#### Sample records for kinetic equations

1. Investigation of the kinetic model equations.

PubMed

Liu, Sha; Zhong, Chengwen

2014-03-01

Currently the Boltzmann equation and its model equations are widely used in numerical predictions for dilute gas flows. The nonlinear integro-differential Boltzmann equation is the fundamental equation in the kinetic theory of dilute monatomic gases. By replacing the nonlinear fivefold collision integral term by a nonlinear relaxation term, its model equations such as the famous Bhatnagar-Gross-Krook (BGK) equation are mathematically simple. Since the computational cost of solving model equations is much less than that of solving the full Boltzmann equation, the model equations are widely used in predicting rarefied flows, multiphase flows, chemical flows, and turbulent flows although their predictions are only qualitatively right for highly nonequilibrium flows in transitional regime. In this paper the differences between the Boltzmann equation and its model equations are investigated aiming at giving guidelines for the further development of kinetic models. By comparing the Boltzmann equation and its model equations using test cases with different nonequilibrium types, two factors (the information held by nonequilibrium moments and the different relaxation rates of high- and low-speed molecules) are found useful for adjusting the behaviors of modeled collision terms in kinetic regime. The usefulness of these two factors are confirmed by a generalized model collision term derived from a mathematical relation between the Boltzmann equation and BGK equation that is also derived in this paper. After the analysis of the difference between the Boltzmann equation and the BGK equation, an attempt at approximating the collision term is proposed.

2. Kinetic Equations for Economic Sciences

Bisi, M.; Brugna, C.

2010-04-01

We discuss, both from the analytical and the numerical point of view, a kinetic model for wealth distribution in a simple market economy which models, besides binary trade interactions, also taxation and redistribution of collected wealth.

3. Turbulence kinetic energy equation for dilute suspensions

NASA Technical Reports Server (NTRS)

Abou-Arab, T. W.; Roco, M. C.

1989-01-01

A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

4. Spectrum Analysis of Some Kinetic Equations

Yang, Tong; Yu, Hongjun

2016-11-01

We analyze the spectrum structure of some kinetic equations qualitatively by using semigroup theory and linear operator perturbation theory. The models include the classical Boltzmann equation for hard potentials with or without angular cutoff and the Landau equation with {γ≥q-2}. As an application, we show that the solutions to these two fundamental equations are asymptotically equivalent (mod time decay rate {t^{-5/4}}) as {tto∞} to that of the compressible Navier-Stokes equations for initial data around an equilibrium state.

5. Stochastic thermodynamics for linear kinetic equations

Van den Broeck, C.; Toral, R.

2015-07-01

Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative detailed fluctuation theorem is derived, expressed solely in terms of forward statistics. It is illustrated for a linear kinetic equation with kangaroo rates.

6. Integral kinetic equation in dechanneling problem

Ryabov, V.

1989-11-01

A version of dechanneling theory, based on using an integral kinetic equation in both the phase and transverse energy space, is described. It is derived from the binary collision model and it takes into account consistently the thermal multiple and single scattering of axial and planar channeled particles. The connection between the method developed and that of Oshiyama and of Gartner is discussed.

7. On a Kinetic Equation for Coalescing Particles

Escobedo, Miguel; Laurençot, Philippe; Mischler, Stéphane

Existence of global weak solutions to a spatially inhomogeneous kinetic model for coalescing particles is proved, each particle being identified by its mass, momentum and position. The large time convergence to zero is also shown. The cornestone of our analysis is that, for any nonnegative and convex function, the associated Orlicz norm is a Liapunov functional. Existence and asymptotic behaviour then rely on weak and strong compactness methods in L1 in the spirit of the DiPerna-Lions theory for the Boltzmann equation.

8. Neutrino quantum kinetic equations: The collision term

Blaschke, Daniel N.; Cirigliano, Vincenzo

2016-08-01

We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.

9. Neutrino quantum kinetic equations: The collision term

DOE PAGES

Blaschke, Daniel N.; Cirigliano, Vincenzo

2016-08-01

We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes ofmore » the two helicity states. As a result, the isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.« less

10. Neutrino quantum kinetic equations: The collision term

SciTech Connect

Blaschke, Daniel N.; Cirigliano, Vincenzo

2016-08-01

We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. As a result, the isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.

11. Kinetic equation for spin-polarized plasmas

SciTech Connect

Cowley, S.C.; Kulsrud, R.M.; Valeo, E.

1984-07-01

The usual kinetic description of a plasma is extended to include variables to describe the spin. The distribution function, over phase-space and the new spin variables, provides a sufficient description of a spin-polarized plasma. The evolution equation for the distribution function is given. The equations derived are used to calculate depolarization due to four processes, inhomogeneous fields, collisions, collisions in inhomogeneous fields, and waves. It is found that depolarization by field inhomogeneity on scales large compared with the gyroradius is totally negligible. The same is true for collisional depolarization. Collisions in inhomogeneous fields yield a depolarization rate of order 10/sup -4/S/sup -1/ for deuterons and a negligible rate for tritons in a typical fusion reactor design. This is still sufficiently small on reactor time scales. However, small amplitude magnetic fluctuations (of order one gauss) resonant with the spin precession frequency can lead to significant depolarization (depolarises triton in ten seconds and deuteron in a hundred seconds.)

12. A relativistic correlationless kinetic equation with radiation reaction fully incorporated

Lai, H. M.

1984-06-01

The Landau-Lifshitz expression for the Lorentz-Dirac equation is used to derive a relativistic correlationless kinetic equation for a system of electrons with radiation reaction fully incorporated. Various situations and possible applications are discussed.

13. Moment equations for chromatography based on Langmuir type reaction kinetics.

PubMed

Miyabe, Kanji

2014-08-22

Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.

14. Drift-free kinetic equations for turbulent dispersion.

PubMed

Bragg, A; Swailes, D C; Skartlien, R

2012-11-01

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

15. A classical but new kinetic equation for hydride transfer reactions.

PubMed

Zhu, Xiao-Qing; Deng, Fei-Huang; Yang, Jin-Dong; Li, Xiu-Tao; Chen, Qiang; Lei, Nan-Ping; Meng, Fan-Kun; Zhao, Xiao-Peng; Han, Su-Hui; Hao, Er-Jun; Mu, Yuan-Yuan

2013-09-28

A classical but new kinetic equation to estimate activation energies of various hydride transfer reactions was developed according to transition state theory using the Morse-type free energy curves of hydride donors to release a hydride anion and hydride acceptors to capture a hydride anion and by which the activation energies of 187 typical hydride self-exchange reactions and more than thirty thousand hydride cross transfer reactions in acetonitrile were safely estimated in this work. Since the development of the kinetic equation is only on the basis of the related chemical bond changes of the hydride transfer reactants, the kinetic equation should be also suitable for proton transfer reactions, hydrogen atom transfer reactions and all the other chemical reactions involved with breaking and formation of chemical bonds. One of the most important contributions of this work is to have achieved the perfect unity of the kinetic equation and thermodynamic equation for hydride transfer reactions.

16. Adsorption studies of molasse's wastewaters on activated carbon: modelling with a new fractal kinetic equation and evaluation of kinetic models.

PubMed

Figaro, S; Avril, J P; Brouers, F; Ouensanga, A; Gaspard, S

2009-01-30

Adsorption kinetic of molasses wastewaters after anaerobic digestion (MSWD) and melanoidin respectively on activated carbon was studied at different pH. The kinetic parameters could be determined using classical kinetic equations and a recently published fractal kinetic equation. A linear form of this equation can also be used to fit adsorption data. Even with lower correlation coefficients the fractal kinetic equation gives lower normalized standard deviation values than the pseudo-second order model generally used to fit adsorption kinetic data, indicating that the fractal kinetic model is much more accurate for describing the kinetic adsorption data than the pseudo-second order kinetic model.

17. Kinetic equation for nonlinear resonant wave-particle interaction

Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.

2016-09-01

We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.

18. Solving Kinetic Equations on GPU’s

DTIC Science & Technology

2011-01-01

rarefied gas flows , it is not well suited to the simulation of low Mach number or unsteady flows . Attempts have been made to extend DSMC in order to...simulate nonequilibrium rarefied gas flows . The full nonlinear Boltzmann equation has been solved by means of a semi-regular method which combines a...Valougeorgis, D. and Sharipov, F. (2008). Application of the integro- moment method to steady-state two-dimensional rarefied gas flows subject to boundary

19. The Linearized Kinetic Equation -- A Functional Analytic Approach

Brinkmann, Ralf Peter

2009-10-01

Kinetic models of plasma phenomena are difficult to address for two reasons. They i) are given as systems of nonlinear coupled integro-differential equations, and ii) involve generally six-dimensional distribution functions f(r,v,t). In situations which can be addressed in a linear regime, the first difficulty disappears, but the second one still poses considerable practical problems. This contribution presents an abstract approach to linearized kinetic theory which employs the methods of functional analysis. A kinetic electron equation with elastic electron-neutral interaction is studied in the electrostatic approximation. Under certain boundary conditions, a nonlinear functional, the kinetic free energy, exists which has the properties of a Lyapunov functional. In the linear regime, the functional becomes a quadratic form which motivates the definition of a bilinear scalar product, turning the space of all distribution functions into a Hilbert space. The linearized kinetic equation can then be described in terms of dynamical operators with well-defined properties. Abstract solutions can be constructed which have mathematically plausible properties. As an example, the formalism is applied to the example of the multipole resonance probe (MRP). Under the assumption of a Maxwellian background distribution, the kinetic model of that diagnostics device is compared to a previously investigated fluid model.

20. Turbulent kinetic energy equation and free mixing

NASA Technical Reports Server (NTRS)

Morel, T.; Torda, T. P.; Bradshaw, P.

1973-01-01

Calculation of free shear flows was carried out to investigate the usefulness of several concepts which were previously successfully applied to wall flows. The method belongs to the class of differential approaches. The turbulence is taken into account by the introduction of one additional partial differential equation, the transport equation for the turbulent shear stress. The structure of turbulence is modeled after Bradshaw et al. This model was used successfully in boundary layers and its applicability to other flows is demonstrated. The work reported differs substantially from that of an earlier attempt to use this approach for calculation of free flows. The most important difference is that the region around the center line is treated by invoking the interaction hypothesis (concerning the structure of turbulence in the regions separated by the velocity extrema). The compressibility effects on shear layer spreading at low and moderate Mach numbers were investigated. In the absence of detailed experiments in free flows, the evidence from boundary layers that at low Mach numbers the structure of turbulence is unaffected by the compressibility was relied on. The present model was tested over a range of self-preserving and developing flows including pressure gradients using identical empirical input. The dependence of the structure of turbulence on the spreading rate of the shear layer was established.

1. Controllability in Hybrid Kinetic Equations Modeling Nonequilibrium Multicellular Systems

PubMed Central

Bianca, Carlo

2013-01-01

This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation. PMID:24191137

2. Enzyme Kinetics and the Michaelis-Menten Equation

ERIC Educational Resources Information Center

Biaglow, Andrew; Erickson, Keith; McMurran, Shawnee

2010-01-01

The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to…

3. Spectral function and kinetic equation for a normal Fermi liquid

SciTech Connect

Arshad, M.; Siddique, I.; Kondratyev, A. S.

2007-08-01

On the basis of the Kadanoff-Baym (KB) version of the time-dependent Green's function method, an Ansatz for the approximation of a spectral function is offered. The Ansatz possesses all the advantages of quasiparticle and extended quasiparticle approximations and satisfies the KB equation for a spectral function in the case of slightly nonequilibrium system when disturbances in space and time are taken into consideration in the gradient approximation. This feature opens opportunities for the microscopic derivation of the Landau kinetic equation for the quasiparticle distribution function of the normal Fermi liquid and provides the widening of these equations' temperature range of validity.

4. A kinetic equation with kinetic entropy functions for scalar conservation laws

NASA Technical Reports Server (NTRS)

1990-01-01

A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.

5. 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.

6. On Some Properties of the Landau Kinetic Equation

Bobylev, Alexander; Gamba, Irene; Potapenko, Irina

2015-12-01

We discuss some general properties of the Landau kinetic equation. In particular, the difference between the "true" Landau equation, which formally follows from classical mechanics, and the "generalized" Landau equation, which is just an interesting mathematical object, is stressed. We show how to approximate solutions to the Landau equation by the Wild sums. It is the so-called quasi-Maxwellian approximation related to Monte Carlo methods. This approximation can be also useful for mathematical problems. A model equation which can be reduced to a local nonlinear parabolic equation is also constructed in connection with existence of the strong solution to the initial value problem. A self-similar asymptotic solution to the Landau equation for large v and t is discussed in detail. The solution, earlier confirmed by numerical experiments, describes a formation of Maxwellian tails for a wide class of initial data concentrated in the thermal domain. It is shown that the corresponding rate of relaxation (fractional exponential function) is in exact agreement with recent mathematically rigorous estimates.

7. The H-theorem for the chemical kinetic equations with discrete time and for their generalizations

Adzhiev, S.; Melikhov, I.; Vedenyapin, V.

2017-01-01

In this paper the generalizations of equations of chemical kinetics, including classical and quantum chemical kinetics, is considered. We make time discrete in these equations and prove the H-theorem.

8. Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

SciTech Connect

Balescu, R.; Wang, H. ); Misguich, J.H. )

1994-12-01

The running diffusion coefficient [ital D]([ital t]) is evaluated for a system of charged particles undergoing the effect of a fluctuating magnetic field and of their mutual collisions. The latter coefficient can be expressed either in terms of the mean square displacement (MSD) of a test particle, or in terms of a correlation between a fluctuating distribution function and the magnetic field fluctuation. In the first case a stochastic differential equation of Langevin type for the position of a test particle must be solved; the second problem requires the determination of the distribution function from a kinetic equation. Using suitable simplifications, both problems are amenable to exact analytic solution. The conclusion is that the equivalence of the two approaches is by no means automatically guaranteed. A new type of object, the hybrid kinetic equation'' is constructed: it automatically ensures the equivalence with the Langevin results. The same conclusion holds for the generalized Fokker--Planck equation. The (Bhatnagar--Gross--Krook) (BGK) model for the collisions yields a completely wrong result. A linear approximation to the hybrid kinetic equation yields an inexact behavior, but represents an acceptable approximation in the strongly collisional limit.

9. Solving the Fokker-Planck kinetic equation on a lattice

Moroni, Daniele; Rotenberg, Benjamin; Hansen, Jean-Pierre; Succi, Sauro; Melchionna, Simone

2006-06-01

We propose a discrete lattice version of the Fokker-Planck kinetic equation in close analogy with the lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension D . A generalized Hermite-Gauss procedure is used to construct a discretized kinetic equation and a Chapman-Enskog expansion is applied to adapt the scheme so as to correctly reproduce the macroscopic continuum equations. The linear stability of the algorithm with respect to the finite time step Δt is characterized by the eigenvalues of the collision matrix. A heuristic second-order algorithm in Δt is applied to investigate the time evolution of the distribution function of simple model systems, and compared to known analytical solutions. Preliminary investigations of sedimenting Brownian particles subjected to an orthogonal centrifugal force illustrate the numerical efficiency of the Lattice-Fokker-Planck algorithm to simulate nontrivial situations. Interactions between Brownian particles may be accounted for by adding a standard Bhatnagar-Gross-Krook collision operator to the discretized Fokker-Planck kernel.

10. Coarse-grained kinetic equations for quantum systems

Petrov, E. G.

2013-01-01

The nonequilibrium density matrix method is employed to derive a master equation for the averaged state populations of an open quantum system subjected to an external high frequency stochastic field. It is shown that if the characteristic time τstoch of the stochastic process is much lower than the characteristic time τsteady of the establishment of the system steady state populations, then on the time scale Δ t ˜ τsteady, the evolution of the system populations can be described by the coarse-grained kinetic equations with the averaged transition rates. As an example, the exact averaging is carried out for the dichotomous Markov process of the kangaroo type.

11. Kinetic equations modelling wealth redistribution: A comparison of approaches

Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe

2008-11-01

Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply, e.g., to the market model with risky investments [S. Cordier, L. Pareschi, and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.

12. Kinetic equations modelling wealth redistribution: a comparison of approaches.

PubMed

Düring, Bertram; Matthes, Daniel; Toscani, Giuseppe

2008-11-01

Kinetic equations modelling the redistribution of wealth in simple market economies is one of the major topics in the field of econophysics. We present a unifying approach to the qualitative study for a large variety of such models, which is based on a moment analysis in the related homogeneous Boltzmann equation, and on the use of suitable metrics for probability measures. In consequence, we are able to classify the most important feature of the steady wealth distribution, namely the fatness of the Pareto tail, and the dynamical stability of the latter in terms of the model parameters. Our results apply, e.g., to the market model with risky investments [S. Cordier, L. Pareschi, and G. Toscani, J. Stat. Phys. 120, 253 (2005)], and to the model with quenched saving propensities [A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A 335, 155 (2004)]. Also, we present results from numerical experiments that confirm the theoretical predictions.

13. Exact solutions of kinetic equations in an autocatalytic growth model.

PubMed

Jędrak, Jakub

2013-02-01

Kinetic equations are introduced for the transition-metal nanocluster nucleation and growth mechanism, as proposed by Watzky and Finke [J. Am. Chem. Soc. 119, 10382 (1997)]. Equations of this type take the form of Smoluchowski coagulation equations supplemented with the terms responsible for the chemical reactions. In the absence of coagulation, we find complete analytical solutions of the model equations for the autocatalytic rate constant both proportional to the cluster mass, and the mass-independent one. In the former case, ξ(k)=s(k)(ξ(1))[proportionality]ξ(1)(k)/k was obtained, while in the latter, the functional form of s(k)(ξ(1)) is more complicated. In both cases, ξ(1)(t)=h(μ)(M(μ)(t)) is a function of the moments of the mass distribution. Both functions, s(k)(ξ(1)) and h(μ)(M(μ)), depend on the assumed mechanism of autocatalytic growth and monomer production, and not on other chemical reactions present in a system.

14. A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.

PubMed

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.

15. Accurate spectral numerical schemes for kinetic equations with energy diffusion

Wilkening, Jon; Cerfon, Antoine J.; Landreman, Matt

2015-08-01

We examine the merits of using a family of polynomials that are orthogonal with respect to a non-classical weight function to discretize the speed variable in continuum kinetic calculations. We consider a model one-dimensional partial differential equation describing energy diffusion in velocity space due to Fokker-Planck collisions. This relatively simple case allows us to compare the results of the projected dynamics with an expensive but highly accurate spectral transform approach. It also allows us to integrate in time exactly, and to focus entirely on the effectiveness of the discretization of the speed variable. We show that for a fixed number of modes or grid points, the non-classical polynomials can be many orders of magnitude more accurate than classical Hermite polynomials or finite-difference solvers for kinetic equations in plasma physics. We provide a detailed analysis of the difference in behavior and accuracy of the two families of polynomials. For the non-classical polynomials, if the initial condition is not smooth at the origin when interpreted as a three-dimensional radial function, the exact solution leaves the polynomial subspace for a time, but returns (up to roundoff accuracy) to the same point evolved to by the projected dynamics in that time. By contrast, using classical polynomials, the exact solution differs significantly from the projected dynamics solution when it returns to the subspace. We also explore the connection between eigenfunctions of the projected evolution operator and (non-normalizable) eigenfunctions of the full evolution operator, as well as the effect of truncating the computational domain.

16. Kinetic equations for baryogenesis via sterile neutrino oscillation

SciTech Connect

Asaka, Takehiko; Eijima, Sintaro; Ishida, Hiroyuki E-mail: eijima@muse.sc.niigata-u.ac.jp

2012-02-01

We investigate baryogenesis in the νMSM (neutrino Minimal Standard Model), which is the SM extended by three right-handed neutrinos with masses below the electroweak scale. The baryon asymmetry of the universe can be generated by the mechanism via flavor oscillation of right-handed (sterile) neutrinos which are responsible to masses of active neutrinos confirmed by various experiments. We present the kinetic equations for the matrix of densities of leptons which describe the generation of asymmetries. Especially, the momentum dependence of the matrix of densities is taken into account. By solving these equations numerically, it is found that the momentum distribution is significantly distorted from the equilibrium one, since the production for the modes with lower momenta k << T (T is the temperature of the universe) is enhanced, while suppressed for higher modes. As a result, the most important mode for the yields of sterile neutrinos as well as the baryon asymmetry is k ≅ 2T, which is smaller than (k) inferred from the thermal average. The comparison with the previous works is also discussed.

17. The Application of Discontinuous Galerkin Space and Velocity Discretization to Model Kinetic Equations (PREPRINT)

DTIC Science & Technology

2009-10-07

relative velocity of colliding molecules, and b and ε are geometric impact parameters. The Boltzmann equation is a nonlinear integro - differential equation ...Space and Velocity Discretization to Model Kinetic Equations (PREPRINT) 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Alexander...Galerkin discretization is proposed for the Bhatnagar-Gross-Krook model kinetic equation . This approach allows for a high order polynomial approximation of

18. Verification of continuum drift kinetic equation solvers in NIMROD

SciTech Connect

Held, E. D.; Ji, J.-Y.; Kruger, S. E.; Belli, E. A.; Lyons, B. C.

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.

19. A bin integral method for solving the kinetic collection equation

Wang, Lian-Ping; Xue, Yan; Grabowski, Wojciech W.

2007-09-01

A new numerical method for solving the kinetic collection equation (KCE) is proposed, and its accuracy and convergence are investigated. The method, herein referred to as the bin integral method with Gauss quadrature (BIMGQ), makes use of two binwise moments, namely, the number and mass concentration in each bin. These two degrees of freedom define an extended linear representation of the number density distribution for each bin following Enukashvily (1980). Unlike previous moment-based methods in which the gain and loss integrals are evaluated for a target bin, the concept of source-bin pair interactions is used to transfer bin moments from source bins to target bins. Collection kernels are treated by bilinear interpolations. All binwise interaction integrals are then handled exactly by Gauss quadrature of various orders. In essence the method combines favorable features in previous spectral moment-based and bin-based pair-interaction (or flux) methods to greatly enhance the logic, consistency, and simplicity in the numerical method and its implementation. Quantitative measures are developed to rigorously examine the accuracy and convergence properties of BIMGQ for both the Golovin kernel and hydrodynamic kernels. It is shown that BIMGQ has a superior accuracy for the Golovin kernel and a monotonic convergence behavior for hydrodynamic kernels. Direct comparisons are also made with the method of Berry and Reinhardt (1974), the linear flux method of Bott (1998), and the linear discrete method of Simmel et al. (2002).

20. A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

NASA Technical Reports Server (NTRS)

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.

1. The kinetic equations for rotating and gravitating spheroidal body

Krot, A.

2003-04-01

In papers [1],[2] it has been proposed a statistical model of the gravitational interaction of particles.In the framework of this model bodies have fuzzy outlines and are represented by means of spheroidal forms. A con- sistency of the proposed statistical model the Einstein general relativity [3], [4], [5] has been shown. In work [6], which is a continuation of the paper[2], it has been investigated a slowly evolving in time process of a gravitational compression of a spheroidal body close to an unstable equilibrium state. In the paper [7] the equation of motion of particles inside the weakly gravitating spheroidal body modeled by means of an ideal liquid has been obtained. It has been derived the equations of hyperbolic type for the gravitational field of a weakly gravitating spheroidal body under observable values of velocities of particles composing it [7],[8]. This paper considers the case of gravitational compres- sion of spheroidal body with observable values of parti- cles.This means that distribution function of particles inside weakly rotating spheroidal body is a sum of an isotropic space-homogeneous stationary distribution function and its change (disturbance) under influence of dymanical gravitational field. The change of initial space-homogeneous stationary distribution function satisfyes the Boltzmann kinetic equation. This paper shows that if gravitating spheroidal body is rotating uniformly or is being at rest then distribution function of its particles satisfyes the Liouville theorem. Thus, being in unstable statistical quasiequilibrium the gravi- tating spheroidal body is rotating with constant angular velocity (or, in particular case, is being at rest). The joint distribution function of spheroidal body's particles in to coordinate space and angular velocity space is introduced. References [1] A.M.Krot, Achievements in Modern Radioelectronics, special issue "Cosmic Radiophysics",no. 8, pp.66-81, 1996 (Moscow, Russia). [2] A.M.Krot, Proc. SPIE 13

2. Generalized Klein-Gordon and Dirac Equations from Nonlocal Kinetic Approach

2016-09-01

In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens's nonlocal-in-time kinetic energy approach, which is motivated from Feynman's kinetic energy functional formalism where the position differences are shifted with respect to one another. I proved that these generalized equations are similar to those obtained in literature in the presence of minimal length based on the Quesne-Tkachuk algebra.

3. Formulation and closure of compressible turbulence equations in the light of kinetic theory

NASA Technical Reports Server (NTRS)

Tsuge, S.; Sagara, K.

1976-01-01

Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.

4. Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations

NASA Technical Reports Server (NTRS)

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.

5. Parameter Estimates in Differential Equation Models for Chemical Kinetics

ERIC Educational Resources Information Center

Winkel, Brian

2011-01-01

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

6. Integrating chemical kinetic rate equations by selective use of stiff and nonstiff methods

NASA Technical Reports Server (NTRS)

1985-01-01

The effect of switching between nonstiff and stiff methods on the efficiency of algorithms for integrating chemical kinetic rate equations was examined. Different integration methods were tested by application of the packaged code LSODE to four practical combustion kinetics problems. The problems describe adiabatic, and homogeneous gas phase combustion reactions. It is shown that selective use of nonstiff and stiff methods in different regimes of a typical batch combustion problem is faster than the use of either method for the entire problem. The implications which result in the development of fast integration techniques for combustion kinetic rate equations are discussed.

7. Integrating chemical kinetic rate equations by selective use of stiff and nonstiff methods

NASA Technical Reports Server (NTRS)

1985-01-01

The effect of switching between nonstiff and stiff methods on the efficiency of algorithms for integrating chemical kinetic rate equations is presented. Different integration methods are tested by application of the packaged code LSODE to four practical combustion kinetics problems. The problems describe adiabatic, homogeneous gas-phase combustion reactions. It is shown that selective use of nonstiff and stiff methods in different regimes of a typical batch combustion problem is faster than the use of either method for the entire problem. The implications of this result to the development of fast integration techniques for combustion kinetic rate equations are discussed.

8. Cluster equations for the Glauber kinetic Ising ferromagnet: I. Existence and uniqueness

Kreer, Markus

The infinite set of cluster equations, proposed by Binder and Müller-Krumbhaar for a Glauber kinetic Ising ferromagnet in 1974, generalize the Becker-Döring equations used in classical nucleation theory. For positive symmetric transition rates satisfying certain growth conditions and a detailed balance condition we prove for sufficiently fast decaying initial cluster distributions the existence of a positive cluster distribution with finite density for all finite times solving the cluster equations. Uniqueness is proven under some further conditions on the transition rates. Our existence and uniqueness results apply e.g. for a Glauber kinetic Ising ferromagnet in two dimensions.

9. Dissipative Relativistic Fluid Dynamics: A New Way to Derive the Equations of Motion from Kinetic Theory

SciTech Connect

Denicol, G. S.; Koide, T.; Rischke, D. H.

2010-10-15

We rederive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast with the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of motion for the dissipative currents, we directly use the latter's definition. Although the equations of motion obtained via the two approaches are formally identical, the coefficients are different. We show that, for the one-dimensional scaling expansion, our method is in better agreement with the solution obtained from the Boltzmann equation.

10. A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations

NASA Technical Reports Server (NTRS)

1984-01-01

A comparison of the efficiency of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations is presented. The methods examined include two general-purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient than evaluating the temperature by integrating its time-derivative.

11. Solving Point-Reactor Kinetics Equations Using Exponential Moment Methods

DTIC Science & Technology

2013-03-21

equations of the following form: ( ) ( ) ( ) ( ) ( )i i i dn t t n t c t S t dt               (2) ( ) ( ) ( )i ii i dc t c t n...presented in the function. Exponential moment functions are orderless; that is, the value of the function is invariant under permutations of its...turned into an integral equation by   ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) i i i i i i i i i i i i dn

12. A new code for collisional drift kinetic equation solving

SciTech Connect

Reynolds, J. M.; Velasco, J. L.; Tarancon, A.; Lopez-Bruna, D.; Guasp, J.

2008-11-02

We introduce a new code of plasma transport based on evolving the Boltzmann equation in guiding center approximation where collisions has been taken into account. The spatial geometry is discretized using high order elements in space and a moment expansion in velocity space. First calculations with non-evolving electric field agree with the particle code ISDEP.

13. Calculation of statistic estimates of kinetic parameters from substrate uncompetitive inhibition equation using the median method.

PubMed

Valencia, Pedro L; Astudillo-Castro, Carolina; Gajardo, Diego; Flores, Sebastián

2017-04-01

We provide initial rate data from enzymatic reaction experiments and tis processing to estimate the kinetic parameters from the substrate uncompetitive inhibition equation using the median method published by Eisenthal and Cornish-Bowden (Cornish-Bowden and Eisenthal, 1974; Eisenthal and Cornish-Bowden, 1974). The method was denominated the direct linear plot and consists in the calculation of the median from a dataset of kinetic parameters Vmax and Km from the Michaelis-Menten equation. In this opportunity we present the procedure to applicate the direct linear plot to the substrate uncompetitive inhibition equation; a three-parameter equation. The median method is characterized for its robustness and its insensibility to outlier. The calculations are presented in an Excel datasheet and a computational algorithm was developed in the free software Python. The kinetic parameters of the substrate uncompetitive inhibition equation Vmax , Km and Ks were calculated using three experimental points from the dataset formed by 13 experimental points. All the 286 combinations were calculated. The dataset of kinetic parameters resulting from this combinatorial was used to calculate the median which corresponds to the statistic estimator of the real kinetic parameters. A comparative statistical analyses between the median method and the least squares was published in Valencia et al. [3].

14. Physiologic statokinetic dissociation is eliminated by equating static and kinetic perimetry testing procedures.

PubMed

Phu, Jack; Al-Saleem, Noha; Kalloniatis, Michael; Khuu, Sieu K

2016-11-01

In the present study, we measured the extent of statokinetic dissociation (SKD) in normal observers and then equated the psychophysical tasks into a two-interval forced choice (2IFC) procedure. In Experiment 1, we used the Humphrey visual field analyzer in static perimetry and automated kinetic perimetry modes to measure contrast sensitivity thresholds and the Goldmann manual kinetic perimeter to measure isopters. This was carried out using a Goldmann size II target. Goldmann kinetic perimetry was performed manually with both inward (peripheral to center) and outward (center to periphery) directions of movement to deduce an "average" isopter. This revealed the presence of SKD when superimposed upon the map of static contrast threshold results. There was no evidence of any contribution of examiner technique or instrument-specific differences to SKD. In Experiment 2, we determined the psychometric curves plotting proportion seen as a function of stimulus eccentricity with static and kinetic stimuli with a 2IFC procedure and method of constant stimuli. In an additional experiment, we also showed that subjects were able to reliably discriminate whether a stimulus was static, moving inward, or moving outward, and hence, comparisons could be made between static and kinetic perimetry tasks. Overall, by making the task objective and reducing criterion bias, eccentricity thresholds were equated across static and kinetic perimetry methods; hence, no evidence of SKD was seen. We suggest SKD is inherent to the differences in methodology of threshold measurement in conventional static and kinetic perimetry and individual criterion bias.

15. Formulation and numerical analysis of diatomic molecular dissociation using Boltzmann kinetic equation

Yano, Ryosuke; Suzuki, Kojiro; Kuroda, Hisayasu

2007-01-01

The direct description of chemical reactions by the Boltzmann equation still involves some difficulties in the kinetic theory. In this paper, we describe diatomic molecular dissociation due to transitions of vibrational quantum states resulting from inelastic collisions. These can be described by the Wang Chang-Uhlenbeck (WCU) equation. To avoid direct evaluation of the strong nonlinear collision kernel of the WCU equation, we used a kinetic equation. For accurate description of the dissociation process, we describe improvements we made to the conventional inelastic collision model (the so-called Morse model). Combining this inelastic collision model with the gas mixture model by Oguchi, we formulated a model for representing diatomic molecular dissociations. We validated this model by simulating a hypersonic shock layer with diatomic molecular dissociation.

16. New integration techniques for chemical kinetic rate equations. 2: Accuracy comparison

NASA Technical Reports Server (NTRS)

1985-01-01

A comparison of the accuracy of several techniques recently developed for solving stiff differential equations is presented. The techniques examined include two general purpose codes EEPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREKID, and GCKP84 developed specifically to solve chemical kinetic rate equations. The accuracy comparisons are made by applying these solution procedures 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. The comparisons show that LSODE is 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 an iterative solution of the algebraic enthalpy conservation equation for the temperature can be more accurate and efficient than computing the temperature by integrating its time derivative.

17. New integration techniques for chemical kinetic rate equations. II - Accuracy comparison

NASA Technical Reports Server (NTRS)

1986-01-01

A comparison of the accuracy of several techniques recently developed for solving stiff differential equations is presented. The techniques examined include two general purpose codes EEPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREKID, and GCKP84 developed specifically to solve chemical kinetic rate equations. The accuracy comparisons are made by applying these solution procedures 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. The comparisons show that LSODE is 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 an iterative solution of the algebraic enthalpy conservation equation for the temperature can be more accurate and efficient than computing the temperature by integrating its time derivative.

18. Analytical solution of the kinetic equation for a uniform plasma in a magnetic field

SciTech Connect

Ji, Jeong-Young; Held, Eric D.

2010-07-15

The kinetic equation for a single-component uniform plasma in a magnetic field is analytically solved by the moment method. The linear system of ordinary differential equations for the moments is decomposed into subsystems of lower dimensions by a geometric method. The eigensystem of each subsystem shows that parallel moments decay monotonically, but perpendicular lth harmonic moments decay while oscillating with the l,l-2,...,-th harmonics of gyrofrequency. A generalization to a multicomponent plasma is discussed.

19. Analytical solution of the kinetic equation for a uniform plasma in a magnetic field.

PubMed

Ji, Jeong-Young; Held, Eric D

2010-07-01

The kinetic equation for a single-component uniform plasma in a magnetic field is analytically solved by the moment method. The linear system of ordinary differential equations for the moments is decomposed into subsystems of lower dimensions by a geometric method. The eigensystem of each subsystem shows that parallel moments decay monotonically, but perpendicular lth harmonic moments decay while oscillating with the l,l-2,… ,-th harmonics of gyrofrequency. A generalization to a multicomponent plasma is discussed.

20. Kinetic equations for a density matrix describing nonlinear effects in spectral line wings

SciTech Connect

Parkhomenko, A. I. Shalagin, A. M.

2011-11-15

Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.

1. Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

NASA Technical Reports Server (NTRS)

Pai, S. I.

1973-01-01

The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.

2. A generalized Fisher equation and its utility in chemical kinetics

PubMed Central

Ross, John; Villaverde, Alejandro Fernández; Banga, Julio R.; Vázquez, Sara; Morán, Federico

2010-01-01

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population dynamics and genetics, where it originated. Here we demonstrate that the GFE can also be useful in other fields, specifically in chemistry, with models of two chemical reaction systems for which the mechanisms and rate coefficients correspond reasonably well to experiments. A bad fit of the GFE can be a sign of high levels of measurement noise; for low or moderate levels of noise, fulfillment of the GFE is not degraded. Hence, the GFE presents a noise threshold that may be used to test the validity of experimental measurements without requiring any additional information. In a different approach information about the system (model) is included in the calculations. In that case, the discrepancy with the GFE can be used as an optimization criterion for the determination of rate coefficients in a given reaction mechanism. PMID:20615992

3. A generalized Fisher equation and its utility in chemical kinetics.

PubMed

Ross, John; Fernández Villaverde, Alejandro; Banga, Julio R; Vázquez, Sara; Morán, Federico

2010-07-20

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population dynamics and genetics, where it originated. Here we demonstrate that the GFE can also be useful in other fields, specifically in chemistry, with models of two chemical reaction systems for which the mechanisms and rate coefficients correspond reasonably well to experiments. A bad fit of the GFE can be a sign of high levels of measurement noise; for low or moderate levels of noise, fulfillment of the GFE is not degraded. Hence, the GFE presents a noise threshold that may be used to test the validity of experimental measurements without requiring any additional information. In a different approach information about the system (model) is included in the calculations. In that case, the discrepancy with the GFE can be used as an optimization criterion for the determination of rate coefficients in a given reaction mechanism.

4. New integration techniques for chemical kinetic rate equations. I - Efficiency comparison

NASA Technical Reports Server (NTRS)

1986-01-01

A comparison of the efficiency of several recently developed numerical techniques for solving chemical kinetic rate equations is presented. The solution procedures examined include two general-purpose codes, EPISODE and LSODE, developed as multipurpose differential equation solvers, and three specialzed codes, CHEMEQ, CREK1D, and GCKP84, developed specifically for chemical kinetics. The efficiency comparison is made by applying these codes to two practical combustion kinetics problems. Both problems describe adiabatic, constant-pressure, gas-phase chemical reactions and include all three combustion regimes: induction, heat release, and equilibration. The comparison shows that LSODE is the fastest routine currently available for solving chemical kinetic rate equations. An important finding is that an iterative solution of the algebraic enthalpy conservation equation for temperature can be significantly faster than evaluation of the temperature by integration of its time derivative. Significant increases in computational speed are realized by updating the reaction rate constants only when the temperature change exceeds an amount Delta-T that is problem dependent. An approximate expression for the automatic evaluation of Delta-T is presented and is shown to result in increased computational speed.

5. Solvability of certain inverse problems for the nonstationary kinetic transport equation

Volkov, N. P.

2016-09-01

Linear and nonlinear inverse problems for the nonstationary multispeed anisotropic kinetic transport equation are studied. Sufficient conditions for the existence and uniqueness of weak solutions to these problems in various function spaces are found. The proofs of the corresponding theorems imply that solutions of the inverse problems under study can be obtained by applying the method of successive approximations.

6. General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations

Doktorov, Alexander B.; Kipriyanov, Alexey A.

2014-05-01

General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of "effective" particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.

7. Geodesic acoustic mode in anisotropic plasmas using double adiabatic model and gyro-kinetic equation

SciTech Connect

Ren, Haijun; Cao, Jintao

2014-12-15

Geodesic acoustic mode in anisotropic tokamak plasmas is theoretically analyzed by using double adiabatic model and gyro-kinetic equation. The bi-Maxwellian distribution function for guiding-center ions is assumed to obtain a self-consistent form, yielding pressures satisfying the magnetohydrodynamic (MHD) anisotropic equilibrium condition. The double adiabatic model gives the dispersion relation of geodesic acoustic mode (GAM), which agrees well with the one derived from gyro-kinetic equation. The GAM frequency increases with the ratio of pressures, p{sub ⊥}/p{sub ∥}, and the Landau damping rate is dramatically decreased by p{sub ⊥}/p{sub ∥}. MHD result shows a low-frequency zonal flow existing for all p{sub ⊥}/p{sub ∥}, while according to the kinetic dispersion relation, no low-frequency branch exists for p{sub ⊥}/p{sub ∥}≳ 2.

8. General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations

SciTech Connect

Doktorov, Alexander B.; Kipriyanov, Alexey A.

2014-05-14

General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of “effective” particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.

9. A multi-dimensional kinetic-based upwind solver for the Euler equations

NASA Technical Reports Server (NTRS)

Eppard, W. M.; Grossman, B.

1993-01-01

A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.

10. Kinetics of solute adsorption at solid/aqueous interfaces: searching for the theoretical background of the modified pseudo-first-order kinetic equation.

PubMed

2008-05-20

It is shown that the modified pseudo-first-order (MPFO) kinetic equation proposed recently by Yang and Al-Duri simulates well the behavior of the kinetics governed by the rate of surface reaction and described by our general kinetic equation, based on the statistical rate theory. The linear representation with respect to time, offered by the MPFO equation seems to be a convenient tool for distinguishing between the surface reaction and the diffusional kinetics. Also, a method of distinguishing between the surface reaction and the intraparticle diffusion model based on analyzing the initial kinetic isotherms of sorption is proposed. The applicability of these procedures is demonstrated by the analysis of adsorption kinetics of the reactive yellow dye onto an activated carbon.

11. Functional integral derivation of the kinetic equation of two-dimensional point vortices

Fouvry, Jean-Baptiste; Chavanis, Pierre-Henri; Pichon, Christophe

2016-08-01

We present a brief derivation of the kinetic equation describing the secular evolution of point vortices in two-dimensional hydrodynamics, by relying on a functional integral formalism. We start from Liouville's equation which describes the exact dynamics of a two-dimensional system of point vortices. At the order 1 / N, the evolution of the system is characterised by the first two equations of the BBGKY hierarchy involving the system's 1-body distribution function and its 2-body correlation function. Thanks to the introduction of auxiliary fields, these two evolution constraints may be rewritten as a functional integral. When functionally integrated over the 2-body correlation function, this rewriting leads to a new constraint coupling the 1-body distribution function and the two auxiliary fields. Once inverted, this constraint provides, through a new route, the closed non-linear kinetic equation satisfied by the 1-body distribution function. Such a method sheds new lights on the origin of these kinetic equations complementing the traditional derivation methods.

12. Application of the median method to estimate the kinetic constants of the substrate uncompetitive inhibition equation.

PubMed

Valencia, Pedro L; Astudillo-Castro, Carolina; Gajardo, Diego; Flores, Sebastián

2017-04-07

In 1974, Eisenthal and Cornish-Bowden published the direct linear plot method, which used the median to estimate the Vmax and Km from a set of initial rates as a function of substrate concentrations. The robustness of this non-parametric method was clearly demonstrated by comparing it with the least-squares method. The authors commented that the method cannot readily be generalized to equations of more than two parameters. Unfortunately, this comment has been misread by other authors. Comments such as "this method cannot be extended directly to equations with more than two parameters" were found in some publications. In addition, recently, the most drastic comment was published: "this method cannot be applied for the analysis of substrate inhibition." Given all of these presumptions, we have been motivated to publish a demonstration of the contrary: the median method can be applied to more than two-parameter equations, using as an example, the substrate uncompetitive inhibition equation. A computer algorithm was written to evaluate the effect of simulated experimental error of the initial rates on the estimation of Vmax, Km and KS. The error was assigned to different points of the experimental design. Four different KS/Km ratios were analyzed with the values 10, 100, 1000 and 10,000. The results indicated that the least-squares method was slightly better than the median method in terms of accuracy and variance. However, the presence of outliers affected the estimation of kinetic constants using the least-squares method more severely than the median method. The estimation of KS using the median method to estimate 1/KS was much better than the direct estimation of KS, causing a negative effect of non-linearity of KS in the kinetic equation. Considering that the median method is free from the assumptions of the least-squares method and the arbitrary assumptions implicit in the linearization methods to estimate the kinetic constants Vmax, Km and KS from the substrate

13. Properties-preserving high order numerical methods for a kinetic eikonal equation

Luo, Songting; Payne, Nicholas

2017-02-01

For the BGK (Bhatnagar-Gross-Krook) equation in the large scale hyperbolic limit, the density of particles can be transformed as the Hopf-Cole transformation, where the phase function converges uniformly to the viscosity solution of an effective Hamilton-Jacobi equation, referred to as the kinetic eikonal equation. In this work, we present efficient high order finite difference methods for numerically solving the kinetic eikonal equation. The methods are based on monotone schemes such as the Godunov scheme. High order weighted essentially non-oscillatory techniques and Runge-Kutta procedures are used to obtain high order accuracy in both space and time. The effective Hamiltonian is determined implicitly by a nonlinear equation given as integrals with respect to the velocity variable. Newton's method is applied to solve the nonlinear equation, where integrals with respect to the velocity variable are evaluated either by a Gauss quadrature formula or as expansions with respect to moments of the Maxwellian. The methods are designed such that several key properties such as the positivity of the viscosity solution and the positivity of the effective Hamiltonian are preserved. Numerical experiments are presented to demonstrate the effectiveness of the methods.

14. A Gas-kinetic Scheme for the Two-Fluid MHD Equations with Resistivity

Anderson, Steven; Girimaji, Sharath; da Silva, Eduardo; Siebert, Diogo; Salazar, Juan

2016-11-01

The two-fluid MHD equations are a simplified model of plasma flow wherein a mixture of two species (electrons and ions) is considered. In this model, unlike single-fluid MHD, quasi-neutrality is not enforced, Ohm's Law is not used, and the fluids are not in thermal equilibrium - thus both fluids assume their own density, velocity, and temperature. Here we present a numerical scheme to solve the two-fluid MHD equations based on an extension of the gas-kinetic method. In contrast to previous implementations of the gas-kinetic scheme for MHD, the solution of the non-equilibrium distribution function for each gas at the cell interface is extended to include the effect of the electromagnetic forces as well as the inter-species collisions (resistivity). Closure of the fluid equations with the electromagnetic fields is obtained through Maxwell's equations, and physically correct divergences are enforced via correction potentials. Maxwell's equations are integrated via a simple Lax-Friedrichs type flux-splitting. To separate integration of the source and flux terms in the governing equations we use Strang splitting. Some numerical results are presented to demonstrate accuracy of the scheme and we discuss advantages and potential applications of the scheme. This research was supported by National Science Foundation Grant Number DGE-1252521 and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) of Brazil.

15. Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses

PubMed Central

2010-01-01

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. PMID:21029411

16. Towards an ultra efficient kinetic scheme. Part I: Basics on the BGK equation

Dimarco, Giacomo; Loubere, Raphaël

2013-12-01

In this paper we present a new ultra efficient numerical method for solving kinetic equations. In this preliminary work, we present the scheme in the case of the BGK relaxation operator. The scheme, being based on a splitting technique between transport and collision, can be easily extended to other collisional operators as the Boltzmann collision integral or to other kinetic equations such as the Vlasov equation. The key idea, on which the method relies, is to solve the collision part on a grid and then to solve exactly the transport linear part by following the characteristics backward in time. The main difference between the method proposed and semi-Lagrangian methods is that here we do not need to reconstruct the distribution function at each time step. This allows to tremendously reduce the computational cost of the method and it permits for the first time, to the author's knowledge, to compute solutions of full six dimensional kinetic equations on a single processor laptop machine. Numerical examples, up to the full three dimensional case, are presented which validate the method and assess its efficiency in 1D, 2D and 3D.

17. Equations for the kinetic modeling of supersonically flowing electrically excited lasers

NASA Technical Reports Server (NTRS)

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 then discussed.

18. A gas-kinetic BGK scheme for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Xu, Kun

2000-01-01

This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gas-kinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requirement in the previous scheme, such as the particle collision time being less than the time step for the validity of the BGK Navier-Stokes solution, is removed. Therefore, the applicable regime of the current method is much enlarged and the Navier-Stokes solution can be obtained accurately regardless of the ratio between the collision time and the time step. The gas-kinetic Navier-Stokes solver developed by Chou and Baganoff is the limiting case of the current method, and it is valid only under such a limiting condition. Also, in this paper, the appropriate implementation of boundary condition for the kinetic scheme, different kinetic limiting cases, and the Prandtl number fix are presented. The connection among artificial dissipative central schemes, Godunov-type schemes, and the gas-kinetic BGK method is discussed. Many numerical tests are included to validate the current method.

19. An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit

Wang, Li; Yan, Bokai

2016-05-01

We present a new asymptotic-preserving scheme for the linear Boltzmann equation which, under appropriate scaling, leads to a fractional diffusion limit. Our scheme rests on novel micro-macro decomposition to the distribution function, which splits the original kinetic equation following a reshuffled Hilbert expansion. As opposed to classical diffusion limit, a major difficulty comes from the fat tail in the equilibrium which makes the truncation in velocity space depending on the small parameter. Our idea is, while solving the macro-micro part in a truncated velocity domain (truncation only depends on numerical accuracy), to incorporate an integrated tail over the velocity space that is beyond the truncation, and its major component can be precomputed once with any accuracy. Such an addition is essential to drive the solution to the correct asymptotic limit. Numerical experiments validate its efficiency in both kinetic and fractional diffusive regimes.

20. Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

Gelß, Patrick; Matera, Sebastian; Schütte, Christof

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO2(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

1. The power of integrating kinetic isotope effects into the formalism of the Michaelis-Menten equation.

PubMed

Klinman, Judith P

2014-01-01

The final arbiter of enzyme mechanism is the ability to establish and test a kinetic mechanism. Isotope effects play a major role in expanding the scope and insight derived from the Michaelis-Menten equation. The integration of isotope effects into the formalism of the Michaelis-Menten equation began in the 1970s and has continued until the present. This review discusses a family of eukaryotic copper proteins, including dopamine β-monooxygenase, tyramine β-monooxygenase and peptidylglycine α-amidating enzyme, which are responsible for the synthesis of neuroactive compounds, norepinephrine, octopamine and C-terminally carboxamidated peptides, respectively. The review highlights the results of studies showing how combining kinetic isotope effects with initial rate parameters permits the evaluation of: (a) the order of substrate binding to multisubstrate enzymes; (b) the magnitude of individual rate constants in complex, multistep reactions; (c) the identification of chemical intermediates; and (d) the role of nonclassical (tunnelling) behaviour in C-H activation.

2. Solving the master equation without kinetic Monte Carlo: Tensor train approximations for a CO oxidation model

SciTech Connect

Gelß, Patrick Matera, Sebastian Schütte, Christof

2016-06-01

In multiscale modeling of heterogeneous catalytic processes, one crucial point is the solution of a Markovian master equation describing the stochastic reaction kinetics. Usually, this is too high-dimensional to be solved with standard numerical techniques and one has to rely on sampling approaches based on the kinetic Monte Carlo method. In this study we break the curse of dimensionality for the direct solution of the Markovian master equation by exploiting the Tensor Train Format for this purpose. The performance of the approach is demonstrated on a first principles based, reduced model for the CO oxidation on the RuO{sub 2}(110) surface. We investigate the complexity for increasing system size and for various reaction conditions. The advantage over the stochastic simulation approach is illustrated by a problem with increased stiffness.

3. Comparison of Mathematical Equation and Neural Network Modeling for Drying Kinetic of Mendong in Microwave Oven

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.

4. A Steady-State Approximation to the Two-Dimensional Master Equation for Chemical Kinetics Calculations.

PubMed

Nguyen, Thanh Lam; Stanton, John F

2015-07-16

In the field of chemical kinetics, the solution of a two-dimensional master equation that depends explicitly on both total internal energy (E) and total angular momentum (J) is a challenging problem. In this work, a weak-E/fixed-J collisional model (i.e., weak-collisional internal energy relaxation/free-collisional angular momentum relaxation) is used along with the steady-state approach to solve the resulting (simplified) two-dimensional (E,J)-grained master equation. The corresponding solutions give thermal rate constants and product branching ratios as functions of both temperature and pressure. We also have developed a program that can be used to predict and analyze experimental chemical kinetics results. This expedient technique, when combined with highly accurate potential energy surfaces, is cable of providing results that may be meaningfully compared to experiments. The reaction of singlet oxygen with methane proceeding through vibrationally excited methanol is used as an illustrative example.

5. Hamiltonian fluid reductions of electromagnetic drift-kinetic equations for an arbitrary number of moments

Tassi, E.

2015-11-01

We present an infinite family of Hamiltonian electromagnetic fluid models for plasmas, derived from drift-kinetic equations. An infinite hierarchy of fluid equations is obtained from a Hamiltonian drift-kinetic system by taking moments of a generalized distribution function and using Hermite polynomials as weight functions of the velocity coordinate along the magnetic guide field. Each fluid model is then obtained by truncating the hierarchy to a finite number N + 1 of equations by means of a closure relation. We show that, for any positive N, a linear closure relation between the moment of order N + 1 and the moment of order N guarantees that the resulting fluid model possesses a Hamiltonian structure, thus respecting the Hamiltonian character of the parent drift-kinetic model. An orthogonal transformation is identified which maps the fluid moments to a new set of dynamical variables in terms of which the Poisson brackets of the fluid models become a direct sum and which unveils remarkable dynamical properties of the models in the two-dimensional (2D) limit. Indeed, when imposing translational symmetry with respect to the direction of the magnetic guide field, all models belonging to the infinite family can be reformulated as systems of advection equations for Lagrangian invariants transported by incompressible generalized velocities. These are reminiscent of the advection properties of the parent drift-kinetic model in the 2D limit and are related to the Casimirs of the Poisson brackets of the fluid models. The Hamiltonian structure of the generic fluid model belonging to the infinite family is illustrated treating a specific example of a fluid model retaining five moments in the electron dynamics and two in the ion dynamics. We also clarify the connection existing between the fluid models of this infinite family and some fluid models already present in the literature.

6. A critical analysis of the accuracy of several numerical techniques for combustion kinetic rate equations

NASA Technical Reports Server (NTRS)

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.

7. Implementation and verification of Chapman-Enskog-like drift kinetic equations in NIMROD

Held, Eric; Jepson, Joseph; Ji, Jeong-Young; Nimrod Team

2016-10-01

Rigorous closure of the extended magnetohydrodynamic equations used in plasma fluid codes incorporates important effects for tokamak plasmas such as perturbed bootstrap current physics and generalized viscosity at low collisionality. In this work we discuss continuum numerical solutions of the Chapman-Enskog-like electron and ion drift kinetic equations which have been implemented recently in the NIMROD code. Among other things, these solutions supply the CGL electron stress closure for Ohms Law and CGL ion stress closure for the plasma flow evolution equation. Such closures are paramount to understanding the macroscopic stability properties of high-performance tokamak plasmas. Verification of the orthogonal nature of the Maxwellian and non-Maxwellian parts of the distribution function inherent in the adopted Chapman-Enskog-like approach is provided along with simulation results of neoclassical transport and the Spitzer thermalization and conduction problems.

8. Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach.

PubMed

Kim, Young C; Hummer, Gerhard

2012-04-01

Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. .

9. A Numerical Method for Integrating the Kinetic Equation of Coalescence and Breakup of Cloud Droplets.

Enukashvily, Isaac M.

1980-11-01

An extension of Bleck' method and of the method of moments is developed for the numerical integration of the kinetic equation of coalescence and breakup of cloud droplets. The number density function nk(x,t) in each separate cloud droplet packet between droplet mass grid points (xk,xk+1) is represented by an expansion in orthogonal polynomials with a given weighting function wk(x,k). The expansion coefficients describe the deviations of nk(x,t) from wk(x,k). In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved, and the problem of solving the kinetic equation is replaced by one of solving a set of coupled differential equations for the moments of the number density function nk(x,t). Equations for these moments in each droplet packet are derived. The method is tested against existing solutions of the coalescence equation. Numerical results are obtained when Bleck's uniform distribution hypothesis for nk(x,t) and Golovin's asymptotic solution of the coalescence equation is chosen for the, weighting function wk(x, k). A comparison between numerical results computed by Bleck's method and by the method of this study is made. It is shown that for the correct computation of the coalescence and breakup interactions between cloud droplet packets it is very important that the, approximation of the nk(x,t) between grid points (xk,xk+1) satisfies the conservation conditions for the number concentration, liquid water content and other moments of the cloud droplet packets. If these conservation conditions are provided, even the quasi-linear approximation of the nk(x,t) in comparison with Berry's six-point interpolation will give reasonable results which are very close to the existing analytic solutions.

10. About and beyond the Henri-Michaelis-Menten rate equation for single-substrate enzyme kinetics.

PubMed

Bajzer, Zeljko; Strehler, Emanuel E

2012-01-20

For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S](0). In our formula the rate is already expressed through [S](0), and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S](0). Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S](0).

11. Utilization of integrated Michaelis-Menten equation to determine kinetic constants.

PubMed

Bezerra, Rui M F; Dias, Albino A

2007-03-01

Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only substrate or product concentrations as a function of reaction time. To overcome this problem we present a methodology which uses the integrated form of Michaelis-Menten equation. The method presented has a theoretical and pedagogic basis which is not as arbitrary as other approaches. Here we present and describe the methodology for analyzing time course data together with some examples of the essential computer procedures to implement these analyses. To simplify the understanding of this methodology the experimental examples are confined to linear inhibitions and experimental points utilized are the same from which the initial rates are determined.

12. Analytical solution of Luedeking-Piret equation for a batch fermentation obeying Monod growth kinetics.

PubMed

Garnier, Alain; Gaillet, Bruno

2015-12-01

Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia.

13. Convective kinetic energy equation under the mass-flux subgrid-scale parameterization

Yano, Jun-Ichi

2015-03-01

The present paper originally derives the convective kinetic energy equation under mass-flux subgrid-scale parameterization in a formal manner based on the segmentally-constant approximation (SCA). Though this equation is long since presented by Arakawa and Schubert (1974), a formal derivation is not known in the literature. The derivation of this formulation is of increasing interests in recent years due to the fact that it can explain basic aspects of the convective dynamics such as discharge-recharge and transition from shallow to deep convection. The derivation is presented in two manners: (i) for the case that only the vertical component of the velocity is considered and (ii) the case that both the horizontal and vertical components are considered. The equation reduces to the same form as originally presented by Arakwa and Schubert in both cases, but with the energy dissipation term defined differently. In both cases, nevertheless, the energy "dissipation" (loss) term consists of the three principal contributions: (i) entrainment-detrainment, (ii) outflow from top of convection, and (iii) pressure effects. Additionally, inflow from the bottom of convection contributing to a growth of convection is also formally counted as a part of the dissipation term. The eddy dissipation is also included for a completeness. The order-of-magnitude analysis shows that the convective kinetic energy "dissipation" is dominated by the pressure effects, and it may be approximately described by Rayleigh damping with a constant time scale of the order of 102-103 s. The conclusion is also supported by a supplementary analysis of a cloud-resolving model (CRM) simulation. The Appendix discusses how the loss term ("dissipation") of the convective kinetic energy is qualitatively different from the conventional eddy-dissipation process found in turbulent flows.

14. An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations

SciTech Connect

Sun, Wenjun; Jiang, Song; Xu, Kun

2015-03-15

The solutions of radiative transport equations can cover both optical thin and optical thick regimes due to the large variation of photon's mean-free path and its interaction with the material. In the small mean free path limit, the nonlinear time-dependent radiative transfer equations can converge to an equilibrium diffusion equation due to the intensive interaction between radiation and material. In the optical thin limit, the photon free transport mechanism will emerge. In this paper, we are going to develop an accurate and robust asymptotic preserving unified gas kinetic scheme (AP-UGKS) for the gray radiative transfer equations, where the radiation transport equation is coupled with the material thermal energy equation. The current work is based on the UGKS framework for the rarefied gas dynamics [14], and is an extension of a recent work [12] from a one-dimensional linear radiation transport equation to a nonlinear two-dimensional gray radiative system. The newly developed scheme has the asymptotic preserving (AP) property in the optically thick regime in the capturing of diffusive solution without using a cell size being smaller than the photon's mean free path and time step being less than the photon collision time. Besides the diffusion limit, the scheme can capture the exact solution in the optical thin regime as well. The current scheme is a finite volume method. Due to the direct modeling for the time evolution solution of the interface radiative intensity, a smooth transition of the transport physics from optical thin to optical thick can be accurately recovered. Many numerical examples are included to validate the current approach.

15. Cosmic rays in a random magnetic field: Breakdown of the quasilinear derivation of the kinetic equation

NASA Technical Reports Server (NTRS)

Kaiser, T. B.; Jones, F. C.; Birmingham, T. J.

1972-01-01

The problem of deriving a kinetic equation for the cosmic ray distribution function in a random magnetic field is considered. A model is adopted which is mathematically simple but which contains the essential physics. The perturbation expansion upon which the quasi-linear treatment is based is investigated. The existence of resonant particles causes the breakdown of the adiabatic approximation frequently used in this theory. Resonant particles cause a general secular growth of higher order terms in the expansion which invalidates the entire perturbative approach.

16. Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.

PubMed

Capolupo, A; Giampaolo, S M; Illuminati, F

2013-10-01

Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.

17. Plasma drift-kinetic equation calculations in three-dimensional magnetic geometries

SciTech Connect

Reynolds, J. M.; Lopez-Bruna, D.

2010-07-15

A new code to simulate three-dimensional plasmas in complex toroidal geometries is presented. It solves drift-kinetic equations for the one-particle distribution function f based on their projection onto a functional basis consisting of an arbitrary number of Legendre-Laguerre polynomials. In this paper, these theoretical aspects of the code are exposed together with their relation with the standard formalism. Comparisons with neoclassical theory for the large aspect ratio case and first calculations in the geometry of the TJ-II Heliac are also presented.

18. On Self-Similar Solutions to a Kinetic Equation Arising in Weak Turbulence Theory for the Nonlinear Schrödinger Equation

Kierkels, A. H. M.; Velázquez, J. J. L.

2016-06-01

We construct a family of self-similar solutions with fat tails to a quadratic kinetic equation. This equation describes the long time behaviour of weak solutions with finite mass to the weak turbulence equation associated to the nonlinear Schrödinger equation. The solutions that we construct have finite mass, but infinite energy. In Kierkels and Velázquez (J Stat Phys 159:668-712, 2015) self-similar solutions with finite mass and energy were constructed. Here we prove upper and lower exponential bounds on the tails of these solutions.

19. Diffusion-induced growth of nanowires: Generalized boundary conditions and self-consistent kinetic equation

Dubrovskii, V. G.; Hervieu, Yu. Yu.

2014-09-01

In this work, we present a theoretical analysis of the diffusion-induced growth of "vapor-liquid-solid" nanowires, based on the stationary equations with generalized boundary conditions. We discuss why and how the earlier results are modified when the adatom chemical potential is discontinuous at the nanowire base. Several simplified models for the adatom diffusion flux are discussed, yielding the 1 /Rp radius dependence of the length, with p ranging from 0.5 to 2. The self-consistent approach is used to couple the diffusion transport with the kinetics of 2D nucleation under the droplet. This leads to a new growth equation that contains only two dimensional parameters and the power exponents p and q, where q=1 or 2 depends on the nucleus position. We show that this equation describes the size-dependent depression of the growth rate of narrow nanowires much better than the Gibbs-Thomson correction in several important cases. Overall, our equation fits very well the experimental data on the length-radius correlations of III-V and group IV nanowires obtained by different epitaxy techniques.

20. Analysis of the methods for the derivation of binary kinetic equations in the theory of fluorescence concentration quenching

SciTech Connect

Doktorov, A. B.

2014-09-14

In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed.

1. Analysis of the methods for the derivation of binary kinetic equations in the theory of fluorescence concentration quenching.

PubMed

Doktorov, A B

2014-09-14

In the framework of unified many-particle approach the familiar problem of fluorescence concentration quenching in the presence of pumping (light pulse) of arbitrary intensity is considered. This process is a vivid and the simplest example of multistage bulk reaction including bimolecular irreversible quenching reaction and reversible monomolecular transformation as elementary stages. General relation between the kinetics of multistage bulk reaction and that of the elementary stage of quenching has been established. This allows one to derive general kinetic equations (of two types) for the multistage reaction in question on the basis of general kinetic equations (differential and integro-differential) of elementary stage of quenching. Relying on the same unified many-particle approach we have developed binary approximations with the use of two (frequently employed in the literature) many-particle methods (such as simple superposition approximation and the method of extracting pair channels in three-particle correlation evolution) to the derivation of non-Markovian binary kinetic equations. The possibility of reducing the obtained binary equations to the Markovian equations of formal chemical kinetics has been considered. As an example the exact solution of the problem (for the specific case) is examined, and the applicability of two many particle methods of derivation of binary equations is analyzed.

2. Bayesian inference for kinetic models of biotransformation using a generalized rate equation.

PubMed

Ying, Shanshan; Zhang, Jiangjiang; Zeng, Lingzao; Shi, Jiachun; Wu, Laosheng

2017-03-06

Selecting proper rate equations for the kinetic models is essential to quantify biotransformation processes in the environment. Bayesian model selection method can be used to evaluate the candidate models. However, comparisons of all plausible models can result in high computational cost, while limiting the number of candidate models may lead to biased results. In this work, we developed an integrated Bayesian method to simultaneously perform model selection and parameter estimation by using a generalized rate equation. In the approach, the model hypotheses were represented by discrete parameters and the rate constants were represented by continuous parameters. Then Bayesian inference of the kinetic models was solved by implementing Markov Chain Monte Carlo simulation for parameter estimation with the mixed (i.e., discrete and continuous) priors. The validity of this approach was illustrated through a synthetic case and a nitrogen transformation experimental study. It showed that our method can successfully identify the plausible models and parameters, as well as uncertainties therein. Thus this method can provide a powerful tool to reveal more insightful information for the complex biotransformation processes.

3. The solution of the point kinetics equations via converged accelerated Taylor series (CATS)

SciTech Connect

Ganapol, B.; Picca, P.; Previti, A.; Mostacci, D.

2012-07-01

This paper deals with finding accurate solutions of the point kinetics equations including non-linear feedback, in a fast, efficient and straightforward way. A truncated Taylor series is coupled to continuous analytical continuation to provide the recurrence relations to solve the ordinary differential equations of point kinetics. Non-linear (Wynn-epsilon) and linear (Romberg) convergence accelerations are employed to provide highly accurate results for the evaluation of Taylor series expansions and extrapolated values of neutron and precursor densities at desired edits. The proposed Converged Accelerated Taylor Series, or CATS, algorithm automatically performs successive mesh refinements until the desired accuracy is obtained, making use of the intermediate results for converged initial values at each interval. Numerical performance is evaluated using case studies available from the literature. Nearly perfect agreement is found with the literature results generally considered most accurate. Benchmark quality results are reported for several cases of interest including step, ramp, zigzag and sinusoidal prescribed insertions and insertions with adiabatic Doppler feedback. A larger than usual (9) number of digits is included to encourage honest benchmarking. The benchmark is then applied to the enhanced piecewise constant algorithm (EPCA) currently being developed by the second author. (authors)

4. Kinetic boundary layers in gas mixtures: Systems described by nonlinearly coupled kinetic and hydrodynamic equations and applications to droplet condensation and evaporation

SciTech Connect

Widder, M.E.; Titulaer, U.M. )

1993-03-01

The authors consider a mixture of heavy vapor molecules and a light carrier gas surrounding a liquid droplet. The vapor is described by a variant of the Klein-Kramers equation; the gas is described by the Navier-Stokes equations; the droplet acts as a heat source due to the released heat of condensation. The exchange of momentum and energy between the constituents of the mixture is taken into account by force terms in the kinetic equation and source terms in the Navier-Stokes equations. These are chosen to obtain maximal agreement with the irreversible thermodynamics of a gas mixture. The structure of the kinetic boundary layer around the sphere is determined from the self-consistent solution of this set of coupled equations with appropriate boundary conditions at the surface of the sphere. The kinetic equation is rewritten as a set of coupled moment equations. A complete set of solutions of these moment equations is constructed by numerical integration inward from the region far away from the droplet, where the background inhomogeneities are small. A technique developed earlier is used to deal with the numerical instability of the moment equations. The solutions obtained for given temperature and pressure profiles in the gas are then combined linearly such that they obey the boundary conditions at the droplet surface; from this solution source terms for the Navier-Stokes equation of the gas are constructed and used to determine improved temperature and pressure profiles for the background gas. For not too large temperature differneces between the droplet and the gas at infinity, self-consistency is reached after a few iterations. The method is applied to the condensation of droplets from a supersaturated vapor as well as to strong evaporation of droplets under the influence of an external heat source, where corrections of up to 40% are obtained.

5. Coalescence kinetics in surfactant stabilized emulsions: Evolution equations from direct numerical simulations

SciTech Connect

R. Skartlien; E. Sollum; A. Akselsen; P. Meakin; B. Grimes; J. Sjoblom

2012-12-01

Lattice Boltzmann simulations were used to study the coalescence kinetics in emulsions with amphiphilic surfactant, under neutrally buoyant conditions, and with a significant kinematic viscosity contrast between the phases (emulating water in oil emulsions). The 3D simulation domain was large enough (256 3rd power -- 10 7th power grid points) to obtain good statistics with droplet numbers ranging from a few thousand at early times to a few hundred near equilibrium. Increased surfactant contents slowed down the coalescence rate between droplets due to the Gibbs-Marangoni effect, and the coalescence was driven by a quasi-turbulent velocity field. The kinetic energy decayed at a relatively slow rate at early times, due to conversion of interfacial energy to kinetic energy in the flow during coalescence. Phenomenological, coupled differential equations for the mean droplet diameter D(t) and the number density nd(t) were obtained from the simulation data and from film draining theories. Local (in time) power law exponents for the growth of the mean diameter (and for the concomitant decrease of nd) were established in terms of the instantaneous values of the kinetic energy, coalescence probability, Gibbs elasticity, and interfacial area. The model studies indicated that true power laws for the growth of the droplet size and decrease of the number of droplets with time may not be justified, since the exponents derived using the phenomenological model were time dependent. In contrast to earlier simulation results for symmetric blends with surfactant, we found no evidence for stretched logarithmic scaling of the formD -- [ln (ct)]a for the morphology length, or exponential scalings associated with arrested growth, on the basis of the phenomenological model.

6. Sub-Alfvénic reduced full-f Kinetic MHD equations to study flute like instabilities

Sengupta, W.; Hassam, A.; Antonsen, T. M., Jr.

2016-10-01

We develop a set of reduced sub-Alfvénic fluid as well as kinetic MHD equations which are suitable for studying flute like instabilities in MHD ordering. The full-f kinetic equations are obtained by reducing Kulsrud's complete set of kinetic MHD system and includes trapped ion dynamics in a toroidal geometry. The nonlinear equations show the presence of Mercier modes, electromagnetic effects, GAMs and Rosenbluth-Hinton zero frequency zonal flows. Linear stability based on our equations shall be compared to the well known Kruskal-Oberman Kinetic MHD stability criteria. In the supersonic limit, for large q, our system can be shown to be equivalent to CGL double adiabatic theory. In the marginal stability limit, we shall discuss trapped particle stabilization of interchange modes. Comparison will also be made to the sub-Alfvénic reduced MHD fluid equations in a large aspect ratio tokamak. We shall show that the trapped particle effects in kinetic theory can be treated as a boundary layer of width the square root of the inverse aspect ratio in phase space. Work supported by DOE.

7. 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.

8. Elementary solutions of coupled model equations in the kinetic theory of gases

NASA Technical Reports Server (NTRS)

Kriese, J. T.; Siewert, C. E.; Chang, T. S.

1974-01-01

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

9. Kinetic substrate quantification by fitting the enzyme reaction curve to the integrated Michaelis-Menten equation.

PubMed

Liao, Fei; Tian, Kao-Cong; Yang, Xiao; Zhou, Qi-Xin; Zeng, Zhao-Chun; Zuo, Yu-Ping

2003-03-01

The reliability of kinetic substrate quantification by nonlinear fitting of the enzyme reaction curve to the integrated Michaelis-Menten equation was investigated by both simulation and preliminary experimentation. For simulation, product absorptivity epsilon was 3.00 mmol(-1) L cm(-1) and K(m) was 0.10 mmol L(-1), and uniform absorbance error sigma was randomly inserted into the error-free reaction curve of product absorbance A(i) versus reaction time t(i) calculated according to the integrated Michaelis-Menten equation. The experimental reaction curve of arylesterase acting on phenyl acetate was monitored by phenol absorbance at 270 nm. Maximal product absorbance A(m) was predicted by nonlinear fitting of the reaction curve to Eq. (1) with K(m) as constant. There were unique A(m) for best fitting of both the simulated and experimental reaction curves. Neither the error in reaction origin nor the variation of enzyme activity changed the background-corrected value of A(m). But the range of data under analysis, the background absorbance, and absorbance error sigma had an effect. By simulation, A(m) from 0.150 to 3.600 was predicted with reliability and linear response to substrate concentration when there was 80% consumption of substrate at sigma of 0.001. Restriction of absorbance to 0.700 enabled A(m) up to 1.800 to be predicted at sigma of 0.001. Detection limit reached A(m) of 0.090 at sigma of 0.001. By experimentation, the reproducibility was 4.6% at substrate concentration twice the K(m), and A(m) linearly responded to phenyl acetate with consistent absorptivity for phenol, and upper limit about twice the maximum of experimental absorbance. These results supported the reliability of this new kinetic method for enzymatic analysis with enhanced upper limit and precision.

10. Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations

Wu, Fuke; Tian, Tianhai; Rawlings, James B.; Yin, George

2016-05-01

The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

11. Verification of particle-in-cell simulations against exact solutions of kinetic equations

Turner, Miles

2015-09-01

Demonstrating correctness of computer simulations (or verification) has become a matter of increasing concern in recent years. The strongest type of verification is a demonstration that the simulation converges to an exact solution of the mathematical model that is supposed to be solved. Of course, this is possible only if such an exact solution is available. In this paper, we are interested in kinetic simulation using the particle-in-cell method, and consequently a relevant exact solution must be a solution of a kinetic equation. While we know of no such solutions that exercise all the features of a typical particle-in-cell simulation, in this paper we show that the mathematical literature contains several such solutions that involve a large fraction of the functionality of such a code, and which collectively exercise essentially all of the code functionality. These solutions include the plane diode, the neutron criticality problem, and the calculation of ion energy distribution functions in oscillating fields. In each of theses cases, we can show the the particle-in-cell simulation converges to the exact solution in the expected way. These demonstrations are strong evidence of correct implementation. Work supported by Science Foundation Ireland under grant 08/SRC/I1411.

12. PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

SciTech Connect

Tsai, Shang-Hsi; Yang, Jaw-Yen

2015-07-20

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

13. Velocity Fourier transform solution of a model collision operator. [to obtain kinetic equation for waves in magnetized plasmas

NASA Technical Reports Server (NTRS)

Catto, P. J.

1979-01-01

A simpler technique than those introduced by Lenard and Bernstein (1958), and Dougherty (1964) is employed to obtain the perturbed species density from a specified kinetic equation for a plasma in a given uniform magnetic field. The technique is a generalization of the velocity-Fourier transform method employed by Karpman (1967) for B sub 0 identical to zero, and relies on the fact that in transform space the model collision operator, used to obtain the kinetic equation for waves in a magnetized plasma, contains only first derivatives. The technique is illustrated by evaluating the perturbed density of an arbitrary species.

14. Unified fluid/kinetic description of plasma microinstabilities. Part I: Basic equations in a sheared slab geometry

SciTech Connect

Chang, Z.; Callen, J.D. )

1992-05-01

Unified fluid/kinetic equations for the plasma perturbed density ({ital {tilde n}}), parallel flow velocity ({ital {tilde u}}{sub {parallel}}) and temperature ({ital {tilde T}}) are developed in a sheared slab geometry by calculating the fluid moment closure relations kinetically. At first, a set of (unclosed) nonlinear perturbed fluid equations for {ital {tilde n}}, {ital {tilde u}}{sub {parallel}} and {ital {tilde T}} is developed using a drift ordering analysis and a new gyroviscous force ((spec. char. missing){center dot}{Pi}{sub {ital g}}). Thereafter, to develop linear closure relations for {bold b}{center dot}{del}{center dot}{tilde {Pi}}{sub {parallel}} and {ital {tilde q}}{sub {parallel}}, a drift-kinetic version of a new Chapman--Enskog-like (CEL) equation is developed and solved by using a moment approach and a physically realistic collision operator (Lorentz scattering operator plus the momentum restoring terms). The resultant closure relations for {bold b}{center dot}(spec. char. missing){center dot}{tilde {Pi}}{sub {parallel}} and {ital {tilde q}}{sub {parallel}} unify the fluid and kinetic approaches. In the collisional fluid limit the equations reduce to the well-known Braginskii equations. In the adiabatic limit they reproduce the usual kinetic results, including Landau damping. It is shown that this new CEL approach is more compatible with a fluidlike description of plasmas than the usual drift/gyrokinetic approach. Remarkably simplified forms of the closure relations are presented. The results are compared with other Landau damping models and shown to be more accurate, complete, and physically realistic. Applications of this set of equations to various microinstabilities in tokamak plasmas are presented in a separate paper (Part II) (Phys. Fluids B {bold 4}, 1182 (1992)).

15. Gas-kinetic unified algorithm for hypersonic flows covering various flow regimes solving Boltzmann model equation in nonequilibrium effect

SciTech Connect

Li, Zhihui; Ma, Qiang; Wu, Junlin; Jiang, Xinyu; Zhang, Hanxin

2014-12-09

Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.

16. A Proposal for a Subcritical Reactivity Meter based on Gandini and Salvatores' point kinetics equations for Multiplying Subcritical Systems

SciTech Connect

Pinto, Leticia N.; Dos Santos, Adimir

2015-07-01

Multiplying Subcritical Systems were for a long time poorly studied and its theoretical description remains with plenty open questions. Great interest on such systems arose partly due to the improvement of hybrid concepts, such as the Accelerator-Driven Systems (ADS). Along with the need for new technologies to be developed, further study and understanding of subcritical systems are essential also in more practical situations, such as in the case of a PWR criticalization in their physical startup tests. Point kinetics equations are fundamental to continuously monitor the reactivity behavior to a possible variation of external sources intensity. In this case, quickly and accurately predicting power transients and reactivity becomes crucial. It is known that conventional Reactivity Meters cannot operate in subcritical levels nor describe the dynamics of multiplying systems in these conditions, by the very structure of the classical kinetic equations. Several theoretical models have been proposed to characterize the kinetics of such systems with special regard to the reactivity, as the one developed by Gandini and Salvatores among others. This work presents a discussion about the derivation of point kinetics equations for subcritical systems and the importance of considering the external source. From the point of view of the Gandini and Salvatores' point kinetics model and based on the experimental results provided by Lee and dos Santos, it was possible to develop an innovative approach. This article proposes an algorithm that describes the subcritical reactivity with external source, contributing to the advancement of studies in the field. (authors)

17. Applications of nonlinear science and kinetic equations to the spread of epidemics

Macinnis, David Robert

The study of the spread of epidemics is currently growing into a successful subfield of a combination of nonlinear science and statistical mechanics. Topics studied in this field include kinetic and mean field levels of epidemiological models. This thesis consists of the analysis of such topics and specifically directed at the Hantavirus, West Nile virus, and the Bubonic Plague. A successful reaction-diffusion equation approach developed recently by Abramson and Kenkre was able to describe spatiotemporal patterns of the Hantavirus model. From measurements of the parameters of their model it was found that the mice, the carriers of the infection, must be regarded as moving diffusively within attractive potentials representative of home ranges. Several attempts have been made to incorporate home ranges into their model. Two of these attempts are discussed within this thesis. A model to explain the transmission of the West Nile virus within bird and mosquito populations was recently developed by Kenkre, Parmenter, Peixoto, and Sadasiv who showed how spatially resolved issues could be discussed but restricted their analysis to mean field considerations. This thesis extends that study by investigating spatial resolution of the infected populations. Traveling waves of the bird and mosquito populations are found in the West Nile context. Infection control of various epidemics has become increasingly important to limit the potential force of infection into the human population. This thesis contains a quantitative attempt at a theory of such control (for the West Nile virus) via spraying of the mosquito population. Mean field and kinetic level models are proposed in this thesis to describe the transmission of the Bubonic Plague which involves flea and mammal populations. The various populations are found to undergo a variety of bifurcations as well as hysteresis in their steady state regime. Spatially resolved analysis of the populations is also presented.

18. The clinical impact of hip joint centre regression equation error on kinematics and kinetics during paediatric gait.

PubMed

Kiernan, D; Malone, A; O'Brien, T; Simms, C K

2015-01-01

Regression equations based on pelvic anatomy are routinely used to estimate the hip joint centre during gait analysis. While the associated errors have been well documented, the clinical significance of these errors has not been reported. This study investigated the clinical agreement of three commonly used regression equation sets (Bell et al., Davis et al. and Orthotrak software) against the equations of Harrington et al. Full 3-dimensional gait analysis was performed on 18 healthy paediatric subjects. Kinematic and kinetic data were calculated using each set of regression equations and compared to Harrington et al. In addition, the Gait Profile Score and GDI-Kinetic were used to assess clinical significance. Bell et al. was the best performing set with differences in Gait Profile Score (0.13°) and GDI-Kinetic (0.84 points) falling below the clinical significance threshold. Small deviations were present for the Orthotrak set for hip abduction moment (0.1 Nm/kg), however differences in Gait Profile Score (0.27°) and GDI-Kinetic (2.26 points) remained below the clinical threshold. Davis et al. showed least agreement with a clinically significant difference in GDI-Kinetic score (4.36 points). It is proposed that Harrington et al. or Bell et al. regression equation sets are used during gait analysis especially where inverse dynamic data are calculated. Orthotrak is a clinically acceptable alternative however clinicians must be aware of the effects of error on hip abduction moment. The Davis et al. set should be used with caution for inverse dynamic analysis as error could be considered clinically meaningful.

19. Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

PubMed Central

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

20. Kinetics of solute adsorption at solid/solution interfaces: a theoretical development of the empirical pseudo-first and pseudo-second order kinetic rate equations, based on applying the statistical rate theory of interfacial transport.

PubMed

2006-08-24

For practical applications of solid/solution adsorption processes, the kinetics of these processes is at least as much essential as their features at equilibrium. Meanwhile, the general understanding of this kinetics and its corresponding theoretical description are far behind the understanding and the level of theoretical interpretation of adsorption equilibria in these systems. The Lagergren empirical equation proposed at the end of 19th century to describe the kinetics of solute sorption at the solid/solution interfaces has been the most widely used kinetic equation until now. This equation has also been called the pseudo-first order kinetic equation because it was intuitively associated with the model of one-site occupancy adsorption kinetics governed by the rate of surface reaction. More recently, its generalization for the two-sites-occupancy adsorption was proposed and called the pseudo-second-order kinetic equation. However, the general use and the wide applicability of these empirical equations during more than one century have not resulted in a corresponding fundamental search for their theoretical origin. Here the first theoretical development of these equations is proposed, based on applying the new fundamental approach to kinetics of interfacial transport called the Statistical Rate Theory. It is shown that these empirical equations are simplified forms of a more general equation developed here, for the case when the adsorption kinetics is governed by the rate of surface reactions. The features of that general equation are shown by presenting exhaustive model investigations, and the applicability of that equation is tested by presenting a quantitative analysis of some experimental data reported in the literature.

1. An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations

SciTech Connect

Sun, Wenjun; Jiang, Song; Xu, Kun; Li, Shu

2015-12-01

This paper presents an extension of previous work (Sun et al., 2015 [22]) of the unified gas kinetic scheme (UGKS) for the gray radiative transfer equations to the frequency-dependent (multi-group) radiative transfer system. Different from the gray radiative transfer equations, where the optical opacity is only a function of local material temperature, the simulation of frequency-dependent radiative transfer is associated with additional difficulties from the frequency-dependent opacity. For the multiple frequency radiation, the opacity depends on both the spatial location and the frequency. For example, the opacity is typically a decreasing function of frequency. At the same spatial region the transport physics can be optically thick for the low frequency photons, and optically thin for high frequency ones. Therefore, the optical thickness is not a simple function of space location. In this paper, the UGKS for frequency-dependent radiative system is developed. The UGKS is a finite volume method and the transport physics is modeled according to the ratio of the cell size to the photon's frequency-dependent mean free path. When the cell size is much larger than the photon's mean free path, a diffusion solution for such a frequency radiation will be obtained. On the other hand, when the cell size is much smaller than the photon's mean free path, a free transport mechanism will be recovered. In the regime between the above two limits, with the variation of the ratio between the local cell size and photon's mean free path, the UGKS provides a smooth transition in the physical and frequency space to capture the corresponding transport physics accurately. The seemingly straightforward extension of the UGKS from the gray to multiple frequency radiation system is due to its intrinsic consistent multiple scale transport modeling, but it still involves lots of work to properly discretize the multiple groups in order to design an asymptotic preserving (AP) scheme in all

2. Use of a generalized fisher equation for global optimization in chemical kinetics.

PubMed

Villaverde, Alejandro F; Ross, John; Morán, Federico; Balsa-Canto, Eva; Banga, Julio R

2011-08-04

A new approach for parameter estimation in chemical kinetics has been recently proposed (Ross et al. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 12777). It makes use of an optimization criterion based on a Generalized Fisher Equation (GFE). Its utility has been demonstrated with two reaction mechanisms, the chlorite-iodide and Oregonator, which are computationally stiff systems. In this Article, the performance of the GFE-based algorithm is compared to that obtained from minimization of the squared distances between the observed and predicted concentrations obtained by solving the corresponding initial value problem (we call this latter approach "traditional" for simplicity). Comparison of the proposed GFE-based optimization method with the "traditional" one has revealed their differences in performance. This difference can be seen as a trade-off between speed (which favors GFE) and accuracy (which favors the traditional method). The chlorite-iodide and Oregonator systems are again chosen as case studies. An identifiability analysis is performed for both of them, followed by an optimal experimental design based on the Fisher Information Matrix (FIM). This allows to identify and overcome most of the previously encountered identifiability issues, improving the estimation accuracy. With the new data, obtained from optimally designed experiments, it is now possible to estimate effectively more parameters than with the previous data. This result, which holds for both GFE-based and traditional methods, stresses the importance of an appropriate experimental design. Finally, a new hybrid method that combines advantages from the GFE and traditional approaches is presented.

3. Collision integral in the kinetic equation for a rarefied electron gas with allowance for its spin polarization

SciTech Connect

Sasorov, P. V.; Fomin, I. V.

2015-06-15

The collision integral in the kinetic equation for a rarefied spin-polarized gas of fermions (electrons) is derived. The collisions between these fermions and the collisions with much heavier particles (ions) forming a randomly located stationary background (gas) are taken into account. An important new circumstance is that the particle-particle scattering amplitude is not assumed to be small, which could be obtained, for example, in the first Born approximation. The derived collision integral can be used in the kinetic equation, including that for a relatively cold rarefied spin-polarized plasma with a characteristic electron energy below α{sup 2}m{sub e}c{sup 2}, where α is the fine-structure constant.

4. Estimation of kinetic parameters for enzyme-inhibition reaction models using direct time-dependent equations for reactant concentrations.

PubMed

Goličnik, Marko

2012-03-01

To facilitate the determination of a reaction type and its kinetics constants for reversible inhibitors of Michaelis-Menten-type enzymes using progress-curve analysis, I present here an explicit equation for direct curve fitting to full time-course data of inhibited enzyme-catalyzed reactions. This algebraic expression involves certain elementary functions where their values are readily available using any standard nonlinear regression program. Hence this allows easy analysis of experimentally observed kinetics without any data conversion prior to fitting. Its implementation gives correct parameter estimates that are in very good agreement with results obtained using both the numerically integrated Michaelis-Menten rate equation or its exact closed-form solution which is expressed in terms of the Lambert W function.

5. Solution to Michaelis-Menten enzyme kinetic equation via undetermined gauge functions: Resolving the nonlinearity of Lineweaver-Burk plot

Murugan, R.

2002-09-01

A composite approximate solution of Michaelis-Menten enzyme kinetic equation, which could describe both transient and slow dynamics, was obtained by ordinary perturbation methods in terms of undetermined gauge functions up to a first-order level. It was found that the zeroth-order perturbation function itself solved the paradox due to steady-state approximation and predicted well the maximum enzyme-substrate complex ([ES]max) and time tm to attain it. Extensive kinetic simulations using a chemical kinetic simulator proved the validity of these results. A comparison between simulated and predicted results showed that error in the prediction of tm was negligible when perturbation parameter falls in the range of (0<ɛ≪1). Apart from these, also the effect of transient dynamics on the linearity of Lineweaver-Burk plot (especially near the origin) has been explained.

6. Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis-Menten and approximate kinetic equations.

PubMed

Costa, Rafael S; Machado, Daniel; Rocha, Isabel; Ferreira, Eugénio C

2010-05-01

The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters, represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis-Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action, convenience kinetics, lin-log and power-law). Using the mechanistic model for Escherichia coli central carbon metabolism as a benchmark, we investigate the alternative modeling approaches through comparative simulations analyses. The good dynamic behavior and the powerful predictive capabilities obtained using the hybrid model composed of Michaelis-Menten and the approximate lin-log kinetics indicate that this is a possible suitable approach to model complex large-scale networks where the exact rate laws are unknown.

7. A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations

SciTech Connect

Liu, Chang; Xu, Kun; Sun, Quanhua; Cai, Qingdong

2016-06-01

Fluid dynamic equations are valid in their respective modeling scales, such as the particle mean free path scale of the Boltzmann equation and the hydrodynamic scale of the Navier–Stokes (NS) equations. With a variation of the modeling scales, theoretically there should have a continuous spectrum of fluid dynamic equations. Even though the Boltzmann equation is claimed to be valid in all scales, many Boltzmann solvers, including direct simulation Monte Carlo method, require the cell resolution to the order of particle mean free path scale. Therefore, they are still single scale methods. In order to study multiscale flow evolution efficiently, the dynamics in the computational fluid has to be changed with the scales. A direct modeling of flow physics with a changeable scale may become an appropriate approach. The unified gas-kinetic scheme (UGKS) is a direct modeling method in the mesh size scale, and its underlying flow physics depends on the resolution of the cell size relative to the particle mean free path. The cell size of UGKS is not limited by the particle mean free path. With the variation of the ratio between the numerical cell size and local particle mean free path, the UGKS recovers the flow dynamics from the particle transport and collision in the kinetic scale to the wave propagation in the hydrodynamic scale. The previous UGKS is mostly constructed from the evolution solution of kinetic model equations. Even though the UGKS is very accurate and effective in the low transition and continuum flow regimes with the time step being much larger than the particle mean free time, it still has space to develop more accurate flow solver in the region, where the time step is comparable with the local particle mean free time. In such a scale, there is dynamic difference from the full Boltzmann collision term and the model equations. This work is about the further development of the UGKS with the implementation of the full Boltzmann collision term in the region

8. Utilization of Integrated Michaelis-Menten Equation to Determine Kinetic Constants

ERIC Educational Resources Information Center

Bezerra, Rui M. F.; Dias, Albino A.

2007-01-01

Students of biochemistry and related biosciences are urged to solve problems where kinetic parameters are calculated from initial rates obtained at different substrate concentrations. Troubles begin when they go to the laboratory to perform kinetic experiments and realize that usual laboratory instruments do not measure initial rates but only…

9. Nucleation and growth in materials and on surfaces: Kinetic Monte Carlo simulations and rate equation theory

Shi, Feng

This dissertation is organized in two parts, the first part is about fundamental characteristics of multiple dimensional systems, the second part is about parallel KMC calculation of coarsening process. In Part I, we first study the fundamental characteristics of nucleation and growth in 3 dimensional (3D) systems using a simplified model of nucleation and growth. One of the main goals of this work is to compare with previous work on 2D nucleation and growth in order to understand the effects of dimensionality. The scaling of the average island-size, island density, monomer density, island-size distribution (ISD), capture number distribution (CND), and capture zone distribution (CZD) are studied as a function of the fraction of occupied sites (coverage) and the ratio D/F of the monomer hopping rate D to the (per site) monomer creation rate F. Our model may be viewed as a simple model of the early-stages of vacancy cluster nucleation and growth under irradiation. Good agreement is found between our mean-field (MF) rate-equation results for the average island and monomer densities and our simulation results. In addition, we find that due to the decreased influence of correlations and fluctuations in 3D as compared to 2D, the scaled CND depends only weakly on the island-size. As a result the scaled ISD is significantly sharper than obtained in 2D and diverges with increasing D/F. However, the scaled ISD obtained in kinetic Monte Carlo (KMC) simulations appears to diverge more slowly with increasing D/F than the MF prediction while the divergence occurs at a value of the scaled island-size which is somewhat beyond the MF prediction. These results are supported by an analysis of the asymptotic CND. The final goal for understanding the mechanism of nucleation and growth is to develop a theory to concisely and precisely disclose the law underlying the nucleation and growth process. From the theoretical point view, dimension can be taken as a variable to develop theory. In

10. Rarefied gas flow simulations using high-order gas-kinetic unified algorithms for Boltzmann model equations

Li, Zhi-Hui; Peng, Ao-Ping; Zhang, Han-Xin; Yang, Jaw-Yen

2015-04-01

This article reviews rarefied gas flow computations based on nonlinear model Boltzmann equations using deterministic high-order gas-kinetic unified algorithms (GKUA) in phase space. The nonlinear Boltzmann model equations considered include the BGK model, the Shakhov model, the Ellipsoidal Statistical model and the Morse model. Several high-order gas-kinetic unified algorithms, which combine the discrete velocity ordinate method in velocity space and the compact high-order finite-difference schemes in physical space, are developed. The parallel strategies implemented with the accompanying algorithms are of equal importance. Accurate computations of rarefied gas flow problems using various kinetic models over wide ranges of Mach numbers 1.2-20 and Knudsen numbers 0.0001-5 are reported. The effects of different high resolution schemes on the flow resolution under the same discrete velocity ordinate method are studied. A conservative discrete velocity ordinate method to ensure the kinetic compatibility condition is also implemented. The present algorithms are tested for the one-dimensional unsteady shock-tube problems with various Knudsen numbers, the steady normal shock wave structures for different Mach numbers, the two-dimensional flows past a circular cylinder and a NACA 0012 airfoil to verify the present methodology and to simulate gas transport phenomena covering various flow regimes. Illustrations of large scale parallel computations of three-dimensional hypersonic rarefied flows over the reusable sphere-cone satellite and the re-entry spacecraft using almost the largest computer systems available in China are also reported. The present computed results are compared with the theoretical prediction from gas dynamics, related DSMC results, slip N-S solutions and experimental data, and good agreement can be found. The numerical experience indicates that although the direct model Boltzmann equation solver in phase space can be computationally expensive

11. Steady-state benchmarks of DK4D: A time-dependent, axisymmetric drift-kinetic equation solver

SciTech Connect

Lyons, B. C.; Jardin, S. C.; Ramos, J. J.

2015-05-15

The DK4D code has been written to solve a set of time-dependent, axisymmetric, finite-Larmor-radius drift-kinetic equations (DKEs) for the non-Maxwellian part of the electron and ion distribution functions using the full, linearized Fokker–Planck–Landau collision operator. The plasma is assumed to be in the low- to finite-collisionality regime, as is found in the cores of modern and future magnetic confinement fusion experiments. Each DKE is formulated such that the perturbed distribution function carries no net density, parallel momentum, or kinetic energy. Rather, these quantities are contained within the background Maxwellians and would be evolved by an appropriate set of extended magnetohydrodynamic (MHD) equations. This formulation allows for straight-forward coupling of DK4D to existing extended MHD time evolution codes. DK4D uses a mix of implicit and explicit temporal representations and finite element and spectral spatial representations. These, along with other computational methods used, are discussed extensively. Steady-state benchmarks are then presented comparing the results of DK4D to expected analytic results at low collisionality, qualitatively, and to the Sauter analytic fits for the neoclassical conductivity and bootstrap current, quantitatively. These benchmarks confirm that DK4D is capable of solving for the correct, gyroaveraged distribution function in stationary magnetic equilibria. Furthermore, the results presented demonstrate how the exact drift-kinetic solution varies with collisionality as a function of the magnetic moment and the poloidal angle.

12. Kinetic theory of transport processes in partially ionized reactive plasma, I: General transport equations

Zhdanov, V. M.; Stepanenko, A. A.

2016-03-01

In this paper we derive the set of general transport equations for multicomponent partially ionized reactive plasma in the presence of electric and magnetic fields taking into account the internal degrees of freedom and electronic excitation of plasma particles. Our starting point is a generalized Boltzmann equation with the collision integral in the Wang-Chang and Uhlenbeck form and a reactive collision integral. We obtain a set of conservation equations for such plasma and employ a linearized variant of Grad's moment method to derive the system of moment (or transport) equations for the plasma species nonequilibrium parameters. Full and reduced transport equations, resulting from the linearized system of moment equations, are presented, which can be used to obtain transport relations and expressions for transport coefficients of electrons and heavy plasma particles (molecules, atoms and ions) in partially ionized reactive plasma.

13. Kinetics of the creatine kinase reaction in neonatal rabbit heart: An empirical analysis of the rate equation

SciTech Connect

McAuliffe, J.J. ); Perry, S.B. ); Brooks, E.E. ); Ingwall, J.S. Harvard Medical School, Boston, MA )

1991-03-12

Here the authors define the kinetics of the creatine kinase (CK) reaction in an intact mammalian heart containing the full rnage of CK isoenzymes. Previously derived kinetic constants were refit for the reaction occurring at 37C. Steady-state metabolite concentrations from {sup 31}P NMR and standard biochemical techniques were determined. {sup 31}P magnetization transfer data were obtained to determine unidirectional creatine kinase fluxes in hearts with differing total creatine contents and differing mitochondrial CK activities during KCl arrest and isovolumic work for both the forward reaction (MgATP synthesis) and reverse reaction (phosphocreatine synthesis). The NMR kinetic data and substrate concentrations data were used in conjunction with a kinetic model based on MM-CK in solution to determine the applicability of the solution-based kinetic models to the CK kinetics of the intact heart. The results indicated that no single set of rate equation constants could describe both the KCl-arrested and working hearts. Analysis of the results indicated that the CK reaction is rate limited in the direction of ATP synthesis, the size of the guanidino substrate pool drives the measured CK flux in the intact heart, and during isovolumic work, the CK reaction operates under saturating conditions; that is, the substrate concentrations are at least 2-fold greater than the K{sub m} or K{sub im} for each substrate. However, during KCl arrest the reaction does not operate under saturating conditions and the CK reaction velocity is strongly influenced by the guanidino substrate pool size.

14. AdS/CFT connection between Boltzmann and Einstein equations: Kinetic theory and pure gravity in AdS space

SciTech Connect

2010-04-15

The AdS/CFT correspondence defines a sector with universal strongly coupled dynamics in the field theory as the dual of pure gravity in AdS described by Einstein's equation with a negative cosmological constant. We explain here, from the field-theoretic viewpoint how the dynamics in this sector gets determined by the expectation value of the energy-momentum tensor alone. We first show that the Boltzmann equation has very special solutions which could be functionally completely determined in terms of the energy-momentum tensor alone. We call these solutions conservative solutions. We indicate why conservative solutions should also exist when we refine this kinetic description to go closer to the exact microscopic theory or even move away from the regime of weak coupling so that no kinetic description could be employed. We argue that these conservative solutions form the universal sector dual to pure gravity at strong coupling and large N. Based on this observation, we propose a regularity condition on the energy-momentum tensor so that the dual solution in pure gravity has a smooth future horizon. We also study if irreversibility emerges only at long time scales of observation, unlike the case of the Boltzmann equation.

15. Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

NASA Technical Reports Server (NTRS)

1986-01-01

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

16. Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis

SciTech Connect

Zhao, Renjie; Evans, James W.; Oliveira, Tiago J.

2016-04-08

Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessed as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.

17. Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis

DOE PAGES

Zhao, Renjie; Evans, James W.; Oliveira, Tiago J.

2016-04-08

Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessedmore » as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.« less

18. Galerkin method for unsplit 3-D Dirac equation using atomically/kinetically balanced B-spline basis

SciTech Connect

Fillion-Gourdeau, F.; Lorin, E.; Bandrauk, A.D.

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.

19. Collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines

SciTech Connect

Parkhomenko, A I; Shalagin, Anatolii M

2011-11-30

Using the eikonal approximation, we have calculated effective collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines. We have established the relation between the probabilities of absorption and stimulated emission and the characteristics of the radiation and elementary scattering event. The example of the power interaction potential shows that quantum mechanical calculation of the collision frequencies in the eikonal approximation and previously known spectral line wing theory give similar results for the probability of radiation absorption.

20. Analytical and semianalytical solutions to the kinetic equation with Coulomb collision term and a monoenergetic source function

SciTech Connect

Goncharov, P. R.; Kuteev, B. V.; Ozaki, T.; Sudo, S.

2010-11-15

Analytical and semianalytical solutions have been obtained using a practical dimensionless form of Boltzmann kinetic equation assuming spatial homogeneity, azimuthal symmetry, and Maxwellian distributions of target plasma species. In contrast with formerly considered simplified equations with truncated collision terms, the exact Landau-Boltzmann collision operator is used, which conserves the number of particles, nullifies the collision term at statistical equilibrium, and describes the Maxwellization process naturally observed in correct solutions. A comparison with previous stationary and time-dependent analytical solutions is given. The new semianalytical results can be used in numerical modeling, for verification of solutions in more complex models, and in experimental data analysis, especially concerning nuclear processes and advanced localized, angle-resolved suprathermal particle diagnostics.

1. A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

NASA Technical Reports Server (NTRS)

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.

2. Modeling real-time PCR kinetics: Richards reparametrized equation for quantitative estimation of European hake (Merluccius merluccius).

PubMed

Sánchez, Ana; Vázquez, José A; Quinteiro, Javier; Sotelo, Carmen G

2013-04-10

Real-time PCR is the most sensitive method for detection and precise quantification of specific DNA sequences, but it is not usually applied as a quantitative method in seafood. In general, benchmark techniques, mainly cycle threshold (Ct), are the routine method for quantitative estimations, but they are not the most precise approaches for a standard assay. In the present work, amplification data from European hake (Merluccius merluccius) DNA samples were accurately modeled by three sigmoid reparametrized equations, where the lag phase parameter (λc) from the Richards equation with four parameters was demonstrated to be the perfect substitute for Ct for PCR quantification. The concentrations of primers and probes were subsequently optimized by means of that selected kinetic parameter. Finally, the linear correlation among DNA concentration and λc was also confirmed.

3. On the connection between the kinetic drumhead model and the Cahn-Hilliard equation in the presence of a gravitational field

Shiwa, Y.

1988-02-01

The equation of motion for an interface in the presence of a gravitational field is considered, when the order parameter is conserved. The kinetic drumhead model is derived directly from the Cahn-Hilliard equation without recourse to the drumhead free energy. We append a systematic derivation of the drumhead free-energy functional for the interface in a nonuniform external field.

4. A covariant Fokker-Planck equation for a simple gas from relativistic kinetic theory

SciTech Connect

Chacon-Acosta, Guillermo; Dagdug, Leonardo; Morales-Tecotl, Hugo A.

2010-12-14

A manifestly covariant Fokker-Planck differential equation is derived for the case of a relativistic simple gas by taking a small momentum transfer approximation within the collision integral of the relativistic Boltzmann equation. We follow closely previous work, with the main difference that we keep manifest covariance at every stage of the analysis. In addition, we use the covariant Juettner distribution function to find a relativistic generalization of the Einstein's fluctuation-dissipation relation.

5. Adsorption Neutralization Model and Floc Growth Kinetics Properties of Aluminum Coagulants Based on Sips and Boltzmann Equations.

PubMed

Wu, Zhen; Zhang, Xian; Zhou, Chunjiao; Pang, Jing-Lin; Zhang, Panyue

2017-02-22

Single-molecule aluminum salt AlCl3, medium polymerized polyaluminum chloride (PAC), and high polymerized polyaluminum chloride (HPAC) were prepared in a laboratory. The characteristics and coagulation properties of these prepared aluminum salts were investigated. The Langmuir, Freundlich, and Sips adsorption isotherms were first used to describe the adsorption neutralization process in coagulation, and the Boltzmann equation was used to fit the reaction kinetics of floc growth in flocculation. It was novel to find that the experimental data fitted well with the Sips and Boltzmann equation, and the significance of parameters in the equations was discussed simultaneously. Through the Sips equation, the adsorption neutralization reaction was proved to be spontaneous and the adsorption neutralization capacity was HPAC > PAC > AlCl3. Sips equation also indicated that the zeta potential of water samples would reach a limit with the increase of coagulant dosage, and the equilibrium zeta potential values were 30.25, 30.23, and 27.25 mV for AlCl3, PAC, and HPAC, respectively. The lower equilibrium zeta potential value of HPAC might be the reason why the water sample was not easy to achieve restabilization at a high coagulant dosage. Through the Boltzmann equation modeling, the maximum average floc size formed by AlCl3, PAC, and HPAC were 196.0, 188.0, and 203.6 μm, respectively, and the halfway time of reactions were 31.23, 17.08, and 9.55 min, respectively. The HPAC showed the strongest floc formation ability and the fastest floc growth rate in the flocculation process, which might be caused by the stronger adsorption and bridging functions of Alb and Alc contained in HPAC.

6. Modeling statistics and kinetics of the natural aggregation structures and processes with the solution of generalized logistic equation

Maslov, Lev A.; Chebotarev, Vladimir I.

2017-02-01

The generalized logistic equation is proposed to model kinetics and statistics of natural processes such as earthquakes, forest fires, floods, landslides, and many others. This equation has the form dN(A)/dA = s dot (1-N(A)) dot N(A)q dot A-α, q>0q>0 and A>0A>0 is the size of an element of a structure, and α≥0. The equation contains two exponents α and q taking into account two important properties of elements of a system: their fractal geometry, and their ability to interact either to enhance or to damp the process of aggregation. The function N(A)N(A) can be understood as an approximation to the number of elements the size of which is less than AA. The function dN(A)/dAdN(A)/dA where N(A)N(A) is the general solution of this equation for q=1 is a product of an increasing bounded function and power-law function with stretched exponential cut-off. The relation with Tsallis non-extensive statistics is demonstrated by solving the generalized logistic equation for q>0q>0. In the case 0equation models super-additive, and the case q>1q>1 it models sub-additive structures. The Gutenberg-Richter (G-R) formula results from interpretation of empirical data as a straight line in the area of stretched exponent with small α. The solution is applied for modeling distribution of foreshocks and aftershocks in the regions of Napa Valley 2014, and Sumatra 2004 earthquakes fitting the observed data well, both qualitatively and quantitatively.

7. Exact solution of the one- and three-dimensional quantum kinetic equations with velocity-dependent collision rates: Comparative analysis

Privalov, T.; Shalagin, A.

1999-06-01

The interaction of a plane monochromatic traveling wave with two-level particles suffering collisions with buffer-gas particles is considered. Collision rates are assumed to be velocity dependent. The collision integral is obtained on the basis of the strong-collision model, generalized to the case of velocity-dependent collision rates (the so-called ``kangaroo'' model). We obtained the exact analytical solution of the problem for arbitrary intensity of radiation, arbitrary ratio of homogeneous and Doppler widths of the absorption line, and arbitrary mass ratio between absorbing- and buffer-gas particles. The obtained analytical solutions of the quantum kinetic equations allowed us to analyze the spectral shape of the strong-field absorption line as well as the probe-field absorption line (the nonlinear part of the work done by the probe field) and the frequency dependence of the light-induced drift (LID) velocity. A comprehensive comparative analysis for the three- and one-dimensional versions of the model is given. On the basis of this analysis, we reach the conclusion that the one-dimensional quantum kinetic equation has quite a wide range of application. We also reveal the conditions for the strongest manifestation of the velocity dependence of the collision rates, which affects most strongly the anomalous LID.

8. A numerical method for integrating the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes

NASA Technical Reports Server (NTRS)

Emukashvily, I. M.

1982-01-01

An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.

9. Evaluation of the recrystallization kinetics of hot-melt extruded polymeric solid dispersions using an improved Avrami equation.

PubMed

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.

10. Discussion of the Separation of Chemical and Relaxational Kinetics of Chemically Activated Intermediates in Master Equation Simulations.

PubMed

Döntgen, Malte; Leonhard, Kai

2017-03-02

Chemical activation of intermediates, such as hydrogen abstraction products, is emerging as a basis for a fully new reaction type: hot β-scission. While for thermally equilibrated intermediates chemical kinetics are typically orders of magnitude slower than relaxational kinetics, chemically activated intermediates raise the issue of inseparable chemical and relaxational kinetics. Here, this separation problem is discussed in the framework of master equation simulations, proposing three cases often encountered in chemistry: insignificant chemical activation, predominant chemical activation, and the transition between these two limits. These three cases are illustrated via three example systems: methoxy (CH3Ȯ), diazenyl (ṄNH), and methyl formate radicals (CH3OĊO). For diazenyl, it is found that hot β-scission fully replaces the sequence of hydrogen abstraction and β-scission of thermally equilibrated diazenyl. Building on the example systems, a rule of thumb is proposed that can be used to intuitively judge the significance of hot β-scission: if the reverse hydrogen abstraction barrier height is comparable to or larger than the β-scission barrier height, hot β-scission should be considered in more detail.

11. Approaches to the solution of coupled multiexponential transient-state rate kinetic equations: A critical review.

PubMed

Fisher, Harvey F

2016-08-01

The transient-state kinetic approach has failed to reach its full potential despite its advantage over the steady-state approach in its ability to observe mechanistic events directly and in real time. This failure has been due in part to the lack of any rigorously derived and readily applicable body of theory corresponding to that which currently characterizes the steady-state approach. In order to clarify the causes of this discrepancy and to suggest a route to its solution we examine the capabilities and limitations of the various forms of transient-state kinetic approaches to the mathematical resolution of enzymatic reaction mechanisms currently available. We document a lack of validity inherent in their basic assumptions and suggest the need for a potentially more rigorous analytic approach.

12. Kinetic involvement of acetaldehyde substrate inhibition on the rate equation of yeast aldehyde dehydrogenase.

PubMed

Eggert, Matthew W; Byrne, Mark E; Chambers, Robert P

2012-10-01

13. Difference in kinematics and kinetics between high- and low-velocity resistance loading equated by volume: implications for hypertrophy training.

PubMed

Mohamad, Nur Ikhwan; Cronin, John B; Nosaka, Ken K

2012-01-01

Although it is generally accepted that a high load is necessary for muscle hypertrophy, it is possible that a low load with a high velocity results in greater kinematics and kinetics than does a high load with a slow velocity. The purpose of this study was to determine if 2 training loads (35 and 70% 1 repetition maximum [1RM]) equated by volume, differed in terms of their session kinematic and kinetic characteristics. Twelve subjects were recruited in this acute randomized within-subject crossover design study. Two bouts of a half-squat exercise were performed 1 week apart, one with high load-low velocity (HLLV = 3 sets of 12 reps at 70% 1RM) and the other with low-load high-velocity (LLHV = 6 sets of 12 reps at 35% 1RM). Time under tension (TUT), average force, peak force (PF), average power (AP), peak power (PP), work (TW), and total impulse (TI) were calculated and compared between loads for the eccentric and concentric phases. For average eccentric and concentric single repetition values, significantly (p < 0.05) greater (∼15-22%) PP outputs were associated with the LLHV loading, whereas significantly greater (∼7-61%) values were associated with the HLLV condition for most other variables of interest. However, in terms of total session kinematics and kinetics, the LLHV protocol resulted in significantly greater (∼16-61%) eccentric and concentric TUT, PF, AP, PP, and TW. The only variable that was significantly greater for the HLLV protocol than for the LLHV protocol was TI (∼20-24%). From these results, it seems that the LLHV protocol may offer an equal if not better training stimulus for muscular adaptation than the HLLV protocol, because of the greater time under tension, power, force, and work output when the total volume of the exercise is equated.

14. Pharmaceutical solid-state kinetic stability investigation by using moisture-modified Arrhenius equation and JMP statistical software.

PubMed

Fu, Mingkun; Perlman, Michael; Lu, Qing; Varga, Csanad

2015-03-25

An accelerated stress approach utilizing the moisture-modified Arrhenius equation and JMP statistical software was utilized to quantitatively assess the solid state stability of an investigational oncology drug MLNA under the influence of temperature (1/T) and humidity (%RH). Physical stability of MLNA under stress conditions was evaluated by using XRPD, DSC, TGA, and DVS, while chemical stability was evaluated by using HPLC. The major chemical degradation product was identified as a hydrolysis product of MLNA drug substance, and was subsequently subjected to an investigation of kinetics based on the isoconversion concept. A mathematical model (ln k=-11,991×(1/T)+0.0298×(%RH)+29.8823) based on the initial linear kinetics observed for the formation of this degradant at all seven stress conditions was built by using the moisture-modified Arrhenius equation and JMP statistical software. Comparison of the predicted versus experimental lnk values gave a mean deviation value of 5.8%, an R(2) value of 0.94, a p-value of 0.0038, and a coefficient of variation of the root mean square error CV(RMSE) of 7.9%. These statistics all indicated a good fit to the model for the stress data of MLNA. Both temperature and humidity were shown to have a statistically significant impact on stability by using effect leverage plots (p-value<0.05 for both 1/T and %RH). Inclusion of a term representing the interaction of relative humidity and temperature (%RH×1/T) was shown not to be justified by using Analysis of Covariance (ANCOVA), which supported the use of the moisture-corrected Arrhenius equation modeling theory. The model was found to be of value to aid setting of specifications and retest period, and storage condition selection. A model was also generated using only four conditions, as an example from a resource saving perspective, which was found to provide a good fit to the entire set of data.

15. Statistically-Averaged Rate Equations Obtained in Kinetic Description of Intense Nonneutral Beam Propagation Through a Periodic Solenoidal Focusing Field

Lee, W. Wei-Li; Davidson, Ronald C.; Stoltz, Peter

1997-11-01

This paper presents a detailed formulation and analysis of the rate equations for statistically-averaged quantities for an intense nonneutral beam propagating through a periodic solenoidal focusing field. B^sol(x) = B_z(z)hatez - (1/2)B'_z(z)(xhatex + yhate_y), where B_z(z+S) = B_z(z), and S = const. is the axial periodicity length. The anaysis assumes a thin beam with characteristic beam radius rb << S, and is based on the nonlinear Vlasov-Maxwell equations. Particularly important in experimental applications and in numerical simulations schemes, such as the nonlinear δ f- scheme,(Q. Qian, W. Lee, and R. Davidson, Phys. Plasmas 4), 1915 (1997). is an understanding of the self-consistent nonlinear evolution of various quantities averaged over the distribution of beam particles f_b(x,p,t). Self-consistent rate equations are derived for the nonlinear evolution of the mean-square beam radius , mean kinetic energy (1/2), field energy ɛ_F(z), unnormalized beam emittance ɛ(z), center of mass motion, etc., and the nonlinear beam dynamics is analysed over a wide range of system parameters.

16. Analysis of kinetic, stoichiometry and regulation of glucose and glutamine metabolism in hybridoma batch cultures using logistic equations

PubMed Central

Acosta, María Lourdes; Sánchez, Asterio; García, Francisco; Molina, Emilio

2007-01-01

Batch cultures were carried out to study the kinetic, stoichiometry, and regulation of glucose and glutamine metabolism of a murine hybridoma line. Asymmetric logistic equations (ALEs) were used to fit total and viable cell density, and nutrient and metabolite/product concentrations. Since these equations were analytically differentiable, specific rates and yield coefficients were readily calculated. Asymmetric logistic equations described satisfactorily uncontrolled batch cultures, including death phase. Specific growth rate showed a Monod-type dependence on initial glucose and glutamine concentrations. Yield coefficients of cell and lactate from glucose, and cell and ammonium from glutamine were all found to change dramatically at low residual glucose and glutamine concentrations. Under stoichiometric glucose limitation, the glucose-to-cell yield increased and glucose-to-lactate yield decreased, indicating a metabolic shift. Under stoichiometric glutamine limitation the glutamine-to-cell and glutamine-to-ammonium yields increased, but also glucose-to-cell yield increased and the glucose-to-lactate yield decreased. Monoclonal antibody production was mainly non-growth associated, independently of glucose and glutamine levels. PMID:19003011

17. A Covariant Generalization of the Real-Time Green's Functions Method in the Theory of Kinetic Equations

Smolyansky, S. A.; Prozorkevich, A. V.; Maino, G.; Mashnik, S. G.

1999-11-01

A generalized quantum relativistic kinetic equation (RKE) of the Kadanoff-Baym type is obtained on the basis of the Heisenberg equations of motion where the time evolution and space translation are separated from each other by means of the covariant method. The same approach is used also for a covariant modification of the real-time Green's functions method based on the Wigner representation. The suggested approach does not contain arbitrariness' elements and uncertainties which often arise from derivation of RKE on the basis of the motion equations of the Kadanoff-Baym type for the correlation functions in the case of systems with inner degrees of freedom. Possibilities of the proposed method are demonstrated by examples of derivation of RKE of the Vlasov type and collision integrals of the Boltzmann- Uehling-Uhlenbeck (BUU) type in the frame of the σω-version of quantum hadrodynamics, for the simplest case of spin saturated nuclear matter without antinuclear component. Here, the quasiparticle approximation in a covariant performance is used. A generalization of the method for the description of strong non-equilibrium states based on the non-equilibrium statistical operator is then proposed as well.

18. Thermostatted kinetic equations as models for complex systems in physics and life sciences.

PubMed

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.

19. Treatment of Severe Metabolic Alkalosis with Continuous Renal Replacement Therapy: Bicarbonate Kinetic Equations of Clinical Value.

PubMed

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.

20. 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.

1. Renormalization group equations and matching in a general quantum field theory with kinetic mixing

Fonseca, Renato M.; Malinský, Michal; Staub, Florian

2013-11-01

We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework.

2. A Kinetic Theory Development of the Equations of Motion of a Diatomic Gas.

DTIC Science & Technology

1986-09-01

excitation, or nuclear excitation. At moderate temperatures, however, both quantum mechanics and statistical thermodynamics show the rigid rotor to be an...distribution function Yf L,’(P , Nt) in the gas phase * space (PNqN) of systems of N molecules is the fundamental equation of classical statistical mechanics ...and Liquids, John Wiley and Sons., New York, 1954. 3. McQuarrie , D. A., Statistical Ther.modynamics, Harper & Row, New York, 1973. h..-A: 4. Bolz, R. G

3. Efficient kinetic method for fluid simulation beyond the Navier-Stokes equation.

PubMed

Zhang, Raoyang; Shan, Xiaowen; Chen, Hudong

2006-10-01

We present a further theoretical extension to the kinetic-theory-based formulation of the lattice Boltzmann method of Shan [J. Fluid Mech. 550, 413 (2006)]. In addition to the higher-order projection of the equilibrium distribution function and a sufficiently accurate Gauss-Hermite quadrature in the original formulation, a regularization procedure is introduced in this paper. This procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the Galerkin sense. Using this formulation, we construct a specific lattice Boltzmann model that accurately incorporates up to third-order hydrodynamic moments. Numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice Boltzmann models, so that fluid flows at finite Knudsen number Kn can be more quantitatively simulated. Results from force-driven Poiseuille flow simulations predict the Knudsen's minimum and the asymptotic behavior of flow flux at large Kn.

4. Solution of Linearized Drift Kinetic Equations in Neoclassical Transport Theory by the Method of Matched Asymptotic Expansions

Wong, S. K.; Chan, V. S.; Hinton, F. L.

2001-10-01

The classic solution of the linearized drift kinetic equations in neoclassical transport theory for large-aspect-ratio tokamak flux-surfaces relies on the variational principle and the choice of ``localized" distribution functions as trialfunctions.(M.N. Rosenbluth, et al., Phys. Fluids 15) (1972) 116. Somewhat unclear in this approach are the nature and the origin of the ``localization" and whether the results obtained represent the exact leading terms in an asymptotic expansion int he inverse aspect ratio. Using the method of matched asymptotic expansions, we were able to derive the leading approximations to the distribution functions and demonstrated the asymptotic exactness of the existing results. The method is also applied to the calculation of angular momentum transport(M.N. Rosenbluth, et al., Plasma Phys. and Contr. Nucl. Fusion Research, 1970, Vol. 1 (IAEA, Vienna, 1971) p. 495.) and the current driven by electron cyclotron waves.

5. Analysis of Electromagnetic Wave Propagation in a Magnetized Re-Entry Plasma Sheath Via the Kinetic Equation

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2009-01-01

Based on a theoretical model of the propagation of electromagnetic waves through a hypersonically induced plasma, it has been demonstrated that the classical radiofrequency communications blackout that is experienced during atmospheric reentry can be mitigated through the appropriate control of an external magnetic field of nominal magnitude. The model is based on the kinetic equation treatment of Vlasov and involves an analytical solution for the electric and magnetic fields within the plasma allowing for a description of the attendant transmission, reflection and absorption coefficients. The ability to transmit through the magnetized plasma is due to the magnetic windows that are created within the plasma via the well-known whistler modes of propagation. The case of 2 GHz transmission through a re-entry plasma is considered. The coefficients are found to be highly sensitive to the prevailing electron density and will thus require a dynamic control mechanism to vary the magnetic field as the plasma evolves through the re-entry phase.

6. An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions.

PubMed

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

7. Numerical approach for solving kinetic equations in two-dimensional case on hybrid computational clusters

Malkov, Ewgenij A.; Poleshkin, Sergey O.; Kudryavtsev, Alexey N.; Shershnev, Anton A.

2016-10-01

The paper presents the software implementation of the Boltzmann equation solver based on the deterministic finite-difference method. The solver allows one to carry out parallel computations of rarefied flows on a hybrid computational cluster with arbitrary number of central processor units (CPU) and graphical processor units (GPU). Employment of GPUs leads to a significant acceleration of the computations, which enables us to simulate two-dimensional flows with high resolution in a reasonable time. The developed numerical code was validated by comparing the obtained solutions with the Direct Simulation Monte Carlo (DSMC) data. For this purpose the supersonic flow past a flat plate at zero angle of attack is used as a test case.

8. Bogoliubov-Born-Green-Kirkwood-Yvon chain and kinetic equations for the level dynamics in an externally perturbed quantum system

Qureshi, Mumnuna A.; Zhong, Johnny; Betouras, Joseph J.; Zagoskin, Alexandre M.

2017-03-01

Theoretical description and simulation of large quantum coherent systems out of equilibrium remains a daunting task. Here we are developing an approach to it based on the Pechukas-Yukawa formalism, which is especially convenient in the case of an adiabatically slow external perturbation, though it is not restricted to adiabatic systems. In this formalism the dynamics of energy levels in an externally perturbed quantum system as a function of the perturbation parameter is mapped on that of a fictitious one-dimensional classical gas of particles with cubic repulsion. Equilibrium statistical mechanics of this Pechukas gas allows us to reproduce the random matrix theory of energy levels. In the present work, we develop the nonequilibrium statistical mechanics of the Pechukas gas, starting with the derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) chain of equations for the appropriate generalized distribution functions. Sets of approximate kinetic equations can be consistently obtained by breaking this chain at a particular point (i.e., approximating all higher-order distribution functions by the products of the lower-order ones). When complemented by the equations for the level occupation numbers and interlevel transition amplitudes, they allow us to describe the nonequilibrium evolution of the quantum state of the system, which can describe better a large quantum coherent system than the currently used approaches. In particular, we find that corrections to the factorized approximation of the distribution function scale as 1 /N , where N is the number of the "Pechukas gas particles" (i.e., energy levels in the system).

9. Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion

PubMed Central

Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J.; Grima, Ramon; Hasenauer, Jan

2016-01-01

Quantitative mechanistic models are valuable tools for disentangling biochemical pathways and for achieving a comprehensive understanding of biological systems. However, to be quantitative the parameters of these models have to be estimated from experimental data. In the presence of significant stochastic fluctuations this is a challenging task as stochastic simulations are usually too time-consuming and a macroscopic description using reaction rate equations (RREs) is no longer accurate. In this manuscript, we therefore consider moment-closure approximation (MA) and the system size expansion (SSE), which approximate the statistical moments of stochastic processes and tend to be more precise than macroscopic descriptions. We introduce gradient-based parameter optimization methods and uncertainty analysis methods for MA and SSE. Efficiency and reliability of the methods are assessed using simulation examples as well as by an application to data for Epo-induced JAK/STAT signaling. The application revealed that even if merely population-average data are available, MA and SSE improve parameter identifiability in comparison to RRE. Furthermore, the simulation examples revealed that the resulting estimates are more reliable for an intermediate volume regime. In this regime the estimation error is reduced and we propose methods to determine the regime boundaries. These results illustrate that inference using MA and SSE is feasible and possesses a high sensitivity. PMID:27447730

10. Kinetic theory of spin-polarized systems in electric and magnetic fields with spin-orbit coupling. I. Kinetic equation and anomalous Hall and spin-Hall effects

Morawetz, K.

2015-12-01

The coupled kinetic equation for density and spin Wigner functions is derived including spin-orbit coupling, electric and magnetic fields, and self-consistent Hartree mean fields suited for SU(2) transport. The interactions are assumed to be with scalar and magnetic impurities as well as scalar and spin-flip potentials among the particles. The spin-orbit interaction is used in a form suitable for solid state physics with Rashba or Dresselhaus coupling, graphene, extrinsic spin-orbit coupling, and effective nuclear matter coupling. The deficiencies of the two-fluid model are worked out consisting of the appearance of an effective in-medium spin precession. The stationary solution of all these systems shows a band splitting controlled by an effective medium-dependent Zeeman field. The self-consistent precession direction is discussed and a cancellation of linear spin-orbit coupling at zero temperature is reported. The precession of spin around this effective direction caused by spin-orbit coupling leads to anomalous charge and spin currents in an electric field. Anomalous Hall conductivity is shown to consist of the known results obtained from the Kubo formula or Berry phases and a symmetric part interpreted as an inverse Hall effect. Analogously the spin-Hall and inverse spin-Hall effects of spin currents are discussed which are present even without magnetic fields showing a spin accumulation triggered by currents. The analytical dynamical expressions for zero temperature are derived and discussed in dependence on the magnetic field and effective magnetizations. The anomalous Hall and spin-Hall effect changes sign at higher than a critical frequency dependent on the relaxation time.

11. Full-time kinetics of self-assembly and disassembly in micellar solution via the generalized Smoluchowski equation with fusion and fission of surfactant aggregates

Shchekin, Alexander K.; Babintsev, Ilya A.; Adzhemyan, Loran Ts.

2016-11-01

Full-time kinetics of self-assembly and disassembly of spherical micelles with their fusion and fission in non-ionic micellar solutions has been considered in detail on the basis of direct numerical solutions of the generalized Smoluchowski equations describing the evolution of the time-dependent concentrations of molecular aggregates for every aggregation number. The cases of instant increase of the monomer concentration up or dilution of a surfactant solution below the critical micelle concentration at large initial deviations from the final equilibrium state have been studied. Different stages in assembly or disassembly of micelles have been described and compared with the results of the stepwise mechanism of monomer attachment-detachment described by the Becker-Döring kinetic equations. A relation of the full-time kinetics to micellar relaxation at small deviations from the equilibrium state has been checked.

12. Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

13. Solution of drift kinetic equation in stellarators and tokamaks with broken symmetry using the code NEO-2

Kernbichler, W.; Kasilov, S. V.; Kapper, G.; Martitsch, A. F.; Nemov, V. V.; Albert, C.; Heyn, M. F.

2016-11-01

NEO-2 is a linearized drift kinetic equation solver for three-dimensional toroidal magnetic fields. It has been designed in order to treat effectively—besides all other regimes—the long mean free path regime, avoiding any simplifications on device geometry or on the Coulomb collision model. The code is based on the field line integration technique combined with a multiple domain decomposition approach, which allows for introduction of an adaptive grid in velocity space. This makes NEO-2 capable of effectively resolving all boundary layers between various classes of trapped particles and passing particles, and also allows for straightforward code parallelization. In stellarators, NEO-2 is used mainly for computations of neoclassical transport coefficients in regimes with slow plasma rotation and for the evaluation of the generalized Spitzer function, which plays the role of a current drive efficiency. In tokamaks with small ideal non-axisymmetric magnetic field perturbations, NEO-2 is used for evaluation of the toroidal torque resulting from these perturbations (neoclassical toroidal viscosity). The limitation to slow plasma rotation pertinent to usage in stellarators has been removed in this case with the help of a quasilinear approach, which is valid due to the smallness of the perturbation field.

14. Technical note: application of α-QSS to the numerical integration of kinetic equations in tropospheric chemistry

Liu, F.; Schaller, E.; Mott, D. R.

2005-08-01

A major task in many applications of atmospheric chemistry transport problems is the numerical integration of stiff systems of Ordinary Differential Equations (ODEs) describing the chemical transformations. A faster solver that is easier to couple to the other physics in the problem is still needed. The integration method, α-QSS, corresponding to the solver CHEMEQ2 aims at meeting the demands of a process-split, reacting-flow simulation (Mott 2000; Mott and Oran, 2001). However, this integrator has yet to be applied to the numerical integration of kinetic equations in tropospheric chemistry. A zero-dimensional (box) model is developed to test how well CHEMEQ2 works on the tropospheric chemistry equations. This paper presents the testing results. The reference chemical mechanisms herein used are Regional Atmospheric Chemistry Mechanism (RACM) (Stockwell et al., 1997) and its secondary lumped successor Regional Lumped Atmospheric Chemical Scheme (ReLACS) (Crassier et al., 2000). The box model is forced and initialized by the DRY scenarios of Protocol Ver. 2 developed by EUROTRAC (Poppe et al., 2001). The accuracy of CHEMEQ2 is evaluated by comparing the results to solutions obtained with VODE. This comparison is made with parameters of the error tolerance, relative difference with respect to VODE scheme, trade off between accuracy and efficiency, global time step for integration etc. The study based on the comparison concludes that the single-point α-QSS approach is fast and moderately accurate as well as easy to couple to reacting flow simulation models, which makes CHEMEQ2 one of the best candidates for three-dimensional atmospheric Chemistry Transport Modelling (CTM) studies. In addition the RACM mechanism may be replaced by ReLACS mechanism for tropospheric chemistry transport modelling. The testing results also imply that the accuracy for chemistry numerical simulations is highly different from species to species. Therefore ozone is not the good choice for

15. Numerical simulation of flood inundation using a well-balanced kinetic scheme for the shallow water equations with bulk recharge and discharge

Ersoy, Mehmet; Lakkis, Omar; Townsend, Philip

2016-04-01

The flow of water in rivers and oceans can, under general assumptions, be efficiently modelled using Saint-Venant's shallow water system of equations (SWE). SWE is a hyperbolic system of conservation laws (HSCL) which can be derived from a starting point of incompressible Navier-Stokes. A common difficulty in the numerical simulation of HSCLs is the conservation of physical entropy. Work by Audusse, Bristeau, Perthame (2000) and Perthame, Simeoni (2001), proposed numerical SWE solvers known as kinetic schemes (KSs), which can be shown to have desirable entropy-consistent properties, and are thus called well-balanced schemes. A KS is derived from kinetic equations that can be integrated into the SWE. In flood risk assessment models the SWE must be coupled with other equations describing interacting meteorological and hydrogeological phenomena such as rain and groundwater flows. The SWE must therefore be appropriately modified to accommodate source and sink terms, so kinetic schemes are no longer valid. While modifications of SWE in this direction have been recently proposed, e.g., Delestre (2010), we depart from the extant literature by proposing a novel model that is "entropy-consistent" and naturally extends the SWE by respecting its kinetic formulation connections. This allows us to derive a system of partial differential equations modelling flow of a one-dimensional river with both a precipitation term and a groundwater flow model to account for potential infiltration and recharge. We exhibit numerical simulations of the corresponding kinetic schemes. These simulations can be applied to both real world flood prediction and the tackling of wider issues on how climate and societal change are affecting flood risk.

16. Competing solutions of Landau’s kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

Li, David Z.; Anderson, R. H.; Miller, M. D.; Crowell, Ethan

2014-07-01

We examine in detail the method introduced by Sanchez-Castro, Bedell, and Wiegers (SBW) to solve Landau’s linearized kinetic equation, and compare it with the well-known standard method introduced by Abrikosov and Khalatnikov (AK). The SBW approach, hardly known, differs from AK in the way that moments are taken with respect to the angular functions of the Fourier transformed kinetic equation. We compare the SBW and AK solutions for zero-sound and first-sound propagation speeds and attenuation both analytically in the zero and full polarization limits, and numerically at arbitrary polarization using Landau parameters appropriate for thin 3He films. We find that the lesser known method not only yields results in close agreement with the standard method, but in most cases does so with far less analytic and computational effort.

17. Numerical modeling of the sound propagation through a rarefied gas in a semi-infinite space on the basis of linearized kinetic equation.

PubMed

Sharipov, Felix; Kalempa, Denize

2008-10-01

The sound propagation through a rarefied gas is investigated on the basis of the linearized kinetic equation. A plate oscillating in the direction normal to its own plane is considered as a sound wave source. It is assumed a fully established oscillation so that the solution of the kinetic equation depends on time harmonically, while its dependence on the spatial coordinates is obtained numerically. The problem is solved over a wide range of the oscillation speed parameter defined as a ratio of the intermolecular collision frequency to the sound frequency. In order to evaluate the influence of the momentum and energy accommodation coefficients on the solution of the problem, the Cercignani-Lampis scattering kernel is applied as the boundary condition. An analysis of wave characteristics near the source surface shows that they are significantly different from those far from the surface even if the oscillation is slow, i.e., the solution is not harmonic in the space.

18. Utilization of integrated Michaelis-Menten equations for enzyme inhibition diagnosis and determination of kinetic constants using Solver supplement of Microsoft Office Excel.

PubMed

Bezerra, Rui M F; Fraga, Irene; Dias, Albino A

2013-01-01

Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion.

19. Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

Davidenko, V. D.; Zinchenko, A. S.; Harchenko, I. K.

2016-12-01

Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.

20. Single-Photon Detection by a Dirty Current-Carrying Superconducting Strip Based on the Kinetic-Equation Approach

Vodolazov, D. Yu.

2017-03-01

Using a kinetic-equation approach, we study the dynamics of electrons and phonons in current-carrying superconducting nanostrips after the absorption of a single photon of the near-infrared or optical range. We find that the larger the Ce/Cph|Tc ratio (where Tc is the critical temperature of a superconductor and Ce and Cph are specific heat capacities of electrons and phonons, respectively), the larger the portion of the photon's energy goes to electrons. The electrons become more strongly heated and hence can thermalize faster during the initial stage of hot-spot formation. The thermalization time τth can be less than 1 ps for superconductors with Ce/Cph|Tc≫1 and a small diffusion coefficient of D ≃0.5 cm2/s when thermalization occurs, mainly due to electron-phonon and phonon-electron scattering in a relatively small volume of approximately ξ2d (ξ is a superconducting coherence length, while d <ξ is a thickness of the strip). For longer time spans, due to diffusion of hot electrons' effective temperature inside the hot spot decreases, the size of the hot spot increases, the superconducting state becomes unstable, and the normal domain spreads in the strip at a current larger than the so-called detection current. We find the dependence of the detection current on the photon's energy, the location of its absorption in the strip, the width of the strip, and the magnetic field, and we compare this dependence with existing experiments. Our results demonstrate that materials with Ce/Cph|Tc≪1 are bad candidates for single-photon detectors due to a small transfer of the photon's energy to electronic system and a large τth . We also predict that even a several-micron-wide dirty superconducting bridge is able to detect a single near-infrared or optical photon if its critical current exceeds 70% of the depairing current and Ce/Cph|Tc≳1 .

1. Boltzmann equation modelling of Learning Dynamics. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

Shizgal, Bernie

2016-03-01

The paper by Burini et al. [7] presents an interesting use of the Boltzmann equation of kinetic theory to model real learning processes. The authors provide a comprehensive discussion of the basic concepts involved in their modelling work. The Boltzmann equation as used by physicists and chemists to model a variety of transport processes in many diverse fields is based on the notion of the binary collisions between identifiable particles in the defined system [9]. The particles exchange energy on collision and the distribution function, which depends on the three velocity components and the three spatial coordinates, varies with time. The classical or quantum collision dynamics between particles play a central role in the definition of the kernels in the integral operators that define the Boltzmann equation [8].

2. On the accuracy of a one-dimensional approach to the solution of kinetic equations with velocity-dependent collision frequencies

Parkhomenko, A. I.; Shalagin, A. M.

2014-11-01

The solution of many problems in light-induced gas kinetics can be simplified significantly using quantum kinetic equations in the context of the so-called one-dimensional approximation, in which the initial equations are averaged over transverse (relative to the direction of radiation) velocities. The errors introduced in such an approach are usually assumed to be small; however, this has been confirmed quantitatively only on the basis of the simplest (two- and three-level) particle models. We analyze the accuracy of the one-dimensional approximation for multilevel particles quantitatively for the light-induced drift (LID) effect in cesium atoms in the atmosphere of inert buffer gases. It is shown that in the case of the so-called "normal" LID, one-dimensional kinetic equations can always be used instead of three-dimensional equations without a risk of losing some important fine details in the dependence of the drift velocity on the radiation frequency. In the case of anomalous LID, the error of the one-dimensional approximation is also insignificant, but it can be disregarded only in the case of light buffer particles. For comparable masses of resonant and buffer particles, the one-dimensional approximation may give a noticeable error in determination of drift velocity amplitudes; however, the positions of drift velocity zeros and extrema depending on radiation-frequency detuning can be described successfully. Results show that the error introduced by using the one-dimensional approximation for multilevel particles turns out to be more significant than for the simplest particle models.

3. On the accuracy of a one-dimensional approach to the solution of kinetic equations with velocity-dependent collision frequencies

SciTech Connect

Parkhomenko, A. I. Shalagin, A. M.

2014-11-15

The solution of many problems in light-induced gas kinetics can be simplified significantly using quantum kinetic equations in the context of the so-called one-dimensional approximation, in which the initial equations are averaged over transverse (relative to the direction of radiation) velocities. The errors introduced in such an approach are usually assumed to be small; however, this has been confirmed quantitatively only on the basis of the simplest (two- and three-level) particle models. We analyze the accuracy of the one-dimensional approximation for multilevel particles quantitatively for the light-induced drift (LID) effect in cesium atoms in the atmosphere of inert buffer gases. It is shown that in the case of the so-called “normal” LID, one-dimensional kinetic equations can always be used instead of three-dimensional equations without a risk of losing some important fine details in the dependence of the drift velocity on the radiation frequency. In the case of anomalous LID, the error of the one-dimensional approximation is also insignificant, but it can be disregarded only in the case of light buffer particles. For comparable masses of resonant and buffer particles, the one-dimensional approximation may give a noticeable error in determination of drift velocity amplitudes; however, the positions of drift velocity zeros and extrema depending on radiation-frequency detuning can be described successfully. Results show that the error introduced by using the one-dimensional approximation for multilevel particles turns out to be more significant than for the simplest particle models.

4. Coupling the advection-dispersion equation with fully kinetic reversible/irreversible sorption terms to model radiocesium soil profiles in Fukushima Prefecture.

PubMed

Kurikami, Hiroshi; Malins, Alex; Takeishi, Minoru; Saito, Kimiaki; Iijima, Kazuki

2017-02-17

Radiocesium is an important environmental contaminant in fallout from nuclear reactor accidents and atomic weapons testing. A modified Diffusion-Sorption-Fixation (mDSF) model, based on the advection-dispersion equation, is proposed to describe the vertical migration of radiocesium in soils following fallout. The model introduces kinetics for the reversible binding of radiocesium. We test the model by comparing its results to depth profiles measured in Fukushima Prefecture, Japan, since 2011. The results from the mDSF model are a better fit to the measurement data (as quantified by R(2)) than results from a simple diffusion model and the original DSF model. The introduction of reversible sorption kinetics means that the exponential-shape depth distribution can be reproduced immediately following fallout. The initial relaxation mass depth of the distribution is determined by the diffusion length, which depends on the distribution coefficient, sorption rate and dispersion coefficient. The mDSF model captures the long tails of the radiocesium distribution at large depths, which are caused by different rates for kinetic sorption and desorption. The mDSF model indicates that depth distributions displaying a peak in activity below the surface are possible for soils with high organic matter content at the surface. The mDSF equations thus offers a physical basis for various types of radiocesium depth profiles observed in contaminated environments.

5. Multistep generalized transformation method applied to solving equations of discrete and continuous time-fractional enzyme kinetics

Vosika, Z.; Mitić, V. V.; Vasić, A.; Lazović, G.; Matija, L.; Kocić, Lj. M.

2017-03-01

In this paper, Caputo based Michaelis-Menten kinetic model based on Time Scale Calculus (TSC) is proposed. The main reason for its consideration is a study of tumor cells population growth dynamics. In the particular case discrete-continuous time kinetics, Michaelis-Menten model is numerically treated, using a new algorithm proposed by authors, called multistep generalized difference transformation method (MSGDETM). In addition numerical simulations are performed and is shown that it represents the upgrade of the multi-step variant of generalized differential transformation method (MSGDTM). A possible conditions for its further development are discussed and possible experimental verification is described.

6. Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: equations and parameter refinement.

PubMed Central

Mulquiney, P J; Kuchel, P W

1999-01-01

Over the last 25 years, several mathematical models of erythrocyte metabolism have been developed. Although these models have identified the key features in the regulation and control of erythrocyte metabolism, many important aspects remain unexplained. In particular, none of these models have satisfactorily accounted for 2,3-bisphosphoglycerate (2,3-BPG) metabolism. 2,3-BPG is an important modulator of haemoglobin oxygen affinity, and hence an understanding of the regulation of 2,3-BPG concentration is important for understanding blood oxygen transport. A detailed, comprehensive, and hence realistic mathematical model of erythrocyte metabolism is presented that can explain the regulation and control of 2,3-BPG concentration and turnover. The model is restricted to the core metabolic pathways, namely glycolysis, the 2,3-BPG shunt and the pentose phosphate pathway (PPP), and includes membrane transport of metabolites, the binding of metabolites to haemoglobin and Mg(2+), as well as pH effects on key enzymic reactions and binding processes. The model is necessarily complex, since it is intended to describe the regulation and control of 2,3-BPG metabolism under a wide variety of physiological and experimental conditions. In addition, since H(+) and blood oxygen tension are important external effectors of 2,3-BPG concentration, it was important that the model take into account the large array of kinetic and binding phenomena that result from changes in these effectors. Through an iterative loop of experimental and simulation analysis many values of enzyme-kinetic parameters of the model were refined to yield close conformity between model simulations and 'real' experimental data. This iterative process enabled a single set of parameters to be found which described well the metabolic behaviour of the erythrocyte under a wide variety of conditions. PMID:10477269

7. Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

NASA Technical Reports Server (NTRS)

Avissar, Roni; Chen, Fei

1993-01-01

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes

8. The comparison of the estimation of enzyme kinetic parameters by fitting reaction curve to the integrated Michaelis-Menten rate equations of different predictor variables.

PubMed

Liao, Fei; Zhu, Xiao-Yun; Wang, Yong-Mei; Zuo, Yu-Ping

2005-01-31

The estimation of enzyme kinetic parameters by nonlinear fitting reaction curve to the integrated Michaelis-Menten rate equation ln(S(0)/S)+(S(0)-S)/K(m)=(V(m)/K(m))xt was investigated and compared to that by fitting to (S(0)-S)/t=V(m)-K(m)x[ln(S(0)/S)/t] (Atkins GL, Nimmo IA. The reliability of Michaelis-Menten constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. Biochem J 1973;135:779-84) with uricase as the model. Uricase reaction curve was simulated with random absorbance error of 0.001 at 0.075 mmol/l uric acid. Experimental reaction curve was monitored by absorbance at 293 nm. For both CV and deviation <20% by simulation, K(m) from 5 to 100 micromol/l was estimated with Eq. (1) while K(m) from 5 to 50 micromol/l was estimated with Eq. (2). The background absorbance and the error in the lag time of steady-state reaction resulted in negative K(m) with Eq. (2), but did not affect K(m) estimated with Eq. (1). Both equations gave better estimation of V(m). The computation time and the goodness of fit with Eq. (1) were 40-fold greater than those with Eq. (2). By experimentation, Eq. (1) yielded K(m) consistent with the Lineweaver-Burk plot analysis, but Eq. (2) gave many negative parameters. Apparent K(m) by Eq. (1) linearly increased, while V(m) were constant, vs. xanthine concentrations, and the inhibition constant was consistent with the Lineweaver-Burk plot analysis. These results suggested that the integrated rate equation that uses the predictor variable of reaction time was reliable for the estimation of enzyme kinetic parameters and applicable for the characterization of enzyme inhibitors.

9. Off-line form of the Michaelis-Menten equation for studying the reaction kinetics in a polymer microchip integrated with enzyme microreactor.

PubMed

Liu, Ai-Lin; Zhou, Ting; He, Feng-Yun; Xu, Jing-Juan; Lu, Yu; Chen, Hong-Yuan; Xia, Xing-Hua

2006-06-01

We firstly transformed the traditional Michaelis-Menten equation into an off-line form which can be used for evaluating the Michaelis-Menten constant after the enzymatic reaction. For experimental estimation of the kinetics of enzymatic reactions, we have developed a facile and effective method by integrating an enzyme microreactor into direct-printing polymer microchips. Strong nonspecific adsorption of proteins was utilized to effectively immobilize enzymes onto the microchannel wall, forming the integrated on-column enzyme microreactor in a microchip. The properties of the integrated enzyme microreactor were evaluated by using the enzymatic reaction of glucose oxidase (GOx) with its substrate glucose as a model system. The reaction product, hydrogen peroxide, was electrochemically (EC) analyzed using a Pt microelectrode. The data for enzyme kinetics using our off-line form of the Michaelis-Menten equation was obtained (K(m) = 2.64 mM), which is much smaller than that reported in solution (K(m) = 6.0 mM). Due to the hydrophobic property and the native mesoscopic structure of the poly(ethylene terephthalate) film, the immobilized enzyme in the microreactor shows good stability and bioactivity under the flowing conditions.

10. An efficient and accurate two-stage fourth-order gas-kinetic scheme for the Euler and Navier-Stokes equations

Pan, Liang; Xu, Kun; Li, Qibing; Li, Jiequan

2016-12-01

For computational fluid dynamics (CFD), the generalized Riemann problem (GRP) solver and the second-order gas-kinetic scheme (GKS) provide a time-accurate flux function starting from a discontinuous piecewise linear flow distributions around a cell interface. With the adoption of time derivative of the flux function, a two-stage Lax-Wendroff-type (L-W for short) time stepping method has been recently proposed in the design of a fourth-order time accurate method for inviscid flow [21]. In this paper, based on the same time-stepping method and the second-order GKS flux function [42], a fourth-order gas-kinetic scheme is constructed for the Euler and Navier-Stokes (NS) equations. In comparison with the formal one-stage time-stepping third-order gas-kinetic solver [24], the current fourth-order method not only reduces the complexity of the flux function, but also improves the accuracy of the scheme. In terms of the computational cost, a two-dimensional third-order GKS flux function takes about six times of the computational time of a second-order GKS flux function. However, a fifth-order WENO reconstruction may take more than ten times of the computational cost of a second-order GKS flux function. Therefore, it is fully legitimate to develop a two-stage fourth order time accurate method (two reconstruction) instead of standard four stage fourth-order Runge-Kutta method (four reconstruction). Most importantly, the robustness of the fourth-order GKS is as good as the second-order one. In the current computational fluid dynamics (CFD) research, it is still a difficult problem to extend the higher-order Euler solver to the NS one due to the change of governing equations from hyperbolic to parabolic type and the initial interface discontinuity. This problem remains distinctively for the hypersonic viscous and heat conducting flow. The GKS is based on the kinetic equation with the hyperbolic transport and the relaxation source term. The time-dependent GKS flux function

11. Establishment of steady-state metabolism of ethanol in perfused rat liver: the quantitative analysis using kinetic mechanism-based rate equations of alcohol dehydrogenase.

PubMed

Yao, Chung-Tay; Lai, Ching-Long; Hsieh, Hsiu-Shan; Chi, Chin-Wen; Yin, Shih-Jiun

2010-09-01

12. Basic Equations in Statics and Kinetics of Protein Polymerization and the Mechanism of the Formation and Dissociation of Amyloid Fibrils Revealed by Pressure Perturbation.

PubMed

Tachibana, Hideki

2015-01-01

Studies of the pressure-dissociation of several amyloid or amyloid-like fibrils have shown that the fibril state is considerably voluminous. Quantitative characterization of the protein fibrillation reaction with respect to volumetric parameters is necessary to elucidate mechanisms of amyloid fibrillation in molecular terms such as protein cavity and hydration. Here we discuss, firstly, basic equations in statics and kinetics of protein polymerization as employed to obtain thermodynamic, volumetric, and kinetic parameters. Equilibrium treatment of the reactions with the scheme such as one-step polymerization, linear-association polymerization, or nucleation-dependent polymerization, and kinetic treatment of seeded linear-polymerization or spontaneous nucleation-elongation polymerization are described. In particular we will detail kinetics of the dissociation of fibrils which have been produced under the linear-association mechanism and therefore the length-distribution of which conforms to a geometric sequence in the degree of polymerization with a common ratio r, which is less than, and usually very close to, unity. In this case, an observed macroscopic rate of dissociation is shown to be a product of the microscopic elementary dissociation rate constant and a factor (1-r), extremely reduced compared with the intrinsic elementary rate. Secondly, we discuss protein conformational states in fibrillogenesis with molecular and volumetric observations reported, such as the unfolded state responsible for the association with seeds and the extension of amyloid fibrils, the transition state in which protein cavity formation and dehydration occur to intermediate levels, and the fibril state in which they occur to final respective levels which, in some cases, depend on the maturity of the fibril.

13. Direct discrete simulation of the kinetic Landau-Fokker-Planck equation with an alternating external electromagnetic field

SciTech Connect

Karpov, S. A.; Potapenko, I. F.

2015-10-15

A stochastic method of simulation of Coulomb interaction is considered. The main idea of the method is to approximate the nonlinear Landau kinetic collision integral by the Boltzmann integral. In its realization, the method can be attributed to a wide class of Monte Carlo-type methods. It is easily combined with the existing particle methods used to simulate collisionless plasmas. This is important for simulation of the dynamics of both laboratory and space plasmas when the mean free path of plasma particles is comparable with the plasma inhomogeneity scale length. Illustrative examples of relaxation of two-temperature plasma being subject to a high-frequency alternating electric field are given, and differences from their classical description are considered. The method satisfies the conservation laws for the number of particles, momentum, and energy and is simple and efficient in implementation.

14. Feasibility of creating a specialized reactimeter based on the inverse solution to kinetics equation with a current-mode neutron detector

Koshelev, A. S.; Arapov, A. V.; Ovchinnikov, M. A.

2016-12-01

The file-evaluation results of a reactimeter based on the inverse solution to the kinetics equation (ISKE) are presented, which were obtained using an operating hardware-measuring complex with a KNK-4 neutron detector working in the current mode. The processing of power-recording files of the BR-1M, BR-K1, and VIR-2M reactors of the Russian Federal Nuclear Center—All-Russian Research Institute of Experimental Physics, which was performed with the use of Excel simulation of the ISKE formalism, demonstrated the feasibility of implementation of the reactivity monitoring (during the operation of these reactors at stationary power) beginning from the level of 5 × 10-4βeff.

15. Kinetic balance and variational bounds failure in the solution of the Dirac equation in a finite Gaussian basis set

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.; Faegri, Knut, Jr.

1990-01-01

The paper investigates bounds failure in calculations using Gaussian basis sets for the solution of the one-electron Dirac equation for the 2p1/2 state of Hg(79+). It is shown that bounds failure indicates inadequacies in the basis set, both in terms of the exponent range and the number of functions. It is also shown that overrepresentation of the small component space may lead to unphysical results. It is concluded that it is important to use matched large and small component basis sets with an adequate size and exponent range.

16. Kinetic description of intense nonneutral beam propagation through a periodic solenoidal focusing field based on the nonlinear Vlasov-Maxwell equations

SciTech Connect

Davidson, R.C.; Chen, C.

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.

17. Effect of the adsorbate kinetic diameter on the accuracy of the Dubinin-Radushkevich equation for modeling adsorption of organic vapors on activated carbon.

PubMed

2012-11-30

18. Investigations of a compartmental model for leucine kinetics using non-linear mixed effects models with ordinary and stochastic differential equations.

PubMed

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.

19. Comparison of the lattice Boltzmann equation and discrete unified gas-kinetic scheme methods for direct numerical simulation of decaying turbulent flows.

PubMed

Wang, Peng; Wang, Lian-Ping; Guo, Zhaoli

2016-10-01

The main objective of this work is to perform a detailed comparison of the lattice Boltzmann equation (LBE) and the recently developed discrete unified gas-kinetic scheme (DUGKS) methods for direct numerical simulation (DNS) of the decaying homogeneous isotropic turbulence and the Kida vortex flow in a periodic box. The flow fields and key statistical quantities computed by both methods are compared with those from the pseudospectral method at both low and moderate Reynolds numbers. The results show that the LBE is more accurate and efficient than the DUGKS, but the latter has a superior numerical stability, particularly for high Reynolds number flows. In addition, we conclude that the DUGKS can adequately resolve the flow when the minimum spatial resolution parameter k_{max}η>3, where k_{max} is the maximum resolved wave number and η is the flow Kolmogorov length. This resolution requirement can be contrasted with the requirements of k_{max}η>1 for the pseudospectral method and k_{max}η>2 for the LBE. It should be emphasized that although more validations should be conducted before the DUGKS can be called a viable tool for DNS of turbulent flows, the present work contributes to the overall assessment of the DUGKS, and it provides a basis for further applications of DUGKS in studying the physics of turbulent flows.

20. The chemical master equation approach to nonequilibrium steady-state of open biochemical systems: linear single-molecule enzyme kinetics and nonlinear biochemical reaction networks.

PubMed

Qian, Hong; Bishop, Lisa M

2010-09-20

We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with concentration fluctuations. We discuss the linear, unimolecular single-molecule enzyme kinetics, phosphorylation-dephosphorylation cycle (PdPC) with bistability, and network exhibiting oscillations. Emphasis is paid to the comparison between the stochastic dynamics and the prediction based on the traditional approach based on the Law of Mass Action. We introduce the difference between nonlinear bistability and stochastic bistability, the latter has no deterministic counterpart. For systems with nonlinear bistability, there are three different time scales: (a) individual biochemical reactions, (b) nonlinear network dynamics approaching to attractors, and (c) cellular evolution. For mesoscopic systems with size of a living cell, dynamics in (a) and (c) are stochastic while that with (b) is dominantly deterministic. Both (b) and (c) are emergent properties of a dynamic biochemical network; We suggest that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting. The cellular evolution proceeds with transitions among the attractors of (b) in a "punctuated equilibrium" manner.

1. Stochastic chemical kinetics and the total quasi-steady-state assumption: application to the stochastic simulation algorithm and chemical master equation.

PubMed

Macnamara, Shev; Bersani, Alberto M; Burrage, Kevin; Sidje, Roger B

2008-09-07

Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four examples: Michaelis-Menten enzyme kinetics, double phosphorylation, the Goldbeter-Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.

2. The Chemical Master Equation Approach to Nonequilibrium Steady-State of Open Biochemical Systems: Linear Single-Molecule Enzyme Kinetics and Nonlinear Biochemical Reaction Networks

PubMed Central

Qian, Hong; Bishop, Lisa M.

2010-01-01

We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with concentration fluctuations. We discuss the linear, unimolecular single-molecule enzyme kinetics, phosphorylation-dephosphorylation cycle (PdPC) with bistability, and network exhibiting oscillations. Emphasis is paid to the comparison between the stochastic dynamics and the prediction based on the traditional approach based on the Law of Mass Action. We introduce the difference between nonlinear bistability and stochastic bistability, the latter has no deterministic counterpart. For systems with nonlinear bistability, there are three different time scales: (a) individual biochemical reactions, (b) nonlinear network dynamics approaching to attractors, and (c) cellular evolution. For mesoscopic systems with size of a living cell, dynamics in (a) and (c) are stochastic while that with (b) is dominantly deterministic. Both (b) and (c) are emergent properties of a dynamic biochemical network; We suggest that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting. The cellular evolution proceeds with transitions among the attractors of (b) in a “punctuated equilibrium” manner. PMID:20957107

3. Introduction to Kinetic Model Equations

DTIC Science & Technology

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

4. STOMP Subsurface Transport Over Multiple Phases Version 1.0 Addendum: ECKEChem Equilibrium-Conservation-Kinetic Equation Chemistry and Reactive Transport

SciTech Connect

White, Mark D.; McGrail, B. Peter

2005-12-01

flow and transport simulator, STOMP (Subsurface Transport Over Multiple Phases). Prior to these code development activities, the STOMP simulator included sequential and scalable implementations for numerically simulating the injection of supercritical CO2 into deep saline aquifers. Additionally, the sequential implementations included operational modes that considered nonisothermal conditions and kinetic dissolution of CO2 into the saline aqueous phase. This addendum documents the advancement of these numerical simulation capabilities to include reactive transport in the STOMP simulator through the inclusion of the recently PNNL developed batch geochemistry solution module ECKEChem (Equilibrium-Conservation-Kinetic Equation Chemistry). Potential geologic reservoirs for sequestering CO2 include deep saline aquifers, hydrate-bearing formations, depleted or partially depleted natural gas and petroleum reservoirs, and coal beds. The mechanisms for sequestering carbon dioxide in geologic reservoirs include physical trapping, dissolution in the reservoir fluids, hydraulic trapping (hysteretic entrapment of nonwetting fluids), and chemical reaction. This document and the associated code development and verification work are concerned with the chemistry of injecting CO2 into geologic reservoirs. As geologic sequestration of CO2 via chemical reaction, namely precipitation reactions, are most dominate in deep saline aquifers, the principal focus of this document is the numerical simulation of CO2 injection, migration, and geochemical reaction in deep saline aquifers. The ECKEChem batch chemistry module was developed in a fashion that would allow its implementation into all operational modes of the STOMP simulator, making it a more versatile chemistry component. Additionally, this approach allows for verification of the ECKEChem module against more classical reactive transport problems involving aqueous systems.

5. O2(a1Δg) + Mg, Fe, and Ca: Experimental kinetics and formulation of a weak collision, multiwell master equation with spin-hopping

Plane, J. M. C.; Whalley, C. L.; Frances-Soriano, L.; Goddard, A.; Harvey, J. N.; Glowacki, D. R.; Viggiano, A. A.

2012-07-01

utilized density functional theory along with multireference and explicitly correlated CCSD(T)-F12 electronic structure calculations to examine the lowest lying singlet and triplet surfaces. In addition to mapping stationary points, we used a genetic algorithm to locate minimum energy crossing points between the two surfaces. Simulations of the Ca + O2(a) kinetics were then carried out using a combination of both standard and non-adiabatic Rice-Ramsperger-Kassel-Marcus (RRKM) theory implemented within a weak collision, multiwell master equation model. In terms of atmospheric significance, only in the case of Ca does reaction with O2(a) compete with O3 during the daytime between 85 and 110 km.

6. Kinetic: A system code for analyzing nuclear thermal propulsion rocket engine transients

NASA Technical Reports Server (NTRS)

Schmidt, Eldon; Lazareth, Otto; Ludewig, Hans

1993-01-01

The topics are presented in viewgraph form and include the following: outline of kinetic code; a kinetic information flow diagram; kinetic neutronic equations; turbopump/nozzle algorithm; kinetic heat transfer equations per node; and test problem diagram.

7. Equivalence of on-Lattice Stochastic Chemical Kinetics with the Well-Mixed Chemical Master Equation in the Limit of Fast Diffusion.

PubMed

Stamatakis, Michail; Vlachos, Dionisios G

2011-12-14

Well-mixed and lattice-based descriptions of stochastic chemical kinetics have been extensively used in the literature. Realizations of the corresponding stochastic processes are obtained by the Gillespie stochastic simulation algorithm and lattice kinetic Monte Carlo algorithms, respectively. However, the two frameworks have remained disconnected. We show the equivalence of these frameworks whereby the stochastic lattice kinetics reduces to effective well-mixed kinetics in the limit of fast diffusion. In the latter, the lattice structure appears implicitly, as the lumped rate of bimolecular reactions depends on the number of neighbors of a site on the lattice. Moreover, we propose a mapping between the stochastic propensities and the deterministic rates of the well-mixed vessel and lattice dynamics that illustrates the hierarchy of models and the key parameters that enable model reduction.

8. A comparative examination of the adsorption mechanism of an anionic textile dye (RBY 3GL) onto the powdered activated carbon (PAC) using various the isotherm models and kinetics equations with linear and non-linear methods

Açıkyıldız, Metin; Gürses, Ahmet; Güneş, Kübra; Yalvaç, Duygu

2015-11-01

The present study was designed to compare the linear and non-linear methods used to check the compliance of the experimental data corresponding to the isotherm models (Langmuir, Freundlich, and Redlich-Peterson) and kinetics equations (pseudo-first order and pseudo-second order). In this context, adsorption experiments were carried out to remove an anionic dye, Remazol Brillant Yellow 3GL (RBY), from its aqueous solutions using a commercial activated carbon as a sorbent. The effects of contact time, initial RBY concentration, and temperature onto adsorbed amount were investigated. The amount of dye adsorbed increased with increased adsorption time and the adsorption equilibrium was attained after 240 min. The amount of dye adsorbed enhanced with increased temperature, suggesting that the adsorption process is endothermic. The experimental data was analyzed using the Langmuir, Freundlich, and Redlich-Peterson isotherm equations in order to predict adsorption isotherm. It was determined that the isotherm data were fitted to the Langmuir and Redlich-Peterson isotherms. The adsorption process was also found to follow a pseudo second-order kinetic model. According to the kinetic and isotherm data, it was found that the determination coefficients obtained from linear method were higher than those obtained from non-linear method.

9. Kinetics of pyrite formation by the H 2S oxidation of iron (II) monosulfide in aqueous solutions between 25 and 125°C: The rate equation

Rickard, David

1997-01-01

A kinetic study of the reaction FeS+ H2S=FeS2+ H2 where FeS is precipitated FeS, H 2S (aq) is aqueous H 2S, FeS 2 is pyrite, and H 2(g) is hydrogen gas, shows that the rate between 25 and 125°C can be described by the equation dFeS2/dt = k(FeS) >(cH2S) where k the second order rate constant varies between 1.03 × 10 -4L mol -1 s -1 at 25°C and 3.20 × 10 -3 L mol -1 s -1 at 125°C. The rate constant shows a sigmoidal temperature dependence with an average Arrhenius activation energy of 35 kJ mol -1. The reaction is surprisingly fast at ambient temperatures with up to 50% reaction being completed within one day. The direct dependence of the rate on cH 2S (aq) means that the rate is pH dependent for any fixed total sulfide concentration. In typical sulfidic aquatic systems and sediments 9 × 10 -13 to 9 × 10 -8 mol FeS 2 per L sediment will be formed each day by this process. This is equivalent to approximately 3 × 10 -10 to 3 × 10 -5 mol FeS 2 per g sediment per year. At pH = 7, for the same total sulfide and FeS constraints, the rate of pyrite formation 1.5 × 10 -9 to 1.5 × 10 -4 mol FeS 2 per g sediment per year. In hydrothermal systems, such as deep ocean vents, the rate of pyrite formation by oxidation of FeS by H 2S at 125°C assuming a typical H 2S concentration of 1 mM is 3.2 × 10 -6 mol L -1 s -1 per mol FeS. A 1 million tonne pyrite deposit could form from a solution containing 1 mmol FeS and 1 mmol H 2S by this process in 1000 years at a flow rate of 0.3 Ls -1. The fluid would have a H 2 concentration of 3 × 10 -9 M. The process is by far the most rapid of the pyrite-forming reactions hitherto identified. Alternative pyrite-forming processes involving HS -, rather than H 2S, as the reaction requires an additional oxidising agent to maintain electron balance. These pathways may involve reactants such as polysulfides or intermediaries such as greigite, Fe 3S 4. In natural systems, therefore, the H 2S process will tend to be favored in strictly

10. Solving Simple Kinetics without Integrals

ERIC Educational Resources Information Center

de la Pen~a, Lisandro Herna´ndez

2016-01-01

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

11. Enskog-like kinetic models for vehicular traffic

SciTech Connect

Klar, A.; Wegener, R.

1997-04-01

In the present paper a general criticism of kinetic equations for vehicular traffic is given. The necessity of introducing an Enskog-type correction into these equations is shown. An Enskog-like kinetic traffic flow equation is presented and fluid dynamic equations are derived. This derivation yields new coefficients for the standard fluid dynamic equations of vehicular traffic. Numerical simulations for inhomogeneous traffic flow situations are shown together with a comparison between kinetic and fluid dynamics models.

12. Modeling of Reactor Kinetics and Dynamics

SciTech Connect

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.

13. Understanding Product Optimization: Kinetic versus Thermodynamic Control.

ERIC Educational Resources Information Center

Lin, King-Chuen

1988-01-01

Discusses the concept of kinetic versus thermodynamic control of reactions. Explains on the undergraduate level (1) the role of kinetic and thermodynamic control in kinetic equations, (2) the influence of concentration and temperature upon the reaction, and (3) the application of factors one and two to synthetic chemistry. (MVL)

14. Kinetic Atom.

ERIC Educational Resources Information Center

Wilson, David B.

1981-01-01

Surveys the research of scientists like Joule, Kelvin, Maxwell, Clausius, and Boltzmann as it comments on the basic conceptual issues involved in the development of a more precise kinetic theory and the idea of a kinetic atom. (Author/SK)

15. A Kinetic-fluid Model

SciTech Connect

First Author = C.Z. Cheng; Jay R. Johnson

1998-07-10

A nonlinear kinetic-fluid model for high-beta plasmas with multiple ion species which can be applied to multiscale phenomena is presented. The model embeds important kinetic effects due to finite ion Larmor radius (FLR), wave-particle resonances, magnetic particle trapping, etc. in the framework of simple fluid descriptions. When further restricting to low frequency phenomena with frequencies less than the ion cyclotron frequency the kinetic-fluid model takes a simpler form in which the fluid equations of multiple ion species collapse into single-fluid density and momentum equations and a low frequency generalized Ohm's law. The kinetic effects are introduced via plasma pressure tensors for ions and electrons which are computed from particle distribution functions that are governed by the Vlasov equation or simplified plasma dynamics equations such as the gyrokinetic equation. The ion FLR effects provide a finite parallel electric field, a perpendicular velocity that modifies the ExB drift, and a gyroviscosity tensor, all of which are neglected in the usual one-fluid MHD description. Eigenmode equations are derived which include magnetosphere-ionosphere coupling effects for low frequency waves (e.g., kinetic/inertial Alfven waves and ballooning-mirror instabilities).

16. Enzyme Kinetics.

ERIC Educational Resources Information Center

Moe, Owen; Cornelius, Richard

1988-01-01

Conveys an appreciation of enzyme kinetic analysis by using a practical and intuitive approach. Discusses enzyme assays, kinetic models and rate laws, the kinetic constants (V, velocity, and Km, Michaels constant), evaluation of V and Km from experimental data, and enzyme inhibition. (CW)

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

18. Nonlinear gyrokinetic equations

SciTech Connect

Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

1983-03-01

Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

19. Multiflow approach to plasma kinetics

SciTech Connect

Ignatov, A. M.

2015-10-15

Instead of the commonly used Vlasov equation, one is able to treat kinetic phenomena in collisionless plasma with the help of the infinite set of hydrodynamic equations. The present paper deals with the linear approximation of multiflow hydrodynamics. It is shown that single-particle and collective excitations analogous to Van Kampen waves are explicitly separated. Expressions for the energy of all eigenmodes are obtained.

20. Analytic solutions of the relativistic Boltzmann equation

Hatta, Yoshitaka; Martinez, Mauricio; Xiao, Bo-Wen

2015-04-01

We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the Israel-Stewart equation in the literature. This allows us to compare the solutions of the kinetic and hydrodynamic equations at an analytical level. We then derive a novel boost-invariant solution of the Boltzmann equation which has an unconventional dependence on the proper time. The existence of such a solution is also suggested in second-order hydrodynamics and fluid-gravity correspondence.

1. THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES

EPA Science Inventory

The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...

2. Mass Conservation and Chemical Kinetics.

ERIC Educational Resources Information Center

Barbara, Thomas M.; Corio, P. L.

1980-01-01

Presents a method for obtaining all mass conservation conditions implied by a given mechanism in which the conditions are used to simplify integration of the rate equations and to derive stoichiometric relations. Discusses possibilities of faulty inference of kinetic information from a given stoichiometry. (CS)

3. Equation poems

Prentis, Jeffrey J.

1996-05-01

One of the most challenging goals of a physics teacher is to help students see that the equations of physics are connected to each other, and that they logically unfold from a small number of basic ideas. Derivations contain the vital information on this connective structure. In a traditional physics course, there are many problem-solving exercises, but few, if any, derivation exercises. Creating an equation poem is an exercise to help students see the unity of the equations of physics, rather than their diversity. An equation poem is a highly refined and eloquent set of symbolic statements that captures the essence of the derivation of an equation. Such a poetic derivation is uncluttered by the extraneous details that tend to distract a student from understanding the essential physics of the long, formal derivation.

4. Penetration equations

SciTech Connect

Young, C.W.

1997-10-01

In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.

5. Aerosol kinetic code "AERFORM": Model, validation and simulation results

Gainullin, K. G.; Golubev, A. I.; Petrov, A. M.; Piskunov, V. N.

2016-06-01

The aerosol kinetic code "AERFORM" is modified to simulate droplet and ice particle formation in mixed clouds. The splitting method is used to calculate condensation and coagulation simultaneously. The method is calibrated with analytic solutions of kinetic equations. Condensation kinetic model is based on cloud particle growth equation, mass and heat balance equations. The coagulation kinetic model includes Brownian, turbulent and precipitation effects. The real values are used for condensation and coagulation growth of water droplets and ice particles. The model and the simulation results for two full-scale cloud experiments are presented. The simulation model and code may be used autonomously or as an element of another code.

6. Mathematics analysis of polymerase chain reaction kinetic curves.

PubMed

Sochivko, D G; Fedorov, A A; Varlamov, D A; Kurochkin, V E; Petrov, R V

2016-01-01

The paper reviews different approaches to the mathematical analysis of polymerase chain reaction (PCR) kinetic curves. The basic principles of PCR mathematical analysis are presented. Approximation of PCR kinetic curves and PCR efficiency curves by various functions is described. Several PCR models based on chemical kinetics equations are suggested. Decision criteria for an optimal function to describe PCR efficiency are proposed.

7. Kinetics of excitation in TL and OSL detectors

Mandowski, A.; Orzechowski, J.; Mandowska, E.

2010-10-01

Kinetic equations for the semi-localized transitions (SLT) model are presented describing charge carrier's kinetics for the excitation and fast relaxation stages. The formulation allows for dose dependence studies of thermoluminescence (TL) and optically stimulated luminescence (OSL) detectors based on the SLT model. The sets of equations were solved numerically demonstrating temporal evolution of all variables of the SLT model during excitation and fast relaxation. The influence of the dose rate on excitation kinetics is shown.

8. Kinetics of enzyme action on surface-attached substrates: a practical guide to progress curve analysis in any kinetic situation.

PubMed

Anne, Agnès; Demaille, Christophe

2012-10-16

In the present work, exact kinetic equations describing the action of an enzyme in solution on a substrate attached to a surface have been derived in the framework of the Michaelis-Menten mechanism but without resorting to the often-used steady-state approximation. The here-derived kinetic equations are cast in a workable format, allowing us to introduce a simple and universal procedure for the quantitative analysis of enzyme surface kinetics that is valid for any kinetic situation. The results presented here should allow experimentalists studying the kinetics of enzyme action on immobilized substrates to analyze their data in a perfectly rigorous way.

9. Fokker Planck equation with fractional coordinate derivatives

Tarasov, Vasily E.; Zaslavsky, George M.

2008-11-01

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations, with averaging with respect to a fast variable, is used. The main assumption is that the correlation function of probability densities of particles to make a step has a power-law dependence. As a result, we obtain a Fokker-Planck equation with fractional coordinate derivative of order 1<α<2.

10. Homogeneous nucleation kinetics

NASA Technical Reports Server (NTRS)

Rasmussen, D. H.; Appleby, M. R.; Leedom, G. L.; Babu, S. V.; Naumann, R. J.

1983-01-01

Homogeneous nucleation kinetics are rederived in a manner fundamentally similar to the approach of classical nucleation theory with the following modifications and improvements. First, the cluster is a parent phase cluster and does not require energization to the parent state. Second, the thermodynamic potential used to describe phase stability is a continuous function along the pathway of phase decomposition. Third, the kinetics of clustering corresponds directly to the diffusional flux of monomers through the cluster distribution and are formally similar to classical theory with the resulting kinetic equation modified by two terms in the preexponential factor. These terms correct for the influence of a supersaturation dependent clustering within the parent phase and for the influence of an asymmetrical cluster concentration as a function of cluster size at the critical cluster size. Fourth, the supersaturation dependence of the nucleation rate is of the same form as that given by classical nucleation theory. This supersaturation dependence must however be interpreted in terms of a size dependent surface tension. Finally, there are two scaling laws which describe supersaturation to either constant nucleation rate or to the thermodynamically determined physical spinodal.

11. Production of a sterile species: Quantum kinetics

SciTech Connect

Ho, Chiu Man; Boyanovsky, D.; Ho, C.M.

2007-04-23

Production of a sterile species is studied within an effective model of active-sterile neutrino mixing in a medium in thermal equilibrium. The quantum kinetic equations for the distribution functions and coherences are obtained from two independent methods: the effective action and the quantum master equation. The decoherence time scale for active-sterile oscillations is tau(dec)=2/Gamma(aa), but the evolution of the distribution functions is determined by the two different time scales associated with the damping rates of the quasiparticle modes in the medium: Gamma(1)=Gamma(aa)cos^2theta(m); Gamma(2)=Gamma(aa)sin^2theta(m) where Gamma(aa) is the interaction rate of the active species in the absence of mixing and theta(m) the mixing angle in the medium. These two time scales are widely different away from Mikheyev-Smirnov-Wolfenstein resonances and preclude the kinetic description of active-sterile production in terms of a simple rate equation. We give the complete set of quantum kinetic equations for the active and sterile populations and coherences and discuss in detail the various approximations. A generalization of the active-sterile transition probability in a medium is provided via the quantum master equation. We derive explicitly the usual quantum kinetic equations in terms of the"polarization vector" and show their equivalence to those obtained from the quantum master equation and effective action.

12. Beautiful equations

Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul

2014-07-01

In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).

13. Group-kinetic theory of turbulence

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1986-01-01

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

14. Kinetic Transport in Crystals

Marklof, Jens

2010-03-01

One of the central challenges in kinetic theory is the derivation of macroscopic evolution equations--describing, for example, the dynamics of an electron gas--from the underlying fundamental microscopic laws of classical or quantum mechanics. An iconic mathematical model in this research area is the Lorentz gas, which describes an ensemble of non-interacting point particles in an infinite array of spherical scatterers. In the case of a disordered scatterer configuration, the classical results by Gallavotti, Spohn and Boldrighini-Bunimovich-Sinai show that the time evolution of a macroscopic particle cloud is governed, in the limit of small scatterer density (Boltzmann-Grad limit), by the linear Boltzmann equation. In this lecture I will discuss the recent discovery that for a periodic configuration of scatterers the linear Boltzmann equation fails, and the random flight process that emerges in the Boltzmann-Grad limit is substantially more complicated. The key ingredient in the description of the limiting stochastic process is the renormalization dynamics on the space of lattices, a powerful technique that has recently been successfully applied also to other open problems in mathematical physics, including KAM theory and quantum chaos. This lecture is based on joint work with Andreas Strömbergsson, Uppsala.

15. Kinetic model of network traffic

Antoniou, I.; Ivanov, V. V.; Kalinovsky, Yu. L.

2002-05-01

We present the first results on the application of the Prigogine-Herman kinetic approach (Kinetic Theory of Vehicular Traffic, American Elsevier Publishing Company, Inc., New York, 1971) to the network traffic. We discuss the solution of the kinetic equation for homogeneous time-independent situations and for the desired speed distribution function, obtained from traffic measurements analysis. For the log-normal desired speed distribution function the solution clearly shows two modes corresponding to individual flow patterns (low-concentration mode) and to collective flow patterns (traffic jam mode). For low-concentration situations we found almost linear dependence of the information flow versus the concentration and that the higher the average speed the lower the concentration at which the optimum flow takes place. When approaching the critical concentration there are no essential differences in the flow for different desired average speeds, whereas for the individual flow regions there are dramatic differences.

16. A kinetic-theory approach to turbulent chemically reacting flows

NASA Technical Reports Server (NTRS)

Chung, P. M.

1976-01-01

The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.

17. Tolrestat kinetics

SciTech Connect

Hicks, D.R.; Kraml, M.; Cayen, M.N.; Dubuc, J.; Ryder, S.; Dvornik, D.

1984-10-01

The kinetics of tolrestat, a potent inhibitor of aldose reductase, were examined. Serum concentrations of tolrestat and of total /sup 14/C were measured after dosing normal subjects and subjects with diabetes with /sup 14/C-labeled tolrestat. In normal subjects, tolrestat was rapidly absorbed and disappearance from serum was biphasic. Distribution and elimination t 1/2s were approximately 2 and 10 to 12 hr, respectively, after single and multiple doses. Unchanged tolrestat accounted for the major portion of /sup 14/C in serum. Radioactivity was rapidly and completely excreted in urine and feces in an approximate ratio of 2:1. Findings were much the same in subjects with diabetes. In normal subjects, the kinetics of oral tolrestat were independent of dose in the 10 to 800 mg range. Repetitive dosing did not result in unexpected cumulation. Tolrestat was more than 99% bound to serum protein; it did not compete with warfarin for binding sites but was displaced to some extent by high concentrations of tolbutamide or salicylate.

18. Marcus equation

DOE R&D Accomplishments Database

1998-09-21

In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

19. Consistent lattice Boltzmann equations for phase transitions

Siebert, D. N.; Philippi, P. C.; Mattila, K. K.

2014-11-01

Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling.

20. Non-markovian boltzmann equation

SciTech Connect

Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.

1997-08-01

A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov{endash}Born{endash}Green{endash}Kirkwood{endash}Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. {copyright} 1997 Academic Press, Inc.

1. On the relationships between Michaelis–Menten kinetics, reverse Michaelis–Menten kinetics, Equilibrium Chemistry Approximation kinetics and quadratic kinetics

DOE PAGES

Tang, J. Y.

2015-09-03

The Michaelis–Menten kinetics and the reverse Michaelis–Menten kinetics are two popular mathematical formulations used in many land biogeochemical models to describe how microbes and plants would respond to changes in substrate abundance. However, the criteria of when to use which of the two are often ambiguous. Here I show that these two kinetics are special approximations to the Equilibrium Chemistry Approximation kinetics, which is the first order approximation to the quadratic kinetics that solves the equation of enzyme-substrate complex exactly for a single enzyme single substrate biogeochemical reaction with the law of mass action and the assumption of quasi-steady-state formore » the enzyme-substrate complex and that the product genesis from enzyme-substrate complex is much slower than the equilibration between enzyme-substrate complexes, substrates and enzymes. In particular, I showed that the derivation of the Michaelis–Menten kinetics does not consider the mass balance constraint of the substrate, and the reverse Michaelis–Menten kinetics does not consider the mass balance constraint of the enzyme, whereas both of these constraints are taken into account in the Equilibrium Chemistry Approximation kinetics. By benchmarking against predictions from the quadratic kinetics for a wide range of substrate and enzyme concentrations, the Michaelis–Menten kinetics was found to persistently under-predict the normalized sensitivity ∂ ln v / ∂ ln k2+ of the reaction velocity v with respect to the maximum product genesis rate k2+, persistently over-predict the normalized sensitivity ∂ ln v / ∂ ln k1+ of v with respect to the intrinsic substrate affinity k1+, persistently over-predict the normalized sensitivity ∂ ln v / ∂ ln [ E ]T of v with respect the total enzyme concentration [ E ]T and persistently under-predict the normalized sensitivity ∂ ln v / ∂ ln [ S ]T of v with respect to the total substrate concentration [ S ]T. Meanwhile, the

2. Kinetic buffers.

PubMed

Alibrandi, Giuseppe; Fabbrizzi, Luigi; Licchelli, Maurizio; Puglisi, Antonio

2015-01-12

This paper proposes a new type of molecular device that is able to act as an inverse proton sponge to slowly decrease the pH inside a reaction vessel. This makes the automatic monitoring of the concentration of pH-sensitive systems possible. The device is a composite formed of an alkyl chloride, which kinetically produces acidity, and a buffer that thermodynamically modulates the variation in pH value. Profiles of pH versus time (pH-t plots) have been generated under various experimental conditions by computer simulation, and the device has been tested by carrying out automatic spectrophotometric titrations, without using an autoburette. To underline the wide variety of possible applications, this new system has been used to realize and monitor HCl uptake by a di-copper(II) bistren complex in a single run, in a completely automatic experiment.

3. Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrödinger equation for C2H4

Avila, Gustavo; Carrington, Tucker

2011-08-01

In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, the Lanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the πtμπ term. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which μ is evaluated at equilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtain the final energy levels. The quadrature scheme is designed, so that integrals for the most important terms in the potential will be exact. The procedure is tested on C2H4. All 12 coordinates are treated explicitly. We need only ˜1.52 × 108 quadrature points. A product Gauss grid with which one could calculate the same energy levels has at least 5.67 × 1013 points.

4. Algebraic operator approach to gas kinetic models

Il'ichov, L. V.

1997-02-01

Some general properties of the linear Boltzmann kinetic equation are used to present it in the form ∂ tϕ = - Â†Âϕ with the operators ÂandÂ† possessing some nontrivial algebraic properties. When applied to the Keilson-Storer kinetic model, this method gives an example of quantum ( q-deformed) Lie algebra. This approach provides also a natural generalization of the “kangaroo model”.

5. Hybrid fluid/kinetic model for parallel heat conduction

SciTech Connect

Callen, J.D.; Hegna, C.C.; Held, E.D.

1998-12-31

It is argued that in order to use fluid-like equations to model low frequency ({omega} < {nu}) phenomena such as neoclassical tearing modes in low collisionality ({nu} < {omega}{sub b}) tokamak plasmas, a Chapman-Enskog-like approach is most appropriate for developing an equation for the kinetic distortion (F) of the distribution function whose velocity-space moments lead to the needed fluid moment closure relations. Further, parallel heat conduction in a long collision mean free path regime can be described through a combination of a reduced phase space Chapman-Enskog-like approach for the kinetics and a multiple-time-scale analysis for the fluid and kinetic equations.

6. The origins of enzyme kinetics.

PubMed

Cornish-Bowden, Athel

2013-09-02

The equation commonly called the Michaelis-Menten equation is sometimes attributed to other authors. However, although Victor Henri had derived the equation from the correct mechanism, and Adrian Brown before him had proposed the idea of enzyme saturation, it was Leonor Michaelis and Maud Menten who showed that this mechanism could also be deduced on the basis of an experimental approach that paid proper attention to pH and spontaneous changes in the product after formation in the enzyme-catalysed reaction. By using initial rates of reaction they avoided the complications due to substrate depletion, product accumulation and progressive inactivation of the enzyme that had made attempts to analyse complete time courses very difficult. Their methodology has remained the standard approach to steady-state enzyme kinetics ever since.

7. Determining enzyme kinetics via isothermal titration calorimetry.

PubMed

Demarse, Neil A; Killian, Marie C; Hansen, Lee D; Quinn, Colette F

2013-01-01

Isothermal titration calorimetry (ITC) has emerged as a powerful tool for determining the thermodynamic properties of chemical or physical equilibria such as protein-protein, ligand-receptor, and protein-DNA binding interactions. The utility of ITC for determining kinetic information, however, has not been fully recognized. Methods for collecting and analyzing data on enzyme kinetics are discussed here. The step-by-step process of converting the raw heat output rate into the kinetic parameters of the Michaelis-Menten equation is explicitly stated. The hydrolysis of sucrose by invertase is used to demonstrate the capability of the instrument and method.

8. Multiple temperature kinetic model and gas-kinetic method for hypersonic non-equilibrium flow computations

Xu, Kun; He, Xin; Cai, Chunpei

2008-07-01

It is well known that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy. For the high speed diatomic molecular flow in the transitional regime, the inaccuracies are partially attributed to the single temperature approximations in the Navier-Stokes equations. Here, we propose a continuum multiple temperature model based on the Bhatnagar-Gross-Krook (BGK) equation for the non-equilibrium flow computation. In the current model, the Landau-Teller-Jeans relaxation model for the rotational energy is used to evaluate the energy exchange between the translational and rotational modes. Due to the multiple temperature approximation, the second viscosity coefficient in the Navier-Stokes equations is replaced by the temperature relaxation term. In order to solve the multiple temperature kinetic model, a multiscale gas-kinetic finite volume scheme is proposed, where the gas-kinetic equation is numerically solved for the fluxes to update the macroscopic flow variables inside each control volume. Since the gas-kinetic scheme uses a continuous gas distribution function at a cell interface for the fluxes evaluation, the moments of a gas distribution function can be explicitly obtained for the multiple temperature model. Therefore, the kinetic scheme is much more efficient than the DSMC method, especially in the near continuum flow regime. For the non-equilibrium flow computations, i.e., the nozzle flow and hypersonic rarefied flow over flat plate, the computational results are validated in comparison with experimental measurements and DSMC solutions.

9. A century of enzyme kinetic analysis, 1913 to 2013.

PubMed

Johnson, Kenneth A

2013-09-02

This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis-Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function.

10. Kinetic Measurements for Enzyme Immobilization.

PubMed

Cooney, Michael J

2017-01-01

Enzyme kinetics is the study of the chemical reactions that are catalyzed by enzymes, with a focus on their reaction rates. The study of an enzyme's kinetics considers the various stages of activity, reveals the catalytic mechanism of this enzyme, correlates its value to assay conditions, and describes how a drug or a poison might inhibit the enzyme. Victor Henri initially reported that enzyme reactions were initiated by a bond between the enzyme and the substrate. By 1910, Michaelis and Menten were advancing their work by studying the kinetics of an enzyme saccharase which catalyzes the hydrolysis of sucrose into glucose and fructose. They published their analysis and ever since the Michaelis-Menten equation has been used as the standard to describe the kinetics of many enzymes. Unfortunately, soluble enzymes must generally be immobilized to be reused for long times in industrial reactors. In addition, other critical enzyme properties have to be improved like stability, activity, inhibition by reaction products, and selectivity towards nonnatural substrates. Immobilization is by far the chosen process to achieve these goals.Although the Michaelis-Menten approach has been regularly adapted to the analysis of immobilized enzyme activity, its applicability to the immobilized state is limited by the barriers the immobilization matrix places upon the measurement of compounds that are used to model enzyme kinetics. That being said, the estimated value of the Michaelis-Menten coefficients (e.g., V max, K M) can be used to evaluate effects of immobilization on enzyme activity in the immobilized state when applied in a controlled manner. In this review enzyme activity and kinetics are discussed in the context of the immobilized state, and a few novel protocols are presented that address some of the unique constraints imposed by the immobilization barrier.

11. Kinetic measurements for enzyme immobilization.

PubMed

Cooney, Michael J

2011-01-01

Enzyme kinetics is the study of the chemical reactions that are catalyzed by enzymes, with a focus on their reaction rates. The study of an enzyme's kinetics considers the various stages of activity, reveals the catalytic mechanism of the enzyme, correlates its value to assay conditions, and describes how a drug or a poison might inhibit the enzyme. Victor Henri initially reported that enzyme reactions were initiated by a bond between the enzyme and the substrate. By 1910, Michaelis and Menten had advanced this work by studying the kinetics of the enzyme saccharase, which catalyzes the hydrolysis of sucrose into glucose and fructose. They published their analysis, and ever since, the Michaelis-Menten equation has been used as the standard to describe the kinetics of many enzymes. Unfortunately, soluble enzymes must generally be immobilized to be reused for long times in industrial reactors. In addition, other critical enzyme properties have to be improved like stability, activity, inhibition by reaction products, selectivity toward nonnatural substrates. Immobilization is by far the chosen process to achieve these goals.Although the Michaelis-Menten approach has been regularly adopted for the analysis of immobilized enzyme activity, its applicability to the immobilized state is limited by the barriers the immobilization matrix places upon the measurement of compounds that are used to model enzyme kinetics. That being said, the estimated value of the Michaelis-Menten coefficients (e.g., V(max), K(M)) can be used to evaluate effects of immobilization on enzyme activity in the immobilized state when applied in a controlled manner. In this review, enzyme activity and kinetics are discussed in the context of the immobilized state, and a few novel protocols are presented that address some of the unique constraints imposed by the immobilization barrier.

12. A new rate equation for desorption at the solid/solution interface

2017-03-01

In this article, a new integrated kinetics Langmuir equation for desorption from the solid surface is derived. This new equation is simple and easy to be used. Several sets of kinetic data points are generated to analyze the accuracy of the new rate equation. By applying theoretical and experimental data, the applicability of the new equation is proved. The analysis of the new equation explains its relation with the pseudo first-order rate equation, and it shows the conditions of its possible application based on Langmuir model. The accuracy of theoretical derivation of pseudo first-order rate equation is proved.

13. An introduction to the Dieterici Equation and the van der Waal Equation

Sheldon, John

2003-11-01

The derivation of the ideal gas law by using the kinetic theory of gases is usually presented in an undergraduate physics thermodynamics texts and physical chemistry texts. Following these derivations is the introduction of nonideal effects and the empirical equations of state: the van der Waals equation and the Dieterici equation. These are sometimes are simply given without comment as to the origin of the terms in them. An introduction to a "derivation" of these equations, appropriate for the undergraduate thermodynamics course, is given herein. Empirical equations are not rigorously derived, but rather they are invented, the so-called derivation simply serves to make the empirical terms appear reasonable.The barometric equation is exploited to get an expression for the effective attractive molecular forces. The differential form of the barometric is derived using kinetic theory, then from the barometric equation we get the Dieterici Equation an expansion of the Dieterici Equation, yields the van der Waals Equation of state. The relationship between the empirical constants is also discussed

14. Kinetics of the humid aging of magnetic recording tape

NASA Technical Reports Server (NTRS)

Bertram, H. N.; Cuddihy, E. F.

1982-01-01

The kinetics of the hydrolysis of polyester urethane binders of magnetic recording tape is described. Kinetic data were generated from measurements of acetone-extractable hydrolyzed binder products versus time for various humidity-temperature environments. These data can be described by a linear, single product, reversible rate equation. This equation, coupled with measurements on the effect of hydrolysis on recorded tape performance, is used to predict proper environmental storage conditions for magnetic tape.

15. Kinetics with chemical reactions and nonequilibrium structures in open systems

Aristov, Vladimir; Frolova, Anna; Zabelok, Sergei

2013-10-01

Simulations of flows on the basis of kinetic equations for mixtures with chemical reactions are performed. The Nonuniform Relaxation Problems (NRP) are formulated and solved. The Unified Flow Solver (UFS) is used for 1D and 2D NRP. The nonequilibrium kinetics can provide results outside the traditional theory of macroscopic phenomena based on the Navier-Stokes equations. Nonequilibrium flows with different properties in relaxation zones are described.

16. Simplification of the unified gas kinetic scheme

Chen, Songze; Guo, Zhaoli; Xu, Kun

2016-08-01

The unified gas kinetic scheme (UGKS) is an asymptotic preserving (AP) scheme for kinetic equations. It is superior for transition flow simulation and has been validated in the past years. However, compared to the well-known discrete ordinate method (DOM), which is a classical numerical method solving the kinetic equations, the UGKS needs more computational resources. In this study, we propose a simplification of the unified gas kinetic scheme. It allows almost identical numerical cost as the DOM, but predicts numerical results as accurate as the UGKS. In the simplified scheme, the numerical flux for the velocity distribution function and the numerical flux for the macroscopic conservative quantities are evaluated separately. The equilibrium part of the UGKS flux is calculated by analytical solution instead of the numerical quadrature in velocity space. The simplification is equivalent to a flux hybridization of the gas kinetic scheme for the Navier-Stokes (NS) equations and the conventional discrete ordinate method. Several simplification strategies are tested, through which we can identify the key ingredient of the Navier-Stokes asymptotic preserving property. Numerical tests show that, as long as the collision effect is built into the macroscopic numerical flux, the numerical scheme is Navier-Stokes asymptotic preserving, regardless the accuracy of the microscopic numerical flux for the velocity distribution function.

17. Zakharov equations in quantum dusty plasmas

SciTech Connect

Sayed, F.; Vladimirov, S. V.; Ishihara, O.

2015-08-15

By generalizing the formalism of modulational interactions in quantum dusty plasmas, we derive the kinetic quantum Zakharov equations in dusty plasmas that describe nonlinear coupling of high frequency Langmuir waves to low frequency plasma density variations, for cases of non-degenerate and degenerate plasma electrons.

18. Kinetic theory of relativistic plasmas

NASA Technical Reports Server (NTRS)

Gould, R. J.

1981-01-01

The thermalization of particle kinetic motion by binary collisions is considered for a plasma with a Boltzmann constant-temperature product approximately equal to 10 to 100 times the product of the electron mass with the square of the speed of light. At this temperature, the principal mechanism for relaxation of electron motion is via radiationless electron-electron collisions (Moller scattering). Ions are nonrelativistic, but are energetic enough so that their Coulomb scattering can be treated in the Born approximation. Relaxation times are computed and Boltzmann-equation Fokker-Planck operators are derived for the various binary-collision processes. The expression for the rate of kinetic energy exchange between electron and ion gases is derived for the case where the gases are at different temperatures.

19. The correct kinetic Bohm criterion

2016-09-01

Space charge sheaths are characteristic for bounded plasmas and are a key element in plasma-surface interactions. Hence, one of the most fundamental concepts in plasma physics - the Bohm criterion - is related to the definition of a sheath edge. However, its kinetic formulation is stirring controversies for a long time - from questioning its validity at high collisionality to claiming a divergence in its formulation. Here, based on a solution of the Boltzmann equation for ions with charge-exchange collisions and ionization both of these disputes are resolved: 1) The obtained form of the kinetic Bohm criterion removes the divergence in the ionic part. 2) It also introduces a new equally important term that describes collisional and geometric effects. This new term reestablishes the validity of the criterion at high collisionality. 3) It also restores agreement with the fluid counterpart of the criterion. The developed theory is supported by non-invasive spatially resolved measurements and a numerical model.

20. Incorporating qualitative knowledge in enzyme kinetic models using fuzzy logic.

PubMed

Lee, B; Yen, J; Yang, L; Liao, J C

1999-03-20

Modeling of metabolic pathway dynamics requires detailed kinetic equations at the enzyme level. In particular, the kinetic equations must account for metabolite effectors that contribute significantly to the pathway regulation in vivo. Unfortunately, most kinetic rate laws available in the literature do not consider all the effectors simultaneously, and much kinetic information exists in a qualitative or semiquantitative form. In this article, we present a strategy to incorporate such information into the kinetic equation. This strategy uses fuzzy logic-based factors to modify algebraic rate laws that account for partial kinetic characteristics. The parameters introduced by the fuzzy factors are then optimized by use of a hybrid of simplex and genetic algorithms. The resulting model provides a flexible form that can simulate various kinetic behaviors. Such kinetic models are suitable for pathway modeling without complete enzyme mechanisms. Three enzymes in Escherichia coli central metabolism are used as examples: phosphoenolpyruvate carboxylase; phosphoenolpyruvate carboxykinase; and pyruvate kinase I. Results show that, with fuzzy logic-augmented models, the kinetic data can be much better described. In particular, complex behavior, such as allosteric inhibition, can be captured using fuzzy rules. The resulting models, even though they do not provide additional physical meaning in enzyme mechanisms, allow the model to incorporate semiquantitative information in metabolic pathway models.

1. Kinetic Theory and Fluid Dynamics

Sone, Yoshio

This monograph gives a comprehensive description of the relationship and connections between kinetic theory and fluid dynamics, mainly for a time-independent problem in a general domain. Ambiguities in this relationship are clarified, and the incompleteness of classical fluid dynamics in describing the behavior of a gas in the continuum limit—recently reported as the ghost effect—is also discussed. The approach used in this work engages an audience of theoretical physicists, applied mathematicians, and engineers. By a systematic asymptotic analysis, fluid-dynamic-type equations and their associated boundary conditions that take into account the weak effect of gas rarefaction are derived from the Boltzmann system. Comprehensive information on the Knudsen-layer correction is also obtained. Equations and their boundary conditions are carefully classified depending on the physical context of problems. Applications are presented to various physically interesting phenomena, including flows induced by temperature fields, evaporation and condensation problems, examples of the ghost effect, and bifurcation of flows. Key features: * many applications and physical models of practical interest * experimental works such as the Knudsen compressor are examined to supplement theory * engineers will not be overwhelmed by sophisticated mathematical techniques * mathematicians will benefit from clarity of definitions and precise physical descriptions given in mathematical terms * appendices collect key derivations and formulas, important to the practitioner, but not easily found in the literature Kinetic Theory and Fluid Dynamics serves as a bridge for those working in different communities where kinetic theory or fluid dynamics is important: graduate students, researchers and practitioners in theoretical physics, applied mathematics, and various branches of engineering. The work can be used in graduate-level courses in fluid dynamics, gas dynamics, and kinetic theory; some parts

2. Lattice Boltzmann equation method for the Cahn-Hilliard equation

Zheng, Lin; Zheng, Song; Zhai, Qinglan

2015-01-01

In this paper a lattice Boltzmann equation (LBE) method is designed that is different from the previous LBE for the Cahn-Hilliard equation (CHE). The starting point of the present CHE LBE model is from the kinetic theory and the work of Lee and Liu [T. Lee and L. Liu, J. Comput. Phys. 229, 8045 (2010), 10.1016/j.jcp.2010.07.007]; however, because the CHE does not conserve the mass locally, a modified equilibrium density distribution function is introduced to treat the diffusion term in the CHE. Numerical simulations including layered Poiseuille flow, static droplet, and Rayleigh-Taylor instability have been conducted to validate the model. The results show that the predictions of the present LBE agree well with the analytical solution and other numerical results.

3. Kinetic Effects in Dynamic Wetting

Sprittles, James E.

2017-03-01

The maximum speed at which a liquid can wet a solid is limited by the need to displace gas lubrication films in front of the moving contact line. The characteristic height of these films is often comparable to the mean free path in the gas so that hydrodynamic models do not adequately describe the flow physics. This Letter develops a model which incorporates kinetic effects in the gas, via the Boltzmann equation, and can predict experimentally observed increases in the maximum speed of wetting when (a) the liquid's viscosity is varied, (b) the ambient gas pressure is reduced, or (c) the meniscus is confined.

4. On the full Boltzmann equations for leptogenesis

SciTech Connect

Garayoa, J.; Pastor, S.; Pinto, T.; Rius, N.; Vives, O. E-mail: pastor@ific.uv.es E-mail: nuria@ific.uv.es

2009-09-01

We consider the full Boltzmann equations for standard and soft leptogenesis, instead of the usual integrated Boltzmann equations which assume kinetic equilibrium for all species. Decays and inverse decays may be inefficient for thermalising the heavy-(s)neutrino distribution function, leading to significant deviations from kinetic equilibrium. We analyse the impact of using the full kinetic equations in the case of a previously generated lepton asymmetry, and find that the washout of this initial asymmetry due to the interactions of the right-handed neutrino is larger than when calculated via the integrated equations. We also solve the full Boltzmann equations for soft leptogenesis, where the lepton asymmetry induced by the soft SUSY-breaking terms in sneutrino decays is a purely thermal effect, since at T = 0 the asymmetry in leptons cancels the one in sleptons. In this case, we obtain that in the weak washout regime (K ∼< 1) the final lepton asymmetry can change up to a factor four with respect to previous estimates.

PubMed

Lorsch, Jon R

2014-01-01

Enzymes are key components of most biological processes. Characterization of enzymes is therefore frequently required during the study of biological systems. Steady-state kinetics provides a simple and rapid means of assessing the substrate specificity of an enzyme. When combined with site-directed mutagenesis (see Site-Directed Mutagenesis), it can be used to probe the roles of particular amino acids in the enzyme in substrate recognition and catalysis. Effects of interaction partners and posttranslational modifications can also be assessed using steady-state kinetics. This overview explains the general principles of steady-state enzyme kinetics experiments in a practical, rather than theoretical, way. Any biochemistry textbook will have a section on the theory of Michaelis-Menten kinetics, including derivations of the relevant equations. No specific enzymatic assay is described here, although a method for monitoring product formation or substrate consumption over time (an assay) is required to perform the experiments described.

6. Solid State Kinetic Parameters and Chemical Mechanism of the Dehydration of CoCl2.6H2O.

ERIC Educational Resources Information Center

Ribas, Joan; And Others

1988-01-01

Presents an experimental example illustrating the most common methods for the determination of kinetic parameters. Discusses the different theories and equations to be applied and the mechanism derived from the kinetic results. (CW)

7. Classical non-Markovian Boltzmann equation

SciTech Connect

2014-08-01

The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

8. Ordinary differential equation for local accumulation time.

PubMed

Berezhkovskii, Alexander M

2011-08-21

Cell differentiation in a developing tissue is controlled by the concentration fields of signaling molecules called morphogens. Formation of these concentration fields can be described by the reaction-diffusion mechanism in which locally produced molecules diffuse through the patterned tissue and are degraded. The formation kinetics at a given point of the patterned tissue can be characterized by the local accumulation time, defined in terms of the local relaxation function. Here, we show that this time satisfies an ordinary differential equation. Using this equation one can straightforwardly determine the local accumulation time, i.e., without preliminary calculation of the relaxation function by solving the partial differential equation, as was done in previous studies. We derive this ordinary differential equation together with the accompanying boundary conditions and demonstrate that the earlier obtained results for the local accumulation time can be recovered by solving this equation.

9. On Coupled Rate Equations with Quadratic Nonlinearities

PubMed Central

Montroll, Elliott W.

1972-01-01

Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013

10. Classical non-Markovian Boltzmann equation

2014-08-01

The modeling of particle transport involves anomalous diffusion, ⟨x2(t) ⟩ ∝ tα with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

11. Chemical and Biological Kinetics

Emanuel', N. M.

1981-10-01

Examples of the application of the methods and ideas of chemical kinetics in various branches of chemistry and biology are considered and the results of studies on the kinetics and mechanisms of autoxidation and inhibited and catalysed oxidation of organic substances in the liquid phase are surveyed. Problems of the kinetics of the ageing of polymers and the principles of their stabilisation are discussed and certain trends in biological kinetics (kinetics of tumour growth, kinetic criteria of the effectiveness of chemotherapy, problems of gerontology, etc.) are considered. The bibliography includes 281 references.

12. Representing Rate Equations for Enzyme-Catalyzed Reactions

ERIC Educational Resources Information Center

2011-01-01

Rate equations for enzyme-catalyzed reactions are derived and presented in a way that makes it easier for the nonspecialist to see how the rate of an enzyme-catalyzed reaction depends upon kinetic constants and concentrations. This is done with distribution equations that show how the rate of the reaction depends upon the relative quantities of…

13. Comparative evaluation of adsorption kinetics of diclofenac and isoproturon by activated carbon.

PubMed

Torrellas, Silvia A; Rodriguez, Araceli R; Escudero, Gabriel O; Martín, José María G; Rodriguez, Juan G

2015-01-01

Adsorption mechanism of diclofenac and isoproturon onto activated carbon has been proposed using Langmuir and Freundlich isotherms. Adsorption capacity and optimum adsorption isotherms were predicted by nonlinear regression method. Different kinetic equations, pseudo-first-order, pseudo-second-order, intraparticle diffusion model and Bangham kinetic model, were applied to study the adsorption kinetics of emerging contaminants on activated carbon in two aqueous matrices.

14. Transport Equations In Tokamak Plasmas

Callen, J. D.

2009-11-01

Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for: neoclassical effects on the parallel Ohm's law (trapped particle effects on resistivity, bootstrap current); fluctuation-induced transport; heating, current-drive and flow sources and sinks; small B field non-axisymmetries; magnetic field transients etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed recently using a kinetic-based framework. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales (and constraints they impose) are considered sequentially: compressional Alfv'en waves (Grad-Shafranov equilibrium, ion radial force balance); sound waves (pressure constant along field lines, incompressible flows within a flux surface); and ion collisions (damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on the plasma fluid: 7 ambipolar collision-based ones (classical, neoclassical, etc.) and 8 non-ambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients etc.). The plasma toroidal rotation equation [1] results from setting to zero the net radial current induced by the non-ambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the non-ambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The resultant transport equations will be presented and contrasted with the usual ones. [4pt] [1] J.D. Callen, A.J. Cole, C.C. Hegna, ``Toroidal Rotation In

15. Transport equations in tokamak plasmas

SciTech Connect

Callen, J. D.; Hegna, C. C.; Cole, A. J.

2010-05-15

Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm's law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfven waves (Grad-Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones (classical, neoclassical, etc.) and eight nonambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients, etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The 'mean field' effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The

16. Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

Kolobov, V. I.; Arslanbekov, R. R.

2012-02-01

This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or continuum solvers in different parts of computational domains. We first review the discrete velocity method for solving Boltzmann and Wang Chang-Uhlenbeck kinetic equations for rarefied gases. Then, peculiarities of AMR implementation with octree Cartesian mesh are discussed. A Unified Flow Solver (UFS) uses AMAR method with adaptive Cartesian mesh to dynamically introduce kinetic patches for multi-scale simulations of gas flows. We describe fluid plasma models with AMR capabilities and illustrate how physical models affect simulation results for gas discharges, especially in the areas where electron kinetics plays an important role. We introduce Eulerian solvers for plasma kinetic equations and illustrate the concept of adaptive mesh in velocity space. Specifics of electron kinetics in collisional plasmas are described focusing on deterministic methods of solving kinetic equations for electrons under different conditions. We illustrate the appearance of distinct groups of electrons in the cathode region of DC discharges and discuss the physical models appropriate for each group. These kinetic models are currently being incorporated into AMAR methodology for multi-scale plasma simulations.

17. Parabolic approximation method for the mode conversion-tunneling equation

SciTech Connect

Phillips, C.K.; Colestock, P.L.; Hwang, D.Q.; Swanson, D.G.

1987-07-01

The derivation of the wave equation which governs ICRF wave propagation, absorption, and mode conversion within the kinetic layer in tokamaks has been extended to include diffraction and focussing effects associated with the finite transverse dimensions of the incident wavefronts. The kinetic layer considered consists of a uniform density, uniform temperature slab model in which the equilibrium magnetic field is oriented in the z-direction and varies linearly in the x-direction. An equivalent dielectric tensor as well as a two-dimensional energy conservation equation are derived from the linearized Vlasov-Maxwell system of equations. The generalized form of the mode conversion-tunneling equation is then extracted from the Maxwell equations, using the parabolic approximation method in which transverse variations of the wave fields are assumed to be weak in comparison to the variations in the primary direction of propagation. Methods of solving the generalized wave equation are discussed. 16 refs.

18. Kinetic energy budgets in areas of intense convection

NASA Technical Reports Server (NTRS)

Fuelberg, H. E.; Berecek, E. M.; Ebel, D. M.; Jedlovec, G. J.

1980-01-01

A kinetic energy budget analysis of the AVE-SESAME 1 period which coincided with the deadly Red River Valley tornado outbreak is presented. Horizontal flux convergence was found to be the major kinetic energy source to the region, while cross contour destruction was the major sink. Kinetic energy transformations were dominated by processes related to strong jet intrusion into the severe storm area. A kinetic energy budget of the AVE 6 period also is presented. The effects of inherent rawinsonde data errors on widely used basic kinematic parameters, including velocity divergence, vorticity advection, and kinematic vertical motion are described. In addition, an error analysis was performed in terms of the kinetic energy budget equation. Results obtained from downward integration of the continuity equation to obtain kinematic values of vertical motion are described. This alternate procedure shows promising results in severe storm situations.

19. Kinetic properties of fractal stellar media

Chumak, O. V.; Rastorguev, A. S.

2017-01-01

Kinetic processes in fractal stellar media are analysed in terms of the approach developed in our earlier paper involving a generalization of the nearest neighbour and random force distributions to fractal media. Diffusion is investigated in the approximation of scale-dependent conditional density based on an analysis of the solutions of the corresponding Langevin equations. It is shown that kinetic parameters (time-scales, coefficients of dynamic friction, diffusion, etc.) for fractal stellar media can differ significantly both qualitatively and quantitatively from the corresponding parameters for a quasi-uniform random media with limited fluctuations. The most important difference is that in the fractal case, kinetic parameters depend on spatial scalelength and fractal dimension of the medium studied. A generalized kinetic equation for stellar media (fundamental equation of stellar dynamics) is derived in the Fokker-Planck approximation with the allowance for the fractal properties of the spatial stellar density distribution. Also derived are its limit forms that can be used to describe small departures of fractal gravitating medium from equilibrium.

20. Kinetic Models for the Trading of Goods

Toscani, Giuseppe; Brugna, Carlo; Demichelis, Stefano

2013-05-01

In this paper we introduce kinetic equations for the evolution of the probability distribution of two goods among a huge population of agents. The leading idea is to describe the trading of these goods by means of some fundamental rules in price theory, in particular by using Cobb-Douglas utility functions for the binary exchange, and the Edgeworth box for the description of the common exchange area in which utility is increasing for both agents. This leads to a Boltzmann-type equation in which the post-interaction variables depend in a nonlinear way from the pre-interaction ones. Other models will be derived, by suitably linearizing this Boltzmann equation. In presence of uncertainty in the exchanges, it is shown that the solution to some of the linearized kinetic equations develop Pareto tails, where the Pareto index depends on the ratio between the gain and the variance of the uncertainty. In particular, the result holds true for the solution of a drift-diffusion equation of Fokker-Planck type, obtained from the linear Boltzmann equation as the limit of quasi-invariant trades.

1. Kinetic and hydrodynamic models of chemotactic aggregation

Chavanis, Pierre-Henri; Sire, Clément

2007-10-01

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean-field Fokker-Planck equation governing the evolution of the distribution function of the system in phase space. By taking the successive moments of this kinetic equation and using a local thermodynamic equilibrium condition, we derive a set of hydrodynamic equations involving a damping term. In the limit of small frictions, we obtain a hyperbolic model describing the formation of network patterns (filaments) and in the limit of strong frictions we obtain a parabolic model which is a generalization of the standard Keller-Segel model describing the formation of clusters (clumps). Our approach connects and generalizes several models introduced in the chemotactic literature. We discuss the analogy between bacterial colonies and self-gravitating systems and between the chemotactic collapse and the gravitational collapse (Jeans instability). We also show that the basic equations of chemotaxis are similar to nonlinear mean-field Fokker-Planck equations so that a notion of effective generalized thermodynamics can be developed.

2. Kinetics of Propargyl Radical Dissociation.

PubMed

Klippenstein, Stephen J; Miller, James A; Jasper, Ahren W

2015-07-16

Due to the prominent role of the propargyl radical for hydrocarbon growth within combustion environments, it is important to understand the kinetics of its formation and loss. The ab initio transition state theory-based master equation method is used to obtain theoretical kinetic predictions for the temperature and pressure dependence of the thermal decomposition of propargyl, which may be its primary loss channel under some conditions. The potential energy surface for the decomposition of propargyl is first mapped at a high level of theory with a combination of coupled cluster and multireference perturbation calculations. Variational transition state theory is then used to predict the microcanonical rate coefficients, which are subsequently implemented within the multiple-well multiple-channel master equation. A variety of energy transfer parameters are considered, and the sensitivity of the thermal rate predictions to these parameters is explored. The predictions for the thermal decomposition rate coefficient are found to be in good agreement with the limited experimental data. Modified Arrhenius representations of the rate constants are reported for utility in combustion modeling.

3. Basic lubrication equations

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

4. Efficient Asymptotic Preserving Deterministic methods for the Boltzmann Equation

DTIC Science & Technology

2011-04-01

release, distribution unlimited 13. SUPPLEMENTARY NOTES See also ADA579248. Models and Computational Methods for Rarefied Flows (Modeles et methodes de...nonlinear collisional kinetic equation. The most well-known example is represented by the Boltzmann equation of rarefied gas dynamics (Cercignani, 1988...et al. (2010). Although the scope of our insights is wider, here we will focus mainly on the classical Boltzmann equation of rarefied gas dynamics

5. Power-law spatial dispersion from fractional Liouville equation

SciTech Connect

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

6. Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks.

PubMed

2014-08-01

Stochasticity in the dynamics of small reacting systems requires discrete-probabilistic models of reaction kinetics instead of traditional continuous-deterministic ones. The master probability equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks. With the first solution of chemical master equations, a wide range of experimental observations of small-system interactions may be mathematically conceptualized.

7. Solution of Chemical Master Equations for Nonlinear Stochastic Reaction Networks

PubMed Central

2014-01-01

Stochasticity in the dynamics of small reacting systems requires discrete-probabilistic models of reaction kinetics instead of traditional continuous-deterministic ones. The master probability equation is a complete model of randomly evolving molecular populations. Because of its ambitious character, the master equation remained unsolved for all but the simplest of molecular interaction networks. With the first solution of chemical master equations, a wide range of experimental observations of small-system interactions may be mathematically conceptualized. PMID:25215268

8. Traffic flow equations coming from the Grad's method.

Velasco, Rosa M.; Méndez, Alma R.

2006-11-01

The usual Grad's method in kinetic theory of gases is developed to construct a new model in traffic flow problems. This is applied to the kinetic equation called as the Paveri-Fontana equation which tells us how the distribution function evolves in time [1]. We assume a special model for the desired velocity of drivers [2] and the Grad's method provides us with a closure relation in the macroscopic equations. The simulation results for this model allow us to find the behavior of density, mean velocity and the velocity variance in the system. All the results are consistent with the validity region of the kinetic equation and with the qualitative behavior proper to traffic models. We show some comparisons with other models in the literature [3]. [1] S.L Paveri-Fontana; Transp. Res. 9 (1975), 225. [2] R.M. Velasco, W. Marques Jr.; Phys. Rev. E72 (2005), 046102. [3] D. Helbing; Phys. Rev. E51 (1995), 3164.

9. Variational Derivation of Dissipative Equations

Sogo, Kiyoshi

2017-03-01

A new variational principle is formulated to derive various dissipative equations. Model equations considered are the damping equation, Bloch equation, diffusion equation, Fokker-Planck equation, Kramers equation and Smoluchowski equation. Each equation and its time reversal equation are simultaneously obtained in our variational principle.

10. Neutral Vlasov kinetic theory of magnetized plasmas

SciTech Connect

Tronci, Cesare; Camporeale, Enrico

2015-02-15

The low-frequency limit of Maxwell equations is considered in the Maxwell-Vlasov system. This limit produces a neutral Vlasov system that captures essential features of plasma dynamics, while neglecting radiation effects. Euler-Poincaré reduction theory is used to show that the neutral Vlasov kinetic theory possesses a variational formulation in both Lagrangian and Eulerian coordinates. By construction, the new model recovers all collisionless neutral models employed in plasma simulations. Then, comparisons between the neutral Vlasov system and hybrid kinetic-fluid models are presented in the linear regime.

11. Kinetic Approach for Laser-Induced Plasmas

SciTech Connect

Omar, Banaz; Rethfeld, Baerbel

2008-10-22

Non-equilibrium distribution functions of electron gas and phonon gas excited with ultrashort intense laser pulses are calculated for laser-induced plasmas occurring in solids. The excitation during femtosecond irradiation and the subsequent thermalization of the free electrons, as well as the dynamics of phonons are described by kinetic equations. The microscopic collision processes, such as absorption by inverse bremsstrahlung, electron-electron collisions, and electron-phonon interactions are considered by complete Boltzmann collision integrals. We apply our kinetic approach for gold by taking s-band electron into account and compare it with the case of excitation of d-band electrons.

12. Resonance Van Hove singularities in wave kinetics

Shi, Yi-Kang; Eyink, Gregory L.

2016-10-01

Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space D =(N - 2) d (d physical space dimension, N the number of waves in resonance) and the degree of degeneracy δ of the critical points. Following Van Hove, we show that non-degenerate singularities lead to finite phase measures for D > 2 but produce divergences when D ≤ 2 and possible breakdown of wave kinetics if the collision integral itself becomes too large (or even infinite). Similar divergences and possible breakdown can occur for degenerate singularities, when D - δ ≤ 2, as we find for several physical examples, including electron-hole kinetics in graphene. When the standard kinetic equation breaks down, then one must develop a new singular wave kinetics. We discuss approaches from pioneering 1971 work of Newell & Aucoin on multi-scale perturbation theory for acoustic waves and field-theoretic methods based on exact Schwinger-Dyson integral equations for the wave dynamics.

13. Studying dissolution with a model integrating solid-liquid interface kinetics and diffusion kinetics.

PubMed

Gao, Jeff Y

2012-12-18

A dissolution model that integrates the solid-liquid interface kinetics and the mass transport kinetics is introduced. Such a model reduces to the Noyes-Whitney equation under special conditions, but offers expanded range of applicability and flexibility fitting dissolution profiles when interfacial kinetics and interfacial concentration deviate from the assumptions implied in the Noyes-Whitney equation. General solutions to the integrated dissolution model derived for noninteractive solutes as well as for solutes participating in ionization equilibrium are discussed. Parameters defining the integrated dissolution model are explained conceptually along with practical ways for their determinations. Conditions under which the model exhibits supersaturation features are elaborated. Simulated dissolution profiles using the integrated dissolution model for published experimental data exhibiting supersaturation features are illustrated.

14. Kinetics equation replacement function for a particular continuous intake scenario.

PubMed

Potter, Charles A

2013-01-01

An important paper by Skrable et al. included a retention function for compartment contents during a continuous intake, including the same time variable in both the numerator and denominator of the replacement function. In fact, the time in the denominator should have been represented as a constant describing the ultimate period length for the continuous intake, whether greater than, less than, or equal to the time variable for the associated measurement.

15. Solutions of the chemical kinetic equations for initially inhomogeneous mixtures.

NASA Technical Reports Server (NTRS)

Hilst, G. R.

1973-01-01

Following the recent discussions by O'Brien (1971) and Donaldson and Hilst (1972) of the effects of inhomogeneous mixing and turbulent diffusion on simple chemical reaction rates, the present report provides a more extensive analysis of when inhomogeneous mixing has a significant effect on chemical reaction rates. The analysis is then extended to the development of an approximate chemical sub-model which provides much improved predictions of chemical reaction rates over a wide range of inhomogeneities and pathological distributions of the concentrations of the reacting chemical species. In particular, the development of an approximate representation of the third-order correlations of the joint concentration fluctuations permits closure of the chemical sub-model at the level of the second-order moments of these fluctuations and the mean concentrations.

16. Enzyme kinetics of oxidative metabolism: cytochromes P450.

PubMed

Korzekwa, Ken

2014-01-01

The cytochrome P450 enzymes (CYPs) are the most important enzymes in the oxidative metabolism of hydrophobic drugs and other foreign compounds (xenobiotics). The versatility of these enzymes results in some unusual kinetic properties, stemming from the simultaneous interaction of multiple substrates with the CYP active site. Often, the CYPs display kinetics that deviate from standard hyperbolic saturation or inhibition kinetics. Non-Michaelis-Menten or "atypical" saturation kinetics include sigmoidal, biphasic, and substrate inhibition kinetics (see Chapter 3 ). Interactions between substrates include competitive inhibition, noncompetitive inhibition, mixed inhibition, partial inhibition, activation, and activation followed by inhibition (see Chapter 4 ). Models and equations that can result in these kinetic profiles will be presented and discussed.

17. Relativistic Langevin equation for runaway electrons

Mier, J. A.; Martin-Solis, J. R.; Sanchez, R.

2016-10-01

The Langevin approach to the kinetics of a collisional plasma is developed for relativistic electrons such as runaway electrons in tokamak plasmas. In this work, we consider Coulomb collisions between very fast, relativistic electrons and a relatively cool, thermal background plasma. The model is developed using the stochastic equivalence of the Fokker-Planck and Langevin equations. The resulting Langevin model equation for relativistic electrons is an stochastic differential equation, amenable to numerical simulations by means of Monte-Carlo type codes. Results of the simulations will be presented and compared with the non-relativistic Langevin equation for RE electrons used in the past. Supported by MINECO (Spain), Projects ENE2012-31753, ENE2015-66444-R.

18. Chemical Equation Balancing.

ERIC Educational Resources Information Center

Blakley, G. R.

1982-01-01

Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

19. Unified fluid/kinetic description of magnetized plasmas

SciTech Connect

Chang, Zuoyang; Callen, J.D.

1991-06-01

Unified fluid/kinetic equations for the plasma perturbed density ({tilde n}), parallel flow velocity ({tilde u}{sub {parallel}}) and temperature ({tilde T}) are developed in a sheared slab geometry by calculating the fluid moment closure relations kinetically. At first, a set of (unclosed) nonlinear perturbed fluid equations for {tilde n}, {tilde u}{sub {parallel}} and {tilde T} is developed using a drift ordering analysis and a new gyroviscous force ({del} {center dot} {product}{sub g}). Thereafter, to develop linear closure relations for b {center dot} {del} {center dot} {tilde product}{sub {parallel}} and {tilde q}{sub {parallel}}, a drift-kinetic version of a Chapman-Enskog-like (CEL) equation is developed and solved by using a moment approach and a physically realistic collision operator (Lorentz scattering operator plus the momentum restoring terms.) The resultant closure relations for b {center dot} {del} {center dot} {tilde product}{sub {parallel}} and {tilde q}{sub {parallel}} unify both the fluid and kinetic approaches. In the collisional fluid limit the equations reduce to the well-known Braginskii equations. In the adiabatic limit they reproduce the usual kinetic results, including Landau damping. It is shown that the CEL approach is more compatible with a fluid-like description of plasmas than the usual drift/gyro kinetic approach. A remarkable simplification of these complicated closure relations is achieved by using single power of plasma dispersion functions with modified arguments. The results are compared with other recently developed Landau damping models and shown to be more accurate, complete and physically meaningful. The resultant set of nonlinear fluid/kinetic equations (with linear closure relations) will be applied to various microinstabilities in tokamak plasmas and drift type microturbulence in a separate paper. 19 refs., 7 refs., 1 tab.

20. Kinetic theory of runaway air-breakdown

SciTech Connect

Roussel-Dupre, R.A.; Gurevich, A.V.; Tunnell, T.; Milikh, G.M.

1993-09-01

The kinetic theory for a new air breakdown mechanism advanced in a previous paper is developed. The relevant form of the Boltzmann equation is derived and the particle orbits in both velocity space and configuration space are computed. A numerical solution of the Boltzmann equation, assuming a spatially uniform electric field, is obtained and the temporal evolution of the electron velocity distribution function is described. The results of our analysis are used to estimate the magnitude of potential x-ray emissions from discharges in thunderstorms.

1. Kinetic theory of runaway air breakdown

SciTech Connect

Roussel-Dupre, R.A. ); Gurevich, A.V. ); Tunnell, T. ); Milikh, G.M. )

1994-03-01

The kinetic theory for an air breakdown mechanism advanced in a previous paper [Phys. Lett. A 165, 463 (1992)] is developed. The relevant form of the Boltzmann equation is derived and the particle orbits in both velocity space and configuration space are computed. A numerical solution of the Boltzmann equation, assuming a spatially uniform electric field, is obtained and the temporal evolution of the electron velocity distribution function is described. The results of our analysis are used to estimate the magnitude of potential x-ray emissions from discharges in thunderstorms.

2. Drift kinetic theory of neoclassical tearing mode physics

Wilson, Howard; Connor, Jack; Hill, Peter; Imada, Koki

2016-10-01

Orbit averaged equations for the particle responses to a small magnetic island are derived, expanding the drift kinetic equation in the ratio of island width to tokamak plasma minor radius, assumed small. Analytic solutions demonstrate that the particles follow drift orbits which have the same geometry as the magnetic island flux surfaces, but are shifted radially by an amount that is proportional to the poloidal Larmor radius (in opposite directions for opposite signs of parallel velocity). The distribution function is flattened across these drift island structures, rather than across the magnetic island. Numerical solutions of our equations confirm the existence of the drift orbits. We employ a model momentum-conserving collision operator to evaluate the consequences for neoclassical tearing mode threshold physics, implementing numerical solutions to our orbit-averaged drift kinetic equations in a ``Modified Rutherford Equation''. Supported by the EPSRC, Grant Number EP/N009363/1.

3. Kinetics of helium bubble formation in nuclear materials

SciTech Connect

Bonilla, L L; Carpio, A; Neu, J C; Wolfer, W G

2005-10-13

The formation and growth of helium bubbles due to self-irradiation in plutonium has been modeled by a discrete kinetic equations for the number densities of bubbles having k atoms. Analysis of these equations shows that the bubble size distribution function can be approximated by a composite of: (1) the solution of partial differential equations describing the continuum limit of the theory but corrected to take into account the effects of discreteness, and (2) a local expansion about the advancing leading edge of the distribution function in size space. Both approximations contribute to the memory term in a close integrodifferential equation for the monomer concentration of single helium atoms. The present theory is compared to the numerical solution of the full kinetic model and to previous approximation of Schaldach and Wolfer involving a truncated system of moment equations.

4. Kinetics of microbial growth on pentachlorophenol.

PubMed Central

Klecka, G M; Maier, W J

1985-01-01

Batch and fed-batch experiments were conducted to examine the kinetics of pentachlorophenol utilization by an enrichment culture of pentachlorophenol-degrading bacteria. The Haldane modification of the Monod equation was found to describe the relationship between the specific growth rate and substrate concentration. Analysis of the kinetic parameters indicated that the maximum specific growth rate and yield coefficients are low, with values of 0.074 h-1 and 0.136 g/g, respectively. The Monod constant (Ks) was estimated to be 60 micrograms/liter, indicating a high affinity of the microorganisms for the substrate. However, high concentrations (KI = 1,375 micrograms/liter) were shown to be inhibitory for metabolism and growth. These kinetic parameters can be used to define the optimal conditions for the removal of pentachlorophenol in biological treatment systems. PMID:3977315

5. Kinetic-energy-momentum tensor in electrodynamics

Sheppard, Cheyenne J.; Kemp, Brandon A.

2016-01-01

We show that the Einstein-Laub formulation of electrodynamics is invalid since it yields a stress-energy-momentum (SEM) tensor that is not frame invariant. Two leading hypotheses for the kinetic formulation of electrodynamics (Chu and Einstein-Laub) are studied by use of the relativistic principle of virtual power, mathematical modeling, Lagrangian methods, and SEM transformations. The relativistic principle of virtual power is used to demonstrate the field dynamics associated with energy relations within a relativistic framework. Lorentz transformations of the respective SEM tensors demonstrate the relativistic frameworks for each studied formulation. Mathematical modeling of stationary and moving media is used to illustrate the differences and discrepancies of specific proposed kinetic formulations, where energy relations and conservation theorems are employed. Lagrangian methods are utilized to derive the field kinetic Maxwell's equations, which are studied with respect to SEM tensor transforms. Within each analysis, the Einstein-Laub formulation violates special relativity, which invalidates the Einstein-Laub SEM tensor.

6. The quasicontinuum Fokker-Plank equation

SciTech Connect

Alexander, Francis J

2008-01-01

We present a regularized Fokker-Planck equation with more accurate short-time and high-frequency behavior for continuous-time, discrete-state systems. The regularization preserves crucial aspects of state-space discreteness lost in the standard Kramers-Moyal expansion. We apply the method to a simple example of biochemical reaction kinetics and to a two-dimensional symmetric random walk, and suggest its application to more complex systerns.

7. Study of kinetic effects arising in simulations of Farley-Buneman instability

SciTech Connect

Kovalev, D. V.; Smirnov, A. P.; Dimant, Ya. S.

2009-05-15

The Farley-Buneman instability, which has been observed in the E region of the Earth's ionosphere, is studied using fluid equations for electrons, a four-dimensional (in coordinate-velocity space) kinetic equation for ions, and Poisson's equation. Numerical simulations with allowance for Landau damping show that the Farley-Buneman instability results in anisotropy of the ion velocity distribution function.

8. Kinetic approach for describing biological systems

Aristov, V. V.; Ilyin, O. V.

2016-11-01

We attempt to consider a biological structure as an open nonequilibrium system the properties of which can be described on the basis of kinetic approach with the help of appropriate kinetic equations. This approach allows us to evaluate in principle scales of sizes and to connect these values to the inner characteristics of the processes of kinetic interaction and advection. One can compare the results with some empirical data concerning these characteristics for bio-systems, in particular mammals, and also for some parts of the systems, say sizes of green leaves. A sense of the nonequilibrium entropy as a measure of complexity of bio-organisms is discussed. Besides the estimations of bio-systems on a global scale, possible methods to describe restricted regions (associated e.g. with living cells) as nonequilibrium open structure with specific boundaries are also discussed. A new boundary 1D problem is formulated and solved for kinetic equations with the membrane-like boundaries conditions. Non-classical transport properties in the system are found.

9. Kinetic theory for interacting Luttinger liquids

Buchhold, Michael; Diehl, Sebastian

2015-10-01

We derive a closed set of equations for the kinetics and non-equilibrium dynamics of interacting Luttinger Liquids with cubic resonant interactions. In the presence of these interactions, the Luttinger phonons become dressed but still well defined quasi-particles, characterized by a life-time much larger then the inverse energy. This enables the separation of forward time dynamics and relative time dynamics into slow and fast dynamics and justifies the so-called Wigner approximation, which can be seen as a "local-time approximation" for the relative dynamics. Applying field theoretical methods in the Keldysh framework, i.e. kinetic and Dyson-Schwinger equations, we derive a closed set of dynamic equations, describing the kinetics of normal and anomalous phonon densities, the phonon self-energy and vertex corrections for a Gaussian non-equilibrium initial state. In the limit of low phonon densities, the results from self-consistent Born approximation are recaptured, including Andreev's scaling solution for the quasi-particle life-time in a thermal state. As an application, we compute the relaxation of an excited state to its thermal equilibrium. While the intermediate time dynamics displays exponentially fast relaxation, the last stages of thermalization are governed by algebraic laws. This can be traced back to the importance of energy and momentum conservation at the longest times, which gives rise to dynamical slow modes.

10. A note on the reverse Michaelis-Menten kinetics

SciTech Connect

Wang, Gangsheng; Post, Wilfred M

2013-01-01

We theoretically derive a general equation describing the enzyme kinetics that can be further simplified to the typical Michaelis-Menten (M-M) kinetics and the reverse M-M equation (RM-M) proposed by Schimel and Weintraub (2003). We discuss the conditions under which the RM-M is valid with this theoretical derivation. These conditions are contrary to the assumptions of Schimel and Weintraub (2003) and limit the applicability of the model in field soil environments. Nonetheless, Schimel and Weintraub s RM-M model is useful and has the ability to produce a non-linear response of SOM decomposition to enzyme concentration consistent with observations. Regardless of the theoretical basis, if we assume that the M-M and the RM-M could be equivalent, our sensitivity analysis indicates that enzyme plays a more sensitive role in the M-M kinetics compared with in the RM-M kinetics.

11. Kinetic mean-field theories

Karkheck, John; Stell, George

1981-08-01

A kinetic mean-field theory for the evolution of the one-particle distribution function is derived from maximizing the entropy. For a potential with a hard-sphere core plus tail, the resulting theory treats the hard-core part as in the revised Enskog theory. The tail, weighted by the hard-sphere pair distribution function, appears linearly in a mean-field term. The kinetic equation is accompanied by an entropy functional for which an H theorem was proven earlier. The revised Enskog theory is obtained by setting the potential tail to zero, the Vlasov equation is obtained by setting the hard-sphere diameter to zero, and an equation of the Enskog-Vlasov type is obtained by effecting the Kac limit on the potential tail. At equilibrium, the theory yields a radial distribution function that is given by the hard-sphere reference system and thus furnishes through the internal energy a thermodynamic description which is exact to first order in inverse temperature. A second natural route to thermodynamics (from the momentum flux which yields an approximate equation of state) gives somewhat different results; both routes coincide and become exact in the Kac limit. Our theory furnishes a conceptual basis for the association in the heuristically based modified Enskog theory (MET) of the contact value of the radial distribution function with the ''thermal pressure'' since this association follows from our theory (using either route to thermodynamics) and moreover becomes exact in the Kac limit. Our transport theory is readily extended to the general case of a soft repulsive core, e.g., as exhibited by the Lennard-Jones potential, via by-now-standard statistical-mechanical methods involving an effective hard-core potential, thus providing a self-contained statistical-mechanical basis for application to such potentials that is lacking in the standard versions of the MET. We obtain very good agreement with experiment for the thermal conductivity and shear viscosity of several

12. Transport equations for partially ionized reactive plasma in magnetic field

Zhdanov, V. M.; Stepanenko, A. A.

2016-06-01

Transport equations for partially ionized reactive plasma in magnetic field taking into account the internal degrees of freedom and electronic excitation of plasma particles are derived. As a starting point of analysis the kinetic equation with a binary collision operator written in the Wang-Chang and Uhlenbeck form and with a reactive collision integral allowing for arbitrary chemical reactions is used. The linearized variant of Grad's moment method is applied to deduce the systems of moment equations for plasma and also full and reduced transport equations for plasma species nonequilibrium parameters.

13. On the relationships between the Michaelis–Menten kinetics, reverse Michaelis–Menten kinetics, equilibrium chemistry approximation kinetics, and quadratic kinetics

DOE PAGES

Tang, J. Y.

2015-12-01

The Michaelis–Menten kinetics and the reverse Michaelis–Menten kinetics are two popular mathematical formulations used in many land biogeochemical models to describe how microbes and plants would respond to changes in substrate abundance. However, the criteria of when to use either of the two are often ambiguous. Here I show that these two kinetics are special approximations to the equilibrium chemistry approximation (ECA) kinetics, which is the first-order approximation to the quadratic kinetics that solves the equation of an enzyme–substrate complex exactly for a single-enzyme and single-substrate biogeochemical reaction with the law of mass action and the assumption of a quasi-steadymore » state for the enzyme–substrate complex and that the product genesis from enzyme–substrate complex is much slower than the equilibration between enzyme–substrate complexes, substrates, and enzymes. In particular, I show that the derivation of the Michaelis–Menten kinetics does not consider the mass balance constraint of the substrate, and the reverse Michaelis–Menten kinetics does not consider the mass balance constraint of the enzyme, whereas both of these constraints are taken into account in deriving the equilibrium chemistry approximation kinetics. By benchmarking against predictions from the quadratic kinetics for a wide range of substrate and enzyme concentrations, the Michaelis–Menten kinetics was found to persistently underpredict the normalized sensitivity ∂ ln v / ∂ ln k2+ of the reaction velocity v with respect to the maximum product genesis rate k2+, persistently overpredict the normalized sensitivity ∂ ln v / ∂ ln k1+ of v with respect to the intrinsic substrate affinity k1+, persistently overpredict the normalized sensitivity ∂ ln v / ∂ ln [E]T of v with respect the total enzyme concentration [E]T, and persistently underpredict the normalized sensitivity ∂ ln v / ∂ ln [S]T of v with respect to the total substrate concentration

14. Single wall penetration equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

1991-01-01

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

15. Kinetic behaviour of zymogen activation processes in the presence of an inhibitor.

PubMed Central

Varón, R; Manjabacas, M C; García-Moreno, M; Valero, E; Garcia-Canovas, F

1993-01-01

A global kinetic analysis of a general zymogen activation model, where not only the activating but also the activated enzyme suffer an irreversible inhibition is presented. A reaction in which the enzyme acts upon a substrate is coupled to monitor the process. In addition, we determined the corresponding kinetic equations for a number of particular cases of the general model studied. Finally, a kinetic data analysis and a procedure to discriminate among the different mechanisms considered, which are based on the kinetic equations obtained, are suggested. PMID:8452535

16. Consistent description of kinetics and hydrodynamics of dusty plasma

SciTech Connect

Markiv, B.; Tokarchuk, M.

2014-02-15

A consistent statistical description of kinetics and hydrodynamics of dusty plasma is proposed based on the Zubarev nonequilibrium statistical operator method. For the case of partial dynamics, the nonequilibrium statistical operator and the generalized transport equations for a consistent description of kinetics of dust particles and hydrodynamics of electrons, ions, and neutral atoms are obtained. In the approximation of weakly nonequilibrium process, a spectrum of collective excitations of dusty plasma is investigated in the hydrodynamic limit.

17. The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

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.

18. Kinetic modelling of mitochondrial translation.

PubMed

Korla, Kalyani; Mitra, Chanchal K

2014-01-01

Mitochondrial genome contains 13 protein coding genes, all being part of the oxidative phosphorylation complexes. The process of translation of these protein coding mRNAs in mitochondrial matrix is a good miniature model of translation in cytoplasm. In this work, we have simulated three phases of mitochondrial translation viz. initiation, elongation and termination (including ribosome recycling). The kinetic equations for these phases have been deduced based on the information available in literature. Various factors involved in the process have been included explicitly. Kinetic simulation was done using Octave, open source software. Scripts were written individually for each phase. Initiation begins with mitoribosome, mRNA, fMet-tRNA and initiation factors. The final product of the initiation script, the initiation complex, was introduced as the start point in the successive step, i.e. elongation. Elongation is a particular extensive process where the various aminoacyl-tRNAs already present in the matrix check for matching with the triplet codon in A-site of mitoribosome. This script consists of two parts: one with the time behaviour of the factors involved in the molecular process (using ordinary differential equation solver) and the other including the reading of triplet codon on the mRNA and incorporating the corresponding aminoacyl-tRNA, and then at each step elongating the peptide chain (using loops and conditions). The peptide chain thus formed in the elongation step (in the loops and conditions segment) was released in the termination step. This was followed by mitoribosome recycling where the mitoribosome reached the native state and was ready for the next cycle of translation.

19. Reflections on Chemical Equations.

ERIC Educational Resources Information Center

Gorman, Mel

1981-01-01

The issue of how much emphasis balancing chemical equations should have in an introductory chemistry course is discussed. The current heavy emphasis on finishing such equations is viewed as misplaced. (MP)

20. Parametrically defined differential equations

Polyanin, A. D.; Zhurov, A. I.

2017-01-01

The paper deals with nonlinear ordinary differential equations defined parametrically by two relations. It proposes techniques to reduce such equations, of the first or second order, to standard systems of ordinary differential equations. It obtains the general solution to some classes of nonlinear parametrically defined ODEs dependent on arbitrary functions. It outlines procedures for the numerical solution of the Cauchy problem for parametrically defined differential equations.

1. Fractional kinetics in drug absorption and disposition processes.

PubMed

Dokoumetzidis, Aristides; Macheras, Panos

2009-04-01

We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the "zero-" and "first-order" processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag-Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag-Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data.

2. Hybrid Parallelization of Adaptive MHD-Kinetic Module in Multi-Scale Fluid-Kinetic Simulation Suite

SciTech Connect

Borovikov, Sergey; Heerikhuisen, Jacob; Pogorelov, Nikolai

2013-04-01

The Multi-Scale Fluid-Kinetic Simulation Suite has a computational tool set for solving partially ionized flows. In this paper we focus on recent developments of the kinetic module which solves the Boltzmann equation using the Monte-Carlo method. The module has been recently redesigned to utilize intra-node hybrid parallelization. We describe in detail the redesign process, implementation issues, and modifications made to the code. Finally, we conduct a performance analysis.

3. The Pendulum Equation

ERIC Educational Resources Information Center

Fay, Temple H.

2002-01-01

We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

4. Extended monod kinetics for substrate, product, and cell inhibition.

PubMed

Han, K; Levenspiel, O

1988-08-05

A generalized form of Monod kinetics is proposed to account for all kinds of product, cell, and substrate inhibition. This model assumes that there exists a critical inhibitor concentration above which cells cannot grow, and that the constants of the Monod equation are functions of this limiting inhibitor concentration. Methods for evaluating the constants of this rate form are presented. Finally the proposed kinetic form is compared with the available data in the literature, which unfortunately is very sparse. In all cases, this equation form fitted the data very well.

5. Numerical methods for high-dimensional probability density function equations

Cho, H.; Venturi, D.; Karniadakis, G. E.

2016-01-01

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

6. Numerical methods for high-dimensional probability density function equations

SciTech Connect

Cho, H.; Venturi, D.; Karniadakis, G.E.

2016-01-15

In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker–Planck and Dostupov–Pugachev equations), random wave theory (Malakhov–Saichev equations) and coarse-grained stochastic systems (Mori–Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.

7. Exact and Approximate Solutions for the Decades-Old Michaelis-Menten Equation: Progress-Curve Analysis through Integrated Rate Equations

ERIC Educational Resources Information Center

Golicnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate "V", and the Michaelis constant "K"[subscript M]) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to…

8. Ion kinetic transport in TJ-II

SciTech Connect

Velasco, J. L.; Tarancon, A.; Castejon, F.; Fernandez, L. A.; Martin-Mayor, V.

2008-11-02

The ion Drift Kinetic Equation (DKE) which describes the ion collisional transport is solved for the TJ-II device plasmas. This non-linear equation is computed by performing a mean field iterative calculation. In each step of the calculation, a Fokker-Planck equation is solved by means of the Langevin approach: one million particles are followed in a realistic TJ-II magnetic configuration, taking into account collisions and electric field. This allows to avoid the assumptions made in the usual neoclassical approach, namely considering radially narrow particle trajectories, diffusive transport, energy conservation and infinite parallel transport. As a consequence, global features of transport, not present in the customary neoclassical models, appear: non-diffusive transport and asymmetries on the magnetic surfaces.

9. Kinetic modeling of non-ideal explosives

SciTech Connect

Fried, L E; Howard, W M; Souers, P C

1999-03-01

We have implemented a Wood-Kirkwood kinetic detonation model based on multi-species equations of state and multiple reaction rate laws. Finite rate laws are used for the slowest chemical reactions, while other reactions are given infinite rates and are kept in constant thermodynamic equilibrium. We model a wide range of ideal and non-ideal composite energetic materials. In addition, we develop an exp-6 equation of state for the product fluids that reproduces a wide range experimental shock Hugoniot and static compression data. For unreacted solids, including solid and liquid Al and Al{sub 2}O{sub 3}, we use a Murnaghan form for the equation of state. We find that we can replicate experimental detonation velocities to within a few per cent for a wide range of explosives, while obtaining good agreement with estimated reaction zone lengths. The detonation velocity as a function of charge radius is also correctly reproduced.

10. Alpha-effect dynamos with zero kinetic helicity.

PubMed

Rädler, Karl-Heinz; Brandenburg, Axel

2008-02-01

A simple explicit example of a Roberts-type dynamo is given in which the alpha effect of mean-field electrodynamics exists in spite of pointwise vanishing kinetic helicity of the fluid flow. In this way, it is shown that alpha-effect dynamos do not necessarily require nonzero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition, numerical solutions of the original dynamo equations are given that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity.

11. {alpha}-effect dynamos with zero kinetic helicity

SciTech Connect

Raedler, Karl-Heinz; Brandenburg, Axel

2008-02-15

A simple explicit example of a Roberts-type dynamo is given in which the {alpha} effect of mean-field electrodynamics exists in spite of pointwise vanishing kinetic helicity of the fluid flow. In this way, it is shown that {alpha}-effect dynamos do not necessarily require nonzero kinetic helicity. A mean-field theory of Roberts-type dynamos is established within the framework of the second-order correlation approximation. In addition, numerical solutions of the original dynamo equations are given that are independent of any approximation of that kind. Both theory and numerical results demonstrate the possibility of dynamo action in the absence of kinetic helicity.

12. The Einstein-Vlasov System/Kinetic Theory.

PubMed

Andréasson, Håkan

2011-01-01

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein-Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein-Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.

13. Master equation analysis of deterministic chemical chaos

Wang, Hongli; Li, Qianshu

1998-05-01

The underlying microscopic dynamics of deterministic chemical chaos was investigated in this paper. We analyzed the master equation for the Williamowski-Rössler model by direct stochastic simulation as well as in the generating function representation. Simulation within an ensemble revealed that in the chaotic regime the deterministic mass action kinetics is related neither to the ensemble mean nor to the most probable value within the ensemble. Cumulant expansion analysis of the master equation also showed that the molecular fluctuations do not admit bounded values but increase linearly in time infinitely, indicating the meaninglessness of the chaotic trajectories predicted by the phenomenological equations. These results proposed that the macroscopic description is no longer useful in the chaotic regime and a more microscopic description is necessary in this circumstance.

14. Exact Pressure Evolution Equation for Incompressible Fluids

Tessarotto, M.; Ellero, M.; Aslan, N.; Mond, M.; Nicolini, P.

2008-12-01

An important aspect of computational fluid dynamics is related to the determination of the fluid pressure in isothermal incompressible fluids. In particular this concerns the construction of an exact evolution equation for the fluid pressure which replaces the Poisson equation and yields an algorithm which is a Poisson solver, i.e., it permits to time-advance exactly the same fluid pressure without solving the Poisson equation. In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically and numerically. This amounts to transform an elliptic type fluid equation into a suitable hyperbolic equation, a result which usually is reached only by means of an asymptotic formulation. Besides being a still unsolved mathematical problem, the issue is relevant for at least two reasons: a) the proliferation of numerical algorithms in computational fluid dynamics which reproduce the behavior of incompressible fluids only in an asymptotic sense (see below); b) the possible verification of conjectures involving the validity of appropriate equations of state for the fluid pressure. Another possible motivation is, of course, the ongoing quest for efficient numerical solution methods to be applied for the construction of the fluid fields {ρ,V,p}, solutions of the initial and boundary-value problem associated to the incompressible N-S equations (INSE). In this paper we intend to show that an exact solution to this problem can be achieved adopting the approach based on inverse kinetic theory (IKT) recently developed for incompressible fluids by Tessarotto et al. [7, 6, 7, 8, 9]. In particular we intend to prove that the evolution of the fluid fields can be achieved by means of a suitable dynamical system, to be identified with the so-called Navier-Stokes (N-S) dynamical system. As a consequence it is found that the fluid pressure obeys a well-defined evolution equation. The result appears

15. A closure scheme for chemical master equations.

PubMed

2013-08-27

Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time.

16. A closure scheme for chemical master equations

PubMed Central

2013-01-01

Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time. PMID:23940327

17. Kinetic theory for electrostatic waves due to transverse velocity shears

NASA Technical Reports Server (NTRS)

Ganguli, G.; Lee, Y. C.; Palmadesso, P. J.

1988-01-01

A kinetic theory in the form of an integral equation is provided to study the electrostatic oscillations in a collisionless plasma immersed in a uniform magnetic field and a nonuniform transverse electric field. In the low temperature limit the dispersion differential equation is recovered for the transverse Kelvin-Helmholtz modes for arbitrary values of K parallel, where K parallel is the component of the wave vector in the direction of the external magnetic field assumed in the z direction. For higher temperatures the ion-cyclotron-like modes described earlier in the literature by Ganguli, Lee and Plamadesso are recovered. In this article, the integral equation is reduced to a second-order differential equation and a study is made of the kinetic Kelvin-Helmholtz and ion-cyclotron-like modes that constitute the two branches of oscillation in a magnetized plasma including a transverse inhomogeneous dc electric field.

18. A study of the Sabatier-methanation reaction kinetics

NASA Technical Reports Server (NTRS)

Verostko, C. E.; Forsythe, R. K.

1974-01-01

The kinetics of the Sabatier methanation reaction, the reduction of carbon dioxide with hydrogen to methane and water, was investigated for 58 percent nickel on kieselguhr catalyst and 20 percent ruthenium on alumina catalyst. Differential rate data from an experimental program were correlated with a power function rate equation both for forward and reverse reactions. The kinetic parameters of activation energy, frequency rate constant and reaction order were determined for the rate equation. The values of these parameters were obtained from an Arrhenius plot of the experimental differential rate data. Also the carbon monoxide side reaction effect was measured and included in the correlation of parameters. The reaction was found to fit the rate equation experimentally within the temperature range 421 K, where the reaction effectively begins, the 800 K where the reaction rate drops and departs from the rate equation form.

19. A steady-state kinetic analysis of the prolyl-4-hydroxylase mechanism.

PubMed

Soskel, N T; Kuby, S A

1981-01-01

Published kinetic data by Kivirikko, et al. on the prolyl-4-hydroxylase reaction have been re-evaluated using the overall steady-state velocity equation in the forward and reverse directions for an ordered ter ter kinetic mechanism. Qualitatively, the published data for prolyl-4-hydroxylase appear to fit the predicted patterns for this kinetic mechanism. More kinetic data are needed to confirm these results and to quantitate the kinetic parameters but, tentatively, the order of substrate addition would appear to be alpha-ketoglutarate, oxygen, and peptide; and the order of product release would be hydroxylated peptide (or collagen), carbon dioxide, and succinate.

20. Chemical gas-dynamics beyond Wang Chang-Uhlenbeck's kinetics

SciTech Connect

Kolesnichenko, Evgeniy G.; Gorbachev, Yuriy E.

2014-12-09

Wang Chang-Uhlenbeck equation does not give possibility to take into account intermolecular processes such as redistribution of the energy among different degrees of freedom. The modification of the generalized Wang Chang-Uhlenbeck equation including such processes is proposed. It allows to study for instance the kinetics of non-radiative transitions. Limitations of this approach are connected with the requirements of absence of polarization of rotational momentum and phases of intermolecular vibrations.

1. Chemical gas-dynamics beyond Wang Chang-Uhlenbeck's kinetics

Kolesnichenko, Evgeniy G.; Gorbachev, Yuriy E.

2014-12-01

Wang Chang-Uhlenbeck equation does not give possibility to take into account intermolecular processes such as redistribution of the energy among different degrees of freedom. The modification of the generalized Wang Chang-Uhlenbeck equation including such processes is proposed. It allows to study for instance the kinetics of non-radiative transitions. Limitations of this approach are connected with the requirements of absence of polarization of rotational momentum and phases of intermolecular vibrations.

2. The Continuous Coagulation-FragmentationEquations with Diffusion

Laurençot, Philippe; Mischler, Stéphane

Existence of global weak solutions to the continuous coagulation-fragmentation equations with diffusion is investigated when the kinetic coefficients satisfy a detailed balance condition or the coagulation coefficient enjoys a monotonicity condition. Our approach relies on weak and strong compactness methods in L1 in the spirit of the DiPerna-Lions theory for the Boltzmann equation. Under the detailed balance condition the large-time behaviour is also studied.

3. Generalized quantum kinetic expansion: Time scale separation between intra-cluster and inter-cluster kinetics

SciTech Connect

Tang, Zhoufei; Gong, Zhihao; Wu, Jianlan

2015-09-14

For a general two-cluster network, a new methodology of the cluster-based generalized quantum kinetic expansion (GQKE) is developed in the matrix formalism under two initial conditions: the local cluster equilibrium and system-bath factorized states. For each initial condition, the site population evolution follows exactly a distinct closed equation, where all the four terms involved are systematically expanded over inter-cluster couplings. For the system-bath factorized initial state, the numerical investigation of the two models, a biased (2, 1)-site system and an unbiased (2, 2)-site system, verifies the reliability of the GQKE and the relevance of higher-order corrections. The time-integrated site-to-site rates and the time evolution of site population reveal the time scale separation between intra-cluster and inter-cluster kinetics. The population evolution of aggregated clusters can be quantitatively described by the approximate cluster Markovian kinetics.

4. Chemical Kinetics Database

National Institute of Standards and Technology Data Gateway

SRD 17 NIST Chemical Kinetics Database (Web, free access)   The NIST Chemical Kinetics Database includes essentially all reported kinetics results for thermal gas-phase chemical reactions. The database is designed to be searched for kinetics data based on the specific reactants involved, for reactions resulting in specified products, for all the reactions of a particular species, or for various combinations of these. In addition, the bibliography can be searched by author name or combination of names. The database contains in excess of 38,000 separate reaction records for over 11,700 distinct reactant pairs. These data have been abstracted from over 12,000 papers with literature coverage through early 2000.

5. A "Stationery" Kinetics Experiment.

ERIC Educational Resources Information Center

Hall, L.; Goberdhansingh, A.

1988-01-01

Describes a simple redox reaction that occurs between potassium permanganate and oxalic acid that can be used to prepare an interesting disappearing ink for demonstrating kinetics for introductory chemistry. Discusses laboratory procedures and factors that influence disappearance times. (CW)

6. Thermal kinetic inductance detector

DOEpatents

Cecil, Thomas; Gades, Lisa; Miceli, Antonio; Quaranta, Orlando

2016-12-20

A microcalorimeter for radiation detection that uses superconducting kinetic inductance resonators as the thermometers. The detector is frequency-multiplexed which enables detector systems with a large number of pixels.

7. Functional integral approach to the kinetic theory of inhomogeneous systems

Fouvry, Jean-Baptiste; Chavanis, Pierre-Henri; Pichon, Christophe

2016-10-01

We present a derivation of the kinetic equation describing the secular evolution of spatially inhomogeneous systems with long-range interactions, the so-called inhomogeneous Landau equation, by relying on a functional integral formalism. We start from the BBGKY hierarchy derived from the Liouville equation. At the order 1 / N, where N is the number of particles, the evolution of the system is characterised by its 1-body distribution function and its 2-body correlation function. Introducing associated auxiliary fields, the evolution of these quantities may be rewritten as a traditional functional integral. By functionally integrating over the 2-body autocorrelation, one obtains a new constraint connecting the 1-body DF and the auxiliary fields. When inverted, this constraint allows us to obtain the closed non-linear kinetic equation satisfied by the 1-body distribution function. This derivation provides an alternative to previous methods, either based on the direct resolution of the truncated BBGKY hierarchy or on the Klimontovich equation. It may turn out to be fruitful to derive more accurate kinetic equations, e.g., accounting for collective effects, or higher order correlation terms.

8. Fundamentals of enzyme kinetics.

PubMed

Seibert, Eleanore; Tracy, Timothy S

2014-01-01

This chapter provides a general introduction to the kinetics of enzyme-catalyzed reactions, with a focus on drug-metabolizing enzymes. A prerequisite to understanding enzyme kinetics is having a clear grasp of the meanings of "enzyme" and "catalysis." Catalysts are reagents that can increase the rate of a chemical reaction without being consumed in the reaction. Enzymes are proteins that form a subset of catalysts. These concepts are further explored below.

9. Study of the kinetics of catalytic decomposition of hydrazine vapors on palladium

NASA Technical Reports Server (NTRS)

Khomenko, A. A.; Apelbaum, L. O.

1987-01-01

The decomposition rates of N2H4 on a palladium surface are studied. Experiments were conducted in a circulating unit at atmosphere pressure. The experimental method is described. The laws found for the reaction kinetics are explained by equations.

10. Linear gyrokinetic theory for kinetic magnetohydrodynamic eigenmodes in tokamak plasmas

Qin, H.; Tang, W. M.; Rewoldt, G.

1999-06-01

A two-dimensional (2D) numerical solution method is developed for the recently derived linear gyrokinetic system which describes arbitrary wavelength electromagnetic perturbations in tokamak plasmas. The system consists of the gyrokinetic equation, the gyrokinetic Poisson equation, and the gyrokinetic moment equation. Since familiar magnetohydrodynamic (MHD) results can be recovered entirely from this gyrokinetic model, and all interesting kinetic effects are intrinsically included, this gyrokinetic system offers an approach for kinetic MHD phenomena which is more rigorous, self-consistent, and comprehensive than the previous hybrid models. Meanwhile, drift type microinstabilities can be also investigated systematically in this theoretical framework. The linear gyrokinetic equation is solved for the distribution function in terms of the perturbed fields by integrating along unperturbed particle orbits. The solution is substituted back into the gyrokinetic moment equation and the gyrokinetic Poisson equation. When the boundary conditions are incorporated, an eigenvalue problem is formed. The resulting numerical code, KIN-2DEM, is applied to kinetic ballooning modes, internal kink modes, and toroidal Alfvén eigenmodes (TAEs). The numerical results are benchmarked against the well-established FULL code [G. Rewoldt, W. M. Tang, and M. S. Chance, Phys. Fluids 25, 480 (1982)], the PEST code [J. Manickam, Nucl. Fusion 24, 595 (1984)], and the NOVA-K code [C. Z. Cheng, Phys. Rep. 211, No. 1 (1992)]. More importantly, kinetic effects on MHD modes can be investigated nonperturbatively. In particular, the kinetic effects of the background plasma on internal kink modes and the hot particle destabilization of TAEs are studied numerically.

11. Functional BES equation

Kostov, Ivan; Serban, Didina; Volin, Dmytro

2008-08-01

We give a realization of the Beisert, Eden and Staudacher equation for the planar Script N = 4 supersymetric gauge theory which seems to be particularly useful to study the strong coupling limit. We are using a linearized version of the BES equation as two coupled equations involving an auxiliary density function. We write these equations in terms of the resolvents and we transform them into a system of functional, instead of integral, equations. We solve the functional equations perturbatively in the strong coupling limit and reproduce the recursive solution obtained by Basso, Korchemsky and Kotański. The coefficients of the strong coupling expansion are fixed by the analyticity properties obeyed by the resolvents.

12. Fractional chemotaxis diffusion equations.

PubMed

Langlands, T A M; Henry, B I

2010-05-01

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles.

13. The hydrothermal reaction kinetics of aspartic acid

Cox, Jenny S.; Seward, Terry M.

2007-02-01

Experimental data on the hydrothermal reaction kinetics of aspartic acid were acquired using a custom-built spectrophotometric reaction cell which permits in situ observation under hydrothermal conditions. The results of this study indicate that the reaction kinetics of dilute aspartic acid solutions are significantly different depending on the presence or absence of catalytic surfaces such as standard metal alloys. The spectroscopic data presented here represent the first direct observations, in situ and in real time, of an amino acid reacting in a hydrothermal solution. Quantitative kinetic information, including rate constants, concentration versus time profiles, and calculations of the individual component spectra, was obtained from the data using a chemometric approach based on factor analysis/principle component analysis which treats the rate expressions simultaneously as a system of differential algebraic equations (DAE) of index 1. Identification of the products was confirmed where possible by high pressure anion exchange chromatography with pulsed amperometric detection (HPAEC-PAD). The reaction kinetics of aspartic acid under hydrothermal conditions was observed to be highly complex, in contrast to previous studies which indicated almost exclusively deamination. At lower temperatures (120-170 °C), several different reaction pathways were observed, including decarboxylation and polymerization, and the catalytic effects of reactor surfaces on the aspartic acid system were clearly demonstrated. At higher temperatures (above 170 °C), aspartic acid exhibited highly complex behaviour, with evidence indicating that it can simultaneously dimerize and cyclize, deaminate (by up to two pathways), and decarboxylate (by up to two pathways). These higher temperature kinetics were not fully resolvable in a quantitative manner due to the complexity of the system and the constraints of UV spectroscopy. The results of this study provide strong evidence that the reaction

14. Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

15. Construction and accuracy of partial differential equation approximations to the chemical master equation.

PubMed

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

16. Nucleation kinetics and crystal growth with fluctuating rates at the intermediate stage of phase transitions

Alexandrov, D. V.; Malygin, A. P.

2014-01-01

Crystal growth kinetics accompanied by particle growth with fluctuating rates at the intermediate stage of phase transitions is analyzed theoretically. The integro-differential model of governing equations is solved analytically for size-independent growth rates and arbitrary dependences of the nucleation frequency on supercooling/supersaturation. Two important cases of Weber-Volmer-Frenkel-Zel'dovich and Mier nucleation kinetics are detailed. A Fokker-Plank type equation for the crystal-size density distribution function is solved explicitly.

17. Closure of a kinetic model of plasma in strong turbulence by relaxation

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1978-01-01

A Fokker-Planck kinetic equation for a turbulent plasma is derived by a repeated cascade decomposition. Calculation of the propagator and the kinetic equation determine the transport coefficients (diffusivity and turbulent viscosity) by means of a closure based on a relaxation procedure governing the approach to equilibrium. The k to the minus third power spectral law is obtained, which governs the coupling between the velocity and the electrostatic field fluctuations.

18. [Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].

PubMed

Murase, Kenya

2015-01-01

In this issue, symbolic methods for solving differential equations were firstly introduced. Of the symbolic methods, Laplace transform method was also introduced together with some examples, in which this method was applied to solving the differential equations derived from a two-compartment kinetic model and an equivalent circuit model for membrane potential. Second, series expansion methods for solving differential equations were introduced together with some examples, in which these methods were used to solve Bessel's and Legendre's differential equations. In the next issue, simultaneous differential equations and various methods for solving these differential equations will be introduced together with some examples in medical physics.

19. Kinetic equilibria of very high- β plasmas

Steinhauer, Loren; TAE Team

2015-11-01

Plasma equilibria with many large ion orbits, such as an advanced beam-driven field-reversed configuration, are neither static (Grad-Shafranov) nor describable as a flowing, multi-fluid. A fully-kinetic treatment of the ions is essential for such high- β plasmas. A kinetic equilibrium is needed to properly support realistic stability and transport analyses, both of which are strongly affected by large-orbit ions. A hybrid equilibrium model has been developed with a fully-kinetic treatment of both thermal ions and a rapidly-rotating ``beam-ion'' component, such as produced by neutral beam injection, relevant to the C-2U experiments at TAE. It employs analytic Vlasov solutions in that the distribution depends only on the two constants of motion, the Hamiltonian (H) and the canonical angular momentum (Pθ) . Electrons are treated as a pressure-bearing fluid. Since realistic forms of f (H ,Pθ) are affected by collisions, f is limited to solutions of a simplified Fokker-Planck equation. Importantly, a kinetic end-loss condition applies to unconfined ions, using a particle sink at a rate consistent with Monte-Carlo-like simulations of end loss accounting for a strong end mirror.

20. Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

1. Continuum kinetic and multi-fluid simulations of classical sheaths

Cagas, P.; Hakim, A.; Juno, J.; Srinivasan, B.

2017-02-01

The kinetic study of plasma sheaths is critical, among other things, to understand the deposition of heat on walls, the effect of sputtering, and contamination of the plasma with detrimental impurities. The plasma sheath also provides a boundary condition and can often have a significant global impact on the bulk plasma. In this paper, kinetic studies of classical sheaths are performed with the continuum kinetic code, Gkeyll, which directly solves the Vlasov-Maxwell equations. The code uses a novel version of the finite-element discontinuous Galerkin scheme that conserves energy in the continuous-time limit. The fields are computed using Maxwell equations. Ionization and scattering collisions are included; however, surface effects are neglected. The aim of this work is to introduce the continuum kinetic method and compare its results with those obtained from an already established finite-volume multi-fluid model also implemented in Gkeyll. Novel boundary conditions on the fluids allow the sheath to form without specifying wall fluxes, so the fluids and fields adjust self-consistently at the wall. The work presented here demonstrates that the kinetic and fluid results are in agreement for the momentum flux, showing that in certain regimes, a multi-fluid model can be a useful approximation for simulating the plasma boundary. There are differences in the electrostatic potential between the fluid and kinetic results. Further, the direct solutions of the distribution function presented here highlight the non-Maxwellian distribution of electrons in the sheath, emphasizing the need for a kinetic model. The densities, velocities, and the potential show a good agreement between the kinetic and fluid results. However, kinetic physics is highlighted through higher moments such as parallel and perpendicular temperatures which provide significant differences from the fluid results in which the temperature is assumed to be isotropic. Besides decompression cooling, the heat flux

2. Kinetic theory for dilute cohesive granular gases with a square well potential.

PubMed

Takada, Satoshi; Saitoh, Kuniyasu; Hayakawa, Hisao

2016-07-01

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the validity of our theory by performing the direct simulation Monte Carlo.

3. Kinetics of alcohol fermentations carried out in rotating biological surface reactors

SciTech Connect

Converti, A.; Del Borghi, M.; Zilli, M.; Ferraiolo, G.

1987-01-01

This article aims at deriving kinetic models for the RBS reactor operating with and without cell porous support. Since derivation of the kinetic equations from the Monod model is very complex, an empirical derivation from experimental data of continuous alcohol fermentations is used in this work. 11 references.

4. A KINETIC MODEL FOR CELL DENSITY DEPENDENT BACTERIAL TRANSPORT IN POROUS MEDIA

EPA Science Inventory

A kinetic transport model with the ability to account for variations in cell density of the aqueous and solid phases was developed for bacteria in porous media. Sorption kinetics in the advective-dispersive-sorptive equation was described by assuming that adsorption was proportio...

5. Derivation of the Freundlich Adsorption Isotherm from Kinetics

ERIC Educational Resources Information Center

Skopp, Joseph

2009-01-01

The Freundlich adsorption isotherm is a useful description of adsorption phenomena. It is frequently presented as an empirical equation with little theoretical basis. In fact, a variety of derivations exist. Here a new derivation is presented using the concepts of fractal reaction kinetics. This derivation provides an alternative basis for…

6. Reexamining Michaelis-Menten Enzyme Kinetics for Xanthine Oxidase

ERIC Educational Resources Information Center

Bassingthwaighte, James B.; Chinn, Tamara M.

2013-01-01

Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions…

7. Kinetic approach to the cluster liquid-gas transition

SciTech Connect

Calvo, F.

2005-04-01

Unimolecular rate theories and equilibrium models of cluster dissociation are reconciled through a kinetic Monte Carlo approach. Assuming that fragmentation occurs sequentially, we calculate the time-dependent boiling temperature of slowly heated, free atomic clusters. Our approach is supported by molecular dynamics simulations of clusters made of sodium atoms or C{sub 60} molecules, as well as simplified rate equations.

8. Equilibrium Binding and Steady-State Enzyme Kinetics.

ERIC Educational Resources Information Center

Dunford, H. Brian

1984-01-01

Points out that equilibrium binding and steady-state enzyme kinetics have a great deal in common and that related equations and error analysis can be cast in identical forms. Emphasizes that if one type of problem solution is taught, the other is also taught. Various methods of data analysis are evaluated. (JM)

9. Renormalizing the Kinetic Energy Operator in Elementary Quantum Mechanics

ERIC Educational Resources Information Center

Coutinho, F. A. B.; Amaku, M.

2009-01-01

In this paper, we consider solutions to the three-dimensional Schrodinger equation of the form [psi](r) = u(r)/r, where u(0) [is not equal to] 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly…

10. Thermoluminescence kinetics of pyrite (FeS sub 2 )

SciTech Connect

Silverman, A.N; Levy, P.W.; Kierstead, J.A.

1990-01-01

Thermoluminescence of pyrite (FeS{sub 2}) has been investigated to study the kinetics of single peak glow curves. The material used normally exhibits one large and four small peaks. However a glow curve can be obtained with only the large single peak that is suitable for testing thermoluminescence kinetics. Glow curves from aliquots of a single natural pyrite crystal studied in detail contain two low intensity thermoluminescence (TL) peaks at {approx}90{degree} and {approx}250{degree}C, and two chemiluminescence (CL) peaks at {approx}350{degree} and {approx}430{degree}C. The CL peaks are largely removable by initially heating the sample chamber under vacuum, pumping through liquid nitrogen traps, and recording glow curves immediately after helium is introduced, procedures which reduce system contaminants that react with pyrite. The shape, the variation of the temperature of the peak maximum (T{sub max}) with dose, and the retrapping to recombination cross section ratio {sigma} of the large 250{degree}C peak are better described by the general one trap (GOT) kinetic equation, the basic equation from which the 1st and 2nd order kinetic equations are obtained as special cases (see text), than by the 1st and 2nd order equations. 12 refs., 7 figs.

11. Alternative Analysis of the Michaelis-Menten Equations

ERIC Educational Resources Information Center

2011-01-01

Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…

12. Numerical Solutions of the Complete Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Robinson, David F.; Hassan, H. A.

1997-01-01

This report details the development of a new two-equation turbulence closure model based on the exact turbulent kinetic energy k and the variance of vorticity, zeta. The model, which is applicable to three dimensional flowfields, employs one set of model constants and does not use damping or wall functions, or geometric factors.

13. Kinetic study and mechanism of Niclosamide degradation

Zaazaa, Hala E.; Abdelrahman, Maha M.; Ali, Nouruddin W.; Magdy, Maimana A.; Abdelkawy, M.

2014-11-01

A spectrophotometric kinetic study of Niclosamide alkaline degradation as a function of drug concentration, alkaline concentration and temperature has been established utilizing double divisor-ratio spectra spectrophotometric method. The developed method allowed determination of Niclosamide in presence of its alkaline degradation products; namely; 2-chloro-4-nitro aniline (DEG I) and 5-chloro salicylic acid (DEG II) with characterization of its degradation mechanism. It was found that degradation kinetic of Niclosamide followed pseudo-first order under the established experimental conditions with a degradation rate constant (k) of 0.0829 mol/h and half life (t1/2) of 8.35 h. The overall degradation rate constant as a function of the temperature under the given conditions obeyed Arrhenius equation where the activation energy was calculated to be 3.41 kcal/mol.

14. Processes of aggression described by kinetic method

SciTech Connect

Aristov, V. V.; Ilyin, O.

2014-12-09

In the last 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 USSR based on the kinetic theory. We model this process with the Cauchy boundary problem for the two-element kinetic equations with spatial initial conditions. The solution of the problem is given in the form of traveling wave. The propagation velocity of a frontline 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 frontline velocities are complied with the historical data.

15. Sigmoid kinetics of protein crystal nucleation

Nanev, Christo N.; Tonchev, Vesselin D.

2015-10-01

A non-linear differential equation expressing the new phase nucleation rate in the different steps of the process (non-stationary and stationary nucleation and in the plateau region) is derived from basic principles of the nucleation theory. It is shown that one and the same sigmoid (logistic) function describes both nucleation scenarios: the one according to the classical theory, and the other according to the modern two-stage mechanism of protein crystal formation. Comparison to experimental data on both insulin crystal nucleation kinetics and on bovine β-lactoglobulin crystallization indicates a good agreement with the sigmoidal prediction. Experimental data for electrochemical nucleation and glass crystallization obey the same sigmoid time dependence, and suggest universality of this nucleation kinetics law.

16. On the kinetic foundations of Kaluza's magnetohydrodynamics

Sandoval-Villalbazo, Alfredo; Sagaceta-Mejía, Alma R.; García-Perciante, Ana L.

2015-06-01

Recent work has shown the existence of a relativistic effect present in a single component non-equilibrium fluid, corresponding to a heat flux due to an electric field [J. Non-Equilib. Thermodyn. 38 (2013), 141-151]. The treatment in that work was limited to a four-dimensional Minkowski space-time in which the Boltzmann equation was treated in a special relativistic approach. The more complete framework of general relativity can be introduced to kinetic theory in order to describe transport processes associated to electromagnetic fields. In this context, the original Kaluza's formalism is a promising approach [Sitz. Ber. Preuss. Akad. Wiss. (1921), 966-972; Gen. Rel. Grav. 39 (2007), 1287-1296; Phys. Plasmas 7 (2000), 4823-4830]. The present work contains a kinetic theory basis for Kaluza's magnetohydrodynamics and gives a novel description for the establishment of thermodynamic forces beyond the special relativistic description.

17. Positron kinetics in an idealized PET environment

Robson, R. E.; Brunger, M. J.; Buckman, S. J.; Garcia, G.; Petrović, Z. Lj.; White, R. D.

2015-08-01

The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the ‘gas-phase’ assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.

18. Kinetic study and mechanism of Niclosamide degradation.

PubMed

Zaazaa, Hala E; Abdelrahman, Maha M; Ali, Nouruddin W; Magdy, Maimana A; Abdelkawy, M

2014-11-11

A spectrophotometric kinetic study of Niclosamide alkaline degradation as a function of drug concentration, alkaline concentration and temperature has been established utilizing double divisor-ratio spectra spectrophotometric method. The developed method allowed determination of Niclosamide in presence of its alkaline degradation products; namely; 2-chloro-4-nitro aniline (DEG I) and 5-chloro salicylic acid (DEG II) with characterization of its degradation mechanism. It was found that degradation kinetic of Niclosamide followed pseudo-first order under the established experimental conditions with a degradation rate constant (k) of 0.0829 mol/h and half life (t1/2) of 8.35 h. The overall degradation rate constant as a function of the temperature under the given conditions obeyed Arrhenius equation where the activation energy was calculated to be 3.41 kcal/mol.

19. Processes of aggression described by kinetic method

Aristov, V. V.; Ilyin, O.

2014-12-01

In the last 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 USSR based on the kinetic theory. We model this process with the Cauchy boundary problem for the two-element kinetic equations with spatial initial conditions. The solution of the problem is given in the form of traveling wave. The propagation velocity of a frontline 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 frontline velocities are complied with the historical data.

20. Kinetic Models with Randomly Perturbed Binary Collisions

Bassetti, Federico; Ladelli, Lucia; Toscani, Giuseppe

2011-02-01

We introduce a class of Kac-like kinetic equations on the real line, with general random collisional rules which, in some special cases, identify models for granular gases with a background heat bath (Carrillo et al. in Discrete Contin. Dyn. Syst. 24(1):59-81, 2009), and models for wealth redistribution in an agent-based market (Bisi et al. in Commun. Math. Sci. 7:901-916, 2009). Conditions on these collisional rules which guarantee both the existence and uniqueness of equilibrium profiles and their main properties are found. The characterization of these stationary states is of independent interest, since we show that they are stationary solutions of different evolution problems, both in the kinetic theory of rarefied gases (Cercignani et al. in J. Stat. Phys. 105:337-352, 2001; Villani in J. Stat. Phys. 124:781-822, 2006) and in the econophysical context (Bisi et al. in Commun. Math. Sci. 7:901-916, 2009).

1. Crystallization kinetics of citric acid anhydrate

Nemdili, L.; Koutchoukali, O.; Bouhelassa, M.; Seidel, J.; Mameri, F.; Ulrich, J.

2016-10-01

The solubility curve, metastable zone width (MSZW) and Crystallization kinetics (nucleation and growth) were measured and estimated during batch crystallization of citric acid anhydrate (CAA). The solubility of citric acid in pure water was measured over the temperature range from 15 to 60 °C using a refractometer. The experimental data were correlated by the modified Apelblat equation. The MSZW was determined under four cooling rates for different citric acid concentrations by means of an ultrasonic technique. The primary nucleation kinetics of CAA was calculated based on these data and the polythermal method of Nyvlt. It was found that the MSZW obtained is in good agreement with literature. Crystal growth rates were calculated by two methods. The first one used seeded isothermal growth experiments (desupersaturation curve) and the derivatives method of Garside. The second method used the measurement of the dimension change of a single crystal in a microscopic cell at different supersaturation levels.

2. Purfication kinetics of beryllium during vacuum induction melting

NASA Technical Reports Server (NTRS)

Mukherjee, J. L.; Gupta, K. P.; Li, C. H.

1972-01-01

The kinetics of evaporation in binary alloys were quantitatively treated. The formalism so developed works well for several systems studied. The kinetics of purification of beryllium was studied through evaporation data actually acquired during vacuum induction melting. Normal evaporation equations are shown to be generally valid and useful for understanding the kinetics of beryllium purification. The normal evaporation analysis has been extended to cover cases of limited liquid diffusion. It was shown that under steady-state evaporation, the solute concentration near the surface may be up to six orders of magnitude different from the bulk concentration. Corrections for limited liquid diffusion are definitely needed for the highly evaporative solute elements, such as Zn, Mg, and Na, for which the computed evaporation times are improved by five orders of magnitude. The commonly observed logarithmic relation between evaporation time and final concentration further supports the validity of the normal evaporation equations.

3. Kinetic theory and long range correlations in moderately dense gases

SciTech Connect

Petrosky, T.; Prigogine, I.

1997-01-01

The complex spectral representation of the Liouville operator is applied to moderately dense gases interacting through hard-core potentials in arbitrary d-dimensional spaces. It is shown that Markovian kinetic equations exist for all d. This provides an answer to the long standing question do kinetic equations exist in two dimensional systems. The non-Markovian effects, such as the long-time tails for arbitrary n-mode coupling, are estimated by superposition of the Markovian evolutions in each subspace as introduced in our spectral decomposition. The long-time tail effects invalidate the traditional kinetic theory based on a truncation of BBGKY hierarchy for d < 4, as well as the Green-Kubo formalism, as there appear contributions of order t{sup -1}, t{sup -{1/2}},... coming from multiple mode-mode couplings even for d = 3.

4. Simulations of plasma sheaths using continuum kinetic models

Srinivasan, Bhuvana; Hakim, Ammar

2015-11-01

Understanding plasma sheath physics is important for the performance of devices such as Hall thrusters due to the effect of energetic particles on electrode erosion. Plasma sheath physics is studied using kinetic and multi-fluid models with relevance to secondary electron emissions and plasma-surface interactions. Continuum kinetic models are developed to directly solve the Vlasov-Poisson equation using the discontinuous Galerkin method for each of the ion and electron species. A steady-state sheath is simulated by including a simple model for a neutral fluid. Multi-fluid simulations for the plasma sheath are also performed using the discontinuous Galerkin method to solve a complete set of fluid equations for each of the ion and electron species. The kinetic plasma sheath is compared to a multi-fluid plasma sheath. Supported by Air Force Office of Scientific Research.

5. Kinetics of the synthesis of dimethylsulphide from methanethiol

SciTech Connect

Mashkin, V.Yu.; Grunval`d, V.R.; Borodin, B.P.

1993-12-31

Using the gradient-free method in the presence of an alumina catalyst, we have studied the kinetics of disproportionation of methanethiol to dimethylsulphide and HS and the reaction of methanethiol with methanol at 320-420{degrees}C with initial concentrations of the reactants of 0.5-12 mmole/1 and a conversion of 10-65%. The kinetic orders of the reactions have been established from single-parameter relationships. The mechanism of formation of dimethylsulphide and dimethyl ether has been proposed, according to which the reaction proceeds via stages of dissociative chemisorption of the reactants, leading to surface methoxylation and subsequent reaction of the CH{sub 3}O groups with the methanethiol associatively adsorbed on the basic centres. Kinetic equations have been obtained which describe satisfactorily the process on the heterogeneous surface of the catalyst, and parameters of the model have been found. The equations are consistent with the postulated mechanism of the reaction.

6. Uniqueness of Maxwell's Equations.

ERIC Educational Resources Information Center

Cohn, Jack

1978-01-01

Shows that, as a consequence of two feasible assumptions and when due attention is given to the definition of charge and the fields E and B, the lowest-order equations that these two fields must satisfy are Maxwell's equations. (Author/GA)

7. Linear Equations: Equivalence = Success

ERIC Educational Resources Information Center

Baratta, Wendy

2011-01-01

The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…

8. Reduced Braginskii equations

SciTech Connect

Yagi, M.; Horton, W. )

1994-07-01

A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite [beta] that the perpendicular component of Ohm's law be solved to ensure [del][center dot][bold j]=0 for energy conservation.

9. Functional Cantor equation

Shabat, A. B.

2016-12-01

We consider the class of entire functions of exponential type in relation to the scattering theory for the Schrödinger equation with a finite potential that is a finite Borel measure. These functions have a special self-similarity and satisfy q-difference functional equations. We study their asymptotic behavior and the distribution of zeros.

10. A kinetic study of lipase-catalyzed reversible kinetic resolution involving verification at miniplant-scale.

PubMed

Berendsen, W R; Gendrot, G; Freund, A; Reuss, M

2006-12-05

Lipase-catalyzed kinetic resolution of racemates is a popular method for synthesis of chiral synthons. Most of these resolutions are reversible equilibrium limited reactions. For the first time, an extensive kinetic model is proposed for kinetic resolution reactions, which takes into account the full reversibility of the reaction, substrate inhibition by an acyl donor and an acyl acceptor as well as alternative substrate inhibition by each enantiomer. For this purpose, the reversible enantioselective transesterification of (R/S)-1-methoxy-2-propanol with ethyl acetate catalyzed by Candida antarctica lipase B (CAL-B) is investigated. The detailed model presented here is valid for a wide range of substrate and product concentrations. Following model discrimination and the application of Haldane equations to reduce the degree of freedom in parameter estimation, the 11 free parameters are successfully identified. All parameters are fitted to the complete data set simultaneously. Six types of independent initial rate studies provide a solid data basis for the model. The effect of changes in substrate and product concentration on reaction kinetics is discussed. The developed model is used for simulations to study the behavior of reaction kinetics in a fixed bed reactor. The typical plot of enantiomeric excess versus conversion of substrate and product is evaluated at various initial substrate mixtures. The model is validated by comparison with experimental results obtained with a fixed bed reactor, which is part of a fully automated state-of-the-art miniplant.

11. Multiple alternative substrate kinetics.

PubMed

Anderson, Vernon E

2015-11-01

The specificity of enzymes for their respective substrates has been a focal point of enzyme kinetics since the initial characterization of metabolic chemistry. Various processes to quantify an enzyme's specificity using kinetics have been utilized over the decades. Fersht's definition of the ratio kcat/Km for two different substrates as the "specificity constant" (ref [7]), based on the premise that the important specificity existed when the substrates were competing in the same reaction, has become a consensus standard for enzymes obeying Michaelis-Menten kinetics. The expansion of the theory for the determination of the relative specificity constants for a very large number of competing substrates, e.g. those present in a combinatorial library, in a single reaction mixture has been developed in this contribution. The ratio of kcat/Km for isotopologs has also become a standard in mechanistic enzymology where kinetic isotope effects have been measured by the development of internal competition experiments with extreme precision. This contribution extends the theory of kinetic isotope effects to internal competition between three isotopologs present at non-tracer concentrations in the same reaction mix. This article is part of a special issue titled: Enzyme Transition States from Theory and Experiment.

12. Theory of Stochastic Schrödinger Equation in Complex Vector Space

Muralidhar, Kundeti

2017-03-01

A generalized Schrödinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained by considering the internal complex structure of the particle which is a consequence of stochastic average of particle oscillations in the zeropoint field. Hence, the generalised Schrödinger equation may be called stochastic Schrödinger equation. It is found that the second order correction terms are similar to corresponding relativistic corrections. When higher order correction terms are neglected, the stochastic Schrödinger equation reduces to normal Schrödinger equation. It is found that the Schrödinger equation contains an internal structure in disguise and that can be revealed in the form of internal kinetic energy. The internal kinetic energy is found to be equal to the quantum potential obtained in the Madelung fluid theory or Bohm statistical theory. In the rest frame of the particle, the stochastic Schrödinger equation reduces to a Dirac type equation and its Lorentz boost gives the Dirac equation. Finally, the relativistic Klein-Gordon equation is derived by squaring the stochastic Schrödinger equation. The theory elucidates a logical understanding of classical approach to quantum mechanical foundations.

13. Relativistic Chiral Kinetic Theory

Stephanov, Mikhail

2016-12-01

This very brief review of the recent progress in chiral kinetic theory is based on the results of Refs. [J.-Y. Chen, D. T. Son, M. A. Stephanov, H.-U. Yee, Y. Yin, Lorentz Invariance in Chiral Kinetic Theory, Phys. Rev. Lett. 113 (18) (2014) 182302. doi:10.1103/PhysRevLett.113.182302; J.-Y. Chen, D. T. Son, M. A. Stephanov, Collisions in Chiral Kinetic Theory, Phys. Rev. Lett. 115 (2) (2015) 021601. doi: 10.1103/PhysRevLett.115.021601; M. A. Stephanov, H.-U. Yee, The no-drag frame for anomalous chiral fluid, Phys. Rev. Lett. 116 (12) (2016) 122302. doi: 10.1103/PhysRevLett.116.122302].

14. Estimation of kinetic parameters related to biochemical interactions between hydrogen peroxide and signal transduction proteins

Brito, Paula; Antunes, Fernando

2014-10-01

The lack of kinetic data concerning the biological effects of reactive oxygen species is slowing down the development of the field of redox signaling. Herein, we deduced and applied equations to estimate kinetic parameters from typical redox signaling experiments. H2O2-sensing mediated by the oxidation of a protein target and the switch-off of this sensor, by being converted back to its reduced form, are the two processes for which kinetic parameters are determined. The experimental data required to apply the equations deduced is the fraction of the H2O2 sensor protein in the reduced or in the oxidized state measured in intact cells or living tissues after exposure to either endogenous or added H2O2. Either non-linear fittings that do not need transformation of the experimental data or linearized plots in which deviations from the equations are easily observed can be used. The equations were shown to be valid by fitting to them virtual time courses simulated with a kinetic model. The good agreement between the kinetic parameters estimated in these fittings and those used to simulate the virtual time courses supported the accuracy of the kinetic equations deduced. Finally, equations were successfully tested with real data taken from published experiments that describe redox signaling mediated by the oxidation of two protein tyrosine phosphatases, PTP1B and SHP-2, which are two of the few H2O2-sensing proteins with known kinetic parameters. Whereas for PTP1B estimated kinetic parameters fitted in general the present knowledge, for SHP-2 results obtained suggest that reactivity towards H2O2 as well as the rate of SHP-2 regeneration back to its reduced form are higher than previously thought. In conclusion, valuable quantitative kinetic data can be estimated from typical redox signaling experiments, thus improving our understanding about the complex processes that underline the interplay between oxidative stress and redox signaling responses.

15. Reaction kinetic analysis of reactor surveillance data

Yoshiie, T.; Kinomura, A.; Nagai, Y.

2017-02-01

In the reactor pressure vessel surveillance data of a European-type pressurized water reactor (low-Cu steel), it was found that the concentration of matrix defects was very high, and a large number of precipitates existed. In this study, defect structure evolution obtained from surveillance data was simulated by reaction kinetic analysis using 15 rate equations. The saturation of precipitation and the growth of loops were simulated, but it was not possible to explain the increase in DBTT on the basis of the defect structures. The sub-grain boundary segregation of solutes was discussed for the origin of the DBTT increase.

16. General properties and kinetics of spontaneous baryogenesis

Arbuzova, E. V.; Dolgov, A. D.; Novikov, V. A.

2016-12-01

General features of spontaneous baryogenesis are studied. The relation between the time derivative of the (pseudo) Goldstone field and the baryonic chemical potential is revisited. It is shown that this relation essentially depends upon the representation chosen for the fermionic fields with nonzero baryonic number (quarks). The calculations of the cosmological baryon asymmetry are based on the kinetic equation generalized to the case of nonstationary background. The effects of the finite interval of the integration over time are also taken into consideration. All these effects combined lead to a noticeable deviation of the magnitude of the baryon asymmetry from the canonical results.

17. Wealth redistribution in conservative linear kinetic models

Toscani, G.

2009-10-01

We introduce and discuss kinetic models for wealth distribution which include both taxation and uniform redistribution. The evolution of the continuous density of wealth obeys a linear Boltzmann equation where the background density represents the action of an external subject on the taxation mechanism. The case in which the mean wealth is conserved is analyzed in full details, by recovering the analytical form of the steady states. These states are probability distributions of convergent random series of a special structure, called perpetuities. Among others, Gibbs distribution appears as steady state in case of total taxation and uniform redistribution.

18. Kinetic treatment of radiation reaction effects

Noble, Adam; Gratus, Jonathan; Burton, David; Ersfeld, Bernhard; Islam, M. Ranaul; Kravets, Yevgen; Raj, Gaurav; Jaroszynski, Dino

2011-05-01

Modern accelerators and light sources subject bunches of charged particles to quasiperiodic motion in extremely high electric fields, under which they may emit a substantial fraction of their energy. To properly describe the motion of these particle bunches, we require a kinetic theory of radiation reaction. We develop such a theory based on the notorious Lorentz-Dirac equation, and explore how it reduces to the usual Vlasov theory in the appropriate limit. As a simple illustration of the theory, we explore the radiative damping of Langmuir waves.

19. The Effective Equation Method

Kuksin, Sergei; Maiocchi, Alberto

In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.

20. Kinetic theory based new upwind methods for inviscid compressible flows

NASA Technical Reports Server (NTRS)

Deshpande, S. M.

1986-01-01

Two new upwind methods called the Kinetic Numerical Method (KNM) and the Kinetic Flux Vector Splitting (KFVS) method for the solution of the Euler equations have been presented. Both of these methods can be regarded as some suitable moments of an upwind scheme for the solution of the Boltzmann equation provided the distribution function is Maxwellian. This moment-method strategy leads to a unification of the Riemann approach and the pseudo-particle approach used earlier in the development of upwind methods for the Euler equations. A very important aspect of the moment-method strategy is that the new upwind methods satisfy the entropy condition because of the Boltzmann H-Theorem and suggest a possible way of extending the Total Variation Diminishing (TVD) principle within the framework of the H-Theorem. The ability of these methods in obtaining accurate wiggle-free solution is demonstrated by applying them to two test problems.

1. Michaelis-Menten kinetics under non-isothermal conditions.

PubMed

Lervik, Anders; Kjelstrup, Signe; Qian, Hong

2015-01-14

We extend the celebrated Michaelis-Menten kinetics description of an enzymatic reaction taking into consideration the presence of a thermal driving force. A coupling of chemical and thermal driving forces is expected from the principle of non-equilibrium thermodynamics, and specifically we obtain an additional term to the classical Michaelis-Menten kinetic equation, which describes the coupling in terms of a single parameter. A companion equation for the heat flux is also derived, which actually can exist even in the absence of a temperature difference. Being thermodynamic in nature, this result is general and independent of the detailed mechanism of the coupling. Conditions for the experimental verification of the new equation are discussed.

2. Kinetics and thermodynamics of first-order Markov chain copolymerization

Gaspard, P.; Andrieux, D.

2014-07-01

We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer.

3. Kinetic plots for gas chromatography: theory and experimental verification.

PubMed

Jespers, Sander; Roeleveld, Kevin; Lynen, Frederic; Broeckhoven, Ken; Desmet, Gert

2015-03-20

Mathematical kinetic plot expressions have been established for the correct extrapolation of the kinetic performance measured in a thin-film capillary GC column with fixed length into the performance that can be expected in a longer column used at the same outlet velocity but at either the maximal inlet pressure or at the optimal inlet pressure, i.e., the one leading to an operation at the kinetic performance limit of the given capillary size. To determine this optimal pressure, analytical solutions have been established for the three roots of the corresponding cubic equation. Experimental confirmation of the kinetic plot extrapolations in GC has been obtained measuring the efficiency of a simple test mixture on 30, 60, 90 and 120m long (coupled) columns.

4. Obtaining and estimating kinetic parameters from the literature.

PubMed

Neves, Susana R

2011-09-13

This Teaching Resource provides lecture notes, slides, and a student assignment for a lecture on strategies for the development of mathematical models. Many biological processes can be represented mathematically as systems of ordinary differential equations (ODEs). Simulations with these mathematical models can provide mechanistic insight into the underlying biology of the system. A prerequisite for running simulations, however, is the identification of kinetic parameters that correspond closely with the biological reality. This lecture presents an overview of the steps required for the development of kinetic ODE models and describes experimental methods that can yield kinetic parameters and concentrations of reactants, which are essential for the development of kinetic models. Strategies are provided to extract necessary parameters from published data. The homework assignment requires students to find parameters appropriate for a well-studied biological regulatory system, convert these parameters into appropriate units, and interpret how different values of these parameters may lead to different biological behaviors.

5. Analysis of Transition-Sensitized Turbulent Transport Equations

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Thacker, William D.; Gatski, Thomas B.; Grosch, Chester E,

2005-01-01

The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced cross the boundary layer by the solid boundary. The dominating dynamics in the disturbance kinetic energy and dissipation rate equations are described. These results are then used to formulate transition-sensitized turbulent transport equations, which are solved in a two-step process and applied to zero-pressure-gradient flow over a flat plate. Computed results are in good agreement with experimental data.

6. Kinetic theory of oxygen isotopic exchange between minerals and water

USGS Publications Warehouse

Criss, R.E.; Gregory, R.T.; Taylor, H.P.

1987-01-01

Kinetic and mass conservation equations are used to describe oxygen isotopic exchange between minerals and water in "closed" and open hydrothermal systems. In cases where n coexisting mineral phases having different reaction rates are present, the exchange process is described by a system of n + 1 simultaneous differential equations consisting of n pseudo first-order rate equations and a conservation of mass equation. The simultaneous solutions to these equations generate curved exchange trajectories on ??-?? plots. Families of such trajectories generated under conditions allowing for different fluid mole fractions, different fluid isotopic compositions, or different fluid flow rates are connected by positive-sloped isochronous lines. These isochrons reproduce the effects observed in hydrothermally exchanged mineral pairs including 1) steep positive slopes, 2) common reversals in the measured fractionation factors (??), and 3) measured fractionations that are highly variable over short distances where no thermal gradient can be geologically demonstrated. ?? 1987.

Hassan, N. J.; Pourdarvish, A.; Sadeghi, J.; Olaomi, J. O.

2017-04-01

In this paper, we derive the non-Markovian stochastic equation of motion (SEM) and master equations (MEs) for the open quantum system by using the non-Markovian stochastic Schrödinger equations (SSEs) for the quadrature unraveling in linear and nonlinear cases. The SSEs for quadrature unraveling arise as a special case of a quantum system. Also we derive the Markovian SEM and ME by using linear and nonlinear Itô SSEs for the measurement probabilities. In linear non-Markovian case, we calculate the convolutionless linear quadrature non-Markovian SEM and ME. We take advantage from example and show that corresponding theory.

8. Nonlinear ordinary difference equations

NASA Technical Reports Server (NTRS)

Caughey, T. K.

1979-01-01

Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

9. Numerical solutions of the complete Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Hassan, H. A.

1986-01-01

Using ideas from the kinetic theory, the Navier-Stokes equations are modified in such a way that they can be cast as a set of first order hyperbolic equations. This is achieved by incorporating time dependent terms into the definition of the stress tensor and the heat flux vectors. The boundary conditions are then determined from the theory of characteristics. Because the resulting equations reduce to the traditional Navier-Stokes equations when the steady state is reached, the present approach provides a straightforward scheme for the determination of inflow and outflow boundary conditions. The method is validated by comparing its predictions with known exact solutions of the steady Navier-Stokes equations.

10. Modeling capsid kinetics assembly from the steady state distribution of multi-sizes aggregates

Hozé, Nathanaël; Holcman, David

2014-01-01

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.

11. Kinetic analysis of a Michaelis-Menten mechanism in which the enzyme is unstable.

PubMed Central

Garrido-del Solo, C; García-Cánovas, F; Havsteen, B H; Varón-Castellanos, R

1993-01-01

A kinetic analysis of the Michaelis-Menten mechanism is made for the cases in which the free enzyme, or the enzyme-substrate complex, or both, are unstable, either spontaneously or as a result of the addition of a reagent. The explicit time-course equations of all of the species involved has been derived under conditions of limiting enzyme concentration. The validity of these equations has been checked by using numerical simulations. An experimental design and a kinetic data analysis allowing the evaluation of the parameters and kinetic constants are recommended. PMID:8373361

12. Submesoscale baroclinic instability and the Balance Equations

Grooms, Ian

2015-11-01

Ocean submesoscale baroclinic instability is studied in the framework of the Balance Equations. The Balance Equations are an intermediate model that includes balanced ageostrophic effects with higher accuracy than the quasigeostrophic approximation, but rules out unbalanced wave motions; as such, they are particularly suited to the study of baroclinic instability in submesoscale ocean dynamics. The linear baroclinic instability problem is developed in generality and then specialized to the case of constant vertical shear. The primary finding is that at low Richardson numbers the growth rate of some instability modes is increased compared to larger-scale quasigeostrophic dynamics, and that the increase can be attributed to both ageostrophic baroclinic production and shear production of perturbation energy. This suggests that the nonlinear development of submesoscale baroclinic instability will proceed more vigorously than mesoscale/quasigeostrophic, and may include a downscale/forward transfer of kinetic energy.

13. Ultrarelativistic decoupling transformation for generalized Dirac equations

Noble, J. H.; Jentschura, U. D.

2015-07-01

The Foldy-Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schrödinger-Pauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.

14. Kinetic tetrazolium microtiter assay

NASA Technical Reports Server (NTRS)

Pierson, Duane L. (Inventor); Stowe, Raymond P. (Inventor); Koeing, David W. (Inventor)

1992-01-01

A method for conducting an in vitro cell assay using a tetrazolium indicator is disclosed. The indicator includes a nonionic detergent which solubilizes a tetrazolium reduction product in vitro and has low toxicity for the cells. The incubation of test cells in the presence of zolium bromide and octoxynol (TRITON X-100) permits kinetics of the cell metabolism to be determined.

15. Applications of kinetic theory

SciTech Connect

Gidaspow, D.

1992-01-01

The overall objective of this investigation is to develop experimentally verified models for circulating fluidized bed (CFB) combustors. This report presents the author's derivation of analytical solutions useful in understanding the operation of a CFB. The report is in a form of a chapter that reviews the kinetic theory applications.

16. Kinetics and Catalysis Demonstrations.

ERIC Educational Resources Information Center

Falconer, John L.; Britten, Jerald A.

1984-01-01

Eleven videotaped kinetics and catalysis demonstrations are described. Demonstrations include the clock reaction, oscillating reaction, hydrogen oxidation in air, hydrogen-oxygen explosion, acid-base properties of solids, high- and low-temperature zeolite reactivity, copper catalysis of ammonia oxidation and sodium peroxide decomposition, ammonia…

17. Oxidative desulfurization: kinetic modelling.

PubMed

Dhir, S; Uppaluri, R; Purkait, M K

2009-01-30

Increasing environmental legislations coupled with enhanced production of petroleum products demand, the deployment of novel technologies to remove organic sulfur efficiently. This work represents the kinetic modeling of ODS using H(2)O(2) over tungsten-containing layered double hydroxide (LDH) using the experimental data provided by Hulea et al. [V. Hulea, A.L. Maciuca, F. Fajula, E. Dumitriu, Catalytic oxidation of thiophenes and thioethers with hydrogen peroxide in the presence of W-containing layered double hydroxides, Appl. Catal. A: Gen. 313 (2) (2006) 200-207]. The kinetic modeling approach in this work initially targets the scope of the generation of a superstructure of micro-kinetic reaction schemes and models assuming Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) mechanisms. Subsequently, the screening and selection of above models is initially based on profile-based elimination of incompetent schemes followed by non-linear regression search performed using the Levenberg-Marquardt algorithm (LMA) for the chosen models. The above analysis inferred that Eley-Rideal mechanism describes the kinetic behavior of ODS process using tungsten-containing LDH, with adsorption of reactant and intermediate product only taking place on the catalyst surface. Finally, an economic index is presented that scopes the economic aspects of the novel catalytic technology with the parameters obtained during regression analysis to conclude that the cost factor for the catalyst is 0.0062-0.04759 US \$ per barrel.

18. Regularized Structural Equation Modeling.

PubMed

Jacobucci, Ross; Grimm, Kevin J; McArdle, John J

A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM's utility.

19. Equations For Rotary Transformers

NASA Technical Reports Server (NTRS)

Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.

1988-01-01

Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.

20. Solving Equations Today.

ERIC Educational Resources Information Center

Shumway, Richard J.

1989-01-01

Illustrated is the problem of solving equations and some different strategies students might employ when using available technology. Gives illustrations for: exact solutions, approximate solutions, and approximate solutions which are graphically generated. (RT)

1. Nonlinear differential equations

SciTech Connect

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

2. Discrete wave equation upscaling

Fichtner, Andreas; Hanasoge, Shravan M.

2017-01-01

We present homogenisation technique for the uniformly discretised wave equation, based on the derivation of an effective equation for the low-wavenumber component of the solution. The method produces a down-sampled, effective medium, thus making the solution of the effective equation less computationally expensive. Advantages of the method include its conceptual simplicity and ease of implementation, the applicability to any uniformly discretised wave equation in one, two or three dimensions, and the absence of any constraints on the medium properties. We illustrate our method with a numerical example of wave propagation through a one-dimensional multiscale medium, and demonstrate the accurate reproduction of the original wavefield for sufficiently low frequencies.

3. Invariance principle and model reduction for the Fokker-Planck equation

Karlin, I. V.

2016-11-01

The principle of dynamic invariance is applied to obtain closed moment equations from the Fokker-Planck kinetic equation. The analysis is carried out to explicit formulae for computation of the lowest eigenvalue and of the corresponding eigenfunction for arbitrary potentials. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

4. Kinetics of DNA tile dimerization.

PubMed

Jiang, Shuoxing; Yan, Hao; Liu, Yan

2014-06-24

Investigating how individual molecular components interact with one another within DNA nanoarchitectures, both in terms of their spatial and temporal interactions, is fundamentally important for a better understanding of their physical behaviors. This will provide researchers with valuable insight for designing more complex higher-order structures that can be assembled more efficiently. In this report, we examined several spatial factors that affect the kinetics of bivalent, double-helical (DH) tile dimerization, including the orientation and number of sticky ends (SEs), the flexibility of the double helical domains, and the size of the tiles. The rate constants we obtained confirm our hypothesis that increased nucleation opportunities and well-aligned SEs accelerate tile-tile dimerization. Increased flexibility in the tiles causes slower dimerization rates, an effect that can be reversed by introducing restrictions to the tile flexibility. The higher dimerization rates of more rigid tiles results from the opposing effects of higher activation energies and higher pre-exponential factors from the Arrhenius equation, where the pre-exponential factor dominates. We believe that the results presented here will assist in improved implementation of DNA tile based algorithmic self-assembly, DNA based molecular robotics, and other specific nucleic acid systems, and will provide guidance to design and assembly processes to improve overall yield and efficiency.

5. Kinetics of DNA Tile Dimerization

PubMed Central

2015-01-01

Investigating how individual molecular components interact with one another within DNA nanoarchitectures, both in terms of their spatial and temporal interactions, is fundamentally important for a better understanding of their physical behaviors. This will provide researchers with valuable insight for designing more complex higher-order structures that can be assembled more efficiently. In this report, we examined several spatial factors that affect the kinetics of bivalent, double-helical (DH) tile dimerization, including the orientation and number of sticky ends (SEs), the flexibility of the double helical domains, and the size of the tiles. The rate constants we obtained confirm our hypothesis that increased nucleation opportunities and well-aligned SEs accelerate tile–tile dimerization. Increased flexibility in the tiles causes slower dimerization rates, an effect that can be reversed by introducing restrictions to the tile flexibility. The higher dimerization rates of more rigid tiles results from the opposing effects of higher activation energies and higher pre-exponential factors from the Arrhenius equation, where the pre-exponential factor dominates. We believe that the results presented here will assist in improved implementation of DNA tile based algorithmic self-assembly, DNA based molecular robotics, and other specific nucleic acid systems, and will provide guidance to design and assembly processes to improve overall yield and efficiency. PMID:24794259

6. Relativistic Guiding Center Equations

SciTech Connect

White, R. B.; Gobbin, M.

2014-10-01

In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.

7. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

DOEpatents

Collier, D.M.; Meeks, L.A.; Palmer, J.P.

1960-05-10

A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

8. Silicon nitride equation of state

Brown, Robert C.; Swaminathan, Pazhayannur K.

2017-01-01

This report presents the development of a global, multi-phase equation of state (EOS) for the ceramic silicon nitride (Si3N4).1 Structural forms include amorphous silicon nitride normally used as a thin film and three crystalline polymorphs. Crystalline phases include hexagonal α-Si3N4, hexagonal β-Si3N4, and the cubic spinel c-Si3N4. Decomposition at about 1900 °C results in a liquid silicon phase and gas phase products such as molecular nitrogen, atomic nitrogen, and atomic silicon. The silicon nitride EOS was developed using EOSPro which is a new and extended version of the PANDA II code. Both codes are valuable tools and have been used successfully for a variety of material classes. Both PANDA II and EOSPro can generate a tabular EOS that can be used in conjunction with hydrocodes. The paper describes the development efforts for the component solid phases and presents results obtained using the EOSPro phase transition model to investigate the solid-solid phase transitions in relation to the available shock data that have indicated a complex and slow time dependent phase change to the c-Si3N4 phase. Furthermore, the EOSPro mixture model is used to develop a model for the decomposition products; however, the need for a kinetic approach is suggested to combine with the single component solid models to simulate and further investigate the global phase coexistences.

9. Kinetics of wealth and the Pareto law

Boghosian, Bruce M.

2014-04-01

An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy change due to interactions with other molecules. We pursue this analogy and derive a Boltzmann equation for the time evolution of the wealth distribution of a population of agents for the so-called Yard-Sale Model of wealth exchange. We examine the solutions to this equation by a combination of analytical and numerical methods and investigate its long-time limit. We study an important limit of this equation for small transaction sizes and derive a partial integrodifferential equation governing the evolution of the wealth distribution in a closed economy. We then describe how this model can be extended to include features such as inflation, production, and taxation. In particular, we show that the model with taxation exhibits the basic features of the Pareto law, namely, a lower cutoff to the wealth density at small values of wealth, and approximate power-law behavior at large values of wealth.

10. Kinetics of wealth and the Pareto law.

PubMed

Boghosian, Bruce M

2014-04-01

An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy change due to interactions with other molecules. We pursue this analogy and derive a Boltzmann equation for the time evolution of the wealth distribution of a population of agents for the so-called Yard-Sale Model of wealth exchange. We examine the solutions to this equation by a combination of analytical and numerical methods and investigate its long-time limit. We study an important limit of this equation for small transaction sizes and derive a partial integrodifferential equation governing the evolution of the wealth distribution in a closed economy. We then describe how this model can be extended to include features such as inflation, production, and taxation. In particular, we show that the model with taxation exhibits the basic features of the Pareto law, namely, a lower cutoff to the wealth density at small values of wealth, and approximate power-law behavior at large values of wealth.

11. Derivation of the equations of motion for complex structures by symbolic manipulation

NASA Technical Reports Server (NTRS)

Hale, A. L.; Meirovitch, L.

1978-01-01

This paper outlines a computer program especially tailored to the task of deriving explicit equations of motion for structures with point-connected substructures. The special purpose program is written in FORTRAN and is designed for performing the specific algebraic operations encountered in the derivation of explicit equations of motion. The derivation is by the Lagrangian approach. Using an orderly kinematical procedure and a discretization and/or truncation scheme, it is possible to write the kinetic and potential energy of each substructure in a compact vector-matrix form. Then, if each element of the matrices and vectors encountered in the kinetic and potential energy is a known algebraic expression, the computer program performs the necessary operations to evaluate the kinetic and potential energy of the system explicitly. Lagrange's equations for small motions about equilibrium can be deduced directly from the explicit form of the system kinetic and potential energy.

12. Exact and approximate solutions for the decades-old Michaelis-Menten equation: Progress-curve analysis through integrated rate equations.

PubMed

Goličnik, Marko

2011-01-01

The Michaelis-Menten rate equation can be found in most general biochemistry textbooks, where the time derivative of the substrate is a hyperbolic function of two kinetic parameters (the limiting rate V, and the Michaelis constant K(M) ) and the amount of substrate. However, fundamental concepts of enzyme kinetics can be difficult to understand fully, or can even be misunderstood, by students when based only on the differential form of the Michaelis-Menten equation, and the variety of methods available to calculate the kinetic constants from rate versus substrate concentration "textbook data." Consequently, enzyme kinetics can be confusing if an analytical solution of the Michaelis-Menten equation is not available. Therefore, the still rarely known exact solution to the Michaelis-Menten equation is presented here through the explicit closed-form equation in terms of the Lambert W(x) function. Unfortunately, as the W(x) is not available in standard curve-fitting computer programs, the practical use of this direct solution is limited for most life-science students. Thus, the purpose of this article is to provide analytical approximations to the equation for modeling Michaelis-Menten kinetics. The elementary and explicit nature of these approximations can provide students with direct and simple estimations of kinetic parameters from raw experimental time-course data. The Michaelis-Menten kinetics studied in the latter context can provide an ideal alternative to the 100-year-old problems of data transformation, graphical visualization, and data analysis of enzyme-catalyzed reactions. Hence, the content of the course presented here could gradually become an important component of the modern biochemistry curriculum in the 21st century.

13. Application of a hybrid kinetic-continuum solver to the near wall modelling

Rovenskaya, O.; Croce, G.

2014-11-01

A hybrid method dynamically coupling the direct numerical solution of the S-model kinetic equation and Navier-Stokes equations is applied to a numerical simulation of the flow through the channel of a finite length due to arbitrarily pressure ratios and for a wide range of Knudsen number. The decomposition of the physical domain into kinetic and hydrodynamic sub-domains is updated at each time step. The solution is advanced in time simultaneously in both kinetic and hydrodynamic domains: the coupling is achieved by matching half fluxes at the interface of the kinetic and Navier-Stokes domains, thus taking care of the conservation of momentum, energy and mass through the interface. Solver efficiency is increased via MPI (Message Passing Interface) parallelization. Accuracy and reliability of the method, for different decomposition criteria, are assessed via comparison with a pure kinetic solution.

14. Oxidation kinetics of ferrous sulfate over active carbon

SciTech Connect

Roennholm, M.R.; Waernaa, J.; Salmi, T.; Turunen, I.; Luoma, M.

1999-07-01

Catalyzed oxidation kinetics of dissolved Fe{sup 2+} ions to Fe{sup 3+} over active carbon in concentrated H{sub 2}SO{sub 4}-FeSO{sub 4} solutions was studied with isothermal and isobaric experiments carried out in a laboratory-scale pressurized autoclave. The experiments were performed at temperatures between 60 and 130 C, and the pressure of oxygen (O{sub 2}) was varied between 4 and 10 bar. The kinetic results revealed that the oxidation rate was enhanced by increasing the temperature and pressure and that the catalytic and noncatalytic oxidations proceed as parallel processes. A rate equation was obtained for the catalytic oxidation process, based on the assumption that the oxidation of Fe{sup 2+} with adsorbed oxygen is rate determining. The total oxidation rate was simulated by including a previously determined rate equation for the noncatalytic oxidation into the global model, from which the kinetic parameters of the catalytic oxidation rate were determined. A comparison of the model fit with the experimental data revealed that the proposed rate equation is applicable for the prediction of the Fe{sup 2+} oxidation kinetics in acidic ferrous sulfate solutions.

15. LLNL Chemical Kinetics Modeling Group

SciTech Connect

Pitz, W J; Westbrook, C K; Mehl, M; Herbinet, O; Curran, H J; Silke, E J

2008-09-24

The LLNL chemical kinetics modeling group has been responsible for much progress in the development of chemical kinetic models for practical fuels. The group began its work in the early 1970s, developing chemical kinetic models for methane, ethane, ethanol and halogenated inhibitors. Most recently, it has been developing chemical kinetic models for large n-alkanes, cycloalkanes, hexenes, and large methyl esters. These component models are needed to represent gasoline, diesel, jet, and oil-sand-derived fuels.

16. An Introductory Level Kinetics Investigation.

ERIC Educational Resources Information Center

McGarvey, J. E. B.; Knipe, A. C.

1980-01-01

Provides a list of the reactions commonly used for introductory kinetics studies. These reactions illustrate the kinetics concepts of rate law, rate constant, and reaction order. Describes a kinetic study of the hydrolysis of 3-bromo-3-phenylpropanoic acid which offers many educational advantages. (CS)

17. Nonequilibrium kinetic theory for trapped binary condensates

Edmonds, M. J.; Lee, K. L.; Proukakis, N. P.

2015-12-01

We derive a nonequilibrium finite-temperature kinetic theory for a binary mixture of two interacting atomic Bose-Einstein condensates and use it to explore the degree of hydrodynamicity attainable in realistic experimental geometries. Based on the standard separation-of-time-scales argument of kinetic theory, the dynamics of the condensates of the multicomponent system are shown to be described by dissipative Gross-Pitaevskii equations self-consistently coupled to corresponding quantum Boltzmann equations for the noncondensate atoms: On top of the usual mean-field contributions, our scheme identifies a total of eight distinct collisional processes, whose dynamical interplay is expected to be responsible for the system's equilibration. In order to provide their first characterization, we perform a detailed numerical analysis of the role of trap frequency and geometry on collisional rates for experimentally accessible mixtures of 87Rb-41K and 87Rb-85Rb , discussing the extent to which the system may approach the hydrodynamic regime with regard to some of those processes as a guide for future experimental investigations of ultracold Bose gas mixtures.

18. Quantum kinetic theories in degenerate plasmas

Brodin, Gert; Ekman, Robin; Zamanian, Jens

2017-01-01

In this review we give an overview of the recent work on quantum kinetic theories of plasmas. We focus, in particular, on the case where the electrons are fully degenerate. For such systems, perturbation methods using the distribution function can be problematic. Instead we present a model that considers the dynamics of the Fermi surface. The advantage of this model is that, even though the value of the distribution function can be greatly perturbed outside the equilibrium Fermi surface, deformation of the Fermi surface is small up to very large amplitudes. Next, we investigate the short-scale dynamics for which the Wigner-Moyal equation replaces the Vlasov equation. In particular, we study wave-particle interaction, and deduce that new types of wave damping can occur due to the simultaneous absorption (or emission) of multiple wave quanta. Finally, we consider exchange effects within a quantum kinetic formalism to find a model that is more accurate than those using exchange potentials from density functional theory. We deduce the exchange corrections to the dispersion relations for Langmuir and ion-acoustic waves. In comparison to results based on exchange potentials deduced from density functional theory we find that the latter models are reasonably accurate for Langmuir waves, but rather inaccurate for ion acoustic waves.

19. Ozone kinetics in low-pressure discharges

Guerra, Vasco; Marinov, Daniil; Guaitella, Olivier; Rousseau, Antoine

2012-10-01

Ozone kinetics is quite well established at atmospheric pressure, due to the importance of ozone in atmospheric chemistry and to the development of industrial ozone reactors. However, as the pressure is decreased and the dominant three-body reactions lose importance, the main mechanisms involved in the creation and destruction of ozone are still surrounded by important uncertainties. In this work we develop a self-consistent model for a pulsed discharge and its afterglow operating in a Pyrex reactor with inner radius 1 cm, at pressures in the range 1-5 Torr and discharge currents of 40-120 mA. The model couples the electron Boltzmann equation with a system of equations for the time evolution of the heavy particles. The calculations are compared with time-dependent measurements of ozone and atomic oxygen. Parametric studies are performed in order to clarify the role of vibrationally excited ozone in the overall kinetics and to establish the conditions where ozone production on the surface may become important. It is shown that vibrationally excited ozone does play a significant role, by increasing the time constants of ozone formation. Moreover, an upper limit for the ozone formation at the wall in these conditions is set at 10(-4).

20. [Kinetics of Cu crossing human erythrocyte membrane].

PubMed

Dun, Zhu Ci Ren

2014-12-01

This study was aimed to investigate various factors influencing the proceduction of Cu(II) crossing human erythrocyte membrane, including concentration of Cu²⁺, pH value of the medium, temperature and time of incubation, and to derive kinetic equation of Cu(II) crossing human erythrocyte membrane. Suspension red blood cells were incubated by Cu²⁺, then content of Cu²⁺ crossed human erythrocyte membrane was determined by atomic absorption spectrometry under various conditions after digestion. The results showed that content of Cu²⁺ crossed human erythrocyte membrane increased with the increase of extracellular Cu²⁺ and enhancement of incubation temperature, and the content of Cu²⁺ crossed human erythrocyte membrane showed a increasing tendency when pH reached to 6.2-7.4, and to maximum at pH 7.4, then gradually decreased at range of pH 7.4-9.2. It is concluded that the Cu²⁺ crossing human erythrocyte has been confirmed to be the first order kinetics characteristics within 120 min, and the linear equation is 10³ × Y = 0.0497t +6.5992.

1. The Bernoulli-Poiseuille Equation.

ERIC Educational Resources Information Center

Badeer, Henry S.; Synolakis, Costas E.

1989-01-01

Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)

2. Spatial equation for water waves

Dyachenko, A. I.; Zakharov, V. E.

2016-02-01

A compact spatial Hamiltonian equation for gravity waves on deep water has been derived. The equation is dynamical and can describe extreme waves. The equation for the envelope of a wave train has also been obtained.

3. Introducing Chemical Formulae and Equations.

ERIC Educational Resources Information Center

Dawson, Chris; Rowell, Jack

1979-01-01

Discusses when the writing of chemical formula and equations can be introduced in the school science curriculum. Also presents ways in which formulae and equations learning can be aided and some examples for balancing and interpreting equations. (HM)

4. On the balance equations for a dilute binary mixture in special relativity

SciTech Connect

Moratto, Valdemar; Garcia-Perciante, A. L.; Garcia-Colin, L. S.

2010-12-14

In this work we study the properties of a relativistic mixture of two non-reacting species in thermal local equilibrium. We use the full Boltzmann equation (BE) to find the general balance equations. Following conventional ideas in kinetic theory, we use the concept of chaotic velocity. This is a novel approach to the problem. The resulting equations will be the starting point of the calculation exhibiting the correct thermodynamic forces and the corresponding fluxes; these results will be published elsewhere.

5. Explosive attractor solutions to a universal cubic delay equation

Sanz-Orozco, David

2016-10-01

This presentation describes new explosive attractor solutions to the universal cubic delay equation found in both the fluid and (for a kinetic system) in the plasma literature. Our results will be explained in the notation of the plasma problem, where a cubic delay equation describes the evolution of a wave in a kinetic system, and is characterized by a control parameter ϕ (its value is determined by the linear properties of the kinetic response). The linear eigenvalues do not exist in absence of the kinetic response (with exceptions for ϕ = 0 or π) but with the kinetic contribution, marginally unstable modes emerge when the kinetic drive is at a critical level. The simulation of the temporal evolution reveals the development of an explosive mode, i.e. a mode growing without bound in a finite time. The two main features of the response are: (1) a well-known explosive envelope (t0 - t) - 5 / 2, with t0 the blow-up time of the amplitude; (2) a spectrum with ever-increasing oscillation frequencies that is critically-dependent upon the parameter ϕ. A code has been constructed that resolves these oscillations over many periods by calculating their Fourier transform with respect to the pseudo-time x = - ln (t0 - t) . In addition, our analytic modeling explains the results and quantitatively nearly replicates the attractor solutions found in the simulations. A physical result of these solutions is the development of frequency chirping of the observed wave. This effect continues beyond the applicability of the cubic delay equation, and thus the attractor solutions that we study represent precursors to long-lived phenomena that may be used in an experimental situation to understand the nature of a system's equilibrium. Dr. Herbert L. Berk.

6. 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.

7. Exact Vlasov Solutions of Kinetic Flux Ropes

Ng, C. S.

2014-12-01

Small-scale magnetic flux ropes have been observed to form within the diffusion region in three-dimensional (3D) kinetic simulations of magnetic reconnection. Such 3D structures and the 2D version of them (plasmoids, secondary islands) could have important dynamical effects on the reconnection physics itself. Small-scale flux ropes have also been observed within the interplanetary space. We have found exact time-steady solutions of kinetic flux ropes by generalizing exact solutions of 2D Bernstein-Greene-Kruskal (BGK) modes in a magnetized plasma with finite magnetic field strength [Ng, Bhattacharjee, and Skiff, Phys. Plasmas 13, 055903 (2006)] to cases with azimuthal magnetic fields so that these structures carry electric current as well as steady electric and magnetic fields. Such fully nonlinear solutions now satisfy exactly the Vlasov-Poisson-Ampere system of equations. Solutions like these could describe small-scale flux ropes observed in reconnection diffusion regions or in the interplanetary space. They are also exact nonlinear solutions that can be used to validate numerical schemes for kinetic simulations. This work is supported by a National Science Foundation grant PHY-1004357.

8. Imperfect dark energy from kinetic gravity braiding

SciTech Connect

Deffayet, Cédric; Pujolàs, Oriol; Sawicki, Ignacy; Vikman, Alexander E-mail: oriol.pujolas@cern.ch E-mail: alexander.vikman@nyu.edu

2010-10-01

We introduce a large class of scalar-tensor models with interactions containing the second derivatives of the scalar field but not leading to additional degrees of freedom. These models exhibit peculiar features, such as an essential mixing of scalar and tensor kinetic terms, which we have named kinetic braiding. This braiding causes the scalar stress tensor to deviate from the perfect-fluid form. Cosmology in these models possesses a rich phenomenology, even in the limit where the scalar is an exact Goldstone boson. Generically, there are attractor solutions where the scalar monitors the behaviour of external matter. Because of the kinetic braiding, the position of the attractor depends both on the form of the Lagrangian and on the external energy density. The late-time asymptotic of these cosmologies is a de Sitter state. The scalar can exhibit phantom behaviour and is able to cross the phantom divide with neither ghosts nor gradient instabilities. These features provide a new class of models for Dark Energy. As an example, we study in detail a simple one-parameter model. The possible observational signatures of this model include a sizeable Early Dark Energy and a specific equation of state evolving into the final de-Sitter state from a healthy phantom regime.

9. Adsorption of methylene blue onto bamboo-based activated carbon: kinetics and equilibrium studies.

PubMed

Hameed, B H; Din, A T M; Ahmad, A L

2007-03-22

Bamboo, an abundant and inexpensive natural resource in Malaysia was used to prepare activated carbon by physiochemical activation with potassium hydroxide (KOH) and carbon dioxide (CO(2)) as the activating agents at 850 degrees C for 2h. The adsorption equilibrium and kinetics of methylene blue dye on such carbon were then examined at 30 degrees C. Adsorption isotherm of the methylene blue (MB) on the activated carbon was determined and correlated with common isotherm equations. The equilibrium data for methylene blue adsorption well fitted to the Langmuir equation, with maximum monolayer adsorption capacity of 454.2mg/g. Two simplified kinetic models including pseudo-first-order and pseudo-second-order equation were selected to follow the adsorption processes. The adsorption of methylene blue could be best described by the pseudo-second-order equation. The kinetic parameters of this best-fit model were calculated and discussed.

10. A conservative multi-group approach to the Boltzmann equations for reactive gas mixtures

Bisi, M.; Rossani, A.; Spiga, G.

2015-11-01

Starting from a simple kinetic model for a quaternary mixture of gases undergoing a bimolecular chemical reaction, multi-group integro-differential equations are derived for the particle distribution functions of all species. The procedure takes advantage of a suitable probabilistic formulation, based on the underlying collision frequencies and transition probabilities, of the relevant reactive kinetic equations of Boltzmann type. Owing to an appropriate choice of a sufficiently large number of weight functions, it is shown that the proposed multi-group equations are able to fulfil exactly, at any order of approximation, the correct conservation laws that must be inherited from the original kinetic equations, where speed was a continuous variable. Future developments are also discussed.

11. Kinetic Tetrazolium Microtiter Assay

NASA Technical Reports Server (NTRS)

Pierson, Duane L.; Stowe, Raymond; Koenig, David

1993-01-01

Kinetic tetrazolium microtiter assay (KTMA) involves use of tetrazolium salts and Triton X-100 (or equivalent), nontoxic, in vitro color developer solubilizing colored metabolite formazan without injuring or killing metabolizing cells. Provides for continuous measurement of metabolism and makes possible to determine rate of action of antimicrobial agent in real time as well as determines effective inhibitory concentrations. Used to monitor growth after addition of stimulatory compounds. Provides for kinetic determination of efficacy of biocide, greatly increasing reliability and precision of results. Also used to determine relative effectiveness of antimicrobial agent as function of time. Capability of generating results on day of test extremely important in treatment of water and waste, disinfection of hospital rooms, and in pharmaceutical, agricultural, and food-processing industries. Assay also used in many aspects of cell biology.

12. Kinetic Theory of Gases

Murdin, P.

2000-11-01

The theory, developed in the nineteenth century, notably by Rudolf Clausius (1822-88) and James Clerk Maxwell (1831-79), that the properties of a gas (temperature, pressure, etc) could be described in terms of the motions (and kinetic energy) of the molecules comprising the gases. The theory has wide implications in astrophysics. In particular, the perfect gas law, which relates the pressure, vol...

13. Model-free deconvolution of femtosecond kinetic data.

PubMed

Bányász, Akos; Keszei, Erno

2006-05-18

Though shorter laser pulses can also be produced, pulses of the 100 fs range are typically used in femtosecond kinetic measurements, which are comparable to characteristic times of the studied processes, making detection of the kinetic response functions inevitably distorted by convolution with the pulses applied. A description of this convolution in terms of experiments and measurable signals is given, followed by a detailed discussion of a large number of available methods to solve the convolution equation to get the undistorted kinetic signal, without any presupposed kinetic or photophysical model of the underlying processes. A thorough numerical test of several deconvolution methods is described, and two iterative time-domain methods (Bayesian and Jansson deconvolution) along with two inverse filtering frequency-domain methods (adaptive Wiener filtering and regularization) are suggested to use for the deconvolution of experimental femtosecond kinetic data sets. Adaptation of these methods to typical kinetic curve shapes is described in detail. We find that the model-free deconvolution gives satisfactory results compared to the classical "reconvolution" method where the knowledge of the kinetic and photophysical mechanism is necessary to perform the deconvolution. In addition, a model-free deconvolution followed by a statistical inference of the parameters of a model function gives less biased results for the relevant parameters of the model than simple reconvolution. We have also analyzed real-life experimental data and found that the model-free deconvolution methods can be successfully used to get undistorted kinetic curves in that case as well. A graphical computer program to perform deconvolution via inverse filtering and additional noise filters is also provided as Supporting Information. Though deconvolution methods described here were optimized for femtosecond kinetic measurements, they can be used for any kind of convolved data where measured

14. Sorption kinetics of arsenic on laterite soil in aqueous medium.

PubMed

Maji, Sanjoy K; Pal, Anjali; Pal, Tarasankar; Adak, Asok

2007-06-01

The efficiency of a locally available laterite soil in removing both arsenite and arsenate from aqueous medium by adsorption was evaluated. It was observed that in batch experiment conducted at 0.5 mg/L initial concentration of arsenic, laterite soil could remove up to 98% of arsenite and 95% of arsenate under optimized conditions. The kinetic profiles under various conditions were developed. Both arsenite and arsenate removal followed pseudo--second order reaction kinetic model. Pore and film diffusion coefficients were determined from the half-time equation and film diffusion appeared to be the rate-limiting. This was further supported by multiple interruption tests.

15. Reaction kinetics and diagnostics for oil-shale retorting

Burnham, A. K.

1981-10-01

The advances in pyrolysis chemistry and kinetics and the resulting diagnostic methods based on effluent products for determining retort performance were reviewed. Kerogen pyrolysis kinetics and stoichiometry were generalized by further measurements on a larger number of samples. Analysis by capillary colunn gas chromatography of shale oil samples produced under a variety of field and laboratory conditions resulted in a method for determining the oil yield from a combustion retort. Measurement of sulfur products under a variety of conditions led to an understanding sulfur reactions both those of processing and environmental importance. Equations for estimating the heat of combustion of spent shale were developed by understanding oil shale composition and reactions.

16. A Note on Kinetic Energy, Dissipation and Enstrophy

NASA Technical Reports Server (NTRS)

Wu, Jie-Zhi; Zhou, Ye; Fan, Meng

1998-01-01

The dissipation rate of a Newtonian fluid with constant shear viscosity can be shown to include three constituents: dilatation, vorticity, and surface strain. The last one is found to make no contributions to the change of kinetic energy. These dissipation constituents arc used to identify typical compact turbulent flow structures at high Reynolds numbers. The incompressible version of the simplified kinetic-energy equation is then cast to a novel form, which is free from the work rate done by surface stresses but in which the full dissipation re-enters.

SciTech Connect

2006-11-15

In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the structure of a classical rate equation. The system dynamics may develop strong nonlocal effects such as the dependence of the stationary properties with the system initialization. These equations are derived from alternative microscopic interactions, such as complex environments described in a generalized Born-Markov approximation and tripartite system-environment interactions, where extra unobserved degrees of freedom mediates the entanglement between the system and a Markovian reservoir. Conditions that guarantee the completely positive condition of the solution map are found. Quantum stochastic processes that recover the system dynamics in average are formulated. We exemplify our results by analyzing the dynamical action of nontrivial structured dephasing and depolarizing reservoirs over a single qubit.

18. Nonlocal electrical diffusion equation

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

19. Accurate kinetic parameter estimation during progress curve analysis of systems with endogenous substrate production.

PubMed

Goudar, Chetan T

2011-10-01

We have identified an error in the published integral form of the modified Michaelis-Menten equation that accounts for endogenous substrate production. The correct solution is presented and the error in both the substrate concentration, S, and the kinetic parameters Vm , Km , and R resulting from the incorrect solution was characterized. The incorrect integral form resulted in substrate concentration errors as high as 50% resulting in 7-50% error in kinetic parameter estimates. To better reflect experimental scenarios, noise containing substrate depletion data were analyzed by both the incorrect and correct integral equations. While both equations resulted in identical fits to substrate depletion data, the final estimates of Vm , Km , and R were different and Km and R estimates from the incorrect integral equation deviated substantially from the actual values. Another observation was that at R = 0, the incorrect integral equation reduced to the correct form of the Michaelis-Menten equation. We believe this combination of excellent fits to experimental data, albeit with incorrect kinetic parameter estimates, and the reduction to the Michaelis-Menten equation at R = 0 is primarily responsible for the incorrectness to go unnoticed. However, the resulting error in kinetic parameter estimates will lead to incorrect biological interpretation and we urge the use of the correct integral form presented in this study.

20. The mechanical and chemical equations of motion of muscle contraction

Shiner, J. S.; Sieniutycz, Stanislaw

1997-11-01

Up to now no formulation of muscle contraction has provided both the chemical kinetic equations for the reactions responsible for the contraction and the mechanical equation of motion for the muscle. This has most likely been due to the lack of general formalisms for nonlinear systems with chemical-nonchemical coupling valid under the far from equilibrium conditions under which muscle operates physiologically. We have recently developed such formalisms and apply them here to the formulation of muscle contraction to obtain both the chemical and the mechanical equations. The standard formulation up to now has yielded only the dynamic equations for the chemical variables and has considered these to be functions of both time and an appropriate mechanical variable. The macroscopically observable quantities were then obtained by averaging over the mechanical variable. When attempting to derive the dynamics equations for both the chemistry and mechanics this choice of variables leads to conflicting results for the mechanical equation of motion when two different general formalisms are applied. The conflict can be resolved by choosing the variables such that both the chemical variables and the mechanical variables are considered to be functions of time alone. This adds one equation to the set of differential equations to be solved but is actually a simplification of the problem, since these equations are ordinary differential equations, not the partial differential equations of the now standard formulation, and since in this choice of variables the variables themselves are the macroscopic observables the procedure of averaging over the mechanical variable is eliminated. Furthermore, the parameters occurring in the equations at this level of description should be accessible to direct experimental determination.

1. Stochastic differential equations

SciTech Connect

Sobczyk, K. )

1990-01-01

This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations. It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as numerical). Starting from basic notions and results of the theory of stochastic processes and stochastic calculus (including Ito's stochastic integral), many principal mathematical problems and results related to stochastic differential equations are expounded here for the first time. Applications treated include those relating to road vehicles, earthquake excitations and offshore structures.

2. Kepler Equation solver

NASA Technical Reports Server (NTRS)

Markley, F. Landis

1995-01-01

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.

3. Obtaining Maxwell's equations heuristically

Diener, Gerhard; Weissbarth, Jürgen; Grossmann, Frank; Schmidt, Rüdiger

2013-02-01

Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light, together with Galilean invariance of the Lorentz force, allows us to finalize Maxwell's equations and to introduce arbitrary electrodynamics units naturally.

4. Comparison of Kernel Equating and Item Response Theory Equating Methods

ERIC Educational Resources Information Center

Meng, Yu

2012-01-01

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

5. Accumulative Equating Error after a Chain of Linear Equatings

ERIC Educational Resources Information Center

Guo, Hongwen

2010-01-01

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…

6. Kinetic analysis of a general model of activation of aspartic proteinase zymogens involving a reversible inhibitor. I. Kinetic analysis.

PubMed

Muñoz-López, A; Sotos-Lomas, A; Arribas, E; Masia-Perez, J; Garcia-Molina, F; García-Moreno, M; Varon, R

2007-04-01

Starting from a simple general reaction mechanism of activation of aspartic proteinases zymogens involving a uni- and a bimolecular simultaneous activation route and a reversible inhibition step, the time course equation of the zymogen, inhibitor and activated enzyme concentrations have been derived. Likewise, expressions for the time required for any reaction progress and the corresponding mean activation rates as well as the half-life of the global zymogen activation have been derived. An experimental design and kinetic data analysis is suggested to estimate the kinetic parameters involved in the reaction mechanism proposed.

7. Evaluation of a kinetic model for computer simulation of growth and fermentation by Scheffersomyces (Pichia) stipitis fed D-xylose

Technology Transfer Automated Retrieval System (TEKTRAN)

Scheffersomyces (formly Pichia) stipitis is a potential biocatalyst for converting lignocelluloses to ethanol because the yeast natively ferments xylose. An unstructured kinetic model based upon a system of linear differential equations has been formulated that describes growth and ethanol productio...

8. Animal Guts as Ideal Reactors: An Open-Ended Project for a Course in Kinetics and Reactor Design.

ERIC Educational Resources Information Center

Carlson, Eric D.; Gast, Alice P.

1998-01-01

Presents an open-ended project tailored for a senior kinetics and reactor design course in which basic reactor design equations are used to model the digestive systems of several animals. Describes the assignment as well as the results. (DDR)

9. Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables

NASA Technical Reports Server (NTRS)

Sislian, J. P.

1978-01-01

The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.

10. The Statistical Drake Equation

Maccone, Claudio

2010-12-01

We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density

11. Reduced methanol kinetic mechanisms for combustion applications

SciTech Connect

Yalamanchili, S.; Sirignano, W.A.; Seiser, R.; Seshadri, K.

2005-08-01

Reduced chemical kinetic mechanisms for methanol combustion were investigated by evaluating ignition delay magnitudes and combustion in a continuously stirred reactor. Unsteady computations were made to study the characteristics of the kinetic mechanisms proposed in the literature and to compare the dependence of various parameters on methanol combustion. All computations were done under isobaric conditions, and, to capture the influence of all the reactions involved in the mechanism, a very small time step was used. Finite-difference methods were used to solve the coupled differential equations. The five-step mechanism developed by C.M. Mueller and N. Peters [in: N. Peters, B. Rogg (Eds.), Reduced Kinetic Mechanisms for Applications in Combustion Systems, Springer-Verlag, New York, 1993, pp. 143-155] for premixed flames and both the five-step mechanism and the four-step mechanisms developed by C.M. Mueller, K. Seshadri, J.Y. Chen [ibid, pp. 284-307] for non-premixed flames were considered. It was found that the Mueller et al. five-step mechanism, with some modifications, best supported the spontaneous ignition and continuous stirred reactor combustion. The results were validated by comparing calculated ignition delays with available experimental data of C.T. Bowman [Combust. Flame 25 (1975) 343-354], and calculated final steady-state concentrations with chemical equilibrium calculations [J.-Y. Chen, Combust. Sci. Technol. 78 (1991) 127]. Initial temperature and concentration and the operating pressure of the system have a major effect on the delay of methanol ignition. The residence time of the continuous stirred reactor affects ignition delay and also changes the transient characteristic of chemical composition of the fuel-vapor mixture. The computations are intended to guide and explain many combustion studies that require a methanol kinetic mechanism.

12. Coupling Coefficients In The Kinetic Theory of Rossby Waves

Soomere, T.

Rossby waves serve as an example of wave systems where resonant energy exchange between different wave classes with comparable frequencies can occur. Energy ex- change in such systems can be described with a system of equations called multi- wave (multi-modal) kinetic equation. Multi-wave kinetic equations typically contain two sets of coefficients describing energy exchange intensity. Interaction coefficients describe interaction intensity within a particular set of resonant waves. The coupling coefficients limit energy exchange within specific types of interactions. The interaction coefficients solely depend on the dispersion relations of the interacting wave compo- nents whereas the coupling coefficients represent the structure of the non-linear parts of the wave equations. One of the simplest multi-wave kinetic equations describes slow evolution of the energy spectrum of baroclinic Rossby waves in a multi-layer model ocean. Explicit expressions for the coupling coefficients in the case of a N-layer ocean are obtained and their main properties are established. A part of the expressions is fairly general. It is demonstrated that several types of interactions vanish in the case of simple realistic vertical structures of the ocean. For example, it is well know that in the two-layer case the intensity of energetic changes within resonant sets containing solely baroclinic harmonics crucially depends on the ratio of the depths of the layers. In the case of equal depths, self-interactions of the baroclinic mode fully cease, be- cause the corresponding coupling coefficient vanishes. This property suggests that an improper choice of the model may result in a completely different evolution scenario of the whole system. The detailed analytic expressions for the coupling coefficients of the Rossby wave kinetic equation are derived for a three-layer model ocean. If the re- duced depths of the uppermost and the lowermost layers are equal, a number of differ- ent interaction

13. Single-molecule Michaelis-Menten equations.

PubMed

Kou, S C; Cherayil, Binny J; Min, Wei; English, Brian P; Xie, X Sunney

2005-10-20

This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information than the ensemble data; in particular, it provides crucial information on dynamic disorder, the apparent fluctuation of the catalytic rates due to the interconversion among the enzyme's conformers with different catalytic rate constants. In the presence of dynamic disorder, f(t) exhibits a highly stretched multiexponential decay at high substrate concentrations and a monoexponential decay at low substrate concentrations. We derive a single-molecule Michaelis-Menten equation for the reciprocal of the first moment of f(t), 1/, which shows a hyperbolic dependence on the substrate concentration [S], similar to the ensemble enzymatic velocity. We prove that this single-molecule Michaelis-Menten equation holds under many conditions, in particular when the intercoversion rates among different enzyme conformers are slower than the catalytic rate. However, unlike the conventional interpretation, the apparent catalytic rate constant and the apparent Michaelis constant in this single-molecule Michaelis-Menten equation are complicated functions of the catalytic rate constants of individual conformers. We also suggest that the randomness parameter r, defined as <(t - )2> / t2, can serve as an indicator for dynamic disorder in the catalytic step of the enzymatic reaction, as it becomes larger than unity at high substrate concentrations in the presence of dynamic disorder.

14. Role of cosolutes in the aggregation kinetics of monoclonal antibodies.

PubMed

Nicoud, Lucrèce; Sozo, Margaux; Arosio, Paolo; Yates, Andrew; Norrant, Edith; Morbidelli, Massimo

2014-10-16

We propose a general strategy based on kinetic analysis to investigate how cosolutes affect the aggregation behavior of therapeutic proteins. We apply this approach to study the impact of NaCl and sorbitol on the aggregation kinetics of two monoclonal antibodies, an IgG1 and an IgG2. By using a combination of size exclusion chromatography and light scattering techniques, we study the impact of the cosolutes on the monomer depletion, as well as on the formation of dimers, trimers, and larger aggregates. We analyze these macroscopic effects in the frame of a kinetic model based on Smoluchowski's population balance equations modified to account for nucleation events. By comparing experimental data with model simulations, we discriminate the effect of cosolutes on the elementary steps which contribute to the global aggregation process. In the case of the IgG1, it is found that NaCl accelerates the kinetics of aggregation by promoting specifically aggregation events, while sorbitol delays the kinetics of aggregation by specifically inhibiting protein unfolding. In the case of the IgG2, whose monomer depletion kinetics is limited by dimer formation, NaCl and sorbitol are found respectively to accelerate and inhibit conformational changes and aggregation events to the same extent.

15. Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach

SciTech Connect

Grecu, A. T.; Grecu, D.; Visinescu, Anca; De Nicola, S.; Fedele, R.

2010-01-21

The modulational (Benjamin-Feir) instability for cylindrical and spherical NLS equations (c/s NLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using the Wigner-Moyal transform. The linear stability of the Fourier transform of the two-point correlation function is studied and an implicit integral form for the dispersion relation is found. This is solved for different expressions of the initial spectrum (delta-spectrum, Lorentzian, Gaussian), and in the case of a Lorentzian spectrum the total growth of the instability is calculated. The similarities and differences with the usual one-dimensional NLS equation are emphasized.

16. Do Differential Equations Swing?

ERIC Educational Resources Information Center

Maruszewski, Richard F., Jr.

2006-01-01

One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

17. Modelling by Differential Equations

ERIC Educational Resources Information Center

Chaachoua, Hamid; Saglam, Ayse

2006-01-01

This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

18. Dunkl Hyperbolic Equations

Mejjaoli, Hatem

2008-12-01

We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.

19. Structural Equation Model Trees

ERIC Educational Resources Information Center

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…

ERIC Educational Resources Information Center

Fay, Temple H.

2010-01-01

Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

1. Parallel Multigrid Equation Solver

SciTech Connect

2001-09-07

Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.

2. Quenching equation for scintillation

Kato, Takahisa

1980-06-01

A mathematical expression is postulated showing the relationship between counting rate and quenching agent concentration in a liquid scintillation solution. The expression is more suited to a wider range of quenching agent concentrations than the Stern-Volmer equation. An estimation of the quenched correction is demonstrated using the expression.

3. Kinetic study of brilliant green adsorption from aqueous solution onto white rice husk ash.

PubMed

Tavlieva, Mariana P; Genieva, Svetlana D; Georgieva, Velyana G; Vlaev, Lyubomir T

2013-11-01

The present research was focused on the study of adsorption kinetics of brilliant green (BG) onto white rice husk ash from aqueous solutions. The research was performed in the temperature interval 290-320 K in 10° steps and in the concentration range of 3-100 mg L(-1). Batch studies were conducted in order to determine the optimal adsorbent dose, and the time required to reach the adsorption equilibrium at each temperature. The effect of the initial concentration of brilliant green was studied (pH not adjusted), as well as the effect of temperature. The maximum adsorption capacity of the WRHA for BG at 320 K was determined to be 85.56 mg g(-1). The adsorption kinetic data were analyzed employing several kinetic models: pseudo-first-order equation, pseudo-second-order equation, Elovichequation, Banghman's equation, Diffusion-chemisorption model, and Boyd kinetic expression. It was established that the adsorption process obeyed the pseudo-second-order kinetic model. Based on the rate constants obtained by this kinetic model using Arrhenius and Eyring equations, the activation parameters were determined, namely the activation energy (50.04 kJ mol(-1)), the change of entropy (-318.31 J mol(-1) K(-1)), enthalpy (-47.50 kJ mol(-1)), and Gibbs free energy (range 44.81-54.36 kJ mol(-1)) for the formation of activated complex from the reagents.

4. Towards adaptive kinetic-fluid simulations of low-temperature plasmas

2013-09-01

The emergence of new types of gaseous electronics in multi-phase systems calls for computational tools with adaptive kinetic-fluid simulation capabilities. We will present an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and discuss current efforts towards extending this methodology for weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or fluid solvers in different parts of computational domains. This AMAR methodology was implemented in our Unified Flow Solver (UFS) for mixed rarefied and continuum flows. UFS uses discrete velocity method for solving Boltzmann kinetic equation under rarefied flow conditions coupled to fluid (Navier-Stokes) solvers for continuum flow regimes. The main challenge of extending AMAR to plasmas comes from the distinction of electron and atom mass. We will present multi-fluid, two-temperature plasma models with AMR capabilities for simulations of glow, corona, and streamer discharges. We will briefly discuss specifics of electron kinetics in collisional plasmas, and deterministic methods of solving kinetic equations for different electron groups. Kinetic solvers with Adaptive Mesh in Phase Space (AMPS) will be introduced to solve Boltzmann equation for electrons in the presence of electric fields, elastic and inelastic collisions with atoms. These kinetic and fluid models are currently being incorporated into AMAR methodology for multi-scale simulations of low-temperature plasmas in multi-phase systems. Supported by AFOSR, NASA, and DoE

5. Rainfall kinetic energy-intensity and rainfall momentum-intensity relationships for Cape Verde

Sanchez-Moreno, Juan Francisco; Mannaerts, Chris M.; Jetten, Victor; Löffler-Mang, Martin

2012-08-01

Momentum and kinetic energy of rainfall are widely used indices to describe erosivity, the ability of rainfall to detach soil particles and erode the landscape. An optical laser disdrometer was installed in Santiago Island, Cape Verde, between September 2008 and September 2010 to measure rainfall intensity and size distribution of raindrops. A total time series of 5129 observations of radar reflectivity, visibility, rainfall intensity and number of particles were gathered. Rainfall kinetic energy expenditure KEtime (J m-2 h-1), kinetic energy content KEmm (J m-2 mm-1) and momentum flux MtA (kg m s-1 m-2 s-1) were calculated and fitted to different known experimental equations. The best fit between rainfall intensity and kinetic energy expenditure, kinetic energy content and momentum were obtained with power-law equations. These equations were validated in two independent events corresponding to 2008 and 2009, producing high correlation coefficients. The results show that for Cape Verde, KEtime is a more appropriate index to relate with rainfall intensity, and that kinetic energy expenditure and momentum flux are interchangeable parameters for erosivity estimation. New relationships relating kinetic energy and rainfall intensity, and momentum and rainfall intensity were derived, which contribute to the characterization of rainfall originating from tropical depressions at lower latitudes.

6. Kinetics of stress fibers

Stachowiak, Matthew R.; O'Shaughnessy, Ben

2008-02-01

Stress fibers are contractile cytoskeletal structures, tensile actomyosin bundles which allow sensing and production of force, provide cells with adjustable rigidity and participate in various processes such as wound healing. The stress fiber is possibly the best characterized and most accessible multiprotein cellular contractile machine. Here we develop a quantitative model of the structure and relaxation kinetics of stress fibers. The principal experimentally known features are incorporated. The fiber has a periodic sarcomeric structure similar to muscle fibers with myosin motor proteins exerting contractile force by pulling on actin filaments. In addition the fiber contains the giant spring-like protein titin. Actin is continuously renewed by exchange with the cytosol leading to a turnover time of several minutes. In order that steady state be possible, turnover must be regulated. Our model invokes simple turnover and regulation mechanisms: actin association and dissociation occur at filament ends, while actin filament overlap above a certain threshold in the myosin-containing regions augments depolymerization rates. We use the model to study stress fiber relaxation kinetics after stimulation, as observed in a recent experimental study where some fiber regions were contractile and others expansive. We find that two distinct episodes ensue after stimulation: the turnover-overlap system relaxes rapidly in seconds, followed by the slow relaxation of sarcomere lengths in minutes. For parameter values as they have been characterized experimentally, we find the long time relaxation of sarcomere length is set by the rate at which actin filaments can grow or shrink in response to the forces exerted by the elastic and contractile elements. Consequently, the stress fiber relaxation time scales inversely with both titin spring constant and the intrinsic actin turnover rate. The model's predicted sarcomere velocities and contraction-expansion kinetics are in good

7. Nonlinear equations of 'variable type'

Larkin, N. A.; Novikov, V. A.; Ianenko, N. N.

In this monograph, new scientific results related to the theory of equations of 'variable type' are presented. Equations of 'variable type' are equations for which the original type is not preserved within the entire domain of coefficient definition. This part of the theory of differential equations with partial derivatives has been developed intensively in connection with the requirements of mechanics. The relations between equations of the considered type and the problems of mathematical physics are explored, taking into account quasi-linear equations, and models of mathematical physics which lead to equations of 'variable type'. Such models are related to transonic flows, problems involving a separation of the boundary layer, gasdynamics and the van der Waals equation, shock wave phenomena, and a combustion model with a turbulent diffusion flame. Attention is also given to nonlinear parabolic equations, and nonlinear partial differential equations of the third order.

8. Inverse Kinetic Theory for Incompressible Thermofluids

Cremaschini, C.; Tessarotto, M.

2008-12-01

An interesting issue in fluid dynamics is represented by the possible existence of inverse kinetic theories (IKT) which are able to deliver, in a suitable sense, the complete set of fluid equations which are associated to a prescribed fluid. From the mathematical viewpoint this involves the formal description of a fluid by means of a classical dynamical system which advances in time the relevant fluid fields. The possibility of defining an IKT for the 3D incompressible Navier-Stokes equations (INSE), recently investigated (Ellero et al., 2004-2007) raises the interesting question whether the theory can be applied also to thermofluids, in such a way to satisfy also the second principle of thermodynamics. The goal of this paper is to prove that such a generalization is actually possible, by means of a suitable extended phase-space formulation. We consider, as a reference test, the case of non-isentropic incompressible thermofluids, whose dynamics is described by the Fourier and the incompressible Navier-Stokes equations, the latter subject to the conditions of validity of the Boussinesq approximation.

9. Substrate inhibition kinetics of phenol biodegradation

SciTech Connect

Goudar, C.T.; Ganji, S.H.; Pujar, B.G.; Strevett, K.A.

2000-02-01

Phenol biodegradation was studied in batch experiments using an acclimated inoculum and initial phenol concentrations ranging from 0.1 to 1.3 g/L. Phenol depletion an associated microbial growth were monitored over time to provide information that was used to estimate the kinetics of phenol biodegradation. Phenol inhibited biodegradation at high concentrations, and a generalized substrate inhibition model based on statistical thermodynamics was used to describe the dynamics of microbial growth in phenol. For experimental data obtained in this study, the generalized substrate inhibition model reduced to a form that is analogous to the Andrews equation, and the biokinetic parameters {micro}{sub max}, maximum specific growth; K{sub s}, saturation constant; and K{sub i}, inhibition constant were estimated as 0.251 h{sup {minus}1}, 0.011 g/L, and 0.348 g/L, respectively, using a nonlinear least squares technique. Given the wide variability in substrate inhibition models used to describe phenol biodegradation, an attempt was made to justify selection of particular model based on theoretical considerations. Phenol biodegradation data from nine previously published studies were used in the generalized substrate inhibition model to determine the appropriate form of the substrate inhibition model. In all nine cases, the generalized substrate inhibition model reduced to a form analogous to the Andrews equation suggesting the suitability of the Andrews equation to describe phenol biodegradation data.

10. Order Parameter and Kinetics of Non-Equilibrium Phase Transition Stimulated by the Impact of Volumetric Heat Source

Slyadnikov, E. E.; Turchanovskii, I. Yu.

2017-01-01

The authors formulated an understanding of the order parameter and built a kinetic model for the nonequilibrium first-order "solid body - liquid" phase transition stimulated by the impact of the volumetric heat source. Analytical solutions for kinetic equations were found, and it was demonstrated that depending on the phase transition rate "surface" and "bulk" melting mechanisms are implemented.

11. Catalytic effects in the reaction of polypropylene with benzoyl peroxide and structural-kinetic model of the polymer

SciTech Connect

Mikheev, Yu.A.; Guseva, L.N.; Toptygin, D.Ya.

1987-09-01

The kinetic peculiarities of the chain arylation of polypropylene with benzoyl peroxide and the yields of the transformation products (arylated polypropylene benzene, and benzoic acid) were established. The equation of the reaction rate depends on the way in which the samples were prepared and on the benzoyl peroxide concentration in the polymer. The kinetic peculiarities found were explained by a heterophase mechanism.

12. Chemical kinetics modeling

SciTech Connect

Westbrook, C.K.; Pitz, W.J.

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.

13. Analysis of Crystallization Kinetics

NASA Technical Reports Server (NTRS)

Kelton, Kenneth F.

1997-01-01

A realistic computer model for polymorphic crystallization (i.e., initial and final phases with identical compositions), which includes time-dependent nucleation and cluster-size-dependent growth rates, is developed and tested by fits to experimental data. Model calculations are used to assess the validity of two of the more common approaches for the analysis of crystallization data. The effects of particle size on transformation kinetics, important for the crystallization of many systems of limited dimension including thin films, fine powders, and nanoparticles, are examined.

14. Kinetic model for microbial growth and desulphurisation with Enterobacter sp.

PubMed

Liu, Long; Guo, Zhiguo; Lu, Jianjiang; Xu, Xiaolin

2015-02-01

Biodesulphurisation was investigated by using Enterobacter sp. D4, which can selectively desulphurise and convert dibenzothiophene into 2-hydroxybiphenyl (2-HBP). The experimental values of growth, substrate consumption and product generation were obtained at 95 % confidence level of the fitted values using three models: Hinshelwood equation, Luedeking-Piret and Luedeking-Piret-like equations. The average error values between experimental values and fitted values were less than 10 %. These kinetic models describe all the experimental data with good statistical parameters. The production of 2-HBP in Enterobacter sp. was by "coupled growth".

15. Group-kinetic theory and modeling of atmospheric turbulence

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1989-01-01

A group kinetic method is developed for analyzing eddy transport properties and relaxation to equilibrium. The purpose is to derive the spectral structure of turbulence in incompressible and compressible media. Of particular interest are: direct and inverse cascade, boundary layer turbulence, Rossby wave turbulence, two phase turbulence; compressible turbulence, and soliton turbulence. Soliton turbulence can be found in large scale turbulence, turbulence connected with surface gravity waves and nonlinear propagation of acoustical and optical waves. By letting the pressure gradient represent the elementary interaction among fluid elements and by raising the Navier-Stokes equation to higher dimensionality, the master equation was obtained for the description of the microdynamical state of turbulence.

16. Test-particle method in kinetic theory of a plasma.

NASA Technical Reports Server (NTRS)

Matsuda, K.

1971-01-01

The introduction of a test particle into a system is considered. The system may be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy. The field particles form a cloud which surrounds the test particle. The cloud is described by a conditional probability function which satisfies a certain equation. A generalization of the superposition principle reported by Rostoker (1964) to higher order correlation functions is discussed. Kinetic equations with the generalized Lenard-Balescu term are obtained, taking into account also diffusion by waves. The characteristics regarding the absorption or emission of waves by particles can be calculated.

17. Kinetic model of turbulence in an incompressible fluid

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1978-01-01

A statistical description of turbulence in an incompressible fluid obeying the Navier-Stokes equations is proposed, where pressure is regarded as a potential for the interaction between fluid elements. A scaling procedure divides a fluctuation into three ranks representing the three transport processes of macroscopic evolution, transport property, and relaxation. Closure is obtained by relaxation, and a kinetic equation is obtained for the fluctuation of the macroscopic rank of the distribution function. The solution gives the transfer function and eddy viscosity. When applied to the inertia subrange of the energy spectrum the analysis recovers the Kolmogorov law and its numerical coefficient.

18. Methods for Equating Mental Tests.

DTIC Science & Technology

1984-11-01

1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

19. Simple jumping process with memory: Transport equation and diffusion

Kamińska, A.; Srokowski, T.

2004-06-01

We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple stationary limit. Its master equation is interpreted as the kinetic equation with variable collision rate. The process can be easily applied to model systems which relax to distributions other than Maxwellian. The case of a constant jumping rate corresponds to the diffusion process, either normal or ballistic.

20. Fluid equations in the presence of electron cyclotron current drive