. Lynggaard, C. Stegelmann, P. Stoltze, Surf. Sci. 544 (2003) 5–23]. The model successfully explains both surface science experiments and kinetic experiments at industrial conditions applying...
Strain in the mesoscale kinetic Monte Carlo model for sintering
DEFF Research Database (Denmark)
Bjørk, Rasmus; Frandsen, Henrik Lund; Tikare, V.
2014-01-01
Shrinkage strains measured from microstructural simulations using the mesoscale kinetic Monte Carlo (kMC) model for solid state sintering are discussed. This model represents the microstructure using digitized discrete sites that are either grain or pore sites. The algorithm used to simulate dens...
Kinetic Modelling of Oil Extraction from Neem Seed | Ogunleye ...
African Journals Online (AJOL)
The suitability of three different types of extraction kinetic models (one- step, two –step and three – step models) for neem oil was investigated in this study. Solvent extraction using n-hexane at temperatures range between 303K and 323 K ; 360minutes of extraction time were experimented and the oil yield calculated.
Stochastic Differential Equations in Artificial Pancreas Modelling
DEFF Research Database (Denmark)
Duun-Henriksen, Anne Katrine
Type 1 diabetes accounts for approximately 5% of the total diabetes population. It is caused by the destruction of insulin producing β-cells in the pancreas. Various treatment strategies are available today, some of which include advanced technological devices such as an insulin pump...... and a continuous glucose monitor (CGM). Despite these technological advances in the treatment of type 1 diabetes, the disease still poses an enormous and constant challenge for the patients. To obtain tight glucose control the patients are required to assess how much they will eat prior to the meal. They have...... the benefits and challenges by using SDEs compared to traditional methods on the basis of the results of the project. First of all, we designed a clinical study to obtain high quality data from type 1 diabetes patients to identify the models from. The study included the main factors influencing the glucose...
Sum rule limitations of kinetic particle-production models
International Nuclear Information System (INIS)
Knoll, J.; CEA Centre d'Etudes Nucleaires de Grenoble, 38; Guet, C.
1988-04-01
Photoproduction and absorption sum rules generalized to systems at finite temperature provide a stringent check on the validity of kinetic models for the production of hard photons in intermediate energy nuclear collisions. We inspect such models for the case of nuclear matter at finite temperature employed in a kinetic regime which copes those encountered in energetic nuclear collisions, and find photon production rates which significantly exceed the limits imposed by the sum rule even under favourable concession. This suggests that coherence effects are quite important and the production of photons cannot be considered as an incoherent addition of individual NNγ production processes. The deficiencies of present kinetic models may also apply for the production of probes such as the pion which do not couple perturbatively to the nuclear currents. (orig.)
Mathematical analysis of partial differential equations modeling electrostatic MEMS
Esposito, Pierpaolo; Guo, Yujin
2010-01-01
Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed
Khonde, Ruta Dhanram; Chaurasia, Ashish Subhash
2015-04-01
The present study provides the kinetic model to describe the pyrolysis of sawdust, rice-husk and sugarcane bagasse as biomass. The kinetic scheme used for modelling of primary pyrolysis consisting of the two parallel reactions giving gaseous volatiles and solid char. Estimation of kinetic parameters for pyrolysis process has been carried out for temperature range of 773-1,173 K. As there are serious issues regarding non-convergence of some of the methods or solutions converging to local-optima, the proposed kinetic model is optimized to predict the best values of kinetic parameters for the system using three approaches—Two-dimensional surface fitting non-linear regression technique, MS-Excel Solver Tool and COMSOL software. The model predictions are in agreement with experimental data over a wide range of pyrolysis conditions. The estimated value of kinetic parameters are compared with earlier researchers and found to be matching well.
Model reduction of multiscale chemical langevin equations: a numerical case study.
Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N
2009-01-01
Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.
Quantum-Dot Semiconductor Optical Amplifiers: State Space Model versus Rate Equation Model
Directory of Open Access Journals (Sweden)
Hussein Taleb
2013-01-01
Full Text Available A simple and accurate dynamic model for QD-SOAs is proposed. The proposed model is based on the state space theory, where by eliminating the distance dependence of the rate equation model of the QD-SOA; we derive a state space model for the device. A comparison is made between the rate equation model and the state space model under both steady state and transient regimes. Simulation results demonstrate that the derived state space model not only is much simpler and faster than the rate equation model, but also it is as accurate as the rate equation model.
Multilevel Analysis of Structural Equation Models via the EM Algorithm.
Jo, See-Heyon
The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are estimation bias due to measurement error and the estimation of the effects of the individual's hierarchical social milieu. This paper…
A Structural Equation Model of Conceptual Change in Physics
Taasoobshirazi, Gita; Sinatra, Gale M.
2011-01-01
A model of conceptual change in physics was tested on introductory-level, college physics students. Structural equation modeling was used to test hypothesized relationships among variables linked to conceptual change in physics including an approach goal orientation, need for cognition, motivation, and course grade. Conceptual change in physics…
A Structural Equation Model of Expertise in College Physics
Taasoobshirazi, Gita; Carr, Martha
2009-01-01
A model of expertise in physics was tested on a sample of 374 college students in 2 different level physics courses. Structural equation modeling was used to test hypothesized relationships among variables linked to expert performance in physics including strategy use, pictorial representation, categorization skills, and motivation, and these…
Modeling shell morphology of an epitoniid species with parametric equations
Bernido, Christopher C.; Carpio-Bernido, M. Victoria; Sadudaquil, Jerome A.; Salas, Rochelle I.; Mangyao, Justin Ericson A.; Halasan, Lorenzo C.; Baja, Paz Kenneth S.; Jumawan, Ethel Jade V.
2017-08-01
An epitoniid specimen under the genus Cycloscala is mathematically modeled using parametric equations which allow comparison of growth functions and parameter values with other specimens of the same genus. This mathematical modeling approach may supplement the currently used genetic and microscopy methods in the taxonomic classification of species.
Effects of Employing Ridge Regression in Structural Equation Models.
McQuitty, Shaun
1997-01-01
LISREL 8 invokes a ridge option when maximum likelihood or generalized least squares are used to estimate a structural equation model with a nonpositive definite covariance or correlation matrix. Implications of the ridge option for model fit, parameter estimates, and standard errors are explored through two examples. (SLD)
Kinetic theory model for the flow of a simple gas from a three-dimensional axisymmetric nozzle
Riley, B. R.
1991-01-01
A system of nonlinear integral equations equivalent to the Krook kinetic equations for the steady state is the mathematical basis used to develop a computer code to model the flowfields for low-thrust three-dimensional axisymmetric nozzles. The method of characteristics is used to solve numerically by an iteration process the approximated Boltzmann equation for the number density, temperature, and velocity profiles of a simple gas as it expands into a vacuum. Results predict backscatter and show the effect of the nozzle wall boundary layer on the external flowfields.
One-dimensional hydrodynamical kinetics model of a cylindrical DBD reactor with N2
International Nuclear Information System (INIS)
Flores-Moreno, M; De la Piedad-Beneitez, A; Barocio-Delgado, S; Mercado-Cabrera, A; López-Callejas, R; Peña-Eguiluz, R; Rodríguez-Méndez, B; Muñoz-Castro, A
2012-01-01
A numerical 1-D model of the chemical kinetics related hydrodynamics of room pressure N 2 plasma at 25 degrees C is reported. This generic discharge is assumed to take place between two cylindrical concentric electrodes, coated in a dielectric material, biased between 1 kV and 10 kV at 60Hz - 3kHz. The model includes the integration of particles conservation and the momentum equations as well as the local field approximation and the Poisson equations for the sake of completeness. The outcome shows that an accumulation of electrons takes place in the close vicinity of the higher voltage electrode, due to the electric field convergence to the internal electrode. Thus, this is a region of intense ionization whereas the generation of free radicals would occur away from the internal electrode. The model predicts no significant influence of the electric field on the heavier particles whose density remains practically constant.
Explicit equilibria in a kinetic model of gambling
Bassetti, F.; Toscani, G.
2010-06-01
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which describes the evolution of wealth in a pure gambling process, where the entire sum of wealths of two agents is up for gambling, and randomly shared between the agents. For this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents. Among others, the exponential distribution appears as steady state in case of a uniformly distributed random fraction, while Gamma distribution appears for a random fraction which is Beta distributed. The case in which the gambling game is only conservative-in-the-mean is shown to lead to an explicit heavy tailed distribution.
Maafi, Mounir; Maafi, Wassila
2016-12-01
New semi-empirical rate-law system of equations is proposed for the first time for consecutive photoreactions that involve up to 4 photoreaction steps, AB 4 (4Φ). The equation system was developed, tested, and validated against synthetic kinetic traces generated by fifth-order Runge-Kutta calculations. The model accurately fitted the kinetic traces of Riboflavin photodegradation in ethanol which decomposes via the AB 2 (2Φ) mechanism involving 2 consecutive photoreaction steps. A kinetic elucidation methodology useful for consecutive photoreactions was also proposed to determine all the kinetic parameters and reaction attributes defining AB 2 (2Φ) reactions. The quantum yields of photodegradation, determined for wavelengths in the visible region 400-480 nm, ranged from 0.005 to 0.00756 and 0.0012 to 8 10 -5 for the first and second photoreaction steps, respectively. They were found to increase with wavelength in defined sigmoid functions. For this monochromatic irradiation range, riboflavin proved to be a useful actinometer. Finally, a photodegradation scale based on pseudo-rate-constant values was also proposed for drugs. This scale (including 4 groups) is thought to contribute to rationalizing photodegradation testing and might prove useful in categorizing drugs' photodegradation reactivity. Copyright © 2016 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.
Hybrid Fluid/Kinetic Modeling Of Magnetized High Energy Density Plasmas
Hansen, David; Held, Eric; King, Jacob; Stoltz, Peter; Masti, Robert; Srinivasan, Bhuvana
2017-10-01
MHD modeling with an equation of state (EOS) of the Rayleigh-Taylor (RT) instabily in Z indicates that it is seeded by the electro-thermal instability. Large thermodynamic drives associated with gradients at the interface between the liner and the coronal regions distort distribution functions and likely lead to non-local transport effects in a plasma which varies from weakly to strongly coupled. In this work, we discuss using effective potential theory along with a Chapman-Ensksog-like (CEL) formalism to develop hybrid fluid/kinetic modeling capabilities for these plasmas. Effective potential theory addresses the role of Coulomb collisions on transport across coupling regimes and the CEL approach bridges the gap between full-blow kinetic simulations and the EOS tables, which only depend locally on density and temperature. Quantitative results on the Spitzer problem across coupling coupling regimes will be presented as a first step. DOE Grant No. DE-SC0016525.
Continuous Time Structural Equation Modeling with R Package ctsem
Directory of Open Access Journals (Sweden)
Charles C. Driver
2017-04-01
Full Text Available We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1 and time series (N = 1 data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modeling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.
Applications of modeling of structural equations in nursing: integrative review
Directory of Open Access Journals (Sweden)
Juliane Umann
2017-12-01
Full Text Available We analyzed the scientific production using modeling of structural equations in nursing. We conducted an integrative review in June of 2016 in the databases PUBMED, MEDLINE, and LILACS. We identified 127 articles, and we selected 20 from those. We conducted the analyses – quality and level of evidence – using validated tools and a synoptic table. The articles attended to 80% of STROBE items (95%, level of evidence 5 (95% and published in Asian (50% and North American (30% countries. There was an increase of the scientific production using models of structural equations during the study period and the predominance of investigations aimed at the work organization. The use of modeling of structural equations in nursing is growing. However, studies aimed at assistance and teaching are lacking. This method appeared useful for issues in research in this health field.
Bayesian inference of chemical kinetic models from proposed reactions
Galagali, Nikhil
2015-02-01
© 2014 Elsevier Ltd. Bayesian inference provides a natural framework for combining experimental data with prior knowledge to develop chemical kinetic models and quantify the associated uncertainties, not only in parameter values but also in model structure. Most existing applications of Bayesian model selection methods to chemical kinetics have been limited to comparisons among a small set of models, however. The significant computational cost of evaluating posterior model probabilities renders traditional Bayesian methods infeasible when the model space becomes large. We present a new framework for tractable Bayesian model inference and uncertainty quantification using a large number of systematically generated model hypotheses. The approach involves imposing point-mass mixture priors over rate constants and exploring the resulting posterior distribution using an adaptive Markov chain Monte Carlo method. The posterior samples are used to identify plausible models, to quantify rate constant uncertainties, and to extract key diagnostic information about model structure-such as the reactions and operating pathways most strongly supported by the data. We provide numerical demonstrations of the proposed framework by inferring kinetic models for catalytic steam and dry reforming of methane using available experimental data.
State-to-State Internal Energy Relaxation Following the Quantum-Kinetic Model in DSMC
Liechty, Derek S.
2014-01-01
A new model for chemical reactions, the Quantum-Kinetic (Q-K) model of Bird, has recently been introduced that does not depend on macroscopic rate equations or values of local flow field data. Subsequently, the Q-K model has been extended to include reactions involving charged species and electronic energy level transitions. Although this is a phenomenological model, it has been shown to accurately reproduce both equilibrium and non-equilibrium reaction rates. The usefulness of this model becomes clear as local flow conditions either exceed the conditions used to build previous models or when they depart from an equilibrium distribution. Presently, the applicability of the relaxation technique is investigated for the vibrational internal energy mode. The Forced Harmonic Oscillator (FHO) theory for vibrational energy level transitions is combined with the Q-K energy level transition model to accurately reproduce energy level transitions at a reduced computational cost compared to the older FHO models.
Modelling of elastic heat conductors via objective rate equations
Morro, Angelo
2018-01-01
A thermoelastic solid is modelled by letting the heat flux be given by a rate equation. As any constitutive property, the rate equation has to be objective and consistent with thermodynamics. Accordingly, firstly a theorem is given that characterizes objective time derivatives. This allows the known objective time derivatives to be viewed as particular elements of the set so specified. Next the thermodynamic consistency is established for the constitutive models involving objective time derivatives within appropriate sets. It emerges that the thermodynamic consistency holds provided the stress contains additively terms quadratic in the heat flux vector in a form that is related to the derivative adopted for the rate of the heat flux.
Energy Technology Data Exchange (ETDEWEB)
Smith, H.L. (Arizona State Univ., Tempe (United States))
1993-01-01
It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.
International Nuclear Information System (INIS)
Vu, H.X.; Bezzerides, B.; DuBois, D.F.
1999-01-01
A fully kinetic, reduced-description particle-in-cell (RPIC) model is presented in which deviations from quasineutrality, electron and ion kinetic effects, and nonlinear interactions between low-frequency and high-frequency parametric instabilities are modeled correctly. The model is based on a reduced description where the electromagnetic field is represented by three separate temporal envelopes in order to model parametric instabilities with low-frequency and high-frequency daughter waves. Because temporal envelope approximations are invoked, the simulation can be performed on the electron time scale instead of the time scale of the light waves. The electrons and ions are represented by discrete finite-size particles, permitting electron and ion kinetic effects to be modeled properly. The Poisson equation is utilized to ensure that space-charge effects are included. The RPIC model is fully three dimensional and has been implemented in two dimensions on the Accelerated Strategic Computing Initiative (ASCI) parallel computer at Los Alamos National Laboratory, and the resulting simulation code has been named ASPEN. The authors believe this code is the first particle-in-cell code capable of simulating the interaction between low-frequency and high-frequency parametric instabilities in multiple dimensions. Test simulations of stimulated Raman scattering, stimulated Brillouin scattering, and Langmuir decay instability are presented
Experimental study and kinetic modeling of the hydro-fluorination of uranium dioxide
International Nuclear Information System (INIS)
Pages, Simon
2014-01-01
A kinetic study of hydro-fluorination of uranium dioxide was performed between 375 and 475 C under partial pressures of HF between 42 and 720 mbar. The reaction was followed by thermogravimetry in isothermal and isobaric conditions. The kinetic data obtained coupled with a characterization of the powder before, during and after reaction by SEM, EDS, BET and XRD showed that the powder grains of UO 2 are transformed according a model of instantaneous germination, anisotropic growth and internal development. The rate limiting step of the growth process is the diffusion of HF in the UF 4 layer. A mechanism of growth of the UF 4 layer has been proposed. In the temperature and pressure range studied, the reaction is of first order with respect to HF and follows an Arrhenius law. A rate equation was determined and used to perform kinetic simulations which have shown a very good correlation with experience. Coupling of this rate equation with heat and mass transport phenomena allowed to perform simulations at the scale of a powder's agglomerate. They have shown that some structures of agglomerates influence the rate of diffusion of the gases in the porous medium and thereby influence the reaction rate. Finally kinetic simulations on powder's beds and pellets were carried out and compared with experimental rates. The experimental and simulated kinetic curves have the same paces, but improvements in the simulations are needed to accurately predict rates: the coupling between the three scales (grain, agglomerate, oven) would be a good example. (author) [fr
Nurfaizal, Yusmedi
2015-01-01
Penelitian ini berjudul “MODEL SERVQUAL DENGAN PENDEKATAN STRUCTURAL EQUATION MODELING (Studi Pada Mahasiswa Sistem Informasi)”. Tujuan penelitian ini adalah untuk mengetahui model Servqual dengan pendekatan Structural Equation Modeling pada mahasiswa sistem informasi. Peneliti memutuskan untuk mengambil sampel sebanyak 100 responden. Untuk menguji model digunakan analisis SEM. Hasil penelitian menunjukkan bahwa tangibility, reliability responsiveness, assurance dan emphaty mempunyai pengaruh...
Scattering of surface waves modelled by the integral equation method
Lu, Laiyu; Maupin, Valerie; Zeng, Rongsheng; Ding, Zhifeng
2008-09-01
The integral equation method is used to model the propagation of surface waves in 3-D structures. The wavefield is represented by the Fredholm integral equation, and the scattered surface waves are calculated by solving the integral equation numerically. The integration of the Green's function elements is given analytically by treating the singularity of the Hankel function at R = 0, based on the proper expression of the Green's function and the addition theorem of the Hankel function. No far-field and Born approximation is made. We investigate the scattering of surface waves propagating in layered reference models imbedding a heterogeneity with different density, as well as Lamé constant contrasts, both in frequency and time domains, for incident plane waves and point sources.
Hoyermann, Karlheinz; Mauß, Fabian; Olzmann, Matthias; Welz, Oliver; Zeuch, Thomas
2017-07-19
Partially oxidized intermediates play a central role in combustion and atmospheric chemistry. In this perspective, we focus on the chemical kinetics of alkoxy radicals, peroxy radicals, and Criegee intermediates, which are key species in both combustion and atmospheric environments. These reactive intermediates feature a broad spectrum of chemical diversity. Their reactivity is central to our understanding of how volatile organic compounds are degraded in the atmosphere and converted into secondary organic aerosol. Moreover, they sensitively determine ignition timing in internal combustion engines. The intention of this perspective article is to provide the reader with information about the general mechanisms of reactions initiated by addition of atomic and molecular oxygen to alkyl radicals and ozone to alkenes. We will focus on critical branching points in the subsequent reaction mechanisms and discuss them from a consistent point of view. As a first example of our integrated approach, we will show how experiment, theory, and kinetic modeling have been successfully combined in the first infrared detection of Criegee intermediates during the gas phase ozonolysis. As a second example, we will examine the ignition timing of n-heptane/air mixtures at low and intermediate temperatures. Here, we present a reduced, fuel size independent kinetic model of the complex chemistry initiated by peroxy radicals that has been successfully applied to simulate standard n-heptane combustion experiments.
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.
A Stationary One-Equation Turbulent Model with Applications in Porous Media
de Oliveira, H. B.; Paiva, A.
2017-05-01
A one-equation turbulent model is studied in this work in the steady-state and with homogeneous Dirichlet boundary conditions. The considered problem generalizes two distinct approaches that are being used with success in the applications to model different flows through porous media. The novelty of the problem relies on the consideration of the classical Navier-Stokes equations with a feedback forces field, whose presence in the momentum equation will affect the equation for the turbulent kinetic energy (TKE) with a new term that is known as the production and represents the rate at which TKE is transferred from the mean flow to the turbulence. By assuming suitable growth conditions on the feedback forces field and on the function that describes the rate of dissipation of the TKE, as well as on the production term, we will prove the existence of the velocity field and of the TKE. The proof of their uniqueness is made by assuming monotonicity conditions on the feedback forces field and on the turbulent dissipation function, together with a condition of Lipschitz continuity on the production term. The existence of a unique pressure, will follow by the application of a standard version of de Rham's lemma.
Kinetic modeling of desorption of Cadmium (ii) ion from ...
African Journals Online (AJOL)
Kinetic modeling of desorption of Cadmium (ii) ion from Mercaptoacetic acide modified and unmodified agricultural adsorbents. A A Abia, E D Asuquo. Abstract. No Abstract. Global Journal of Environmental Science Vol. 6 (2) 2007: pp. 89-98. Full Text: EMAIL FREE FULL TEXT EMAIL FREE FULL TEXT · DOWNLOAD FULL ...
Kinetic modeling of kraft delignification of Eucalyptus globulus
Energy Technology Data Exchange (ETDEWEB)
Santos, A.; Rodriguez, F.; Gilarranz, M.A.; Moreno, D.; Garcia-Ochoa, F. [Univ. Complutense, Madrid (Spain). Dept. de Ingenieria Quimica
1997-10-01
A kinetic model for the kraft pulping delignification of Eucalyptus globulus is proposed. This model is discriminated among some kinetic expressions often used in the literature, and the kinetic parameters are determined by fitting of experimental results. A total of 25 isothermal experiments at liquor-to-wood ratios of 50 and 5 L/kg have been carried out. Initial, bulk, and residual delignification stages have been observed during the lignin removal, the transitions being, referring to the lignin initial content, about 82 and 3%. Carbohydrate removal and effective alkali-metal and hydrosulfide consumption have been related with the lignin removal by means of effective stoichiometric coefficients for each stage, coefficients also being calculated by fitting of the experimental data. The kinetic model chosen has been used to simulate typical kraft pulping experiments carried out at nonisothermal conditions, using a temperature ramp. The model yields simulated values close to those obtained experimentally for the wood studied and also ably reproduces the trends of the literature data.
Physiologically-based kinetic modelling in risk assessment
The European Union Reference Laboratory for Alternatives to Animal Testing (EURL ECVAM) hosted a two-day workshop with an aim to discuss the role and application of Physiologically Based Kinetic (PBK) models in regulatory decision making. The EURL ECVAM strategy document on Toxic...
Estimation of Kinetic Parameters in an Automotive SCR Catalyst Model
DEFF Research Database (Denmark)
Åberg, Andreas; Widd, Anders; Abildskov, Jens
2016-01-01
A challenge during the development of models for simulation of the automotive Selective Catalytic Reduction catalyst is the parameter estimation of the kinetic parameters, which can be time consuming and problematic. The parameter estimation is often carried out on small-scale reactor tests...
Study of growth kinetic and modeling of ethanol production by ...
African Journals Online (AJOL)
GREGORY
2011-12-16
Dec 16, 2011 ... oxygen content, octane number and reduction of CO emission (Cardona et al., 2010). Furthermore, E10 (10% ... networks and chemical reaction (Lee, 2008). On the con- trary, structured kinetic models are ... CO2 evolution rate (Sato and Yoshizawa, 1988). In this study, batch ethanol fermentation of glucose ...
Modelling of thermal degradation kinetics of ascorbic acid in ...
African Journals Online (AJOL)
Ascorbic acid (vitamin C) loss in thermally treated pawpaw and potato was modelled mathematically. Isothermal experiments in the temperature range of 50 -80 oC for the drying of pawpaw and 60 -100 oC for the blanch-drying of potato were utilized to determine the kinetics of ascorbic acid loss in both fruit and vegetable.
Modelling of Thermal Degradation Kinetics of Ascorbic Acid in ...
African Journals Online (AJOL)
Ascorbic acid (vitamin C) loss in thermally treated pawpaw and potato was modelled mathematically. Isothermal experiments in the temperature range of 50 -80 oC for the drying of pawpaw and 60 -100 oC for the blanch-drying of potato were utilized to determine the kinetics of ascorbic acid loss in both fruit and vegetable.
Web-based kinetic modelling using JWS Online
Olivier, Brett G.; Snoep, Jacky L.
2004-01-01
Summary: JWS Online is a repository of kinetic models, describing biological systems, which can be interactively run and interrogated over the Internet. It is implemented using a client-server strategy where the clients, in the form of web browser based Java applets, act as a graphical interface to
Kinetic modelling and thermodynamic studies on purification of ...
African Journals Online (AJOL)
Adsorbent capacities have been determined by mathematical fitting of equilibrium data using the most common isotherms: Freundlich isotherm and Langmuir isotherm. Several kinetic models have been applied to the process. Thermodynamic parameters: △So, △Ho, △Go and Ea (kJ/mol) have been determined.
Energetic Mapping of Ni Catalysts by Detailed Kinetic Modeling
DEFF Research Database (Denmark)
Bjørgum, Erlend; Chen, De; Bakken, Mari G.
2005-01-01
precursor seems to result in more steplike sites, kinks, and defects for carbon monoxide dissociation. A detailed kinetic modeling of the TPO results based on elementary reaction steps has been conducted to give an energetic map of supported Ni catalysts. Experimental results from the ideal Ni surface fit...
Grima, R
2010-07-21
Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the
One-Dimensional Modeling of an Entrained Coal Gasification Process Using Kinetic Parameters
Directory of Open Access Journals (Sweden)
Moonkyeong Hwang
2016-02-01
Full Text Available A one-dimensional reactor model was developed to simulate the performance of an entrained flow gasifier under various operating conditions. The model combined the plug flow reactor (PFR model with the well-stirred reactor (WSR model. Reaction kinetics was considered together with gas diffusion for the solid-phase reactions in the PFR model, while equilibrium was considered for the gas-phase reactions in the WSR model. The differential and algebraic equations of mass balance and energy balance were solved by a robust ODE solver, i.e., an semi-implicit Runge–Kutta method, and by a nonlinear algebraic solver, respectively. The computed gasifier performance was validated against experimental data from the literature. The difference in product gas concentration from the equilibrium model, and the underlying mechanisms were discussed further. The optimal condition was found after parameter studies were made for various operating conditions.
Chemical kinetics and combustion modelling with CFX 4
Energy Technology Data Exchange (ETDEWEB)
Stopford, P. [AEA Technology, Computational Fluid Dynamics Services Harwell, Oxfordshire (United Kingdom)
1997-12-31
The presentation describes some recent developments in combustion and kinetics models used in the CFX software of AEA Technology. Three topics are highlighted: the development of coupled solvers in a traditional `SIMPLE`-based CFD code, the use of detailed chemical kinetics mechanism via `look-up` tables and the application of CFD to large-scale multi-burner combustion plant. The aim is identify those physical approximations and numerical methods that are likely to be most useful in the future and those areas where further developments are required. (author) 6 refs.
Rodríguez, J; Clemente, G; Sanjuán, N; Bon, J
2014-01-01
The drying kinetics of thyme was analyzed by considering different conditions: air temperature of between 40°C and 70°C , and air velocity of 1 m/s. A theoretical diffusion model and eight different empirical models were fitted to the experimental data. From the theoretical model application, the effective diffusivity per unit area of the thyme was estimated (between 3.68 × 10(-5) and 2.12 × 10 (-4) s(-1)). The temperature dependence of the effective diffusivity was described by the Arrhenius relationship with activation energy of 49.42 kJ/mol. Eight different empirical models were fitted to the experimental data. Additionally, the dependence of the parameters of each model on the drying temperature was determined, obtaining equations that allow estimating the evolution of the moisture content at any temperature in the established range. Furthermore, artificial neural networks were developed and compared with the theoretical and empirical models using the percentage of the relative errors and the explained variance. The artificial neural networks were found to be more accurate predictors of moisture evolution with VAR ≥ 99.3% and ER ≤ 8.7%.
Alternans promotion in cardiac electrophysiology models by delay differential equations
Gomes, Johnny M.; dos Santos, Rodrigo Weber; Cherry, Elizabeth M.
2017-09-01
Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.
Alternans promotion in cardiac electrophysiology models by delay differential equations.
Gomes, Johnny M; Dos Santos, Rodrigo Weber; Cherry, Elizabeth M
2017-09-01
Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.
A model to predict the permeation kinetics of dimethyl sulfoxide in articular cartilage.
Yu, Xiaoyi; Chen, Guangming; Zhang, Shaozhi
2013-02-01
Cryopreservation of articular cartilage (AC) has excited great interest due to the practical surgical importance of this tissue. Characterization of permeation kinetics of cryoprotective agents (CPA) in AC is important for designing optimal CPA addition/removal protocols to achieve successful cryopreservation. Permeation is predominantly a mass diffusion process. Since the diffusivity is a function of temperature and concentration, analysis of the permeation problem would be greatly facilitated if a predictive method were available. This article describes, a model that was developed to predict the permeation kinetics of dimethyl sulfoxide (DMSO) in AC. The cartilage was assumed as a porous medium, and the effect(s) of composition and thermodynamic nonideality of the DMSO solution were considered in model development. The diffusion coefficient was correlated to the infinite dilution coefficients through a binary diffusion thermodynamic model. The UNIFAC model was used to evaluate the activity coefficient, the Vignes equation was employed to estimate the composition dependence of the diffusion coefficient, and the Siddiqi-Lucas correlation was applied to determine the diffusion coefficients at infinite dilution. Comparisons of the predicted overall DMSO uptake by AC with the experimental data over wide temperature and concentration ranges [1~37°C, 10~47% (w/w)] show that the model can accurately describe the permeation kinetics of DMSO in AC [coefficient of determination (R(2)): 0.961~0.996, mean relative error (MRE): 2.2~9.1%].
Abstract of programs for nuclear reactor calculation and kinetic equations solution
International Nuclear Information System (INIS)
Marakazov, A.A.
1977-01-01
The collection includes about 50 annotations of programmes,developed in the Kurchatov Atomic Energy Institute in 1971-1976. The programmes are intended for calculating the neutron flux, for solving systems of multigroup equations in P 3 approximation, for calculating the reactor cell, for analysing the system stability, breeding ratio etc. The programme annotations are compiled according to the following diagram: 1.Programme title. 2.Computer type. 3.Physical problem. 4.Solution method. 5.Calculation limitations. 6.Characteristic computer time. 7.Programme characteristic features. 8.Bound programmes. 9.Programme state. 10.Literature allusions in the programme. 11.Required memory resourses. 12.Programming language. 13.Operation system. 14.Names of authors and place of programme adjusting
Ensemble Kinetic Modeling of Metabolic Networks from Dynamic Metabolic Profiles
Jia, Gengjie; Stephanopoulos, Gregory; Gunawan, Rudiyanto
2012-01-01
Kinetic modeling of metabolic pathways has important applications in metabolic engineering, but significant challenges still remain. The difficulties faced vary from finding best-fit parameters in a highly multidimensional search space to incomplete parameter identifiability. To meet some of these challenges, an ensemble modeling method is developed for characterizing a subset of kinetic parameters that give statistically equivalent goodness-of-fit to time series concentration data. The method is based on the incremental identification approach, where the parameter estimation is done in a step-wise manner. Numerical efficacy is achieved by reducing the dimensionality of parameter space and using efficient random parameter exploration algorithms. The shift toward using model ensembles, instead of the traditional “best-fit” models, is necessary to directly account for model uncertainty during the application of such models. The performance of the ensemble modeling approach has been demonstrated in the modeling of a generic branched pathway and the trehalose pathway in Saccharomyces cerevisiae using generalized mass action (GMA) kinetics. PMID:24957767
A kinetic model for flavonoid production in tea cell culture.
Shibasaki-Kitakawa, Naomi; Iizuka, Yasuhiro; Takahashi, Atsushi; Yonemoto, Toshikuni
2017-02-01
As one of the strategies for efficient production of a metabolite from cell cultures, a kinetic model is very useful tool to predict productivity under various culture conditions. In this study, we propose a kinetic model for flavonoid production in tea cell culture based on the cell life cycle and expression of PAL, the gene encoding phenylalanine ammonia-lyase (PAL)-the key enzyme in flavonoid biosynthesis. The flavonoid production rate was considered to be related to the amount of active PAL. Synthesis of PAL was modelled based on a general gene expression/translation mechanism, including the transcription of DNA encoding PAL into mRNA and the translation of PAL mRNA into the PAL protein. The transcription of DNA was assumed to be promoted at high light intensity and suppressed by a feedback regulatory mechanism at high flavonoid concentrations. In the model, mRNA and PAL were considered to self-decompose and to be lost by cell rupture. The model constants were estimated by fitting the experimental results obtained from tea cell cultures under various light intensities. The model accurately described the kinetic behaviors of dry and fresh cell concentrations, glucose concentration, cell viability, PAL specific activity, and flavonoid content under a wide range of light intensities. The model simulated flavonoid productivity per medium under various culture conditions. Therefore, this model will be useful to predict optimum culture conditions for maximum flavonoid productivity in cultured tea cells.
Ensemble Kinetic Modeling of Metabolic Networks from Dynamic Metabolic Profiles
Directory of Open Access Journals (Sweden)
Gengjie Jia
2012-11-01
Full Text Available Kinetic modeling of metabolic pathways has important applications in metabolic engineering, but significant challenges still remain. The difficulties faced vary from finding best-fit parameters in a highly multidimensional search space to incomplete parameter identifiability. To meet some of these challenges, an ensemble modeling method is developed for characterizing a subset of kinetic parameters that give statistically equivalent goodness-of-fit to time series concentration data. The method is based on the incremental identification approach, where the parameter estimation is done in a step-wise manner. Numerical efficacy is achieved by reducing the dimensionality of parameter space and using efficient random parameter exploration algorithms. The shift toward using model ensembles, instead of the traditional “best-fit” models, is necessary to directly account for model uncertainty during the application of such models. The performance of the ensemble modeling approach has been demonstrated in the modeling of a generic branched pathway and the trehalose pathway in Saccharomyces cerevisiae using generalized mass action (GMA kinetics.
Numerical modelling of multicomponent LNAPL dissolution kinetics ...
Indian Academy of Sciences (India)
Abstract. Characterization of aquifers contaminated by petroleum hydrocarbons is limited by the use of dissolution mass transfer correlations developed for single com- pounds without considering the effects of the mass transfer limitations in presence of other components. A one-dimensional implicit numerical model is ...
Modelling the kinetics of a triple junction
Czech Academy of Sciences Publication Activity Database
Fischer, F. D.; Svoboda, Jiří; Hackl, K.
2012-01-01
Roč. 60, č. 12 (2012), s. 4704-4711 ISSN 1359-6454 R&D Projects: GA ČR GAP108/10/1781 Institutional support: RVO:68081723 Keywords : Phase-field method * Phase transformation * Grain boundary migration * Thermodynamic modelling Subject RIV: BJ - Thermodynamics Impact factor: 3.941, year: 2012
Kinetics and modeling of anaerobic digestion process
DEFF Research Database (Denmark)
Gavala, Hariklia N.; Angelidaki, Irini; Ahring, Birgitte Kiær
2003-01-01
Anaerobic digestion modeling started in the early 1970s when the need for design and efficient operation of anaerobic systems became evident. At that time not only was the knowledge about the complex process of anaerobic digestion inadequate but also there were computational limitations. Thus...
Case-Deletion Diagnostics for Nonlinear Structural Equation Models
Lee, Sik-Yum; Lu, Bin
2003-01-01
In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…
Asymptotics for Estimating Equations in Hidden Markov Models
DEFF Research Database (Denmark)
Hansen, Jørgen Vinsløv; Jensen, Jens Ledet
Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...
Local Influence Analysis of Nonlinear Structural Equation Models
Lee, Sik-Yum; Tang, Nian-Sheng
2004-01-01
By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…
Non-Grassmann mechanical model of the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Deriglazov, A. A.; Zamudio, G. P.; Castro, P. S. [Department de Matematica, ICE, Universidade Federal de Juiz de Fora, MG (Brazil); Rizzuti, B. F. [ISB, Universidade Federal do Amazonas, Coari-AM (Brazil)
2012-12-15
We construct a new example of the spinning-particle model without Grassmann variables. The spin degrees of freedom are described on the base of an inner anti-de Sitter space. This produces both {Gamma}{sup {mu}} and {Gamma}{sup {mu}{nu}}-matrices in the course of quantization. Canonical quantization of the model implies the Dirac equation. We present the detailed analysis of both the Lagrangian and the Hamiltonian formulations of the model and obtain the general solution to the classical equations of motion. Comparing Zitterbewegung of the spatial coordinate with the evolution of spin, we ask on the possibility of space-time interpretation for the inner space of spin. We enumerate similarities between our analogous model of the Dirac equation and the two-body system subject to confining potential which admits only the elliptic orbits of the order of de Broglie wavelength. The Dirac equation dictates the perpendicularity of the elliptic orbits to the direction of center-of-mass motion.
Multiple Imputation Strategies for Multiple Group Structural Equation Models
Enders, Craig K.; Gottschall, Amanda C.
2011-01-01
Although structural equation modeling software packages use maximum likelihood estimation by default, there are situations where one might prefer to use multiple imputation to handle missing data rather than maximum likelihood estimation (e.g., when incorporating auxiliary variables). The selection of variables is one of the nuances associated…
Sensitivity Analysis in Structural Equation Models: Cases and Their Influence
Pek, Jolynn; MacCallum, Robert C.
2011-01-01
The detection of outliers and influential observations is routine practice in linear regression. Despite ongoing extensions and development of case diagnostics in structural equation models (SEM), their application has received limited attention and understanding in practice. The use of case diagnostics informs analysts of the uncertainty of model…
Meson Spectra: Power Law Potential Model in the Dirac Equation ...
African Journals Online (AJOL)
A single mass-spectra potential model has been used to predict the spectra of both light and heavy mesons (including leptonic decay-widths) in the Dirac equation. In fact a power law potential has been proposed with effective power where is the mass of the constituent quarks (in GeV) of the mesons considered.
Building Context with Tumor Growth Modeling Projects in Differential Equations
Beier, Julie C.; Gevertz, Jana L.; Howard, Keith E.
2015-01-01
The use of modeling projects serves to integrate, reinforce, and extend student knowledge. Here we present two projects related to tumor growth appropriate for a first course in differential equations. They illustrate the use of problem-based learning to reinforce and extend course content via a writing or research experience. Here we discuss…
The Use of Structural Equation Modeling in Counseling Psychology Research
Martens, Matthew P.
2005-01-01
Structural equation modeling (SEM) has become increasingly popular for analyzing data in the social sciences, although several broad reviews of psychology journals suggest that many SEM researchers engage in questionable practices when using the technique. The purpose of this study is to review and critique the use of SEM in counseling psychology…
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.; Salvage, K.M. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Civil and Environmental Engineering; Gwo, J.P. [Oak Ridge National Lab., TN (United States); Zachara, J.M.; Szecsody, J.E. [Pacific Northwest National Lab., Richland, WA (United States)
1998-07-01
The computer program HYDROBIOGEOCHEM is a coupled model of HYDROlogic transport and BIOGEOCHEMical kinetic and/or equilibrium reactions in saturated/unsaturated media. HYDROBIOGEOCHEM iteratively solves the two-dimensional transport equations and the ordinary differential and algebraic equations of mixed biogeochemical reactions. The transport equations are solved for all aqueous chemical components and kinetically controlled aqueous species. HYDROBIOGEOCHEM is designed for generic application to reactive transport problems affected by both microbiological and geochemical reactions in subsurface media. Input to the program includes the geometry of the system, the spatial distribution of finite elements and nodes, the properties of the media, the potential chemical and microbial reactions, and the initial and boundary conditions. Output includes the spatial distribution of chemical and microbial concentrations as a function of time and space, and the chemical speciation at user-specified nodes.
Construction of a kinetics model for liquid-solid transitions built from atomistic simulations
Benedict, Lorin; Zepeda-Ruiz, Luis; Haxhimali, Tomorr; Hamel, Sebastien; Sadigh, Babak; Chernov, Alexander; Belof, Jonathan
We discuss work in progress towards a kinetics model for dynamically-driven liquid-solid transitions built from MD simulations. The growth of solid particles within a liquid is studied for a range of conditions, and careful attention is paid to the construction of an accurate multi-phase (equilibrium) equation of state for the system under consideration, in order to provide a framework upon which the non-equilibrium physics is based. His work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC.
International Nuclear Information System (INIS)
Mukunthan, K.; Hawbolt, E.B.
1996-01-01
The recovery and recrystallization kinetics in an 80 pct cold-rolled Ti-Nb stabilized interstitial-free (IF) steel have been characterized for isothermal (500 to 760 C) and continuous heating (0.025 C s -1 to 20.2 C s -1 ) annealing. Isothermal recovery kinetics, as monitored by {220} X-ray peak resolution measurements, were described using a semiempirical logarithmic equation. The IF steel recovered relatively easily, with approximately 45 to 60 pct of the total peak resolution occurring prior to the onset of recrystallization. An iterative procedure was adopted to separate the diffraction effects associated with the concurrent recovery and recrystallization processes. Microstructural observations indicated that the recrystallization event was heterogeneous, with preferential nucleation and early site saturation at grain boundaries in the cold-rolled material. Isothermal recrystallization kinetics, determined by quantitative metallography, were described using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) and Speich-Fisher (SF) relationships. Recovery and recrystallization kinetics during continuous heating have been modeled using the isothermal kinetic parameters, assuming the validity of the principle of additivity. The results were validated by experimental measurements obtained at heating rates simulating both batch and continuous annealing. Although the Scheil additivity equation overestimated the recrystallization start time for continuous heating conditions, the associated higher temperature and more rapid initial recrystallization resulted in similar overall kinetics
Modelling and determination of the kinetic parameters of the pyrolysis of Dichrostachys cinerea
International Nuclear Information System (INIS)
Abreu Naranjo, Reinier; Romero Romero, Osvaldo
2011-01-01
In the present study were analyzed biomass samples of Dichrostachys cinerea, commonly known in Cuba as marabou, by thermogravimetric method at various heating rates of devolatilization in nitrogen atmosphere at 5, 10 and 20 C min-1. On the kinetic analysis was used a mechanism of three independent reactions of order 1, generally attributed to three chief components of this kind of lignocellulose materials, hemicelluloses, cellulose and lignin. The values of activation energy, pre-exponential factor and contribution factor were similar to those reported in previous research for this type of biomass. The proposed model predicts with acceptable correlation the experimental and calculated curves of the decomposition of D. cinerea, with a deviation factor less than 5% for the temperature range studied. On the other hand, the kinetic parameters of the thermal decomposition coupled at equations of transport phenomena are essential to optimize the design and use of biomass thermochemical conversion processes, hence the importance of the research. (author)
Developments in kinetic modelling of chalcocite particle oxidation
Energy Technology Data Exchange (ETDEWEB)
Jaervi, J.; Ahokainen, T.; Jokilaakso, A. [Helsinki Univ. of Technology, Otaniemi (Finland). Lab. of Materials Processing and Powder Metallurgy
1997-12-31
A mathematical model for simulating chalcocite particle oxidation is presented. Combustion of pure chalcocite with oxygen is coded as a kinetic module which can be connected as a separate part of commercial CFD-package, PHOENICS. Heat transfer, fluid flow and combustion phenomena can be simulated using CFD-calculation together with the kinetic model. Interaction between gas phase and particles are taken into account by source terms. The aim of the kinetic model is to calculate the particle temperature, contents of species inside the particle, oxygen consumption and formation of sulphur dioxide. Four oxidation reactions are considered and the shrinking core model is used to describe the rate of the oxidation reactions. The model is verified by simulating the particle oxidation reactions in a laboratory scale laminar-flow furnace under different conditions and the model predicts the effects of charges correctly. In the future, the model validation will be done after experimental studies in the laminar flow-furnace. (author) 18 refs.
Nonzero solutions of nonlinear integral equations modeling infectious disease
Energy Technology Data Exchange (ETDEWEB)
Williams, L.R. (Indiana Univ., South Bend); Leggett, R.W.
1982-01-01
Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, x(t) = ..integral../sup t//sub t-tau/f(s,x(s))ds, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if x(t) is the proportion of infectives at time t and f(t,x(t)) is the proportion of new infectives per unit time.
Ab initio and kinetic modeling studies of formic acid oxidation
DEFF Research Database (Denmark)
Marshall, Paul; Glarborg, Peter
2015-01-01
A detailed chemical kinetic model for oxidation of formic acid (HOCHO) in flames has been developed, based on theoretical work and data from literature. Ab initio calculations were used to obtain rate coefficients for reactions of HOCHO with H, O, and HO2. Modeling predictions with the mechanism...... have been compared to the experimental results of de Wilde and van Tiggelen (1968) who measured the laminar burning velocities for HOCHO flames over a range of stoichiometries and dilution ratios. The modeling predictions are generally satisfactory. The governing reaction mechanisms are outlined based...... on calculations with the kinetic model. Formic acid is consumed mainly by reaction with OH, yielding OCHO, which dissociates rapidly to CO2 + H, and HOCO, which may dissociate to CO + OH or CO2 + H, or react with H, OH, or O2 to form more stable products. The branching fraction of the HOCHO + OH reaction, as well...
An efficient method for modeling kinetic behavior of channel proteins in cardiomyocytes.
Wang, Chong; Beyerlein, Peter; Pospisil, Heike; Krause, Antje; Nugent, Chris; Dubitzky, Werner
2012-01-01
Characterization of the kinetic and conformational properties of channel proteins is a crucial element in the integrative study of congenital cardiac diseases. The proteins of the ion channels of cardiomyocytes represent an important family of biological components determining the physiology of the heart. Some computational studies aiming to understand the mechanisms of the ion channels of cardiomyocytes have concentrated on Markovian stochastic approaches. Mathematically, these approaches employ Chapman-Kolmogorov equations coupled with partial differential equations. As the scale and complexity of such subcellular and cellular models increases, the balance between efficiency and accuracy of algorithms becomes critical. We have developed a novel two-stage splitting algorithm to address efficiency and accuracy issues arising in such modeling and simulation scenarios. Numerical experiments were performed based on the incorporation of our newly developed conformational kinetic model for the rapid delayed rectifier potassium channel into the dynamic models of human ventricular myocytes. Our results show that the new algorithm significantly outperforms commonly adopted adaptive Runge-Kutta methods. Furthermore, our parallel simulations with coupled algorithms for multicellular cardiac tissue demonstrate a high linearity in the speedup of large-scale cardiac simulations.
Energy Technology Data Exchange (ETDEWEB)
Davidson, R.C. [Princeton Univ., NJ (United States). Princeton Plasma Physics Lab.; Chen, C. [Massachusetts Inst. of Tech., Cambridge, MA (United States). Plasma Science and Fusion Center
1997-08-01
A kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field B{sup sol}({rvec x}) is developed. The analysis is carried out for a thin beam with characteristic beam radius r{sub b} {much_lt} S, and directed axial momentum {gamma}{sub b}m{beta}{sub b}c (in the z-direction) large compared with the transverse momentum and axial momentum spread of the beam particles. Making use of the nonlinear Vlasov-Maxwell equations for general distribution function f{sub b}({rvec x},{rvec p},t) and self-consistent electrostatic field consistent with the thin-beam approximation, the kinetic model is used to investigate detailed beam equilibrium properties for a variety of distribution functions. Examples are presented both for the case of a uniform solenoidal focusing field B{sub z}(z) = B{sub 0} = const. and for the case of a periodic solenoidal focusing field B{sub z}(z + S) = B{sub z}(z). The nonlinear Vlasov-Maxwell equations are simplified in the thin-beam approximation, and an alternative Hamiltonian formulation is developed that is particularly well-suited to intense beam propagation in periodic focusing systems. Based on the present analysis, the Vlasov-Maxwell description of intense nonneutral beam propagation through a periodic solenoidal focusing field {rvec B}{sup sol}({rvec x}) is found to be remarkably tractable and rich in physics content. The Vlasov-Maxwell formalism developed here can be extended in a straightforward manner to investigate detailed stability behavior for perturbations about specific choices of beam equilibria.
A Fokker-Planck based kinetic model for diatomic rarefied gas flows
Gorji, M. Hossein; Jenny, Patrick
2013-06-01
A Fokker-Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker-Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the equipartition theorem in equilibrium and fulfills the Landau-Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown.
Franz, Silvio; Gradenigo, Giacomo; Spigler, Stefano
2016-03-01
We study how the thermodynamic properties of the triangular plaquette model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in kinetically constrained models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model the random-diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "random first-order" kind. Finally, we give support to our conjectures studying the finite-temperature phase diagram of the random-diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free energy and configurational entropy can be computed by means of the cavity equations.
Partial differential equations modeling, analysis and numerical approximation
Le Dret, Hervé
2016-01-01
This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems. .
A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space
Adkins, T.; Schekochihin, A. A.
2018-02-01
A class of simple kinetic systems is considered, described by the one-dimensional Vlasov-Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analogue of the Kraichnan-Batchelor model of chaotic advection. The solution of the model is found in Fourier-Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective route to dissipation (i.e. to thermalisation of electric energy via velocity space). The full Fourier-Hermite spectrum is derived. Its asymptotics are -3/2$ at low wavenumbers and high Hermite moments ( ) and -1/2k-2$ at low Hermite moments and high wavenumbers ( ). These conclusions hold at wavenumbers below a certain cutoff (analogue of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.
El-Seddik, Mostafa M; Galal, Mona M; Radwan, A G; Abdel-Halim, Hisham S
2016-01-01
This paper addresses a modified kinetic-hydraulic model for up-flow anaerobic sludge blanket (UASB) reactor aimed to treat wastewater of biodegradable organic substrates as acetic acid based on Van der Meer model incorporated with biological granules inclusion. This dynamic model illustrates the biomass kinetic reaction rate for both direct and indirect growth of microorganisms coupled with the amount of biogas produced by methanogenic bacteria in bed and blanket zones of reactor. Moreover, the pH value required for substrate degradation at the peak specific growth rate of bacteria is discussed for Andrews' kinetics. The sensitivity analyses of biomass concentration with respect to fraction of volume of reactor occupied by granules and up-flow velocity are also demonstrated. Furthermore, the modified mass balance equations of reactor are applied during steady state using Newton Raphson technique to obtain a suitable degree of freedom for the modified model matching with the measured results of UASB Sanhour wastewater treatment plant in Fayoum, Egypt.
Multi-scale modelling and numerical simulation of electronic kinetic transport
International Nuclear Information System (INIS)
Duclous, R.
2009-11-01
This research thesis which is at the interface between numerical analysis, plasma physics and applied mathematics, deals with the kinetic modelling and numerical simulations of the electron energy transport and deposition in laser-produced plasmas, having in view the processes of fuel assembly to temperature and density conditions necessary to ignite fusion reactions. After a brief review of the processes at play in the collisional kinetic theory of plasmas, with a focus on basic models and methods to implement, couple and validate them, the author focuses on the collective aspect related to the free-streaming electron transport equation in the non-relativistic limit as well as in the relativistic regime. He discusses the numerical development and analysis of the scheme for the Vlasov-Maxwell system, and the selection of a validation procedure and numerical tests. Then, he investigates more specific aspects of the collective transport: the multi-specie transport, submitted to phase-space discontinuities. Dealing with the multi-scale physics of electron transport with collision source terms, he validates the accuracy of a fast Monte Carlo multi-grid solver for the Fokker-Planck-Landau electron-electron collision operator. He reports realistic simulations for the kinetic electron transport in the frame of the shock ignition scheme, the development and validation of a reduced electron transport angular model. He finally explores the relative importance of the processes involving electron-electron collisions at high energy by means a multi-scale reduced model with relativistic Boltzmann terms
Bayesian inference with information content model check for Langevin equations
DEFF Research Database (Denmark)
Krog, Jens F. C.; Lomholt, Michael Andersen
2017-01-01
The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work we introduce an information content model check which may serve as a goodness-of-fit, like the chi-square procedure......, to complement conventional Bayesian analysis. We demonstrate this extended Bayesian framework on a system of Langevin equations, where coordinate dependent mobilities and measurement noise hinder the normal mean squared displacement approach....
A MULTIPLE EQUATION MODEL OF HOUSEHOLD LOCATIONAL AND TRIPMAKING BEHAVIOR,
This Memorandum describes a multiple equation model of household locational and tripmaking behavior , to be used in RAND’s study of urban...workers were aggregated to 254 spatially separate workplace zones. The model explains four types of locational and tripmaking behavior for the white...workers employed in these 254 zones: residential space consumption , automobile ownership, modal choice, and length of journey-to-work. In all, the final
International Nuclear Information System (INIS)
Colombino, A.; Mosiello, R.; Norelli, F.; Jorio, V.M.; Pacilio, N.
1975-01-01
A nuclear system kinetics is formulated according to a stochastic approach. The detailed probability balance equations are written for the probability of finding the mixed population of neutrons and detected neutrons, i.e. detectrons, at a given level for a given instant of time. Equations are integrated in search of a probability profile: a series of cases is analyzed through a progressive criterium. It tends to take into account an increasing number of physical processes within the chosen model. The most important contribution is that solutions interpret analytically experimental conditions of equilibrium (moise analysis) and non equilibrium (pulsed neutron measurements, source drop technique, start up procedures)
Schokker, E.P.
1997-01-01
The kinetics of heat inactivation of the extracellular proteinase from Pseudomonas fluorescens 22F was studied. It was established, by making use of kinetic modelling, that heat inactivation in the temperature range 35 - 70 °C was most likely caused
Chemistry resolved kinetic flow modeling of TATB based explosives
Vitello, Peter; Fried, Laurence E.; William, Howard; Levesque, George; Souers, P. Clark
2012-03-01
Detonation waves in insensitive, TATB-based explosives are believed to have multiple time scale regimes. The initial burn rate of such explosives has a sub-microsecond time scale. However, significant late-time slow release in energy is believed to occur due to diffusion limited growth of carbon. In the intermediate time scale concentrations of product species likely change from being in equilibrium to being kinetic rate controlled. We use the thermo-chemical code CHEETAH linked to an ALE hydrodynamics code to model detonations. We term our model chemistry resolved kinetic flow, since CHEETAH tracks the time dependent concentrations of individual species in the detonation wave and calculates EOS values based on the concentrations. We present here two variants of our new rate model and comparison with hot, ambient, and cold experimental data for PBX 9502.
Structural Equation Modeling with Mplus Basic Concepts, Applications, and Programming
Byrne, Barbara M
2011-01-01
Modeled after Barbara Byrne's other best-selling structural equation modeling (SEM) books, this practical guide reviews the basic concepts and applications of SEM using Mplus Versions 5 & 6. The author reviews SEM applications based on actual data taken from her own research. Using non-mathematical language, it is written for the novice SEM user. With each application chapter, the author "walks" the reader through all steps involved in testing the SEM model including: an explanation of the issues addressed illustrated and annotated testing of the hypothesized and post hoc models expl
Directory of Open Access Journals (Sweden)
Fazlollah Rezvani
Full Text Available Abstract Kinetic behaviors of five Lactobacillus strains were investigated with Contois and Exponential models. Awareness of kinetic behavior of microorganisms is essential for their industrial process design and scale up. The consistency of experimental data was evaluated using Excel software. L. bulgaricus was introduced as the most efficient strain with the highest biomass and lactic acid yield of 0.119 and 0.602 g g-1 consumed lactose, respectively. The biomass and carbohydrate yield of L. fermentum and L. lactis were slightly less and close to L. bulgaricus. Biomass and lactic acid production yield of 0.117 and 0.358 for L. fermentum and 0.114 and 0.437 g g-1 for L.actobacillus lactis were obtained. L. casei and L. delbrueckii had the less biomass yield, nearly 11.8 and 22.7% less than L. bulgaricus, respectively. L. bulgaricus (R 2 = 0.9500 and 0.9156 and L. casei (R 2 = 0.9552 and 0.8401 showed acceptable consistency with both models. The investigation revealed that the above mentioned models are not suitable to describe the kinetic behavior of L. fermentum (R 2 = 0.9367 and 0.6991, L. delbrueckii (R 2 = 0.9493 and 0.7724 and L. lactis (R 2 = 0.8730 and 0.6451. Contois rate equation is a suitable model to describe the kinetic of Lactobacilli. Specific cell growth rate for L. bulgaricus, L. casei, L. fermentum, L. delbrueckii and L. lactis with Contois model in order 3.2, 3.9, 67.6, 10.4 and 9.8-fold of Exponential model.
Rezvani, Fazlollah; Ardestani, Fatemeh; Najafpour, Ghasem
Kinetic behaviors of five Lactobacillus strains were investigated with Contois and Exponential models. Awareness of kinetic behavior of microorganisms is essential for their industrial process design and scale up. The consistency of experimental data was evaluated using Excel software. L. bulgaricus was introduced as the most efficient strain with the highest biomass and lactic acid yield of 0.119 and 0.602gg -1 consumed lactose, respectively. The biomass and carbohydrate yield of L. fermentum and L. lactis were slightly less and close to L. bulgaricus. Biomass and lactic acid production yield of 0.117 and 0.358 for L. fermentum and 0.114 and 0.437gg -1 for L.actobacillus lactis were obtained. L. casei and L. delbrueckii had the less biomass yield, nearly 11.8 and 22.7% less than L. bulgaricus, respectively. L. bulgaricus (R 2 =0.9500 and 0.9156) and L. casei (R 2 =0.9552 and 0.8401) showed acceptable consistency with both models. The investigation revealed that the above mentioned models are not suitable to describe the kinetic behavior of L. fermentum (R 2 =0.9367 and 0.6991), L. delbrueckii (R 2 =0.9493 and 0.7724) and L. lactis (R 2 =0.8730 and 0.6451). Contois rate equation is a suitable model to describe the kinetic of Lactobacilli. Specific cell growth rate for L. bulgaricus, L. casei, L. fermentum, L. delbrueckii and L. lactis with Contois model in order 3.2, 3.9, 67.6, 10.4 and 9.8-fold of Exponential model. Copyright © 2017 Sociedade Brasileira de Microbiologia. Published by Elsevier Editora Ltda. All rights reserved.
[Fundamentally study on mathematical kinetic model of component extraction from FTCM].
He, Fu-Yuan; Deng, Kai-Wen; Luo, Jie-Ying; Liu, Wei; Liu, Wen-Long; Deng, Chang-Qing
2007-03-01
To establish the mathematical kinetic model of the components extracted from the FTMC (formulae of the traditional Chinese medicine) and analyze parameters of the astragaloside IV extracted from the BYHWD (Buyang Huanwu decoction). The model, including algebra and differential groups, have been set up according to the FICK discipline and Noyes-whitney soluted theories, as well as two transfer diffusive processes ((1) from protoplasate to apoplasmic, also from material compartment interior cell membrane to outside compartment; (2) apoplasmic to solution, also from outside compartment to solvent compartment) on components extraction from the FTMC. The equation groups, according to laplace transform, have been given a expression as solutions, which indicate the quantitative changes of the component concentration in solvent vs. time. The model kinetic parameters have been analyzed, meanwhile the parameters of the astragaloside IV in the BYHWD under 100 degrees C, extracted by water, have been analyzed by way of this model: It has been established a mathematical model that consists of three parts of e exponent. The kinetic parameters: M, alpha, N, beta, L, pi, K, k1', k2', rho1, rho2, tmax, Cmax, AUC, w0, P, D of the BYHWD were respectivelly 0.061 27% , 0.280 2 min(-1), - 1.027% , 0.008 965 min(-1), 1.077%, 0.002 665 min(-1), 3.451 x 10(-3) min(-1), 3.188 x 10(-3) min(-1), 0.375 9 min(-1), 1.420 min, 0.754 7 min, 184.9 min, 0. 0572 1 mg x mL(-1), 289.9 min, 0.070 11%, 46.24%, 22. 35%. The kinetic model, applied to isolated system, can have been of the rule of multiplex linear. Each parameters can be analyzed completely.
A stochastic differential equation model for transcriptional regulatory networks
Directory of Open Access Journals (Sweden)
Quirk Michelle D
2007-05-01
Full Text Available Abstract Background This work explores the quantitative characteristics of the local transcriptional regulatory network based on the availability of time dependent gene expression data sets. The dynamics of the gene expression level are fitted via a stochastic differential equation model, yielding a set of specific regulators and their contribution. Results We show that a beta sigmoid function that keeps track of temporal parameters is a novel prototype of a regulatory function, with the effect of improving the performance of the profile prediction. The stochastic differential equation model follows well the dynamic of the gene expression levels. Conclusion When adapted to biological hypotheses and combined with a promoter analysis, the method proposed here leads to improved models of the transcriptional regulatory networks.
Kinetic modelling of laccase mediated delignification of Lantana camara.
Gujjala, Lohit K S; Bandyopadhyay, Tapas K; Banerjee, Rintu
2016-07-01
Enzymatic delignification is seen as a green step in biofuels production owing to its specificity towards lignin and its proper understanding requires a kinetic study to decipher intricate details of the process such as thermodynamic parameters viz., activation energy, entropy change and enthalpy change. A system of two coupled kinetic models has been constructed to model laccase mediated delignification of Lantana camara. From the simulated output, activation energy was predicted to be 45.56 and 56.06 kJ/mol, entropy change was observed to be 1.08 × 10(2) and 1.05 × 10(2)cal/mol-K and enthalpy change was determined to be 3.33 × 10(4) and 3.20 × 10(4)cal/mol, respectively from Tessier's and Michaelis Menten model. While comparing the prediction efficiency, it was noticed that Tessier's model gave better performance. Sensitivity analysis was also conducted and it was observed that the model was most sensitive towards temperature dependent kinetic constants. Copyright © 2016 Elsevier Ltd. All rights reserved.
Hidden physics models: Machine learning of nonlinear partial differential equations
Raissi, Maziar; Karniadakis, George Em
2018-03-01
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.
An autocatalytic kinetic model for describing microbial growth during fermentation.
Ibarz, Albert; Augusto, Pedro E D
2015-01-01
The mathematical modelling of the behaviour of microbial growth is widely desired in order to control, predict and design food and bioproduct processing, stability and safety. This work develops and proposes a new semi-empirical mathematical model, based on an autocatalytic kinetic, to describe the microbial growth through its biomass concentration. The proposed model was successfully validated using 15 microbial growth patterns, covering the three most important types of microorganisms in food and biotechnological processing (bacteria, yeasts and moulds). Its main advantages and limitations are discussed, as well as the interpretation of its parameters. It is shown that the new model can be used to describe the behaviour of microbial growth.
Relativistic Brownian motion: from a microscopic binary collision model to the Langevin equation.
Dunkel, Jörn; Hänggi, Peter
2006-11-01
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still delta correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.
Zhakhovsky, Vasily V; Kryukov, Alexei P; Levashov, Vladimir Yu; Shishkova, Irina N; Anisimov, Sergey I
2018-04-16
Boundary conditions required for numerical solution of the Boltzmann kinetic equation (BKE) for mass/heat transfer between evaporation and condensation surfaces are analyzed by comparison of BKE results with molecular dynamics (MD) simulations. Lennard-Jones potential with parameters corresponding to solid argon is used to simulate evaporation from the hot side, nonequilibrium vapor flow with a Knudsen number of about 0.02, and condensation on the cold side of the condensed phase. The equilibrium density of vapor obtained in MD simulation of phase coexistence is used in BKE calculations for consistency of BKE results with MD data. The collision cross-section is also adjusted to provide a thermal flux in vapor identical to that in MD. Our MD simulations of evaporation toward a nonreflective absorbing boundary show that the velocity distribution function (VDF) of evaporated atoms has the nearly semi-Maxwellian shape because the binding energy of atoms evaporated from the interphase layer between bulk phase and vapor is much smaller than the cohesive energy in the condensed phase. Indeed, the calculated temperature and density profiles within the interphase layer indicate that the averaged kinetic energy of atoms remains near-constant with decreasing density almost until the interphase edge. Using consistent BKE and MD methods, the profiles of gas density, mass velocity, and temperatures together with VDFs in a gap of many mean free paths between the evaporation and condensation surfaces are obtained and compared. We demonstrate that the best fit of BKE results with MD simulations can be achieved with the evaporation and condensation coefficients both close to unity.
Focuss algorithm application in kinetic compartment modeling for PET tracer
International Nuclear Information System (INIS)
Huang Xinrui; Bao Shanglian
2004-01-01
Molecular imaging is in the process of becoming. Its application mostly depends on the molecular discovery process of imaging probes and drugs, from the mouse to the patient, from research to clinical practice. Positron emission tomography (PET) can non-invasively monitor . pharmacokinetic and functional processes of drugs in intact organisms at tracer concentrations by kinetic modeling. It has been known that for all biological systems, linear or nonlinear, if the system is injected by a tracer in a steady state, the distribution of the tracer follows the kinetics of a linear compartmental system, which has sums of exponential solutions. Based on the general compartmental description of the tracer's fate in vivo, we presented a novel kinetic modeling approach for the quantification of in vivo tracer studies with dynamic positron emission tomography (PET), which can determine a parsimonious model consisting with the measured data. This kinetic modeling technique allows for estimation of parametric images from a voxel based analysis and requires no a priori decision about the tracer's fate in vivo, instead determining the most appropriate model from the information contained within the kinetic data. Choosing a set of exponential functions, convolved with the plasma input function, as basis functions, the time activity curve of a region or a pixel can be written as a linear combination of the basis functions with corresponding coefficients. The number of non-zero coefficients returned corresponds to the model order which is related to the number of tissue compartments. The system macro parameters are simply determined using the focal underdetermined system solver (FOCUSS) algorithm. The FOCUSS algorithm is a nonparametric algorithm for finding localized energy solutions from limited data and is a recursive linear estimation procedure. FOCUSS algorithm usually converges very fast, so demands a few iterations. The effectiveness is verified by simulation and clinical
Stepwise kinetic equilibrium models of quantitative polymerase chain reaction.
Cobbs, Gary
2012-08-16
Numerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented. Two models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the literature. They also give better estimates of