Kinetic energy equations for the average-passage equation system
NASA Technical Reports Server (NTRS)
Johnson, Richard W.; Adamczyk, John J.
1989-01-01
Important kinetic energy equations derived from the average-passage equation sets are documented, with a view to their interrelationships. These kinetic equations may be used for closing the average-passage equations. The turbulent kinetic energy transport equation used is formed by subtracting the mean kinetic energy equation from the averaged total instantaneous kinetic energy equation. The aperiodic kinetic energy equation, averaged steady kinetic energy equation, averaged unsteady kinetic energy equation, and periodic kinetic energy equation, are also treated.
Investigation of the kinetic model equations
NASA Astrophysics Data System (ADS)
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.
Kinetic Equations for the Plasma Edge
NASA Astrophysics Data System (ADS)
Abel, Ian; Hammett, Greg
2015-11-01
A hybrid fluid-kinetic framework for studying large-amplitude fluctuations in the edge of tokamak plasmas is presented. We derive equations for the behavior of an anisotropic plasma in the presence of both large fluctuations and steep gradients. The system consists of kinetic equations for electrons and ions, supplemented with fluid equations for the electromagnetic fields. In this way it builds upon both kinetic MHD and from the use of vorticity equations in gyrokinetics. This framework, by including both Alfvénic (including current-driven modes) and drift wave dynamics, can handle fully nonlinear perturbations such as erupting ELM filaments and blob-based turbulence. We not only present equations for such fast behavior, but also develop higher order equations that describe pedestal equilibria and slow scrape-off-layer dynamics. The relationship between this framework and existing collisional edge models is made clear.
Kinetic Equations for Economic Sciences
NASA Astrophysics Data System (ADS)
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.
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.
Spectrum Analysis of Some Kinetic Equations
NASA Astrophysics Data System (ADS)
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.
Stochastic thermodynamics for linear kinetic equations
NASA Astrophysics Data System (ADS)
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.
Benchmarks for the point kinetics equations
Ganapol, B.; Picca, P.; Previti, A.; Mostacci, D.
2013-07-01
A new numerical algorithm is presented for the solution to the point kinetics equations (PKEs), whose accurate solution has been sought for over 60 years. The method couples the simplest of finite difference methods, a backward Euler, with Richardsons extrapolation, also called an acceleration. From this coupling, a series of benchmarks have emerged. These include cases from the literature as well as several new ones. The novelty of this presentation lies in the breadth of reactivity insertions considered, covering both prescribed and feedback reactivities, and the extreme 8- to 9- digit accuracy achievable. The benchmarks presented are to provide guidance to those who wish to develop further numerical improvements. (authors)
Neutrino quantum kinetic equations: The collision term
NASA Astrophysics Data System (ADS)
Blaschke, Daniel N.; Cirigliano, Vincenzo
2016-08-01
We derive the collision term relevant for neutrino quantum kinetic equations in the early universe and compact astrophysical objects, displaying its full matrix structure in both flavor and spin degrees of freedom. We include in our analysis neutrino-neutrino processes, scattering and annihilation with electrons and positrons, and neutrino scattering off nucleons (the latter in the low-density limit). After presenting the general structure of the collision terms, we take two instructive limiting cases. The one-flavor limit highlights the structure in helicity space and allows for a straightforward interpretation of the off-diagonal entries in terms of the product of scattering amplitudes of the two helicity states. The isotropic limit is relevant for studies of the early universe: in this case the terms involving spin coherence vanish and the collision term can be expressed in terms of two-dimensional integrals, suitable for computational implementation.
Neutrino quantum kinetic equations: The collision term
Blaschke, Daniel N.; Cirigliano, Vincenzo
2016-08-25
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
Kinetic Approach for Quantum Hydrodynamic Equations
NASA Astrophysics Data System (ADS)
Tessarotto, M.; Ellero, M.; Nicolini, P.
2008-12-01
A striking feature of standard quantum mechanics (SQM) is its analogy with classical fluid dynamics. In particular it is well known the Schrödinger equation can be viewed as describing a classical compressible and non-viscous fluid, described by two (quantum) fluid fields {ρ,V}, to be identified with the quantum probability density and velocity field. This feature has suggested the construction of a phase-space hidden-variable description based on a suitable inverse kinetic theory (IKT; Tessarotto et al., 2007). The discovery of this approach has potentially important consequences since it permits to identify the classical dynamical system which advances in time the quantum fluid fields. This type of approach, however requires the identification of additional fluid fields. These can be generally identified with suitable directional fluid temperatures TQM,i (for i = 1,2,3), to be related to the expectation values of momentum fluctuations appearing in the Heisenberg inequalities. Nevertheless the definition given previously for them (Tessarotto et al., 2007) is non-unique. In this paper we intend to propose a criterion, based on the validity of a constant H-theorem, which provides an unique definition for the quantum temperatures.
Moment equations for chromatography based on Langmuir type reaction kinetics.
Miyabe, Kanji
2014-08-22
Moment equations were derived for chromatography, in which the reaction kinetics between solute molecules and functional ligands on the stationary phase was represented by the Langmuir type rate equation. A set of basic equations of the general rate model of chromatography representing the mass balance, mass transfer rate, and reaction kinetics in the column were analytically solved in the Laplace domain. The moment equations for the first absolute moment and the second central moment in the real time domain were derived from the analytical solution in the Laplace domain. The moment equations were used for predicting the chromatographic behavior under hypothetical HPLC conditions. The influence of the parameters relating to the adsorption equilibrium and to the reaction kinetics on the chromatographic behavior was quantitatively evaluated. It is expected that the moment equations are effective for a detailed analysis of the influence of the mass transfer rates and of the Langmuir type reaction kinetics on the column efficiency.
A classical but new kinetic equation for hydride transfer reactions.
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.
Kinetic equation for nonlinear resonant wave-particle interaction
NASA Astrophysics Data System (ADS)
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.
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.
The Linearized Kinetic Equation -- A Functional Analytic Approach
NASA Astrophysics Data System (ADS)
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.
Derivation of kinetic equations from non-Wiener stochastic differential equations
NASA Astrophysics Data System (ADS)
Basharov, A. M.
2013-12-01
Kinetic differential-difference equations containing terms with fractional derivatives and describing α -stable Levy processes with 0 < α < 1 have been derived in a unified manner in terms of one-dimensional stochastic differential equations controlled merely by the Poisson processes.
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…
General Entropic Approximations for Canonical Systems Described by Kinetic Equations
NASA Astrophysics Data System (ADS)
Pavan, V.
2011-02-01
In this paper we extend the general construction of entropic approximation for kinetic operators modelling canonical systems. More precisely, this paper aims at pursuing to thermalized systems the works of Levermore, Schneider and Junk on moments problems relying on entropy minimization in order to construct BGK approximations and moments based equations.
Modeling the turbulent kinetic energy equation for compressible, homogeneous turbulence
NASA Technical Reports Server (NTRS)
Aupoix, B.; Blaisdell, G. A.; Reynolds, William C.; Zeman, Otto
1990-01-01
The turbulent kinetic energy transport equation, which is the basis of turbulence models, is investigated for homogeneous, compressible turbulence using direct numerical simulations performed at CTR. It is shown that the partition between dilatational and solenoidal modes is very sensitive to initial conditions for isotropic decaying turbulence but not for sheared flows. The importance of the dilatational dissipation and of the pressure-dilatation term is evidenced from simulations and a transport equation is proposed to evaluate the pressure-dilatation term evolution. This transport equation seems to work well for sheared flows but does not account for initial condition sensitivity in isotropic decay. An improved model is proposed.
Bounce-averaged Kinetic Equations and Neoclassical Polarization Density
First Author = B.H. Fong; T.S. Hahm
1998-07-01
The rigorous formulation of the bounce-averaged equations is presented based upon the Poincare-Cartan one-form andLie perturbation methods. The resulting bounce-averaged Vlasov equation is Hamiltonian, thus suitable for theself-consistent simulation of low-frequency electrostatic turbulence in the trapped ion mode regime. In the bounce-kineticPoisson equation, the "neoclassical polarization density" arises from the difference between bounce-averaged banana centerand real trapped particle densities across a field line. This representation of the neoclassical polarization drift as ashielding term provides a systematic way to study the long-term behavior of the turbulence-driven E x B flow.
Spectral function and kinetic equation for a normal Fermi liquid
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.
A kinetic equation with kinetic entropy functions for scalar conservation laws
NASA Technical Reports Server (NTRS)
Perthame, Benoit; Tadmor, Eitan
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.
Derivation of the Drude conductivity from quantum kinetic equations
NASA Astrophysics Data System (ADS)
Kitamura, Hikaru
2015-11-01
The Drude formula of ac (frequency-dependent) electric conductivity has been established as a simple and practically useful model to understand the electromagnetic response of simple free-electron-like metals. In most textbooks of solid-state physics, the Drude formula is derived from either a classical equation of motion or the semiclassical Boltzmann transport equation. On the other hand, quantum-mechanical derivation of the Drude conductivity, which requires an appropriate treatment of phonon-assisted intraband transitions with small momentum transfer, has not been well documented except for the zero- or high-frequency case. Here, a lucid derivation of the Drude conductivity that covers the entire frequency range is presented by means of quantum kinetic equations in the density-matrix formalism. The derivation is straightforward so that advanced undergraduate students or early-year graduate students will be able to gain insight into the link between the microscopic Schrödinger equation and macroscopic transport.
Dependence of kinetic friction on velocity: master equation approach.
Braun, O M; Peyrard, M
2011-04-01
We investigate the velocity dependence of kinetic friction with a model that makes minimal assumptions on the actual mechanism of friction so that it can be applied at many scales, provided the system involves multicontact friction. Using a recently developed master equation approach, we investigate the influence of two concurrent processes. First, at a nonzero temperature, thermal fluctuations allow an activated breaking of contacts that are still below the threshold. As a result, the friction force monotonically increases with velocity. Second, the aging of contacts leads to a decrease of the friction force with velocity. Aging effects include two aspects: the delay in contact formation and aging of a contact itself, i.e., the change of its characteristics with the duration of stationary contact. All these processes are considered simultaneously with the master equation approach, giving a complete dependence of the kinetic friction force on the driving velocity and system temperature, provided the interface parameters are known.
On Some Properties of the Landau Kinetic Equation
NASA Astrophysics Data System (ADS)
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.
Kinetic equations modelling wealth redistribution: A comparison of approaches
NASA Astrophysics Data System (ADS)
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.
Coarse-grained kinetic equations for quantum systems
NASA Astrophysics Data System (ADS)
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.
Modifications of weighted Monte Carlo algorithms for nonlinear kinetic equations
NASA Astrophysics Data System (ADS)
Korotchenko, M. A.; Mikhailov, G. A.; Rogasinsky, S. V.
2007-12-01
Test problems for the nonlinear Boltzmann and Smoluchowski kinetic equations are used to analyze the efficiency of various versions of weighted importance modeling as applied to the evolution of multiparticle ensembles. For coagulation problems, a considerable gain in computational costs is achieved via the approximate importance modeling of the “free path” of the ensemble combined with the importance modeling of the index of a pair of interacting particles. A weighted modification of the modeling of the initial velocity distribution was found to be the most efficient for model solutions to the Boltzmann equation. The technique developed can be useful as applied to real-life coagulation and relaxation problems for which the model problems considered give approximate solutions.
Hamiltonian fluid reductions of drift-kinetic equations and the link with water-bags
NASA Astrophysics Data System (ADS)
Perin, M.; Chandre, C.; Tassi, E.
2016-07-01
Hamiltonian models for the first three moments of the drift-kinetic distribution function, namely the density, the fluid velocity and the parallel pressure, are derived from the Hamiltonian structure of the drift-kinetic equations. The link with the water-bag closure is established, showing that, unlike the one-dimensional Vlasov equations, these solutions are the only Hamiltonian fluid reductions for the drift-kinetic equation. These models are discussed through their equations of motion and their Casimir invariants.
Verification of continuum drift kinetic equation solvers in NIMROD
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.
Verification of continuum drift kinetic equation solvers in NIMROD
NASA Astrophysics Data System (ADS)
Held, E. D.; Kruger, S. E.; Ji, J.-Y.; Belli, E. A.; Lyons, B. C.
2015-03-01
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.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
The efficiency of several algorithms used for numerical integration of stiff ordinary differential equations was compared. The methods examined included two general purpose codes EPISODE and LSODE and three codes (CHEMEQ, CREK1D and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes were applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code available for the integration of combustion kinetic rate equations. It is shown that an iterative solution of the algebraic energy conservation equation to compute the temperature can be more efficient then evaluating the temperature by integrating its time-derivative.
CHEMSODE: A stiff ODE solver for the equations of chemical kinetics
Aro, C.J.
1995-01-01
This report describes the CHEMSODE package: a collection of FORTRAN subroutines for the automatic integration of systems of ordinary differential equations (ODEs) arising in atmospheric chemical kinetics. The mathematical basis and code are presented here.
Generalized Klein-Gordon and Dirac Equations from Nonlocal Kinetic Approach
NASA Astrophysics Data System (ADS)
El-Nabulsi, Rami Ahmad
2016-09-01
In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens's nonlocal-in-time kinetic energy approach, which is motivated from Feynman's kinetic energy functional formalism where the position differences are shifted with respect to one another. I proved that these generalized equations are similar to those obtained in literature in the presence of minimal length based on the Quesne-Tkachuk algebra.
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…
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.
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.
NASA Astrophysics Data System (ADS)
Saveliev, V. L.
2011-05-01
Pair collisions is the main interaction process in the Boltzmann gas dynamics. By making use of exactly the same physical assumptions as was used by Ludwig Boltzmann we write the kinetic equation for two-particle distribution function of molecules in the gas mixtures. Instead of the collision integral, there are the linear scattering operator and the chaos projector in the right part of this equation. Because the scattering operator is more simple then Boltzmann collision integral this equation opens new opportunities for mathematical description of the Boltzmann gas dynamics.
Integrating chemical kinetic rate equations by selective use of stiff and nonstiff methods
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
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.
Integrating chemical kinetic rate equations by selective use of stiff and nonstiff methods
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
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.
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.
A comparison of the efficiency of numerical methods for integrating chemical kinetic rate equations
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
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.
Contractivity of Transport Distances for the Kinetic Kuramoto Equation
NASA Astrophysics Data System (ADS)
Carrillo, José A.; Choi, Young-Pil; Ha, Seung-Yeal; Kang, Moon-Jin; Kim, Yongduck
2014-07-01
We present synchronization and contractivity estimates for the kinetic Kuramoto model obtained from the Kuramoto phase model in the mean-field limit. For identical Kuramoto oscillators, we present an admissible class of initial data leading to time-asymptotic complete synchronization, that is, all measure valued solutions converge to the traveling Dirac measure concentrated on the initial averaged phase. In the case of non-identical oscillators, we show that the velocity field converges to the average natural frequency proving that the oscillators move asymptotically with the same frequency under suitable assumptions on the initial configuration. If two initial Radon measures have the same natural frequency density function and strength of coupling, we show that the Wasserstein -distance between corresponding measure valued solutions is exponentially decreasing in time. This contraction principle is more general than previous -contraction properties of the Kuramoto phase model.
NASA Astrophysics Data System (ADS)
Seidi, M.; Behnia, S.; Khodabakhsh, R.
2014-09-01
Point reactor kinetics equations with one group of delayed neutrons in the presence of the time-dependent external neutron source are solved analytically during the start-up of a nuclear reactor. Our model incorporates the random nature of the source and linear reactivity variation. We establish a general relationship between the expectation values of source intensity and the expectation values of neutron density of the sub-critical reactor by ignoring the term of the second derivative for neutron density in neutron point kinetics equations. The results of the analytical solution are in good agreement with the results obtained with numerical solution.
Kinetic equation for collective modes of a Fermi system with free surface
NASA Astrophysics Data System (ADS)
Abrosimov, V.; Di Toro, M.; Strutinsky, V.
1993-09-01
A semiclassical approach for studying collective modes of finite Fermi systems is proposed on the basis of the Landau-Vlasov kinetic equation. In the theory the effective surface is explicitly used. The surface-motion equation is deduced. The problem is reduced to solving a linearized kinetic equation with mirror-reflection conditions at the free-moving effective surface. An equation for eigenfrequencies is obtained when the collision integral and the residual quasiparticle interaction in the bulk of the system are neglected. The eigenfrequencies for oscillations with multipolarities L > 0 are complex. A simple analytical solution is found for monopole eigenfrequencies. The properties of the first monopole mode agree with the ones derived in the corresponding RPA approximation.
NASA Astrophysics Data System (ADS)
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.
New integration techniques for chemical kinetic rate equations. 2: Accuracy comparison
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
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.
New integration techniques for chemical kinetic rate equations. II - Accuracy comparison
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
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.
Kinetic equations for a density matrix describing nonlinear effects in spectral line wings
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.
A generalized Fisher equation and its utility in chemical kinetics.
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.
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.
New integration techniques for chemical kinetic rate equations. I - Efficiency comparison
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
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.
Geodesic acoustic mode in anisotropic plasmas using double adiabatic model and gyro-kinetic equation
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.
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.
General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations
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.
Functional integral derivation of the kinetic equation of two-dimensional point vortices
NASA Astrophysics Data System (ADS)
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.
Sub- and superluminal kink-like waves in the kinetic limit of Maxwell-Bloch equations
NASA Astrophysics Data System (ADS)
Janowicz, Maciej; Holthaus, Martin
2011-01-01
Running-wave solutions to three systems of partial differential equations describing wave propagation in atomic media in the kinetic limit have been obtained. Those systems include approximations to (i) standard two-level Maxwell-Bloch equations; (ii) equations describing processes with saturated absorption in three-level systems and (iii) equations describing processes with reversed saturation in four-level systems. It has been shown that in all three cases kink-like solitary waves can emerge if the dynamical equation for the intensity includes a linear contribution to the Lambert-Beer law. Those solitary waves can propagate with either sub- or superluminal velocity of the edge of the kink, and in a direction which can be either the same as or opposite to that of the carrier wave. In addition, simple qualitative information about the behaviour of waves near the wavefronts has been obtained.
Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation
NASA Technical Reports Server (NTRS)
Spangler, Steven R.
1990-01-01
A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.
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
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.
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.
Creation of the set of kinetic equations for a nonideal gas near critical temperatures
NASA Astrophysics Data System (ADS)
Bishaev, A. M.; Rykov, V. A.
2015-01-01
In this article, the derivation of the Boltzmann equation from BBKIY of the chain is generalized for the case when the intermolecular interaction potential has both repulsive and attractive components. In this case, the application of the Bogolyubov method leads to situation when the term taking into account the transfer of molecules from the region where the hypothesis of the molecular chaos occurs into the region where molecules are arranged in a bound state is added to the usual collision integral. A two-particle distribution function of molecules in the bound state is assumed to be quasi-equilibrium with parameters depending on the variables that characterize the Boltzmann gas. Kinetic equations are written for these parameters performing the corresponding averaging over the region of bound states. Thus, this resulted in a closed set of kinetic equations describing nonideal gas. After introducing the corresponding macroparameters, all conservation laws and their consequences invariant relative to the Galileo transform follow from the corresponding set. The equation of state derived for such gas resembles the van der Waals equation by form. When considering the relaxation problem, the H-theorem is proven.
New forms of two-particle and one-particle kinetic equations
NASA Astrophysics Data System (ADS)
Saveliev, V. L.; Yonemura, S.
2012-11-01
Pair collisions are the main interaction process in the Boltzmann gas dynamics. By making use of exactly the same physical assumptions as was done by Ludwig Boltzmann we wrote the kinetic equation for two-particle distribution function of molecules in gas mixtures. Instead of the collision integral, there are the linear scattering operator and the chaos projector in the right part of this equation. We developed a new technique for factorization of the scattering operator on the bases of right inverses to the Casimir operator of the group of rotations. We exactly transformed the Boltzmann collision integral to the Landau-Fokker-Planck like form.
Analysis of atmospheric flow over a surface protrusion using the turbulence kinetic energy equation
NASA Technical Reports Server (NTRS)
Frost, W.; Harper, W. L.; Fichtl, G. H.
1975-01-01
Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Mean-flow results are compared with those given in a previous paper where the same problem was attacked using a Prandtl mixing-length hypothesis. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow. They highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient.
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.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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.
An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit
NASA Astrophysics Data System (ADS)
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.
A kinetic equation for linear stable fractional motion with applications to space plasma physics
Watkins, Nicholas W; Credgington, Daniel; Sanchez, Raul; Rosenberg, SJ; Chapman, Sandra C
2009-01-01
Levy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm) is a model process of this type, combining {alpha}-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk (CTRW), with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst 'sizes' and 'durations' in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.
NASA Astrophysics Data System (ADS)
Chiba, G.; Tsuji, M.; Narabayashi, T.
2014-04-01
In order to better predict a kinetic behavior of a nuclear fission reactor, an improvement of the delayed neutron parameters is essential. The present paper specifies important nuclear data for a reactor kinetics: Fission yield and decay constant data of 86Ge, some bromine isotopes, 94Rb, 98mY and some iodine isotopes. Their importance is quantified as sensitivities with a help of the adjoint kinetic equation, and it is found that they are dependent on an inserted reactivity (or a reactor period). Moreover, dependence of sensitivities on nuclear data files is also quantified using the latest files. Even though the currently evaluated data are used, there are large differences among different data files from a view point of the delayed neutrons.
Collision integrals and the generalized kinetic equation for charged particle beams
Tzenov, S. I.
1998-10-01
In the present paper we study the role of particle interactions on the evolution of a high energy beam. The interparticle forces taken into account are due to space charge alone. We derive the collision integral for a charged particle beam in the form of Balescu-Lenard and Landau and consider its further simplifications. Finally, the transition to the generalized kinetic equation has been accomplished by using the method of adiabatic elimination of fast variables.
Kinetic Formulation of the Kohn-Sham Equations for ab initio Electronic Structure Calculations
NASA Astrophysics Data System (ADS)
Mendoza, M.; Succi, S.; Herrmann, H. J.
2014-08-01
We introduce a new connection between density functional theory and kinetic theory. In particular, we show that the Kohn-Sham equations can be reformulated as a macroscopic limit of the steady-state solution of a suitable single-particle kinetic equation. We derive a Boltzmann-like equation for a gas of quasiparticles, where the potential plays the role of an external source that generates and destroys particles, so as to drive the system towards its ground state. The ions are treated as classical particles by using either the Born-Oppenheimer dynamics or by imposing concurrent evolution with the electronic orbitals. In order to provide quantitative support to our approach, we implement a discrete (lattice) kinetic model and compute the exchange and correlation energies of simple atoms and the geometrical configuration of the methane molecule. Moreover, we also compute the first vibrational mode of the hydrogen molecule, with both Born-Oppenheimer and concurrent dynamics. Excellent agreement with values in the literature is found in all cases.
Kinetic formulation of the Kohn-Sham Equations for ab initio electronic structure calculations.
Mendoza, M; Succi, S; Herrmann, H J
2014-08-29
We introduce a new connection between density functional theory and kinetic theory. In particular, we show that the Kohn-Sham equations can be reformulated as a macroscopic limit of the steady-state solution of a suitable single-particle kinetic equation. We derive a Boltzmann-like equation for a gas of quasiparticles, where the potential plays the role of an external source that generates and destroys particles, so as to drive the system towards its ground state. The ions are treated as classical particles by using either the Born-Oppenheimer dynamics or by imposing concurrent evolution with the electronic orbitals. In order to provide quantitative support to our approach, we implement a discrete (lattice) kinetic model and compute the exchange and correlation energies of simple atoms and the geometrical configuration of the methane molecule. Moreover, we also compute the first vibrational mode of the hydrogen molecule, with both Born-Oppenheimer and concurrent dynamics. Excellent agreement with values in the literature is found in all cases.
NASA Technical Reports Server (NTRS)
Radhadrishnan, Krishnan
1993-01-01
A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.
Proton-pumping mechanism of cytochrome c oxidase: a kinetic master-equation approach.
Kim, Young C; Hummer, Gerhard
2012-04-01
Cytochrome c oxidase is an efficient energy transducer that reduces oxygen to water and converts the released chemical energy into an electrochemical membrane potential. As a true proton pump, cytochrome c oxidase translocates protons across the membrane against this potential. Based on a wealth of experiments and calculations, an increasingly detailed picture of the reaction intermediates in the redox cycle has emerged. However, the fundamental mechanism of proton pumping coupled to redox chemistry remains largely unresolved. Here we examine and extend a kinetic master-equation approach to gain insight into redox-coupled proton pumping in cytochrome c oxidase. Basic principles of the cytochrome c oxidase proton pump emerge from an analysis of the simplest kinetic models that retain essential elements of the experimentally determined structure, energetics, and kinetics, and that satisfy fundamental physical principles. The master-equation models allow us to address the question of how pumping can be achieved in a system in which all reaction steps are reversible. Whereas proton pumping does not require the direct modulation of microscopic reaction barriers, such kinetic gating greatly increases the pumping efficiency. Further efficiency gains can be achieved by partially decoupling the proton uptake pathway from the active-site region. Such a mechanism is consistent with the proposed Glu valve, in which the side chain of a key glutamic acid shuttles between the D channel and the active-site region. We also show that the models predict only small proton leaks even in the absence of turnover. The design principles identified here for cytochrome c oxidase provide a blueprint for novel biology-inspired fuel cells, and the master-equation formulation should prove useful also for other molecular machines. . PMID:21946020
NASA Astrophysics Data System (ADS)
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.
Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna
2014-12-09
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
NASA Astrophysics Data System (ADS)
Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna
2014-12-01
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
From microscopic theory to Boltzmann kinetic equation: Application to vortex dynamics
NASA Astrophysics Data System (ADS)
Blatter, G.; Geshkenbein, V. B.; Kopnin, N. B.
1999-06-01
We show how to lift the problem of calculating the force acting on a topological defect in a superfluid from the microscopic to the semiclassical level: Starting from the microscopic kinetic equations for a clean superconductor, we derive a Boltzmann equation for the quasiparticle distribution function in and around the defect. The velocity q˙ and force p˙ appearing in this Boltzmann equation are given through the Hamiltonian equations q˙=∂pEn(p,q) and p˙=-∂qEn(p,q), where En(p,q) denotes the (nth branch in the) spectrum of the quasiparticles in the vicinity of the defect. Second, we reformulate the microscopic expression for the force acting on the defect in terms of the total momentum transfer of the quasiparticles from the heat bath to the vortex core. We illustrate our result with an application to vortices in s-wave superconductors, where we derive the vortex equation of motion and identify the Magnus, Hall, and dissipative forces.
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.
An asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations
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.
Convective kinetic energy equation under the mass-flux subgrid-scale parameterization
NASA Astrophysics Data System (ADS)
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.
Application of convergence acceleration to the reactor kinetic equations: A comparative study
Picca, P.; Furfaro, R.; Ganapol, B. D.
2013-07-01
This presentation provides a comparison of two methodologies for the solution of reactor kinetic equations, namely for a standard finite difference and a semi-analytical approach. The above-mentioned methods are implemented in a convergence acceleration framework to enhance their efficiency and a comparative study is reported to verify whether it is more convenient to use a rudimentary but fast algorithm (finite difference) with respect to the more refined but computationally intense approach of the semi-analytical method. Performance on several test cases from the literature are compared. (authors)
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.
Capolupo, A; Giampaolo, S M; Illuminati, F
2013-10-01
Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments.
Shtykov, N. M. Palto, S. P.; Umanskii, B. A.
2013-08-15
We report on the results of calculating the conditions for light generation in cholesteric liquid crystals doped with fluorescent dyes using kinetic equations. Specific features of spectral properties of the chiral cholesteric medium as a photonic structure and spatially distributed type of the feedback in the active medium are taken into account. The expression is derived for the threshold pump radiation intensity as a function of the dye concentration and sample thickness. The importance of taking into account the distributed loss level in the active medium for calculating the optimal parameters of the medium and for matching the calculated values with the results of experiments is demonstrated.
Theory of warm ionized gases: equation of state and kinetic Schottky anomaly.
Capolupo, A; Giampaolo, S M; Illuminati, F
2013-10-01
Based on accurate Lennard-Jones-type interaction potentials, we derive a closed set of state equations for the description of warm atomic gases in the presence of ionization processes. The specific heat is predicted to exhibit peaks in correspondence to single and multiple ionizations. Such kinetic analog in atomic gases of the Schottky anomaly in solids is enhanced at intermediate and low atomic densities. The case of adiabatic compression of noble gases is analyzed in detail and the implications on sonoluminescence are discussed. In particular, the predicted plasma electron density in a sonoluminescent bubble turns out to be in good agreement with the value measured in recent experiments. PMID:24229140
NASA Astrophysics Data System (ADS)
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.
Berry curvature and four-dimensional monopoles in the relativistic chiral kinetic equation.
Chen, Jiunn-Wei; Pu, Shi; Wang, Qun; Wang, Xin-Nian
2013-06-28
We derive a relativistic chiral kinetic equation with manifest Lorentz covariance from Wigner functions of spin-1/2 massless fermions in a constant background electromagnetic field. It contains vorticity terms and a four-dimensional Euclidean Berry monopole which gives an axial anomaly. By integrating out the zeroth component of the 4-momentum p, we reproduce the previous three-dimensional results derived from the Hamiltonian approach, together with the newly derived vorticity terms. The phase space continuity equation has an anomalous source term proportional to the product of electric and magnetic fields (FσρF[over ˜]σρ∼EσBσ). This provides a unified interpretation of the chiral magnetic and vortical effects, chiral anomaly, Berry curvature, and the Berry monopole in the framework of Wigner functions.
The solution of the point kinetics equations via converged accelerated Taylor series (CATS)
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)
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.
NASA Astrophysics Data System (ADS)
Doktorov, A. B.
2014-09-01
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.
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.
Muff, S; Caflisch, A
2009-03-12
It is difficult to investigate folding kinetics by conventional atomistic simulations of proteins. The replica exchange molecular dynamics (REMD) simulation technique enhances conformational sampling at the expenses of reduced kinetic information, which in REMD is directly available only for very short time scales. Here, we propose a procedure for obtaining kinetic data from REMD by making use of the equilibrium transitions network (ETN) sampled at the temperature of interest. This information is supplemented by mean folding times extracted from ETNs at higher REMD temperatures and scaled according to the Arrhenius equation. The procedure is applied to a three-stranded antiparallel beta-sheet peptide which has a very heterogeneous denatured state with a broad entropic basin and several enthalpic traps. Despite the complexity of the system and the REMD exchange time of only 0.1 ns, the procedure is able to estimate folding times (ranging from about 0.1 micros at the melting temperature of 330 K to about 8 micros at 286 K) as well as transition times from individual non-native basins to the native state.
Kinetic flux-vector splitting for the Navier-Stokes equations
Chou, S.Y.; Baganoff, D.
1997-01-15
Before a hybrid scheme can be developed combining the direct simulation Monte Carlo (DSMC) method and a Navier-Stokes (NS) representation, one must have access to compatible kinetic-split fluxes from the NS portion of the hybrid scheme. The kinetic theory basis is given for the development of the required fluxes from the Chapman-Enskog velocity distribution function for a simple gas; and these are then extended to a polyatomic gas by use of the Eucken approximation. The derived fluxes are then used to implement boundary conditions at solid surfaces that are based on concepts associated with kinetic theory and the DSMC method. This approach is shown to lead to temperature slip and velocity slip as a natural outcome of the new formulation, a requirement for use in the near-continuum regime where DSMC and NS must be joined. Several different flows, for which solid boundaries are not present, are computed using the derived fluxes, together with a second-order finite-volume scheme, and the results are shown to agree well with several established numerical schemes for the NS equations. 22 refs., 12 figs.
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.
NASA Astrophysics Data System (ADS)
Skartlien, R.; Grimes, B.; Meakin, P.; Sjöblom, J.; Sollum, E.
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 (2563 ˜ 107 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 form D ˜ [ln (ct)]α for the morphology length, or exponential scalings associated with arrested growth, on the basis of the phenomenological model.
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.
Solution of fractional kinetic equation by a class of integral transform of pathway type
NASA Astrophysics Data System (ADS)
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.
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.
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. PMID:27155630
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.
NASA Astrophysics Data System (ADS)
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.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
2014-12-26
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature – specifically, “jumps” in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique – both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
Conditions for critical effects in the mass action kinetics equations for water radiolysis
Wittman, Richard S.; Buck, Edgar C.; Mausolf, Edward J.; McNamara, Bruce K.; Smith, Frances N.; Soderquist, Chuck Z.
2014-11-25
We report on a subtle global feature of the mass action kinetics equations for water radiolysis that results in predictions of a critical behavior in H2O2 and associated radical concentrations. While radiolysis kinetics has been studied extensively in the past, it is only in recent years that high speed computing has allowed the rapid exploration of the solution over widely varying dose and compositional conditions. We explore the radiolytic production of H2O2 under various externally fixed conditions of molecular H2 and O2 that have been regarded as problematic in the literature – specifically, “jumps” in predicted concentrations, and inconsistencies between predictions and experiments have been reported for alpha radiolysis. We computationally map-out a critical concentration behavior for alpha radiolysis kinetics using a comprehensive set of reactions. We then show that all features of interest are accurately reproduced with 15 reactions. An analytical solution for steady-state concentrations of the 15 reactions reveals regions in [H2] and [O2] where the H2O2 concentration is not unique – both stable and unstable concentrations exist. The boundary of this region can be characterized analytically as a function of G-values and rate constants independent of dose rate. Physically, the boundary can be understood as separating a region where a steady-state H2O2 concentration exists, from one where it does not exist without a direct decomposition reaction. We show that this behavior is consistent with reported alpha radiolysis data and that no such behavior should occur for gamma radiolysis. We suggest experiments that could verify or discredit a critical concentration behavior for alpha radiolysis and could place more restrictive ranges on G-values from derived relationships between them.
PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY
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.
Padé Approximants for the Equation of State for Relativistic Hydrodynamics by Kinetic Theory
NASA Astrophysics Data System (ADS)
Tsai, Shang-Hsi; Yang, Jaw-Yen
2015-07-01
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.
Fillion-Gourdeau, F; Herrmann, H J; Mendoza, M; Palpacelli, S; Succi, S
2013-10-18
We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).
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.
NASA Astrophysics Data System (ADS)
Li, Zhihui; Wu, Junlin; Ma, Qiang; Jiang, Xinyu; Zhang, Hanxin
2014-12-01
Based on the Gas-Kinetic Unified Algorithm (GKUA) directly solving the Boltzmann model equation, the effect of rotational non-equilibrium is investigated recurring to the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant. The molecular velocity distribution function is integrated by the weight factor on the internal energy, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The optimization selection technique of discrete velocity ordinate points and numerical quadrature rules for macroscopic flow variables with dynamic updating evolvement are developed to simulate hypersonic flows, and the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in thermodynamic non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of Boltzmann model equation involving non-equilibrium effect is presented for the whole range of flow regimes. The hypersonic flows involving non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-Ma-25, the planar ramp flow with the whole range of Knudsen numbers of 0.0009-Kn-10 and the three-dimensional re-entering flows around tine double-cone body.
NASA Astrophysics Data System (ADS)
Gramstad, Odin; Babanin, Alexander
2016-04-01
An alternative model for the nonlinear interaction term S n l in spectral wave models, the so called generalized kinetic equation (Janssen J Phys Oceanogr 33(4):863-884, 2003; Annenkov and Shrira J Fluid Mech 561:181-207, 2006b; Gramstad and Stiassnie J Fluid Mech 718:280-303, 2013), is discussed and implemented in the third generation wave model WAVEWATCH-III. The generalized kinetic equation includes the effects of near-resonant nonlinear interactions, and is therefore able, in theory, to describe faster nonlinear evolution than the existing forms of S n l which are based on the standard Hasselmann kinetic equation (Hasselmann J Fluid Mech 12:481-500, 1962). Numerical simulations with WAVEWATCH have been carried out to thoroughly test the performance of the new form of S n l , and to compare it to the existing models for S n l in WAVEWATCH; the DIA and WRT. Some differences between the different models for S n l are observed. As expected, the DIA is shown to perform less well compared to the exact terms in certain situations, in particular for narrow wave spectra. Also for the case of turning wind significant differences between the different models are observed. Nevertheless, different from the case of unidirectional waves where the generalized kinetic equation represents a obvious improvement to the standard forms of S n l (Gramstad and Stiassnie 2013), the differences seems to be less pronounced for the more realistic cases considered in this paper.
Applications of nonlinear science and kinetic equations to the spread of epidemics
NASA Astrophysics Data System (ADS)
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.
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.
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-01-01
Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation.
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-08-01
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
Rudzinski, Wladyslaw; Plazinski, Wojciech
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.
NASA Astrophysics Data System (ADS)
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
Richardson, W.H. . E-mail: whr@stanford.edu
2006-06-15
A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.
Use of a generalized fisher equation for global optimization in chemical kinetics.
Villaverde, Alejandro F; Ross, John; Morán, Federico; Balsa-Canto, Eva; Banga, Julio R
2011-08-01
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.
NASA Technical Reports Server (NTRS)
Frost, W.; Harper, W. L.
1975-01-01
Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, STOL vehicles, etc.). Atmospheric flow fields resulting from a semi-elliptical surface obstruction in an otherwise horizontally homogeneous statistically stationary flow are modelled with the boundary-layer/Boussinesq-approximation of the governing equation of fluid mechanics. The turbulence kinetic energy equation is used to determine the dissipative effects of turbulent shear on the mean flow. Iso-lines of turbulence kinetic energy and turbulence intensity are plotted in the plane of the flow and highlight regions of high turbulence intensity in the stagnation zone and sharp gradients in intensity along the transition from adverse to favourable pressure gradient. Discussion of the effects of the disturbed wind field in CTOL and STOL aircraft flight path and obstruction clearance standards is given. The results indicate that closer inspection of these presently recommended standards as influenced by wind over irregular terrains is required.
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.
A unified gas-kinetic scheme for continuum and rarefied flows IV: Full Boltzmann and model equations
NASA Astrophysics Data System (ADS)
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
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…
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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
Steady-state benchmarks of DK4D: A time-dependent, axisymmetric drift-kinetic equation solver
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.
Steady-state benchmarks of DK4D: A time-dependent, axisymmetric drift-kinetic equation solvera)
NASA Astrophysics Data System (ADS)
Lyons, B. C.; Jardin, S. C.; Ramos, J. J.
2015-05-01
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.
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.
Weston, Ralph E; Nguyen, Thanh Lam; Stanton, John F; Barker, John R
2013-02-01
Ab initio microcanonical rate constants were computed using Semi-Classical Transition State Theory (SCTST) and used in two master equation formulations (1D, depending on active energy with centrifugal corrections, and 2D, depending on total energy and angular momentum) to compute temperature-dependent rate constants for the title reactions using a potential energy surface obtained by sophisticated ab initio calculations. The 2D master equation was used at the P = 0 and P = ∞ limits, while the 1D master equation with centrifugal corrections and an empirical energy transfer parameter could be used over the entire pressure range. Rate constants were computed for 75 K ≤ T ≤ 2500 K and 0 ≤ [He] ≤ 10(23) cm(-3). For all temperatures and pressures important for combustion and for the terrestrial atmosphere, the agreement with the experimental rate constants is very good, but at very high pressures and T ≤ 200 K, the theoretical rate constants are significantly smaller than the experimental values. This effect is possibly due to the presence in the experiments of dimers and prereactive complexes, which were not included in the model calculations. The computed H/D kinetic isotope effects are in acceptable agreement with experimental data, which show considerable scatter. Overall, the agreement between experimental and theoretical H/D kinetic isotope effects is much better than in previous work, and an assumption of non-RRKM behavior does not appear to be needed to reproduce experimental observations.
Iyer, Ramakrishnan; Mukhopadhyay, Ayan
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.
NASA Technical Reports Server (NTRS)
Pratt, D. T.; Radhakrishnan, K.
1986-01-01
The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.
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
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.
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.
NASA Astrophysics Data System (ADS)
Gladush, M. G.
2015-09-01
We obtained the system of Maxwell-Bloch equations (MB) that describe the interaction of cw laser with optically active impurity centers (particles) embedded in a dielectric material. The dielectric material is considered as a continuous medium with sufficient laser detuning from its absorption lines. The model takes into account the effects associated with both the real and the imaginary part of the dielectric constant of the material. MB equations were derived within a many-particle quantum-kinetic formalism, which is based on Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for reduced density matrices and correlation operators of material particles and the quantized radiation field modes. It is shown that this method is beneficial to describe the effects of individual and collective behavior of the light emitters and requires no phenomenological procedures. It automatically takes into account the characteristics associated with the presence of non-resonant and resonant particles filling the space between the optical centers.
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.
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.
NASA Astrophysics Data System (ADS)
Yoshizawa, Akira; Abe, Hiroyuki; Matsuo, Yuichi; Fujiwara, Hitoshi; Mizobuchi, Yasuhiro
2012-07-01
A Reynolds-averaged approach to turbulent shear flows is sought with resort to a three-equation method. Its novelty is the introduction of a turbulent-viscosity transport equation through the transport equation for the Reynolds stress in addition to those for the turbulent kinetic energy and the dissipation rate. The latter two equations are used for evaluating the dimensional coefficients in the former. The aim of this model is to enhance the capability to cope with nonstationary and advection effects in various turbulent flows. The adaptability to them is confirmed through the application to homogeneous-shear and supersonic free-shear flows. In particular, the reasonable prediction is obtained in the latter where the growth rate of the shear layer is suppressed with the increase in the convective Mach number. The present model is also applied to a three-dimensional flow past a wing tip as an instance of complex aeronautical flows, and the excessive diffusion of the trailing vortices is shown to be suppressed. The turbulent-viscosity representation for the Reynolds stress is systematically supplemented with nonlinear effects of mean-velocity gradient tensors, and its adequacy is verified in a channel flow.
NASA Astrophysics Data System (ADS)
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.
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. PMID:25224341
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.
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.
Equations for the Cabrera-Mott kinetics of oxidation for spherical nanoparticles
NASA Astrophysics Data System (ADS)
Ermoline, Alexandre; Dreizin, Edward L.
2011-03-01
Equations describing formation of a spherical oxide shell according to the Cabrera-Mott mechanism are presented. Two different configurations of metal and oxidizer are considered: oxidation of a spherical metal particle in surrounding oxidizer, and reduction of a spherical oxide inclusion in a metal matrix. Equations for the former configuration were reported earlier but did not explicitly account for volume changes in the growing oxide shell and shrinking central core. For aluminum oxidation, the correction for these volume changes is significant for spherical particles with diameters less than 10 nm.
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.
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.
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.
Thermostatted kinetic equations as models for complex systems in physics and life sciences
NASA Astrophysics Data System (ADS)
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.
Benisti, Didier; Yampolsky, Nikolai A.; Fisch, Nathaniel J.
2012-01-15
In this paper, we compare two recent models [N. A. Yampolsky and N. J. Fisch, Phys. Plasmas 16, 072104 (2009); D. Benisti, D. J. Strozzi, L. Gremillet, and O. Morice, Phys. Rev. Lett. 103, 155002 (2009)] introduced to predict the nonlinear growth of stimulated Raman scattering in the kinetic regime, and providing moreover a nonlinear description of the collisionless, Landau-like, damping rate of the driven electron plasma wave. We first recall the general theoretical framework common to these two models, based on the derivation of the imaginary part of the electron susceptibility, {chi}{sub i}, and then discuss in detail why the two approaches differ. By comparing the theoretical predictions for {chi}{sub i} to those derived from test particle or Vlasov simulations, we moreover discuss the range of validity of the two models.
Master equation for a kinetic model of a trading market and its analytic solution.
Chatterjee, Arnab; Chakrabarti, Bikas K; Stinchcombe, Robin B
2005-08-01
We analyze an ideal-gas-like model of a trading market with quenched random saving factors for its agents and show that the steady state income (m) distribution P(m) in the model has a power law tail with Pareto index nu exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of P(m) . Precise solutions are then obtained in some special cases. PMID:16196663
NASA Astrophysics Data System (ADS)
Morii, Youhi; Terashima, Hiroshi; Koshi, Mitsuo; Shimizu, Taro; Shima, Eiji
2016-10-01
We herein propose a fast and robust Jacobian-free time integration method named as the extended robustness-enhanced numerical algorithm (ERENA) to treat the stiff ordinary differential equations (ODEs) of chemical kinetics. The formulation of ERENA is based on an exact solution of a quasi-steady-state approximation that is optimized to preserve the mass conservation law through use of a Lagrange multiplier method. ERENA exhibits higher accuracy and faster performance in homogeneous ignition simulations compared to existing popular explicit and implicit methods for stiff ODEs such as VODE, MTS, and CHEMEQ2. We investigate the effects of user-specified threshold values in ERENA, to provide trade-off information between the accuracy and the computational cost.
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.
Kinetic equations and mechanisms for activation and inhibition in enzyme systems.
Laidler, K J
1983-11-01
The rates of enzyme reactions that are activated or inhibited by added modifiers can in some cases be expressed as a rational function of the first degree, v = (alpha 0 + alpha 1[Q] )/(beta 0 + beta 1 [Q] ) where [Q] is the concentration of the modifier and alpha 0, alpha 1, beta 0, and beta 1 are functions of rate constants and sometimes of the enzyme and substrate concentrations; the behaviour is then said to be linear. Three simple mechanisms that give rise to linear kinetics are examined, and the conditions under which there is activation or inhibition are determined. Sometimes there is a transition from activation to inhibition as the substrate concentration is varied. Definitions of competitive, uncompetitive, and noncompetitive activation are suggested, by analogy with the generally accepted definitions for inhibition. In second-degree activation or inhibition the rate can be expressed as the ratio of two quadratic polynomials with positive coefficients. Ten patterns are then possible for plots of v against [Q], and they may be classified with respect to (i) overall activation or inhibition, (ii) initial (at [Q] leads to 0) activation or inhibition, (iii) terminal (at [Q] leads to oo) activation or inhibition, and (iv) whether there is an initial inflexion. The general case of an n:n rational function is also discussed.
NASA Astrophysics Data System (ADS)
Watkins, N. W.; Rosenberg, S.; Sanchez, R.; Chapman, S. C.; Credgington, D.
2008-12-01
Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototype) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold. This problem relates to the burst size measure introduced by Takalo and Consolini into solar-terrestrial physics and further studied by Freeman et al [PRE, 2000] on solar wind Poynting flux near L1. We test how expressions derived by other authors generalise to the non-Gaussian, constant threshold problem. Ongoing work on extension of these LFSM results to multifractals will also be discussed.
NASA Astrophysics Data System (ADS)
Grima, R.
2010-07-01
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 Ω-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 regions of
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
Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion.
Fröhlich, Fabian; Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J; Grima, Ramon; Hasenauer, Jan
2016-07-01
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
Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion.
Fröhlich, Fabian; Thomas, Philipp; Kazeroonian, Atefeh; Theis, Fabian J; Grima, Ramon; Hasenauer, Jan
2016-07-01
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.
Inference for Stochastic Chemical Kinetics Using Moment Equations and System Size Expansion
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
NASA Astrophysics Data System (ADS)
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.
Igor D. Kaganovich; Oleg Polomarov
2003-05-19
In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated.
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.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Caillol, P.; Zeitlin, V.
2000-07-01
An ensemble of random-phase internal gravity waves is considered in the dynamical framework of the Euler-Boussinesq equations. For flows with zero mean potential vorticity, a kinetic equation for the mean spectral energy density of the waves is obtained under hypothesis of Gaussian statistics with zero correlation length. Stationary scaling solutions of this equation are found for almost vertically propagating waves. The resulting spectra are anisotropic in vertical and horizontal wave numbers. For flows with small but non-zero mean potential vorticity, under the same statistical hypothesis applied to the wave part of the flow, it is shown that the vortex part and the wave part decouple. The vortex part obeys a limiting slow dynamics equation exhibiting vertical collapse and layering which may contaminate the wave-part spectra. Relation of these results to the in situ atmospheric measurements and previous work on oceanic gravity waves is discussed.
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. PMID:19062839
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
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].
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.
2000-03-20
Given the space-independent, one energy group reactor kinetics equations and the initial conditions, this prgram determines the time variation of reactivity required to produce the given input of flux-time data.
Bizarro, J.P.; Belo, J.H.; Figueiredo, A.C.
1997-06-01
Knowing that short-time propagators for Fokker{endash}Planck equations are Gaussian, and based on a path-sum formulation, an efficient and simple numerical method is presented to solve the initial-value problem for electron kinetics during rf heating and current drive. The formulation is thoroughly presented and discussed, its advantages are stressed, and general, practical criteria for its implementation are derived regarding the time step and grid spacing. The new approach is illustrated and validated by solving the one-dimensional model for lower-hybrid current drive, which has a well-known steady-state analytical solution. {copyright} {ital 1997 American Institute of Physics.}
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
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
NASA Astrophysics Data System (ADS)
Abourabia, Aly Maher; Wahid, Taha Zakaraia Abdel
2011-05-01
A new approach for studying the influence of a thermal radiation field upon a rarefied neutral gas is introduced. We insert the radiation field effect in the force term of the Boltzmann equation. In a frame co-moving with the fluid, the BGK (Bhatnager-Gross-Krook) model kinetic equation is applied analytically. The one-dimensional steady problem is studied using the Liu-Lees model. We apply the moment method to follow the behavior of the macroscopic properties of the gas, such as the temperature and concentration. They are substituted into the corresponding two-stream Maxwellian distribution functions, permitting the investigation of the non-equilibrium thermodynamic properties of the system (gas + heated plate). The entropy, entropy flux, entropy production, thermodynamic forces and the kinetic coefficients are obtained. We verify the celebrated Onsager reciprocity relations for the system. The ratios between the different contributions of the internal energy changes based upon the total derivatives of the extensive parameters are estimated via the Gibbs formula. The results are applied to the Helium gas for various radiation field intensities due to different plate temperatures. Figures illustrating the calculated variables are drawn to predict their behavior and the results are discussed.
NASA Astrophysics Data System (ADS)
Zizin, M. N.; Ivanov, L. D.
2013-12-01
In the present paper, an attempt is made to analyze the accuracy of calculating the effectiveness of the VVER-1000 reactor scram system by means of the inverted solution of the kinetics equation (ISKE). In the numerical studies in the intellectual ShIPR software system, the actuation of the reactor scram system with the possible jamming of one of the two most effective rods is simulated. First, the connection of functionals calculated in the space-time computation in different approximations with the kinetics equation is considered on the theoretical level. The formulas are presented in a manner facilitating their coding. Then, the results of processing of several such functions by the ISKE are presented. For estimating the effectiveness of the VVER-1000 reactor scram system, it is proposed to use the measured currents of ionization chambers (IC) jointly with calculated readings of IC imitators. In addition, the integral of the delayed neutron (DN) generation rate multiplied by the adjoint DN source over the volume of the reactor, calculated for the instant of time when insertion of safety rods ends, is used. This integral is necessary for taking into account the spatial reactivity effects. Reasonable agreement was attained for the considered example between the effectiveness of the scram system evaluated by this method and the values obtained by steady-state calculations as the difference of the reciprocal effective multiplication factors with withdrawn and inserted control rods. This agreement was attained with the use of eight-group DN parameters.
Yao, Chung-Tay; Lai, Ching-Long; Hsieh, Hsiu-Shan; Chi, Chin-Wen; Yin, Shih-Jiun
2010-09-01
Alcohol dehydrogenase (ADH) catalyzes oxidation of ingested ethanol to acetaldehyde, the first step in hepatic metabolism. The purpose of this study was to establish an ex vivo rat liver perfusion system under defined and verified steady states with respect to the metabolites and the metabolic rates, and to quantitatively correlate the observed rates with simulations based on the kinetic mechanism-based rate equations of rat liver ADH. Class I ADH1 was isolated from male Sprague-Dawley rats and characterized by steady-state kinetics in the Krebs-Ringer perfusion buffer with supplements. Nonrecirculating liver perfusion with constant input of ethanol at near physiological hepatic blood flow rate was performed in situ. Ethanol and the related metabolites acetaldehyde, acetate, lactate, and pyruvate in perfusates were determined. Results of the initial velocity, product, and dead-end inhibition studies showed that rat ADH1 conformed to the Theorell-Chance Ordered Bi Bi mechanism. Steady-state metabolism of ethanol in the perfused liver maintained up to 3h as evidenced by the steady-state levels of ethanol and metabolites in the effluent, and the steady-state ethanol disappearance rates and acetate production rates. The changes of the metabolic rates were qualitatively and in general quantitatively correlated to the results from simulations with the kinetic rate equations of ADH1 under a wide range of ethanol, in the presence of competitive inhibitor 4-methylpyrazole and of uncompetitive inhibitor isobutyramide. Preliminary flux control analysis estimated that apparent C(ADH)(J) in the perfused liver may approximate 0.7 at constant infusion with 1-2 mM ethanol, suggesting that ADH plays a major but not the exclusive role in governing hepatic ethanol metabolism. The reported steady-state rat liver perfusion system may potentially be applicable to other drug or drug-ethanol interaction studies.
Miller, D M
1965-07-01
Equations describing the movement of sugars during induced uphill transport were derived on the assumption of a simple carrier transport mechanism and subjected to experimental verification. Since there was good agreement between the experimental points and the theoretical curves, no changes in the original postulates were required.
Abedi-Varaki, Mehdi; Ganjovi, Alireza; Shojaei, Fahimeh; Hassani, Zahra
2015-01-01
In this work, a zero-dimensional kinetics model is used to study the temporal behavior of different species such as charged particles, radicals and excited states inside a Dielectric Barrier Discharge plasma reactor. It is shown that, the reactor significantly reduces the concentration of nitrogen monoxide as an environmental pollutant. After a drastic increase, a decrease in the concentration of the NO2 molecules inside the reactor is seen. Nitrogen monoxide molecules with a very low concentration are produced inside the reactor and its quick conversion to other products is proved. The obtained results are compared with the existing experimental and simulation findings, whenever possible.
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.
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.
Stability of Planar Fronts for a Non-Local Phase Kinetics Equation with a Conservation Law in D ≤ 3
NASA Astrophysics Data System (ADS)
Carlen, Eric A.; Orlandi, Enza
2012-05-01
We consider, in a D-dimensional cylinder, a non-local evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider sub-critical temperatures, for which there are two local spatially homogeneous equilibria, and show a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibrium; i.e. the planar fronts: We show that an initial perturbation of a front that is sufficiently small in L2 norm, and sufficiently localized yields a solution that relaxes to another front, selected by a conservation law, in the L1 norm at an algebraic rate that we explicitly estimate. We also obtain rates for the relaxation in the L2 norm and the rate of decrease of the excess free energy.
Topham, C M; Brocklehurst, K
1992-01-01
1. The suggestion by Segel & Martin [(1988) J. Theor. Biol. 135, 445-453] that the well-known schematic method for the derivation of rate equations for combined quasi-equilibrium-steady-state models proposed by Cha [(1968) J. Biol. Chem. 243, 820-825] may not be generally applicable was shown to be incorrect. By contrast, Cha's method was shown (a) to yield correct initial-rate equations that are exact and (b) not to require any constraints on the relative magnitudes of rate constants for slow steps outside the quasi-equilibrium segments of the kinetic model, including those suggested by Segel & Martin. 2. Examination of residual King-Altman patterns for the general modifier model of Botts & Morales [(1953) Trans. Faraday Soc. 49, 696-707] revealed the reasons for the erroneous conclusions reached by Segel & Martin. The errors arise from the failure to take account of fluxes in parallel pathways that connect the two isolated groups of enzyme species existing in quasi-equilibrium with the modifier. 3. A similar failure to take explicit account of parallel pathways in a thermodynamic box that delayed proper appreciation of the form of pH-dependence of kcat/Km is briefly discussed. PMID:1540141
Moll-Navarro, M J; Merino, M; Casabó, V G; Nácher, A; Polache, A
1996-11-01
Previous studies showed that the in situ absorption of baclofen in rat jejunum was inhibited by beta-alanine, a nonessential amino acid, and therefore mediated, at least in part, by some beta-amino acid carrier. In this paper a similar study was undertaken using taurine, a sulfonic beta-amino acid, in order to evaluate its effect and to establish a general inhibition model. To achieve this goal, remaining concentrations of inhibitor were also measured and incorporated into the model. Previously, kinetic absorption in situ parameters for taurine in free solution were obtained: Vm = 27.73 +/- 9.99 mM h-1, K(m) = 8.06 +/- 2.82 mM, Ka (passive difussion component) = 0.40 +/- 0.28 h-1. Isotonic solutions containing 0.5 mM baclofen with starting taurine concentrations ranging from 0 to 100 mM were perfused in rat jejunum, and the remaining concentrations of both compounds were measured. The apparent rate pseudoconstant of the drug clearly decreased as the remaining taurine concentration increased. The interaction can be described as a complete competitive inhibition plus a second component, K, noninhibited, K = 0.58 (+/- 0.03) h-1, Ki = 20.62 (+/- 4.04) mM, Vmi = 28.12 (+/- 6.12) mM h-1, Kmi = 11.71 (+/- 2.53) mM, Kai = 0.47 (+/- 0.10) h-1. A residual absorption of baclofen in the presence of high taurine concentrations was observed, which should be attributed to another transport system not associated with the taurine carrier. In order to elucidate whether or not taurine and beta-alanine carriers are two separate entities that baclofen can use for absorption, further experiments using beta-alanine and taurine together as inhibitors (baclofen, 0.5 mM; beta-alanine, 50 mM, and taurine, 50 mM) were developed. Results indicated that baclofen and both amino acids share the same carrier in the intestinal absorption process. We have completed studies using leucine, taurine, and GABA together as inhibitors of drug absorption. An isotonic perfusion solution of 0.5 mM baclofen in
NASA Astrophysics Data System (ADS)
Pöschl, U.; Rudich, Y.; Ammann, M.
2005-04-01
Aerosols and clouds play central roles in atmospheric chemistry and physics, climate, air pollution, and public health. The mechanistic understanding and predictability of aerosol and cloud properties, interactions, transformations, and effects are, however, still very limited. This is due not only to the limited availability of measurement data, but also to the limited applicability and compatibility of model formalisms used for the analysis, interpretation, and description of heterogeneous and multiphase processes. To support the investigation and elucidation of atmospheric aerosol and cloud surface chemistry and gas-particle interactions, we present a comprehensive kinetic model framework with consistent and unambiguous terminology and universally applicable rate equations and parameters. It allows to describe mass transport and chemical reactions at the gas-particle interface and to link aerosol and cloud surface processes with gas phase and particle bulk processes in systems with multiple chemical components and competing physicochemical processes. The key elements and essential aspects of the presented framework are: a simple and descriptive double-layer surface model (sorption layer and quasi-static layer); straightforward flux-based mass balance and rate equations; clear separation of mass transport and chemical reactions; well-defined rate parameters (uptake and accommodation coefficients, reaction and transport rate coefficients); clear distinction between gas phase, gas-surface, and surface-bulk transport (gas phase diffusion correction, surface and bulk accommodation); clear distinction between gas-surface, surface layer, and surface-bulk reactions (Langmuir-Hinshelwood and Eley-Rideal mechanisms); mechanistic description of concentration and time dependencies; flexible inclusion/omission of chemical species and physicochemical processes; flexible convolution/deconvolution of species and processes; and full compatibility with traditional resistor model
Macnamara, Shev; Bersani, Alberto M; Burrage, Kevin; Sidje, Roger B
2008-09-01
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.
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.
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
NASA Technical Reports Server (NTRS)
Shoub, E. C.
1977-01-01
The problem of calculating the steady-state free-electron energy distribution in a hydrogen gas is considered in order to study departures of that distribution from a Maxwellian at sufficiently low degrees of ionization. A model kinetic equation is formulated and solved analytically for the one-particle electron distribution function in a steady-state partially ionized hydrogen gas, and it is shown that the formal solution can be accurately approximated by using the WKB method. The solutions obtained indicate that the high-energy tail of the distribution is susceptible to distortion by imbalanced inelastic collisions for ionization fractions not exceeding about 0.1 and that such departures from a Maxwellian can lead to significant changes in the collisional excitation and ionization rates of ground-state hydrogen atoms. Expressions for the electron-hydrogen collision rates are derived which explicitly display their dependence on the hydrogen departure coefficients. The results are applied in order to compare self-consistent predictions with those based on the a priori assumption of a Maxwellian distribution for models of the thermal ionization equilibrium of hydrogen in the optically thin limit, spectral-line formation by a gas consisting of two-level atoms, and radiative transfer in finite slabs by a gas of four-level hydrogen atoms.
NASA Astrophysics Data System (ADS)
Pöschl, U.; Rudich, Y.; Ammann, M.
2007-12-01
Aerosols and clouds play central roles in atmospheric chemistry and physics, climate, air pollution, and public health. The mechanistic understanding and predictability of aerosol and cloud properties, interactions, transformations, and effects are, however, still very limited. This is due not only to the limited availability of measurement data, but also to the limited applicability and compatibility of model formalisms used for the analysis, interpretation, and description of heterogeneous and multiphase processes. To support the investigation and elucidation of atmospheric aerosol and cloud surface chemistry and gas-particle interactions, we present a comprehensive kinetic model framework with consistent and unambiguous terminology and universally applicable rate equations and parameters. It enables a detailed description of mass transport and chemical reactions at the gas-particle interface, and it allows linking aerosol and cloud surface processes with gas phase and particle bulk processes in systems with multiple chemical components and competing physicochemical processes. The key elements and essential aspects of the presented framework are: a simple and descriptive double-layer surface model (sorption layer and quasi-static layer); straightforward flux-based mass balance and rate equations; clear separation of mass transport and chemical reactions; well-defined and consistent rate parameters (uptake and accommodation coefficients, reaction and transport rate coefficients); clear distinction between gas phase, gas-surface, and surface-bulk transport (gas phase diffusion, surface and bulk accommodation); clear distinction between gas-surface, surface layer, and surface-bulk reactions (Langmuir-Hinshelwood and Eley-Rideal mechanisms); mechanistic description of concentration and time dependences (transient and steady-state conditions); flexible addition of unlimited numbers of chemical species and physicochemical processes; optional aggregation or resolution
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.
Brownian motion from Boltzmann's equation.
NASA Technical Reports Server (NTRS)
Montgomery, D.
1971-01-01
Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.
NASA Astrophysics Data System (ADS)
Babintsev, Ilya A.; Adzhemyan, Loran Ts.; Shchekin, Alexander K.
2014-08-01
The eigenvalues and eigenvectors of the matrix of coefficients of the linearized kinetic equations applied to aggregation in surfactant solution determine the full spectrum of characteristic times and specific modes of micellar relaxation. The dependence of these relaxation times and modes on the total surfactant concentration has been analyzed for concentrations in the vicinity and well above the second critical micelle concentration (cmc2) for systems with coexisting spherical and cylindrical micelles. The analysis has been done on the basis of a discrete form of the Becker-Döring kinetic equations employing the Smoluchowsky diffusion model for the attachment rates of surfactant monomers to surfactant aggregates with matching the rates for spherical aggregates and the rates for large cylindrical micelles. The equilibrium distribution of surfactant aggregates in solution has been modeled as having one maximum for monomers, another maximum for spherical micelles and wide slowly descending branch for cylindrical micelles. The results of computations have been compared with the analytical ones known in the limiting cases from solutions of the continuous Becker-Döring kinetic equation. They demonstrated a fair agreement even in the vicinity of the cmc2 where the analytical theory looses formally its applicability.
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.
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Truskinovsky, Lev; Vainchtein, Anna
2010-09-01
We introduce the concept of kinetic or rate equations for moving defects representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries, link the instantaneous value of the velocity of a defect with an instantaneous value of the driving force. The new approach generalizes kinetic relations by implying a relation between the velocity and the driving force which is nonlocal in time. To make this relation explicit one may need to integrate a system of kinetic equations. We illustrate the difference between kinetic relation and kinetic equations by working out in full detail a prototypical model of an overdamped defect in a one-dimensional discrete lattice. We show that the minimal nonlocal kinetic description, containing now an internal time scale, is furnished by a system of two ordinary differential equations coupling the spatial location of defect with another internal parameter that describes configuration of the core region.
NASA Astrophysics Data System (ADS)
Wang, L. W.; Fecht, H.-J.
2008-12-01
On the basis of the kinetic model for liquids, which gave a quantitative description of liquid substructures, atomic relaxations in a model liquid were calculated. A crossover temperature Tcoop was recognized: relaxations were noncooperative at temperatures above Tcoop while cooperative below Tcoop. The cooperation in relaxation was responsible for the very slow dynamics near glass transition, departing significantly from the Arrhenius relation. This found supports in a large variety of glass forming liquids. The degree of cooperation in relaxation was straightforwardly determined by the number of atoms, N, in the liquid substructure and was responsible for the fragility of liquids: the larger the N was, the more fragile a liquid was.
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…
Nuclear Reactor Kinetics and Control.
JEFFERY,; LEWINS, D.
2009-07-27
Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Nuclear Reactor Kinetics and Control, Pergamon Press, London, 275 pages, 1978. 1. Introductory Review 2. Neutron and Precursor Equations 3. Elementary Solutions of the Kinetics Equations at Low Power 4. Linear Reactor Process Dynamics with Feedback 5. Power Reactor Control Systems 6. Fluctuations and Reactor Noise 7. Safety and Reliability 8. Non Linear Systems; Stability and Control 9. Analogue Computing Addendum: Jay Basken and Jeffery D. Lewins: Power Series Solution of the Reactor Kinetics Equations, Nuclear Science and Engineering: 122, 407-436 (1996) (authorized for distribution with the book: courtesy of the American Nuclear Society)
NASA Astrophysics Data System (ADS)
Carlen, E. A.; Carvalho, M. C.; Orlandi, E.
1999-06-01
This is the first of two papers devoted to the study of a nonlocal evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider subcritical temperatures, for which there are two local equilibria, and begin the proof of a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibria; i.e., the fronts. We shall show in the second paper that an initial perturbation v 0 of a front that is sufficiently small in L 2 norm, and sufficiently localized that ∫ x 2 v 0( x)2 dx<∞, yields a solution that relaxes to another front, selected by a conservation law, in the L 1 norm at an algebraic rate that we explicitly estimate. There we also obtain rates for the relaxation in the L 2 norm and the rate of decrease of the excess free energy. Here we prove a number of estimates essential for this result. Moreover, the estimates proved here suffice to establish the main result in an important special case.
Enskog-like kinetic models for vehicular traffic
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.
Modeling of Reactor Kinetics and Dynamics
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.
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)
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)
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).
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)
Nonlinear gyrokinetic equations
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.
Nuclear Reactor Kinetics and Control.
2009-07-27
Version 00 Dr. J.D. Lewins has now released the following legacy book for free distribution: Nuclear Reactor Kinetics and Control, Pergamon Press, London, 275 pages, 1978. 1. Introductory Review 2. Neutron and Precursor Equations 3. Elementary Solutions of the Kinetics Equations at Low Power 4. Linear Reactor Process Dynamics with Feedback 5. Power Reactor Control Systems 6. Fluctuations and Reactor Noise 7. Safety and Reliability 8. Non Linear Systems; Stability and Control 9. Analogue Computingmore » Addendum: Jay Basken and Jeffery D. Lewins: Power Series Solution of the Reactor Kinetics Equations, Nuclear Science and Engineering: 122, 407-436 (1996) (authorized for distribution with the book: courtesy of the American Nuclear Society)« less
Analytic solutions of the relativistic Boltzmann equation
NASA Astrophysics Data System (ADS)
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.
THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES
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 ...
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.
Yost, F.G.
2000-04-14
The importance of interfacial processes in materials joining has a long history. A significant amount of work has suggested that processes collateral to wetting can affect the extent of wetting and moderate or retard wetting rate. Even very small additions of a constituent, known to react with the substrate, cause pronounced improvement in wetting and are exploited in braze alloys, especially those used for joining to ceramics. In the following a model will be constructed for the wetting kinetics of a small droplet of metal containing a constituent that diffuses to the wetting line and chemically reacts with a flat, smooth substrate. The model is similar to that of Voitovitch et al. and Mortensen et al. but incorporates chemical reaction kinetics such that the result contains both diffusion and reaction kinetics. The model is constructed in the circular cylinder coordinate system, satisfies the diffusion equation under conditions of slow flow, and considers diffusion and reaction at the wetting line to be processes in series. This is done by solving the diffusion equation with proper initial and boundary conditions, computing the diffusive flux at the wetting line, and equating this to both the convective flux and reaction flux. This procedure is similar to equating the current flowing in components of a series circuit. The wetting rate will be computed versus time for a variety of diffusion and reaction conditions. A transition is observed from nonlinear (diffusive) to linear (reactive) behavior as the control parameters (such as the diffusion coefficient) are modified. This is in agreement with experimental observations. The adequacy of the slow flow condition, used in this type of analysis, is discussed and an amended procedure is suggested.
Multiflow approach to plasma kinetics
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.
YOST, FREDERICK G.
1999-09-09
The importance of interfacial processes in materials joining has a long history. A significant amount of work has suggested that processes collateral to wetting can affect the extent of wetting and moderate or retard wetting rate. Even very small additions of a constituent, known to react with the substrate, cause pronounced improvement in wetting and are exploited in braze alloys, especially those used for joining to ceramics. The wide diversity of processes, such as diffusion, chemical reaction, and fluxing, and their possible combinations suggest that various rate laws should be expected for wetting kinetics depending on the controlling processes. These rate laws are expected to differ crucially from the standard fluid controlled wetting models found in the literature. Voitovitch et al. and Mortensen et al. have shown data that suggests diffusion control for some systems and reaction control for others. They also presented a model of wetting kinetics controlled by the diffusion of a constituent contained by the wetting fluid. In the following a model will be constructed for the wetting kinetics of a small droplet of metal containing a constituent that diffuses to the wetting line and chemically reacts with a flat, smooth substrate. The model is similar to that of Voitovitch et al. and Mortensen et al. but incorporates chemical reaction kinetics such that the result contains both diffusion and reaction kinetics. The model is constructed in the circular cylinder coordinate system, satisfies the diffusion equation under conditions of slow flow, and considers diffusion and reaction at the wetting line to be processes in series. This is done by solving the diffusion equation with proper initial and boundary conditions, computing the diffusive flux at the wetting line and equating this to both the convective flux and reaction flux. This procedure is similar to equating the current flowing in components of a series circuit. The wetting rate will be computed versus time
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)
Kinetics of protein aggregation
NASA Astrophysics Data System (ADS)
Knowles, Tuomas
2015-03-01
Aggregation into linear nanostructures, notably amyloid and amyloid-like fibrils, is a common form of behaviour exhibited by a range of peptides and proteins. This process was initially discovered in the context of the aetiology of a range of neurodegenerative diseases, but has recently been recognised to of general significance and has been found at the origin of a number of beneficial functional roles in nature, including as catalytic scaffolds and functional components in biofilms. This talk discusses our ongoing efforts to study the kinetics of linear protein self-assembly by using master equation approaches combined with global analysis of experimental data.
Chemical kinetics of geminal recombination
Levin, P.P.; Khudyakov, I.V.; Brin, E.F.; Kuz'min, V.A.
1988-09-01
The kinetics of geminal recombination of triplet radical pairs formed in photoreduction of benzophenone by p-cresol in glycerin solution was studied by pulsed laser photolysis. The experiments were conducted at several temperatures and in a constant magnetic field of H = 0.34 T. The parameters in six kinetic equations describing geminal recombination were determined with a computer. The values of the sums of the squares of the residual deviations of the approximation were obtained. It was found that the kinetics are best described by the functions proposed by Noyes and Shushin. It was shown that it is necessary to use the mutual diffusion coefficient of the radicals, which is significantly smaller than the sum of the estimations of the experimental values of the radical diffusion coefficients, for describing the kinetics due to the correlations of the molecular motions of the radicals in the cage.
The Arrhenius equation revisited.
Peleg, Micha; Normand, Mark D; Corradini, Maria G
2012-01-01
The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T
NASA Astrophysics Data System (ADS)
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).
Aerosol kinetic code "AERFORM": Model, validation and simulation results
NASA Astrophysics Data System (ADS)
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.
A Gas-Kinetic Scheme for Reactive Flows
NASA Technical Reports Server (NTRS)
Lian,Youg-Sheng; Xu, Kun
1998-01-01
In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.
Kinetic Model of Optical Characteristics of Banknote Paper During Artificial Aging
NASA Astrophysics Data System (ADS)
Kulak, M. I.; Kyrychok, T. Yu.; Miadziak, D. M.; Kyrychok, P. O.
2016-09-01
A phenomenological kinetic equation is obtained for the change in color difference and brightness of banknote paper during aging. A solution is obtained for the kinetic equation. The coefficients of the kinetic function are determined from experimental data. Kinetic functions are constructed for three samples of the banknote paper. By analysis of the coefficients of the kinetic function it is possible to compare the paper according to its resistance towards the aging process.
Mathematics analysis of polymerase chain reaction kinetic curves.
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.
IKT for quantum hydrodynamic equations
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Ellero, Marco; Nicolini, Piero
2007-11-01
A striking feature of standard quantum mechanics (SQM) is its analogy with classical fluid dynamics. In fact, it is well-known that the Schr"odinger equation is equivalent to a closed set of partial differential equations for suitable real-valued functions of position and time (denoted as quantum fluid fields) [Madelung, 1928]. In particular, the corresponding quantum hydrodynamic equations (QHE) can be viewed as the equations of a classical compressible and non-viscous fluid, endowed with potential velocity and quantized velocity circulation. In this reference, an interesting theoretical problem, in its own right, is the construction of an inverse kinetic theory (IKT) for such a type of fluids. In this note we intend to investigate consequences of the IKT recently formulated for QHE [M.Tessarotto et al., Phys. Rev. A 75, 012105 (2007)]. In particular a basic issue is related to the definition of the quantum fluid fields.
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.
Production of a sterile species: Quantum kinetics
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.
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.
NASA Astrophysics Data System (ADS)
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.
On fast reactor kinetics studies
Seleznev, E. F.; Belov, A. A.; Matveenko, I. P.; Zhukov, A. M.; Raskach, K. F.
2012-07-01
The results and the program of fast reactor core time and space kinetics experiments performed and planned to be performed at the IPPE critical facility is presented. The TIMER code was taken as computation support of the experimental work, which allows transient equations to be solved in 3-D geometry with multi-group diffusion approximation. The number of delayed neutron groups varies from 6 to 8. The code implements the solution of both transient neutron transfer problems: a direct one, where neutron flux density and its derivatives, such as reactor power, etc, are determined at each time step, and an inverse one for the point kinetics equation form, where such a parameter as reactivity is determined with a well-known reactor power time variation function. (authors)
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.
Perceptions of the Schrodinger equation
NASA Astrophysics Data System (ADS)
Efthimiades, Spyros
2014-03-01
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived as the quantum equivalent of the non-relativistic classical energy relation. We argue that the Schrodinger equation cannot be a physical postulate, and we show explicitly that its second space derivative term is wrongly associated with the kinetic energy of the particle. The kinetic energy of a particle at a point is proportional to the square of the momentum, that is, to the square of the first space derivative of the wavefunction. Analyzing particle interactions, we realize that particles have multiple virtual motions and that each motion is accompanied by a wave that has constant amplitude. Accordingly, we define the wavefunction as the superposition of the virtual waves of the particle. In simple interaction settings we can tell what particle motions arise and can explain the outcomes in direct and tangible terms. Most importantly, the mathematical foundation of quantum mechanics becomes clear and justified, and we derive the Schrodinger, Dirac, etc. equations as the conditions the wavefunction must satisfy at each space-time point in order to fulfill the respective total energy equation.
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.
NASA Astrophysics Data System (ADS)
Tang, J. Y.
2015-09-01
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 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 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 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
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
Pöschel, Thorsten; Brilliantov, Nikolai V.; Frömmel, Cornelius
2003-01-01
We study the kinetics of prion fibril growth, described by the nucleated polymerization model analytically and by means of numerical experiments. The elementary processes of prion fibril formation lead us to a set of differential equations for the number of fibrils, their total mass, and the number of prion monomers. In difference to previous studies we analyze this set by explicitly taking into account the time-dependence of the prion monomer concentration. The theoretical results agree with experimental data, whereas the generally accepted hypothesis of constant monomer concentration leads to a fibril growth behavior which is not in agreement with experiments. The obtained size distribution of the prion fibril aggregates is shifted significantly toward shorter lengths as compared to earlier results, which leads to a enhanced infectivity of the prion material. Finally, we study the effect of filtering of the inoculated material on the incubation time of the disease. PMID:14645042
Algebraic operator approach to gas kinetic models
NASA Astrophysics Data System (ADS)
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”.
Hybrid fluid/kinetic model for parallel heat conduction
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.
Lam, C. F.; Priest, D. G.
1972-01-01
One of the most generally applicable algorithms for the derivation of steady-state rate equations for complex enzyme reaction mechanisms is that of King and Altman. Several modifications of this algorithm have been suggested; however, each requires the generation of numerous valid and invalid patterns and the subsequent elimination of those that are invalid. A method is presented, employing topological theory of linear graphs, for the systematic generation of only those patterns which are valid. This method is readily adaptable to use on a digital computer. An independent method for the calculation of the number of valid patterns is also presented. This calculation can be used to substantiate the accuracy of the patterns obtained. This calculation is also adaptable to computerization. Examples are included to demonstrate both the generation of patterns and the calculation of their number for specific enzyme mechanisms. PMID:5016111
Shore, B.W.
1981-01-30
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence.
NASA Astrophysics Data System (ADS)
Hur, Min Sup; Yoo, Seung Hoon; Suk, Hyyong
2007-03-01
The electron kinetic effects on Raman backscattering and Raman backward laser amplification were analyzed. The analysis is based on the envelope-kinetic equations of a plasma wave, which are composed of the conventional envelope equation of a fluid plasma and the kinetic term. One major goal of this paper is to close the envelope-kinetic model by analyzing the kinetic term, which was not fully covered in the previous work [M. S. Hur et al., Phys. Rev. Lett. 95, 115003 (2005)]. It was found that the closed envelope-kinetic equation in the nontrapping regime takes the same form as the envelope equation of the fluid plasma used in the three-wave model. For the closure in the trapping-dominant regime, the test particle technique is employed to calculate the kinetic term. Results from the full kinetic and test particle simulations agree well with each other, while the latter has a great advantage in computation speed. The frequency shift and resonance breaking by the trapped particles are discussed with the help of a new diagnostic inserted in the full kinetic averaged particle-in-cell code.
Hur, Min Sup; Yoo, Seung Hoon; Suk, Hyyong
2007-03-15
The electron kinetic effects on Raman backscattering and Raman backward laser amplification were analyzed. The analysis is based on the envelope-kinetic equations of a plasma wave, which are composed of the conventional envelope equation of a fluid plasma and the kinetic term. One major goal of this paper is to close the envelope-kinetic model by analyzing the kinetic term, which was not fully covered in the previous work [M. S. Hur et al., Phys. Rev. Lett. 95, 115003 (2005)]. It was found that the closed envelope-kinetic equation in the nontrapping regime takes the same form as the envelope equation of the fluid plasma used in the three-wave model. For the closure in the trapping-dominant regime, the test particle technique is employed to calculate the kinetic term. Results from the full kinetic and test particle simulations agree well with each other, while the latter has a great advantage in computation speed. The frequency shift and resonance breaking by the trapped particles are discussed with the help of a new diagnostic inserted in the full kinetic averaged particle-in-cell code.
Zakharov equations in quantum dusty plasmas
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.
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)]; 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. PMID:25679741
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. PMID:27627418
Simplification of the unified gas kinetic scheme
NASA Astrophysics Data System (ADS)
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.
Classical non-Markovian Boltzmann equation
Alexanian, Moorad
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.
Kinetic theory of relativistic plasmas
Gould, R.J.
1981-01-01
The thermalization of particle kinetic motion by binary collisions is considered for a plasma with kTapprox.(10--100) mc/sup 2/, where m is the electron mass. 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.
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.
Kinetic Relaxation Models for Energy Transport
NASA Astrophysics Data System (ADS)
Aoki, Kazuo; Markowich, Peter; Takata, Shigeru
2007-04-01
Kinetic equations with relaxation collision kernels are considered under the basic assumption of two collision invariants, namely mass and energy. The collision kernels are of BGK-type with a general local Gibbs state, which may be quite different from the Gaussian. By the use of the diffusive length/time scales, energy transport systems consisting of two parabolic equations with the position density and the energy density as unknowns are derived on a formal level. The H theorem for the kinetic model is presented, and the entropy for the energy transport systems, which is inherited from the kinetic model, is derived. The energy transport systems for specific examples of the global Gibbs state, such as a power law with negative exponent, a cut-off power law with positive exponent, the Maxwellian, Bose-Einstein, and Fermi-Dirac distributions, arepresented.
Transport equations in tokamak plasmas
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
Transport Equations In Tokamak Plasmas
NASA Astrophysics Data System (ADS)
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
Transport equations in tokamak plasmasa)
NASA Astrophysics Data System (ADS)
Callen, J. D.; Hegna, C. C.; Cole, A. J.
2010-05-01
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, 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 Alfvén 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
The maximum principle for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Akysh, Abdigali Sh.
2016-08-01
New connections were established between extreme values of the velocity, the density of kinetic energy (in particular local maximum) and the pressure of the Navier-Stokes equations. Validity of the maximum principle was shown for nonlinear Navier-Stokes equations using these connections, that is fundamentally-key from the mathematical point of view.
Representing Rate Equations for Enzyme-Catalyzed Reactions
ERIC Educational Resources Information Center
Ault, Addison
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…
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.
Practical steady-state enzyme kinetics.
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.
Parabolic approximation method for the mode conversion-tunneling equation
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.
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)
Chemical and Biological Kinetics
NASA Astrophysics Data System (ADS)
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.
Power-law spatial dispersion from fractional Liouville equation
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.
Cesium removal and kinetics equilibrium: Precipitation kinetics
Barnes, M.J.
1999-12-17
This task consisted of both non-radioactive and radioactive (tracer) tests examining the influence of potentially significant variables on cesium tetraphenylborate precipitation kinetics. The work investigated the time required to reach cesium decontamination and the conditions that affect the cesium precipitation kinetics.
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)
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.
Kinetic and hydrodynamic models of chemotactic aggregation
NASA Astrophysics Data System (ADS)
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.
Functional derivative of the kinetic energy functional for spherically symmetric systems.
Nagy, Á
2011-07-28
Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original non-interacting kinetic energy of the density functional theory.
Functional derivative of the kinetic energy functional for spherically symmetric systems.
Nagy, Á
2011-07-28
Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original non-interacting kinetic energy of the density functional theory. PMID:21806089
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.
Kinetic-equation approach to diffusive superconducting hybrid devices
Stoof, T.H.; Nazarov, Y.V.
1996-06-01
We present calculations of the temperature-dependent electrostatic and chemical potential distributions in disordered normal metal-superconductor structures. We show that they differ appreciably in the presence of a superconducting terminal and propose an experiment to measure these two different potential distributions. We also compute the resistance change in these structures due to a recently proposed mechanism which causes a finite effect at zero temperature. The relative resistance change due to this effect is of the order of the interaction parameter in the normal metal. Finally a detailed calculation of the resistance change due to the temperature dependence of Andreev reflection in diffusive systems is presented. We find that the maximal magnitude due to this thermal effect is in general much larger than the magnitude of the interaction effect. {copyright} {ital 1996 The American Physical Society.}
Kinetics of Propargyl Radical Dissociation.
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. PMID:25871530
Kinetics of Propargyl Radical Dissociation.
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.
Neutral Vlasov kinetic theory of magnetized plasmas
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.
Kinetic Approach for Laser-Induced Plasmas
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.
Resonance Van Hove singularities in wave kinetics
NASA Astrophysics Data System (ADS)
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.
Reflected kinetics model for nuclear space reactor kinetics and control scoping calculations
Washington, K.E.
1986-01-01
Renewed interest in space nuclear applications has motivated the study of a specialized reactor kinetics model. Consideration of a kinetics model favorable for study of the feasibility of automatic control of these devices is warranted. The need to bridge this gap between reactor kinetics and automatic control in conjunction with the control drum design characteristic of next generation paper space reactors inspired the development of a new Reflected Kinetics (RK) model. An extension of the conventional point-kinetics (PK) model was done in order to explicitly correlate reactivity and the reflector/absorber control drums characteristic of space nuclear reactor designs. Open-loop computations and numerical comparison to analytic PK equations indicated that the RK model is a functional alternative to equivalent bare point kinetics in the analysis of moderate transients. Variations in the RK reflector-to-core transfer probabilities and coolant flow rate do indeed drive the transient differently than the lumped insertion of equivalent reactivity amounts in the core. These computations illustrated the potential importance of the utilization of variable coolant flow rate to aid control in space reactor systems limited by minimal drum reactivity worth. Additionally the Doppler reactivity shutdown mechanism was concluded to be the primarily reliable means of safety shutdown in such systems. The structure of the RK equations proved to be advantageous for integration of automatic control.
Anomalous Maxwell equations for inhomogeneous chiral plasma
NASA Astrophysics Data System (ADS)
Gorbar, E. V.; Shovkovy, I. A.; Vilchinskii, S.; Rudenok, I.; Boyarsky, A.; Ruchayskiy, O.
2016-05-01
Using the chiral kinetic theory we derive the electric and chiral current densities in inhomogeneous relativistic plasma. We also derive equations for the electric and chiral chemical potentials that close the Maxwell equations in such a plasma. The analysis is done in the regimes with and without a drift of the plasma as a whole. In addition to the currents present in the homogeneous plasma (Hall current, chiral magnetic, chiral separation, and chiral electric separation effects, as well as Ohm's current) we derive several new terms associated with inhomogeneities of the plasma. Apart from various diffusionlike terms, we find also new dissipationless terms that are independent of relaxation time. Their origin can be traced to the Berry curvature modifications of the kinetic theory.
The quasicontinuum Fokker-Plank equation
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.
Modelling heart rate kinetics.
Zakynthinaki, Maria S
2015-01-01
The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise). Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual's cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects) but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women).
Zakynthinaki, Maria S.
2015-01-01
The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise). Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual’s cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects) but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women). PMID:25876164
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)
Interpretation of Bernoulli's Equation.
ERIC Educational Resources Information Center
Bauman, Robert P.; Schwaneberg, Rolf
1994-01-01
Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)
Kinetic theory of runaway air-breakdown
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.
Kinetic theory of runaway air breakdown
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.
Kinetics of helium bubble formation in nuclear materials
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.
Transport equations for partially ionized reactive plasma in magnetic field
NASA Astrophysics Data System (ADS)
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.
Kinetic-energy-momentum tensor in electrodynamics
NASA Astrophysics Data System (ADS)
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.
Using chemical kinetics to model biochemical pathways.
Le Novère, Nicolas; Endler, Lukas
2013-01-01
Chemical kinetics is the study of the rate of reactions transforming some chemical entities into other chemical entities. Over the twentieth century it has become one of the cornerstones of biochemistry. When in the second half of the century basic knowledge of cellular processes became sufficient to understand quantitatively metabolic networks, chemical kinetics associated with systems theory led to the development of what would become an important branch of systems biology. In this chapter we introduce basic concepts of chemical and enzyme kinetics, and show how the temporal evolution of a reaction system can be described by ordinary differential equations. Finally we present a method to apply this type of approach to model any regulatory network.
Establishment of the spectra of kinetic turbulence
NASA Technical Reports Server (NTRS)
Bolshov, L. A.; Dykhne, A. M.; Kiselev, V. P.; Pergament, A. K.
1979-01-01
An analysis of kinetic equations describing the establishment of Langmuir turbulence spectra is presented. Secondary turbulence occurs where stationary distribution consists of many peaks. The position of peaks is established and their amplitudes complete undamped oscillations. It is pointed out that establishing spectra can occur only during adiabatic inclusion of pumping. It is significant here that the adiabiatic condition is more rigid than the ordinary by several hundred times.
Azizian, Saeid; Bashiri, Hadis
2008-10-21
The kinetics of solute adsorption at the solid/solution interface has been studied by statistical rate theory (SRT) at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. A new kinetic equation has been derived for initial times of adsorption on the basis of SRT. For the first time a theoretical interpretation based on SRT has been provided for the modified pseudo-first-order (MPFO) kinetic equation which was proposed empirically by Yang and Al-Duri. It has been shown that the MPFO kinetic equation can be derived from the SRT equation when the system is close to equilibrium. On the basis of numerically generated points ( t, q) by the SRT equation, it has been shown that we can apply the new equation for initial times of adsorption in a larger time range in comparison to the previous q vs radical t linear equation. Also by numerical analysis of the generated kinetic data points, it is shown that application of the MPFO equation for modeling of whole kinetic data causes a large error for the data at initial times of adsorption. The results of numerical analysis are in perfect agreement with our theoretical derivation of the MPFO kinetic equation from the SRT equation. Finally, the results of the present theoretical study were confirmed by analysis of an experimental system. PMID:18788819
Kinetic theory for interacting Luttinger liquids
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Alaia, Alessandro; Puppo, Gabriella
2012-06-01
In this work we present a non stationary domain decomposition algorithm for multiscale hydrodynamic-kinetic problems, in which the Knudsen number may span from equilibrium to highly rarefied regimes. Our approach is characterized by using the full Boltzmann equation for the kinetic regime, the Compressible Euler equations for equilibrium, with a buffer zone in which the BGK-ES equation is used to represent the transition between fully kinetic to equilibrium flows. In this fashion, the Boltzmann solver is used only when the collision integral is non-stiff, and the mean free path is of the same order as the mesh size needed to capture variations in macroscopic quantities. Thus, in principle, the same mesh size and time steps can be used in the whole computation. Moreover, the time step is limited only by convective terms. Since the Boltzmann solver is applied only in wholly kinetic regimes, we use the reduced noise DSMC scheme we have proposed in Part I of the present work. This ensures a smooth exchange of information across the different domains, with a natural way to construct interface numerical fluxes. Several tests comparing our hybrid scheme with full Boltzmann DSMC computations show the good agreement between the two solutions, on a wide range of Knudsen numbers.
A note on the reverse Michaelis-Menten kinetics
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.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
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.
A closure scheme for chemical master equations.
Smadbeck, Patrick; Kaznessis, Yiannis N
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.
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
NASA Astrophysics Data System (ADS)
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-steady 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 [S
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…
Kinetic behaviour of zymogen activation processes in the presence of an inhibitor.
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
Consistent description of kinetics and hydrodynamics of dusty plasma
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.
An integral representation of functions in gas-kinetic models
NASA Astrophysics Data System (ADS)
Perepelitsa, Misha
2016-08-01
Motivated by the theory of kinetic models in gas dynamics, we obtain an integral representation of lower semicontinuous functions on {{{R}}^d,} {d≥1}. We use the representation to study the problem of compactness of a family of the solutions of the discrete time BGK model for the compressible Euler equations. We determine sufficient conditions for strong compactness of moments of kinetic densities, in terms of the measures from their integral representations.
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.
Deng, De-Ming; Chang, Cheng-Hung
2015-05-14
Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems. PMID:25978879
NASA Astrophysics Data System (ADS)
Deng, De-Ming; Chang, Cheng-Hung
2015-05-01
Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.
Deng, De-Ming; Chang, Cheng-Hung
2015-05-14
Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.
Point Genetics: A New Concept to Assess Neutron Kinetics
Klein Meulekamp, R.; Kuijper, J.C.; Schikorr, M.
2005-02-15
Point genetic equations are introduced. These equations are similar to the well-known point kinetic equations but characterize and couple individual fission generations in subcritical systems. Point genetic equations are able to describe dynamic behavior of source-driven subcritical systems on shorter timescales than is possible with point kinetic equations. Point genetic parameters can be used as a first-order characterization of the system and can be calculated using standard Monte Carlo techniques; the implementation in other calculational schemes seems straightforward. A Godiva sphere is considered to show the applicability of the point genetic equations in describing a detector response on short timescales. For this system the point genetic parameters are calculated and compared with reference calculations. Typical dynamic source behavior is considered by studying a transient in which the neutron source energy decreases from 20 to 1 MeV. For all cases studied, the point genetic equations are compared to full space-time kinetic solutions, and it is shown that point genetics performs well.
Uniqueness of thermodynamic projector and kinetic basis of molecular individualism
NASA Astrophysics Data System (ADS)
Gorban, Alexander N.; Karlin, Iliya V.
2004-05-01
Three results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of the thermodynamic projector is proven: There exists only one projector which transforms any vector field equipped with the given Lyapunov function into a vector field with the same Lyapunov function for a given anzatz manifold which is not tangent to the Lyapunov function levels. Second, we use the thermodynamic projector for developing the short memory approximation and coarse-graining for general nonlinear dynamic systems. We prove that in this approximation the entropy production increases. ( The theorem about entropy overproduction.) In example, we apply the thermodynamic projector to derive the equations of reduced kinetics for the Fokker-Planck equation. A new class of closures is developed, the kinetic multipeak polyhedra. Distributions of this type are expected in kinetic models with multidimensional instability as universally as the Gaussian distribution appears for stable systems. The number of possible relatively stable states of a nonequilibrium system grows as 2 m, and the number of macroscopic parameters is in order mn, where n is the dimension of configuration space, and m is the number of independent unstable directions in this space. The elaborated class of closures and equations pretends to describe the effects of “molecular individualism”. This is the third result.
NASA Astrophysics Data System (ADS)
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.
Einstein equation at singularities
NASA Astrophysics Data System (ADS)
Stoica, Ovidiu-Cristinel
2014-02-01
Einstein's equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is constructed in terms of the Ricci part of the Riemann curvature (as the Kulkarni-Nomizu product between Einstein's equation and the metric tensor).
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.
Kinetic modeling of non-ideal explosives
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.
Equilibrium and kinetic data and process design for adsorption of Congo Red onto bentonite.
Bulut, Emrah; Ozacar, Mahmut; Sengil, I Ayhan
2008-06-15
The adsorption of Congo Red onto bentonite in a batch adsorber has been studied. Four kinetic models, the pseudo first- and second-order equations, the Elovich equation and the intraparticle diffusion equation, were selected to follow the adsorption process. Kinetic parameters; rate constants, equilibrium adsorption capacities and correlation coefficients, for each kinetic equation were calculated and discussed. It was shown that the adsorption of Congo Red onto bentonite could be described by the pseudo second-order equation. The experimental isotherm data were analyzed using the Langmuir, Freundlich and Temkin equations. Adsorption of Congo Red onto bentonite followed the Langmuir isotherm. A single stage batch adsorber was designed for different adsorbent mass/treated effluent volume ratios using the Langmuir isotherm. PMID:18055111
Exploring Kinetics of Phenol Biodegradation by Cupriavidus taiwanesis 187
Wei, Yu-Hong; Chen, Wei-Chuan; Chang, Shan-Ming; Chen, Bor-Yann
2010-01-01
Phenol biodegradation in batch systems using Cupriavidus taiwanesis 187 has been experimentally studied. To determine the various parameters of a kinetic model, combinations of rearranged equations have been evaluated using inverse polynomial techniques for parameter estimation. The correlations between lag phase and phase concentration suggest that considering phenol inhibition in kinetic analysis is helpful for characterizing phenol degradation. This study proposes a novel method to determine multiplicity of steady states in continuous stirred tank reactors (CSTRs) in order to identify the most appropriate kinetics to characterize the dynamics of phenol biodegradation. PMID:21614192
Release kinetics of 5-aminosalicylic acid from halloysite.
Aguzzi, C; Viseras, C; Cerezo, P; Salcedo, I; Sánchez-Espejo, R; Valenzuela, C
2013-05-01
This paper investigates desorption of 5-aminosalicilyc acid (5-ASA) adsorbed onto halloysite (HL). Desorption isotherms were fitted according to kinetic laws obtained considering release of 5-ASA from HL as the phase of desorption of the previously adsorbed drug molecules both inside the nanotubes of HL as onto the surface of clay particles and/or in the inter-particle spaces of their aggregates. Desorption isotherms has been also fitted with other equations frequently used in drug release kinetics studies. The best fitting corresponded to the kinetic model proposed; in agreement with the results of adsorption.
Kinetic modeling of cell metabolism for microbial production.
Costa, Rafael S; Hartmann, Andras; Vinga, Susana
2016-02-10
Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations. PMID:26724578
Electron Kinetic Effects on Raman Backscatter in Plasmas
Hur, M.S.; Suk, H.; Lindberg, R.R.; Charman, A.E.; Wurtele, J.S.
2005-09-09
We augment the usual three-wave cold-fluid equations governing Raman backscatter (RBS) with a new kinetic thermal correction, proportional to an average of particle kinetic energy weighted by the ponderomotive phase. From closed-form analysis within a homogeneous kinetic three-wave model and ponderomotively averaged kinetic simulations in a more realistic pulsed case, the magnitude of these new contributions is shown to be a measure of the dynamical detuning between the pump laser, seed laser, and Langmuir wave. Saturation of RBS is analyzed, and the role of trapped particles illuminated. Simple estimates show that a small fraction of trapped particles ({approx}6%) can significantly suppress backscatter. We discuss the best operating regime of the Raman plasma amplifier to reduce these deleterious kinetic effects.
Kinetics of propylene oxidation on multicomponent oxide catalyst
Boreskov, G.K.; Erenburg, E.M.; Andrushkevich, T.V.; Zelenkova, T.V.; Bibin, V.N.; Meshcheryakov, V.D.; Boronina, N.P.; Tyurin, Y.N.
1983-02-01
A kinetic study of propylene oxidation on a multicomponent molybdenum-containing oxide catalyst has been carried out in a circulating-flow unit in the temperature interval 573-663/sup 0/K. The dependences of the reaction product formation rates (acrolein, acrylic acid, acetic acid, CO, and CO/sub 2/) are described by equations that are first-order with respect to the substance being oxidized, these equations differing in the influence of acrolein and water. The conversion of propylene to acrolein is an autocatalytic reaction accelerated by acrolein. Water vapor increases the acid formation and suppresses the reactions of exhaustive oxidation of acrolein and acetic acid, without affecting the post-oxidation of acrylic acid. Kinetic equations are proposed for all of the partial reactions. Nonlinear programming has been used to calculate the constants of the equations and the activation energies.
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.
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.
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.
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.
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)
Octonic Massive Field Equations
NASA Astrophysics Data System (ADS)
Demir, Süleyman; Kekeç, Seray
2016-07-01
In the present paper we propose the octonic form of massive field equations based on the analogy with electromagnetism and linear gravity. Using the advantages of octon algebra the Maxwell-Dirac-Proca equations have been reformulated in compact and elegant way. The energy-momentum relations for massive field are discussed.
A steady-state kinetic analysis of the prolyl-4-hydroxylase mechanism.
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.
Chemical gas-dynamics beyond Wang Chang-Uhlenbeck's kinetics
NASA Astrophysics Data System (ADS)
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.
Chemical gas-dynamics beyond Wang Chang-Uhlenbeck's kinetics
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.
Global kinetic explorer: a new computer program for dynamic simulation and fitting of kinetic data.
Johnson, Kenneth A; Simpson, Zachary B; Blom, Thomas
2009-04-01
We describe a new dynamic kinetic simulation program that allows multiple data sets to be fit simultaneously to a single model based on numerical integration of the rate equations describing the reaction mechanism. Unlike other programs that allow fitting based on numerical integration of rate equations, in the dynamic simulation rate constants, output factors, and starting concentrations of reactants can be scrolled while observing the change in the shape of the simulated reaction curves. Fast dynamic simulation facilitates the exploration of initial parameters that serve as the starting point for nonlinear regression in fitting data and facilitates exploration of the relationships between individual constants and observable reactions. The exploration of parameter space by dynamic simulation provides a powerful tool for learning kinetics and for evaluating the extent to which parameters are constrained by the data. This feature is critical to avoid overly complex models that are not supported by the data.
[Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (2)].
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.
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.
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)
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.
Alternative Analysis of the Michaelis-Menten Equations
ERIC Educational Resources Information Center
Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa
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…
Functional integral approach to the kinetic theory of inhomogeneous systems
NASA Astrophysics Data System (ADS)
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.
Garnier, Josselin; Picozzi, Antonio
2010-03-15
This article presents a unified kinetic formulation of partially coherent nonlinear optical waves propagating in a noninstantaneous response Kerr medium. We derive a kinetic equation that combines the weak Langmuir turbulence kinetic equation and a Vlasov-like equation within a general framework: It describes the evolution of the spectrum of a random field that exhibits a quasistationary statistics in the presence of a noninstantaneous nonlinear response. The kinetic equation sheds new light on the dynamics of partially coherent nonlinear waves and allows for a qualitative interpretation of the interplay between the noninstantaneous nonlinearity and the nonstationary statistics of the incoherent field. It is shown that the incoherent modulational instability of a random nonlinear wave can be suppressed by the noninstantaneous nonlinear response. Moreover, incoherent modulational instability can prevent the generation of spectral incoherent solitons.
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.
The Fluid-Kinetic Particle-in-Cell method for plasma simulations
NASA Astrophysics Data System (ADS)
Markidis, Stefano; Henri, Pierre; Lapenta, Giovanni; Rönnmark, Kjell; Hamrin, Maria; Meliani, Zakaria; Laure, Erwin
2014-08-01
A method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a self-consistent electromagnetic field, the kinetic effects are retained while solving the multi-fluid equations. The Maxwell's and multi-fluid equations are discretized implicitly in time enabling kinetic simulations over time scales typical of the fluid simulations. The Fluid-Kinetic Particle-in-Cell method has been implemented in a three-dimensional electromagnetic code, and tested against the two-stream instability, the Weibel instability, the ion cyclotron resonance and magnetic reconnection problems. The method is a promising approach for coupling fluid and kinetic methods in a unified framework.
Are improper kinetic models hampering drug development?
2014-01-01
Reproducibility of biological data is a significant problem in research today. One potential contributor to this, which has received little attention, is the over complication of enzyme kinetic inhibition models. The over complication of inhibitory models stems from the common use of the inhibitory term (1 + [I]/Ki), an equilibrium binding term that does not distinguish between inhibitor binding and inhibitory effect. Since its initial appearance in the literature, around a century ago, the perceived mechanistic methods used in its production have spurred countless inhibitory equations. These equations are overly complex and are seldom compared to each other, which has destroyed their usefulness resulting in the proliferation and regulatory acceptance of simpler models such as IC50s for drug characterization. However, empirical analysis of inhibitory data recognizing the clear distinctions between inhibitor binding and inhibitory effect can produce simple logical inhibition models. In contrast to the common divergent practice of generating new inhibitory models for every inhibitory situation that presents itself. The empirical approach to inhibition modeling presented here is broadly applicable allowing easy comparison and rational analysis of drug interactions. To demonstrate this, a simple kinetic model of DAPT, a compound that both activates and inhibits γ-secretase is examined using excel. The empirical kinetic method described here provides an improved way of probing disease mechanisms, expanding the investigation of possible therapeutic interventions. PMID:25374788
L2-stability of the Landau equation near global Maxwellians
NASA Astrophysics Data System (ADS)
Ha, Seung-Yeal; Xiao, Qinghua
2015-08-01
We present an L2-stability of the kinetic Landau equation for a single species charged plasma with an inverse power-law interaction force in the perturbative regime of global Maxwellians. Our result demonstrates that the L2-distance between two classical solutions to the Landau equation can be controlled by that between corresponding initial data in a Lipschitz manner. The Coulomb interaction is known to be the singular and marginal case of the theory of the Boltzmann equation where the grazing collisions are the dominant. For some class of classical solutions, we show that our L2-stability result can provide a uniform L2-stability.
From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations.
Colangeli, Matteo; Karlin, Iliya V; Kröger, Martin
2007-05-01
Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model -- a 13 moment Grad system.
General approach to constructing models of the Boltzmann equation
NASA Astrophysics Data System (ADS)
Gorban, Alexander N.; Karlin, Iliya V.
1994-05-01
The problem of thermodynamic parameterization of an arbitrary approximation of reduced description is solved. On the base of this solution a new class of model kinetic equations is constructed that gives a model extension of the chosen approximation to a kinetic model. Model equations describe two processes: rapid relaxation to the chosen approximation along the planes of rapid motions, and the slow motion caused by the chosen approximation. The H-theorem is proved for these models. It is shown, that the rapid process always leads to entropy growth, and also a neighborhood of the approximation is determined inside which the slow process satisfies the H-theorem. Kinetic models for Grad moment approximations and for the Tamm-Mott-Smith approximation are constructed explicitly. In particular, the problem of concordance of the ES-model with the H-theorem is solved.
NASA Astrophysics Data System (ADS)
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.
Hur, Min Sup; Suk, Hyyong
2007-10-01
A new test particle method is presented for self-consistent incorporation of the kinetic effects into the fluid three-wave model. One of the most important kinetic effects is the electron trapping and it has been found that the trapping affects significantly the behavior of Raman backscatter and Raman backward laser amplification. The conventional fluid three-wave model cannot reproduce the kinetic simulations in the trapping regime. The test particle scheme utilizes the same equations for the laser evolution as in the three-wave model. However, the plasma wave is treated by the envelope-kinetic equation, which consists of envelope evolution and the kinetic term. The core of the new scheme is employing test particles to compute the kinetic term self-consistently. The benchmarking results against the averaged particle-in-cell (aPIC) code show excellent agreements, and the computation speed gain over the aPIC is from 2 to 20 depending on parameters.
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.
NASA Astrophysics Data System (ADS)
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Kinetic theory of the presheath and the Bohm criterion
NASA Astrophysics Data System (ADS)
Baalrud, S. D.; Hegna, C. C.
2011-04-01
A kinetic theory of the Bohm criterion is developed that is based on positive-exponent velocity moments of the plasma kinetic equation. This result is contrasted with the conventional kinetic Bohm criterion that is based on a v-1 moment of the Vlasov equation. The salient difference between the two results is that low-velocity particles dominate in the conventional theory, but are essentially unimportant in the new theory. It is shown that the derivation of the conventional kinetic Bohm criterion is flawed. Low-velocity particles can cause unphysical divergences in the conventional theory. These divergent contributions are avoided with this new approach. The two theories are compared using example distribution functions from previous presheath models. The importance of ion-ion and electron-electron collisions to determining the particle distribution functions throughout the presheath is also discussed. A kinetic equation that accounts for wave-particle scattering by convective instabilities is used to show that ion-acoustic instabilities in the presheath of low temperature plasmas (where Te Gt Ti) can cause both ions and electrons to obtain Maxwellian distribution functions near the sheath.
Wave kinetics of random fibre lasers
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
Comparative evaluation of adsorption kinetics of diclofenac and isoproturon by activated carbon.
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. PMID:26301850
Kinetic theory for dilute cohesive granular gases with a square well potential.
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. PMID:27575205
A KINETIC MODEL FOR CELL DENSITY DEPENDENT BACTERIAL TRANSPORT IN POROUS MEDIA
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...
Fluctuating kinetic energy budget during homogeneous flow of a fluid solid mixture
Liljegren, L.M.; Foslein, W.
1996-01-01
Ensemble-averaging theorems are applied to derive transport equations for the fluctuating kinetic energy of a particulate mixture consisting of a continuous fluid and solid particles. The evolution of fluctuating kinetic energy in a homogeneous flow is examined and discussed. {copyright} {ital 1996 American Institute of Physics.}
Kinetic theory for dilute cohesive granular gases with a square well potential.
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.
Kinetic theory for dilute cohesive granular gases with a square well potential
NASA Astrophysics Data System (ADS)
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.
Nonlinear differential equations
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.
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…
Fast algorithms for combustion kinetics calculations: A comparison
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.
1984-01-01
To identify the fastest algorithm currently available for the numerical integration of chemical kinetic rate equations, several algorithms were examined. Findings to date are summarized. The algorithms examined include two general-purpose codes EPISODE and LSODE and three special-purpose (for chemical kinetic calculations) codes CHEMEQ, CRK1D, and GCKP84. In addition, an explicit Runge-Kutta-Merson differential equation solver (IMSL Routine DASCRU) is used to illustrate the problems associated with integrating chemical kinetic rate equations by a classical method. Algorithms were applied to two test problems drawn from combustion kinetics. These problems included all three combustion regimes: induction, heat release and equilibration. Variations of the temperature and species mole fraction are given with time for test problems 1 and 2, respectively. Both test problems were integrated over a time interval of 1 ms in order to obtain near-equilibration of all species and temperature. Of the codes examined in this study, only CREK1D and GCDP84 were written explicitly for integrating exothermic, non-isothermal combustion rate equations. These therefore have built-in procedures for calculating the temperature.
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)
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…
Thermoluminescence kinetics of pyrite (FeS sub 2 )
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.
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…
Relativistic Guiding Center Equations
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.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
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.
Ultrarelativistic decoupling transformation for generalized Dirac equations
NASA Astrophysics Data System (ADS)
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.
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.
Set Equation Transformation System.
2002-03-22
Version 00 SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protectionmore » requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system. Two auxiliary programs, SEP and FTD, are included. SEP performs the quantitative analysis of reduced Boolean equations (minimal cut sets) produced by SETS. The user can manipulate and evaluate the equations to find the probability of occurrence of any desired event and to produce an importance ranking of the terms and events in an equation. FTD is a fault tree drawing program which uses the proprietary ISSCO DISSPLA graphics software to produce an annotated drawing of a fault tree processed by SETS. The DISSPLA routines are not included.« less
Perspective: Stochastic algorithms for chemical kinetics
NASA Astrophysics Data System (ADS)
Gillespie, Daniel T.; Hellander, Andreas; Petzold, Linda R.
2013-05-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.
Pullulan from peat hydrolyzate fermentation kinetics.
Boa, J M; Leduy, A
1987-09-01
The Luedeking-Piret equation was used to fit the kinetic data of pullulan fermentations from peat hydrolyzate substrate. In batch mode, the kinetic parameters m, n, alpha, and beta varied as a function of fermentation conditions: aeration rate, agitation speed, and temperature. In constant-feed fed-batch mode, the parameters Varied according to the feed rates. In peat hydrolyzate medium, the polysaccharide synthesis was strongly growth associated in batch and continuous fermentations but entirely growth associated in fedbatch fermentations. The fed-batch mode of fermentation with an appropriate feed rate is more advantageous with respect to batch and continuous fermentations. Therefore, if the fermentation is started batchwise and then followed by fed-batch mode at a constant feed rate, the overall polysaccharide productivity (g pullulan/L h) is significantly higher than those obtained with batch or continuous fermentations using the same total medium volume.
Crystallization kinetics of citric acid anhydrate
NASA Astrophysics Data System (ADS)
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.
Processes of aggression described by kinetic method
NASA Astrophysics Data System (ADS)
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.
On the kinetic foundations of Kaluza's magnetohydrodynamics
NASA Astrophysics Data System (ADS)
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.
Perspective: Stochastic algorithms for chemical kinetics.
Gillespie, Daniel T; Hellander, Andreas; Petzold, Linda R
2013-05-01
We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stochastic approach, and for the approximations that need to be made in order to regain the traditional continuous-deterministic description. We next take note of some of the more promising strategies for dealing stochastically with stiff systems, rare events, and sensitivity analysis. Finally, we review some recent efforts to adapt and extend the discrete-stochastic approach to systems that are not well-mixed. In that currently developing area, we focus mainly on the strategy of subdividing the system into well-mixed subvolumes, and then simulating diffusional transfers of reactant molecules between adjacent subvolumes together with chemical reactions inside the subvolumes.
Positron kinetics in an idealized PET environment
NASA Astrophysics Data System (ADS)
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.
Sigmoid kinetics of protein crystal nucleation
NASA Astrophysics Data System (ADS)
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.
Processes of aggression described by kinetic method
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.
Kinetic study and mechanism of Niclosamide degradation.
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. PMID:24892546
Kinetic study and mechanism of Niclosamide degradation
NASA Astrophysics Data System (ADS)
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.
Adsorption kinetics of methyl violet onto perlite.
Doğan, Mehmet; Alkan, Mahir
2003-01-01
This study examines adsorption kinetics and activation parameters of methyl violet on perlite. The effect of process parameters like contact time, concentration of dye, temperature and pH on the extent of methyl violet adsorption from solution has been investigated. Results of the kinetic studies show that the adsorption reaction is first order with respect to dye solution concentration with activation energy of 13.2 kJ mol(-1). This low activation energy value indicates that the adsorption reaction is diffusion controlled. The activation parameters using Arrhenius and Eyring equations have been calculated. Adsorption increases with increase of variables such as contact time, initial dye concentration, temperature and pH.
POLARIZATION AND COMPRESSIBILITY OF OBLIQUE KINETIC ALFVEN WAVES
Hunana, P.; Goldstein, M. L.; Passot, T.; Sulem, P. L.; Laveder, D.; Zank, G. P.
2013-04-01
It is well known that a complete description of the solar wind requires a kinetic description and that, particularly at sub-proton scales, kinetic effects cannot be ignored. It is nevertheless usually assumed that at scales significantly larger than the proton gyroscale r{sub L} , magnetohydrodynamics or its extensions, such as Hall-MHD and two-fluid models with isotropic pressures, provide a satisfactory description of the solar wind. Here we calculate the polarization and magnetic compressibility of oblique kinetic Alfven waves and show that, compared with linear kinetic theory, the isotropic two-fluid description is very compressible, with the largest discrepancy occurring at scales larger than the proton gyroscale. In contrast, introducing anisotropic pressure fluctuations with the usual double-adiabatic (or CGL) equations of state yields compressibility values which are unrealistically low. We also show that both of these classes of fluid models incorrectly describe the electric field polarization. To incorporate linear kinetic effects, we use two versions of the Landau fluid model that include linear Landau damping and finite Larmor radius (FLR) corrections. We show that Landau damping is crucial for correct modeling of magnetic compressibility, and that the anisotropy of pressure fluctuations should not be introduced without taking into account the Landau damping through appropriate heat flux equations. We also show that FLR corrections to all the retained fluid moments appear to be necessary to yield the correct polarization. We conclude that kinetic effects cannot be ignored even for kr{sub L} << 1.
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.
Kinetic theory and long range correlations in moderately dense gases
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.
Acyclovir kinetics after intravenous infusion.
de Miranda, P; Whitley, R J; Blum, M R; Keeney, R E; Barton, N; Cocchetto, D M; Good, S; Hemstreet, G P; Kirk, L E; Page, D A; Elion, G B
1979-12-01
The disposition and safety of the antiviral drug acyclovir were studied in 14 subjects with advanced malignancies. Acyclovir was administered by a 1-hr intravenous infusion at doses of 0.5, 1.0, 2.5, and 5.0 mg/kg. At the end of infusion, mean peak plasma levels (+/- SEM), determined by radioimmunoassay, were 6.4 +/- 0.7, 12.1 +/- 2.3, 14.9 +/- 2.7, and 33.7 +/- 7.1 microM. The plasma concentration-time profiles could be described by a biexponential equation. The half-life of acyclovir in the slow disposition phase ranged from 2.2 to 5 hr and the drug was detected in the plasma for at least 18 hr after infusion. The total body clearance ranged from 117 to 396 ml/min/1.73 m2. A proportionality between area under the curve and dose suggests that acyclovir exhibits dose-independent kinetics in the dose range studied. There was wide variation in cumulative urinary excretion of unchanged drug, ranging from 30 to 69% of the dose. From renal clearances of acyclovir, which were higher than creatinine clearances, it appears that both glomerular filtration and tubular secretion contribute to its renal excretion. Analysis of the urine by reverse-phase high-performance liquid chromatography revealed the presence of the metabolite 9-carboxymethoxymethylguanine. There was no indication of toxicity either clinically or from laboratory findings in any of the study subjects. This study demonstrates that in addition to selectivity and low toxicity, the kinetic profile and metabolic disposition of acyclovir make it an attractive candidate for therapy in a variety of herpes infections.
Berendsen, W R; Gendrot, G; Freund, A; Reuss, M
2006-12-01
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.
Multiple alternative substrate kinetics.
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. PMID:26051088
Multiple alternative substrate kinetics.
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.
Kopelman, R
1988-09-23
Classical reaction kinetics has been found to be unsatisfactory when the reactants are spatially constrained on the microscopic level by either walls, phase boundaries, or force fields. Recently discovered theories of heterogeneous reaction kinetics have dramatic consequences, such as fractal orders for elementary reactions, self-ordering and self-unmixing of reactants, and rate coefficients with temporal "memories." The new theories were needed to explain the results of experiments and supercomputer simulations of reactions that were confined to low dimensions or fractal dimensions or both. Among the practical examples of "fractal-like kinetics" are chemical reactions in pores of membranes, excitation trapping in molecular aggregates, exciton fusion in composite materials, and charge recombination in colloids and clouds.
Erbium hydride decomposition kinetics.
Ferrizz, Robert Matthew
2006-11-01
Thermal desorption spectroscopy (TDS) is used to study the decomposition kinetics of erbium hydride thin films. The TDS results presented in this report are analyzed quantitatively using Redhead's method to yield kinetic parameters (E{sub A} {approx} 54.2 kcal/mol), which are then utilized to predict hydrogen outgassing in vacuum for a variety of thermal treatments. Interestingly, it was found that the activation energy for desorption can vary by more than 7 kcal/mol (0.30 eV) for seemingly similar samples. In addition, small amounts of less-stable hydrogen were observed for all erbium dihydride films. A detailed explanation of several approaches for analyzing thermal desorption spectra to obtain kinetic information is included as an appendix.
Dynamical equation of the effective gluon mass
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2011-10-15
In this article, we derive the integral equation that controls the momentum dependence of the effective gluon mass in the Landau gauge. This is accomplished by means of a well-defined separation of the corresponding ''one-loop dressed'' Schwinger-Dyson equation into two distinct contributions, one associated with the mass and one with the standard kinetic part of the gluon. The entire construction relies on the existence of a longitudinally coupled vertex of nonperturbative origin, which enforces gauge invariance in the presence of a dynamical mass. The specific structure of the resulting mass equation, supplemented by the additional requirement of a positive-definite gluon mass, imposes a rather stringent constraint on the derivative of the gluonic dressing function, which is comfortably satisfied by the large-volume lattice data for the gluon propagator, both for SU(2) and SU(3). The numerical treatment of the mass equation, under some simplifying assumptions, is presented for the aforementioned gauge groups, giving rise to a gluon mass that is a nonmonotonic function of the momentum. Various theoretical improvements and possible future directions are briefly discussed.
Ill-Posedness of the Hydrostatic Euler and Singular Vlasov Equations
NASA Astrophysics Data System (ADS)
Han-Kwan, Daniel; Nguyen, Toan T.
2016-09-01
In this paper, we develop an abstract framework to establish ill-posedness, in the sense of Hadamard, for some nonlocal PDEs displaying unbounded unstable spectra. We apply this to prove the ill-posedness for the hydrostatic Euler equations as well as for the kinetic incompressible Euler equations and the Vlasov-Dirac-Benney system.
Asymptotic solution of a linearized Morgenstern equation for small Knudsen numbers
NASA Astrophysics Data System (ADS)
Demina, N. V.
The properties of a kinetic equation with a linearized Morgenstern-Boltzmann operator are examined. The eigenfunctions and eigenvalues are obtained in the context of perturbation theory; the solution to the equation is analyzed asymptotically. Some applications of the results are suggested.
Microbial kinetic for In-Storage-Psychrophilic Anaerobic Digestion (ISPAD).
Madani-Hosseini, Mahsa; Mulligan, Catherine N; Barrington, Suzelle
2014-12-15
In-Storage-Psychrophilic-Anaerobic-Digestion (ISPAD) is a wastewater storage tank converted into an anaerobic digestion (AD) system by means of an airtight floating geo-membrane. For process optimization, ISPAD requires modelling with well-established microbial kinetics coefficients. The present objectives were to: obtain kinetics coefficients for the modelling of ISPAD; compare the prediction of the conventional and decomposition fitting approach, an innovative fitting technique used in other fields of science, and; obtain equations to predict the maximum growth rate (μmax) of microbial communities as a function of temperature. The method consisted in conducting specific Substrate Activity Tests (SAT) using ISPAD inoculum to monitor the rate of degradation of specific substrates at 8, 18 and 35 °C. Microbial kinetics coefficients were obtained by fitting the Monod equations to SAT. The statistical procedure of Least Square Error analysis was used to minimize the Sum of Squared Errors (SSE) between the measured ISPAD experimental data and the Monod equation values. Comparing both fitting methods, the decomposition approach gave higher correlation coefficient (R) for most kinetics values, as compared to the conventional approach. Tested to predict μmax with temperature, the Square Root equation better predicted temperature dependency of both acidogens and propionate degrading acetogens, while the Arrhenius equation better predicted that of methanogens and butyrate degrading acetogens. Increasing temperature from 18 to 35 °C did not affect butyrate degrading acetogens, likely because of their dominance, as demonstrated by microbial population estimation. The estimated ISPAD kinetics coefficients suggest a robust psychrophilic and mesophilic coexisting microbial community demonstrating acclimation to ambient temperature.
Brito, Paula M.; Antunes, Fernando
2014-01-01
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 toward 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 underlie the interplay between oxidative stress and redox signaling responses. PMID:25325054
NASA Astrophysics Data System (ADS)
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.
Brito, Paula M; Antunes, Fernando
2014-01-01
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 toward 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 underlie the interplay between oxidative stress and redox signaling responses.
Wealth redistribution in conservative linear kinetic models
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Clarke, C. J.; Pringle, J. E.
2004-07-01
We show how the viscous evolution of Keplerian accretion discs can be understood in terms of simple kinetic theory. Although standard physics texts give a simple derivation of momentum transfer in a linear shear flow using kinetic theory, many authors, as detailed by Hayashi & Matsuda, have had difficulties applying the same considerations to a circular shear flow. We show here how this may be done, and note that the essential ingredients are to take proper account of, first, isotropy locally in the frame of the fluid and, secondly, the geometry of the mean flow.
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)
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)
Kinetic Plasma Simulation Using a Quadrature-based Moment Method
NASA Astrophysics Data System (ADS)
Larson, David J.
2008-11-01
The recently developed quadrature-based moment method [Desjardins, Fox, and Villedieu, J. Comp. Phys. 227 (2008)] is an interesting alternative to standard Lagrangian particle simulations. The two-node quadrature formulation allows multiple flow velocities within a cell, thus correctly representing crossing particle trajectories and lower-order velocity moments without resorting to Lagrangian methods. Instead of following many particles per cell, the Eulerian transport equations are solved for selected moments of the kinetic equation. The moments are then inverted to obtain a discrete representation of the velocity distribution function. Potential advantages include reduced computational cost, elimination of statistical noise, and a simpler treatment of collisional effects. We present results obtained using the quadrature-based moment method applied to the Vlasov equation in simple one-dimensional electrostatic plasma simulations. In addition we explore the use of the moment inversion process in modeling collisional processes within the Complex Particle Kinetics framework.
Kinetics and thermodynamics of first-order Markov chain copolymerization
Gaspard, P.; Andrieux, D.
2014-07-28
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.
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.
Kinetic plots for gas chromatography: theory and experimental verification.
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.
Kinetic plots for gas chromatography: theory and experimental verification.
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. PMID:25683626
Kinetic theory of oxygen isotopic exchange between minerals and water
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.
Drift-Kinetic Simulations of Neoclassical Transport
Belli, E. A.; Candy, J.
2008-11-01
We present results from numerical studies of neoclassical transport for multi-species plasmas. The code, NEO, provides a first-principles based calculation of the neoclassical transport coefficients directly from solution of the distribution function by solving a hierarchy of equations derived by expanding the fundamental drift-kinetic equation in powers of {rho}{sub *i}, the ratio of the ion gyroradius to system size. It extends previous studies by including the self-consistent coupling of electrons and multiple ion species and strong toroidal rotation effects. Systematic calculations of the second-order particle and energy fluxes and first-order plasma flows and bootstrap current and comparisons with existing theories are given for multi-species plasmas. The ambipolar relation {sigma}{sub a}z{sub a}{gamma}{sub a} = 0, which can only be maintained with complete cross-species collisional coupling, is confirmed. The effects of plasma shaping are also explored.
Kinetic analysis of complex reactions using FEMLAB
Cao, Chunshe; Wang, Yong
2005-06-07
A finite element method software FEMALB has been implemented to the kinetic analysis of complex reaction systems. The established protocol provides fast solutions to the coupled differential-algebraic equations. It shows significant advantages over the conventional coding process with the standard implicit Runge-Kutta (IRK) method. The accuracy and high efficiency have been demonstrated in the simulation of the reaction processes such as glucose/fructose hydrogenation and catalytic cracking of gasoil. As model validation, the numerical results showed satisfactory agreement with the exact solutions. With the powerful capability of solving large matrixes of differential equations (both ODE and PDE) with nonlinear algebraic constrains, such an algorithm has greatly reduced the coding labor in reaction mechanistic studies and provided a unique tool in reactor design and optimization.
Modeling capsid kinetics assembly from the steady state distribution of multi-sizes aggregates
NASA Astrophysics Data System (ADS)
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.
Parallel tridiagonal equation solvers
NASA Technical Reports Server (NTRS)
Stone, H. S.
1974-01-01
Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.
Nonlocal electrical diffusion equation
NASA Astrophysics Data System (ADS)
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.
Long tail kinetics in biophysics?
Nagle, J F
1992-01-01
Long tail kinetics describe a variety of data from complex, disordered materials that cannot be described by conventional kinetics. It is suggested that the kinetics of diffusive motion in complex biological media, such as cytoplasm or biomembranes, might also have long tails. The effects of long tail kinetics are investigated for two standard biophysical measurements, fluorescence recovery after photobleaching (FRAP), and dynamic light scattering (DLS). It is shown that long tail kinetic data would yield significantly distorted and misleading results when analyzed assuming conventional kinetics. PMID:1420883
Toluene and benzyl decomposition mechanisms: elementary reactions and kinetic simulations.
Derudi, Marco; Polino, Daniela; Cavallotti, Carlo
2011-12-28
The high temperature decomposition kinetics of toluene and benzyl were investigated by combining a kinetic analysis with the ab initio/master equation study of new reaction channels. It was found that similarly to toluene, which decomposes to benzyl and phenyl losing atomic hydrogen and methyl, also benzyl decomposition proceeds through two channels with similar products. The first leads to the formation of fulvenallene and hydrogen and has already been investigated in detail in recent publications. In this work it is proposed that benzyl can decompose also through a second decomposition channel to form benzyne and methyl. The channel specific kinetic constants of benzyl decomposition were determined by integrating the RRKM/master equation over the C(7)H(7) potential energy surface. The energies of wells and saddle points were determined at the CCSD(T) level on B3LYP/6-31+G(d,p) structures. A kinetic mechanism was then formulated, which comprises the benzyl and toluene decomposition reactions together with a recently proposed fulvenallene decomposition mechanism, the decomposition kinetics of the fulvenallenyl radical, and some reactions describing the secondary chemistry originated by the decomposition products. The kinetic mechanism so obtained was used to simulate the production of H atoms measured in a wide pressure and temperature range using different experimental setups. The calculated and experimental data are in good agreement. Kinetic constants of the new reaction channels here examined are reported as a function of temperature at different pressures. The mechanism here proposed is not compatible with the assumption often used in literature kinetic mechanisms that benzyl decomposition can be effectively described through a lumped reaction whose products are the cyclopentadienyl radical and acetylene.
Stochastic differential equations
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.
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.
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…
Oxidative desulfurization: kinetic modelling.
Dhir, S; Uppaluri, R; Purkait, M K
2009-01-30
Increasing environmental legislations coupled with enhanced production of petroleum products demand, the deployment of novel technologies to remove organic sulfur efficiently. This work represents the kinetic modeling of ODS using H(2)O(2) over tungsten-containing layered double hydroxide (LDH) using the experimental data provided by Hulea et al. [V. Hulea, A.L. Maciuca, F. Fajula, E. Dumitriu, Catalytic oxidation of thiophenes and thioethers with hydrogen peroxide in the presence of W-containing layered double hydroxides, Appl. Catal. A: Gen. 313 (2) (2006) 200-207]. The kinetic modeling approach in this work initially targets the scope of the generation of a superstructure of micro-kinetic reaction schemes and models assuming Langmuir-Hinshelwood (LH) and Eley-Rideal (ER) mechanisms. Subsequently, the screening and selection of above models is initially based on profile-based elimination of incompetent schemes followed by non-linear regression search performed using the Levenberg-Marquardt algorithm (LMA) for the chosen models. The above analysis inferred that Eley-Rideal mechanism describes the kinetic behavior of ODS process using tungsten-containing LDH, with adsorption of reactant and intermediate product only taking place on the catalyst surface. Finally, an economic index is presented that scopes the economic aspects of the novel catalytic technology with the parameters obtained during regression analysis to conclude that the cost factor for the catalyst is 0.0062-0.04759 US $ per barrel. PMID:18541367
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.
The Statistical Drake Equation
NASA Astrophysics Data System (ADS)
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
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…
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…
A conservative multi-group approach to the Boltzmann equations for reactive gas mixtures
NASA Astrophysics Data System (ADS)
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.
Kinetics of wealth and the Pareto law
NASA Astrophysics Data System (ADS)
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.
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.
Studies on cultivation kinetics for elastase production by Bacillus sp. EL31410.
Chen, Qi-He; He, Guo-Qing; Schwarz, Paul
2004-06-01
It was the first time to study elastase batch cultivation kinetics. This paper discusses the growth kinetics, elastase production, and substrate consumption kinetics model of Bacillus sp. EL31410 in batch cultivation. A simple model was proposed using a logistic equation for growth, the Luedeking-Piret equation for elastase production, and the Luedeking-Piret-like equation for glucose consumption. The model appeared to provide a reasonable description for each parameter during the growth phase. This study could provide some support for studying elastase fermentation kinetics, especially for studying its singular growth phenomenon. However, the model for elastase production is not good for explaining the real process and is still up to research. PMID:15161197
Parallel Multigrid Equation Solver
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.
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…
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…
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]…
Generalized reduced magnetohydrodynamic equations
Kruger, S.E.
1999-02-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.
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…
LLNL Chemical Kinetics Modeling Group
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.
Budgets of divergent and rotational kinetic energy during two periods of intense convection
NASA Technical Reports Server (NTRS)
Buechler, D. E.; Fuelberg, H. E.
1986-01-01
The derivations of the energy budget equations for divergent and rotational components of kinetic energy are provided. The intense convection periods studied are: (1) synoptic scale data of 3 or 6 hour intervals and (2) mesoalphascale data every 3 hours. Composite energies and averaged budgets for the periods are presented; the effects of random data errors on derived energy parameters is investigated. The divergent kinetic energy and rotational kinetic energy budgets are compared; good correlation of the data is observed. The kinetic energies and budget terms increase with convective development; however, the conversion of the divergent and rotational energies are opposite.
Constructive methods of invariant manifolds for kinetic problems
NASA Astrophysics Data System (ADS)
Gorban, Alexander N.; Karlin, Iliya V.; Zinovyev, Andrei Yu.
2004-06-01
The concept of the slow invariant manifold is recognized as the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in the most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space ( the invariance equation). The equation of motion for immersed manifolds is obtained ( the film extension of the dynamics). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability. A collection of methods to derive analytically and to compute numerically the slow invariant manifolds is presented. Among them, iteration methods based on incomplete linearization, relaxation method and the method of invariant grids are developed. The systematic use of thermodynamics structures and of the quasi-chemical representation allow to construct approximations which are in concordance with physical restrictions. The following examples of applications are presented: nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers Kn∼1; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; model reduction in chemical kinetics; derivation and numerical implementation of constitutive equations for polymeric fluids; the limits of macroscopic description for polymer molecules, etc.
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)
Ozone kinetics in low-pressure discharges
NASA Astrophysics Data System (ADS)
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).
Kinetics of cobalt cementation on zinc powder
Polcaro, A.M.; Palmas, S.; Dernini, S.
1995-09-01
The cementation process may be considered an interesting method to treat dilute solutions containing metal ions. The aim of the process may be either the removal of pollutant metals or the recovery of economically valuable metals such as Ag from spent photographic liquors. The kinetics of cobalt cementation on Zn powder from zinc sulfate concentrated solutions in the presence of copper and antimony ions was investigated in stirred tank reactors. The composition of the solutions was in the range usually utilized in industrial zinc electrowinning plants. The results showed that the reaction occurs by means of the formation of crystallization nuclei of noble metals on the zinc powder, followed by the cementation of cobalt ions on these newly-formed nuclei. Mass transfer to the reaction surface is shown to be the controlling step in copper and antimony reduction, and an equation correlating mass transfer coefficients has been determined. A kinetic equation, which interprets the influence of stirring speed and solution composition on cobalt cementation, has also been proposed.
[Kinetics of Cu crossing human erythrocyte membrane].
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.
Kinetics of liquid-phase hydrogenation of phenol on a palladium catalyst
Kotova, V.G.; Kul'kova, N.V.; Temkin, M.I.
1988-08-01
The kinetics of liquid-phase hydrogenation of phenol into cyclohexanone on a Pd catalyst were studied. At atmospheric pressure, the reaction rate is described by the equation previously obtained for liquid-phase hydrogenation of benzoic acid. At pressures of 0.7-4 MPa, the rate obeys a zero-order equation. The preexponential factor of the Arrhenius equation for the number of rotations in the zero-order region correspond to a transmission coefficient of /kappa/ << 1.
A kinetic model for chemical neurotransmission
NASA Astrophysics Data System (ADS)
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.
Imperfect dark energy from kinetic gravity braiding
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.
Adsorption of methylene blue onto bamboo-based activated carbon: kinetics and equilibrium studies.
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.
Problems with the linear q-Fokker Planck equation
NASA Astrophysics Data System (ADS)
Yano, Ryosuke
2015-05-01
In this letter, we discuss the linear q-Fokker Planck equation, whose solution follows Tsallis distribution, from the viewpoint of kinetic theory. Using normal definitions of moments, we can expand the distribution function with infinite moments for 0 ⩽ q < 1, whereas we cannot expand the distribution function with infinite moments for 1 < q owing to emergences of characteristic points in moments. From Grad's 13 moment equations for the linear q-Fokker Planck equation, the dissipation rate of the heat flux via the linear q-Fokker Planck equation diverges at 0 ⩽ q < 2/3. In other words, the thermal conductivity, which defines the heat flux with the spatial gradient of the temperature and the thermal conductivity, which defines the heat flux with the spacial gradient of the density, jumps to zero at q = 2/3, discontinuously.
Sub-Alfvenic Reduced Equations for Tokamak Plasmas
NASA Astrophysics Data System (ADS)
Sengupta, W.; Hassam, A. B.; Antonsen, T. M.
2015-11-01
We present a system of reduced resistive MHD equations which are sub-Alfvenic with respect to ideal ballooning in large aspect ratio tokamak geometry. The low beta system allows dynamic evolution of full profiles. The system has the advantage that it is 2-dimensional in the transverse to º, space variables. This allows significant analytical tractability as well as ease in numerical implementation. The linearized equations are shown to reproduce Mercier modes, resistive ballooning modes, tearing modes, sound waves, GAMs, the Stringer spinup, and Rosenbluth-Hinton zonal flows. The methodology developed allows extension to drift modes as well as to a hybrid system of moment and electromagnetic sub-gyro-drift-kinetic equations. Analytical and numerical benchmarks will be presented. We show that the system, which requires Laplace equation inversion to solve for electromagnetic potentials, is implementable numerically. Work supported by DOE.
Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach
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.
Supersymmetric fifth order evolution equations
Tian, K.; Liu, Q. P.
2010-03-08
This paper considers supersymmetric fifth order evolution equations. Within the framework of symmetry approach, we give a list containing six equations, which are (potentially) integrable systems. Among these equations, the most interesting ones include a supersymmetric Sawada-Kotera equation and a novel supersymmetric fifth order KdV equation. For the latter, we supply some properties such as a Hamiltonian structures and a possible recursion operator.
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.
NASA Astrophysics Data System (ADS)
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...
Chemical, physical, and theoretical kinetics of an ultrafast folding protein.
Kubelka, Jan; Henry, Eric R; Cellmer, Troy; Hofrichter, James; Eaton, William A
2008-12-01
An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein--the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models--a three-state chemical-kinetics model, a physical-kinetics model, and an Ising-like theoretical model that considers 10(5) possible conformations (microstates). In both the physical-kinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 10(5) microstates. The analysis of the data on site-directed mutants using the chemical-kinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-by-residue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical- or physical-kinetics models.
Chemical, physical, and theoretical kinetics of an ultrafast folding protein
Kubelka, Jan; Henry, Eric R.; Cellmer, Troy; Hofrichter, James; Eaton, William A.
2008-01-01
An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein—the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models—a three-state chemical-kinetics model, a physical-kinetics model, and an Ising-like theoretical model that considers 105 possible conformations (microstates). In both the physical-kinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 105 microstates. The analysis of the data on site-directed mutants using the chemical-kinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-by-residue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical- or physical-kinetics models. PMID:19033473
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.
Renormalization group improved Higgs inflation with a running kinetic term
NASA Astrophysics Data System (ADS)
Takahashi, Fuminobu; Takahashi, Ryo
2016-09-01
We study a Higgs inflation model with a running kinetic term, taking account of the renormalization group evolution of relevant coupling constants. Specifically we study two types of the running kinetic Higgs inflation, where the inflaton potential is given by the quadratic or linear term potential in a frame where the Higgs field is canonically normalized. We solve the renormalization group equations at two-loop level and calculate the scalar spectral index and the tensor-to-scalar ratio. We find that, even if the renormalization group effects are included, the quadratic inflation is ruled out by the CMB observations, while the linear one is still allowed.
Sorption kinetics of arsenic on laterite soil in aqueous medium.
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. PMID:17558779
Sorption kinetics of arsenic on laterite soil in aqueous medium.
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.
Low temperature dry scrubbing reaction kinetics and mechanisms: Volume 2
Prudich, M.E.; Sampson, K.J.; Visneski, M.J.; Reddy, S.N.; Ben-Said, L.; Maldei, M. )
1992-03-01
A resistance-in-series kinetic model for the low temperature reaction of sulfur dioxide with limestone is presented. The resistances considered are the gas-phase transport of sulfur dioxide, the liquid-phase diffusion of both the sulfur species and the calcium species and the solid-phase dissolution of limestone. The model uses film theory to predict the liquid concentrations of the dissolved species and assumes an instantaneous reaction between the sulfur species and calcium species. The kinetic model incorporates three rate equations for the removal of sulfur dioxide. When the rate of removal is limited by the diffusion of sulfur dioxide across the gas film surrounding the limestone particle, a gas-phase controlled rate equation is used. When the diffusion of the reacting species through the liquid film covering the limestone particle is the predominant resistance, a liquid-phase controlled rate equation is used. When the rate is limited by the dissolution of limestone, a solid-phase controlled rate equation is used. The kinetic model is incorporated into a flow model for the fixed-bed Limestone Emission Control (LEC) system. The LEC system employs a fixed-bed of standard quarry-sized limestone to remove sulfur dioxide from coal-fired boiler flue gases. The flow modeling equations for the fixed-bed LEC system, which include simultaneous heat and mass transfer as applied to water-phase evaporation and condensation are also presented. The combined kinetic and flow model is subjected to a parametric study and the modeling predictions are compared with experimental results.
Nikolaevskiy equation with dispersion.
Simbawa, Eman; Matthews, Paul C; Cox, Stephen M
2010-03-01
The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral "Goldstone" mode, including electroconvection and reaction-diffusion systems. It is known to exhibit chaotic dynamics at the onset of pattern formation, at least when the dispersive terms in the equation are suppressed, as is commonly the practice in previous analyses. In this paper, the effects of reinstating the dispersive terms are examined. It is shown that such terms can stabilize some of the spatially periodic traveling waves; this allows us to study the loss of stability and transition to chaos of the waves. The secondary stability diagram ("Busse balloon") for the traveling waves can be remarkably complicated. PMID:20365845
Causal electromagnetic interaction equations
Zinoviev, Yury M.
2011-02-15
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
Generalized reduced MHD equations
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson.
NASA Astrophysics Data System (ADS)
Konesky, Gregory
2009-08-01
In the almost half century since the Drake Equation was first conceived, a number of profound discoveries have been made that require each of the seven variables of this equation to be reconsidered. The discovery of hydrothermal vents on the ocean floor, for example, as well as the ever-increasing extreme conditions in which life is found on Earth, suggest a much wider range of possible extraterrestrial habitats. The growing consensus that life originated very early in Earth's history also supports this suggestion. The discovery of exoplanets with a wide range of host star types, and attendant habitable zones, suggests that life may be possible in planetary systems with stars quite unlike our Sun. Stellar evolution also plays an important part in that habitable zones are mobile. The increasing brightness of our Sun over the next few billion years, will place the Earth well outside the present habitable zone, but will then encompass Mars, giving rise to the notion that some Drake Equation variables, such as the fraction of planets on which life emerges, may have multiple values.
Illite Dissolution Rates and Equation (100 to 280 dec C)
Carroll, Susan
2014-10-17
The objective of this suite of experiments was to develop a useful kinetic dissolution expression for illite applicable over an expanded range of solution pH and temperature conditions representative of subsurface conditions in natural and/or engineered geothermal reservoirs. Using our new data, the resulting rate equation is dependent on both pH and temperature and utilizes two specific dissolution mechanisms (a “neutral” and a “basic” mechanism). The form of this rate equation should be easily incorporated into most existing reactive transport codes for to predict rock-water interactions in EGS shear zones.
Transport equation for plasmas in a stationary-homogeneous turbulence
NASA Astrophysics Data System (ADS)
Wang, Shaojie
2016-02-01
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose symmetry has been proved, can be computed in a straightforward way when the fluctuating particle trajectories are provided. As an application, it has been shown that a mean parallel electric filed can drive a particle flux through the Stokes-Einstein relation, independent of the details of the fluctuations.
On the Role of Viscosity in the Eyring Equation.
Kistemaker, Jos C M; Lubbe, Anouk S; Bloemsma, Erik A; Feringa, Ben L
2016-06-17
Transition-state theory allows for the characterization of kinetic processes in terms of enthalpy and entropy of activation by using the Eyring equation. However, for reactions in solution, it fails to take the change of viscosity of solvents with temperature into account. A second-generation unidirectional rotary molecular motor was used as a probe to study the effects of temperature-dependent viscosity changes upon unimolecular thermal isomerization processes. By combining the free-volume model with transition-state theory, a modified version of the Eyring equation was derived, in which the rate is expressed in terms of both temperature and viscosity. PMID:26853537
Simple jumping process with memory: Transport equation and diffusion
NASA Astrophysics Data System (ADS)
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.
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.
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)
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...
Double-Plate Penetration Equations
NASA Technical Reports Server (NTRS)
Hayashida, K. B.; Robinson, J. H.
2000-01-01
This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.
Thermodynamic consequences of the kinetic nature of the glass transition
Koperwas, Kajetan; Grzybowski, Andrzej; Tripathy, Satya N.; Masiewicz, Elzbieta; Paluch, Marian
2015-01-01
In this paper, we consider the glass transition as a kinetic process and establish one universal equation for the pressure coefficient of the glass transition temperature, dTg/dp, which is a thermodynamic characteristic of this process. Our findings challenge the common previous expectations concerning key characteristics of the transformation from the liquid to the glassy state, because it suggests that without employing an additional condition, met in the glass transition, derivation of the two independent equations for dTg/dp is not possible. Hence, the relation among the thermodynamic coefficients, which could be equivalent to the well-known Prigogine-Defay ratio for the process under consideration, cannot be obtained. Besides, by comparing the predictions of our universal equation for dTg/dp and Ehrenfest equations, we find the aforementioned supplementary restriction, which must be met to use the Prigogine-Defay ratio for the glass transition. PMID:26657017
Reduction operators of Burgers equation
Pocheketa, Oleksandr A.; Popovych, Roman O.
2013-01-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special “no-go” case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf–Cole transformation to a parameterized family of Lie reductions of the linear heat equation. PMID:23576819
New application to Riccati equation
NASA Astrophysics Data System (ADS)
Taogetusang; Sirendaoerji; Li, Shu-Min
2010-08-01
To seek new infinite sequence of exact solutions to nonlinear evolution equations, this paper gives the formula of nonlinear superposition of the solutions and Bäcklund transformation of Riccati equation. Based on the tanh-function expansion method and homogenous balance method, new infinite sequence of exact solutions to Zakharov-Kuznetsov equation, Karamoto-Sivashinsky equation and the set of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov equations are obtained with the aid of symbolic computation system Mathematica. The method is of significance to construct infinite sequence exact solutions to other nonlinear evolution equations.
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
ERIC Educational Resources Information Center
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
Differential Equations Compatible with Boundary Rational qKZ Equation
NASA Astrophysics Data System (ADS)
Takeyama, Yoshihiro
2011-10-01
We give diffierential equations compatible with the rational qKZ equation with boundary reflection. The total system contains the trigonometric degeneration of the bispectral qKZ equation of type (Cěen, Cn) which in the case of type GLn was studied by van Meer and Stokman. We construct an integral formula for solutions to our compatible system in a special case.
The compressible adjoint equations in geodynamics: equations and numerical assessment
NASA Astrophysics Data System (ADS)
Ghelichkhan, Siavash; Bunge, Hans-Peter
2016-04-01
The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
Estimating Equating Error in Observed-Score Equating. Research Report.
ERIC Educational Resources Information Center
van der Linden, Wim J.
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and in the population of examinees. This definition underlies, for example, the well-known approximation to the standard error of equating by Lord (1982).…
Potassium kinetics during hemodialysis.
Agar, Baris U; Culleton, Bruce F; Fluck, Richard; Leypoldt, John K
2015-01-01
Hyperkalemia in hemodialysis patients is associated with high mortality, but prescription of low dialysate potassium concentrations to decrease serum potassium levels is associated with a high incidence of sudden cardiac arrest or sudden death. Improved clinical outcomes for these patients may be possible if rapid and substantial intradialysis decreases in serum potassium concentration can be avoided while maintaining adequate potassium removal. Data from kinetic modeling sessions during the HEMO Study of the dependence of serum potassium concentration on time during hemodialysis treatments and 30 minutes postdialysis were evaluated using a pseudo one-compartment model. Kinetic estimates of potassium mobilization clearance (K(M)) and predialysis central distribution volume (V(pre)) were determined in 551 hemodialysis patients. The studied patients were 58.8 ± 14.4 years of age with predialysis body weight of 72.1 ± 15.1 kg; 306 (55.4%) of the patients were female and 337 (61.2%) were black. K(M) and V(pre) for all patients were non-normally distributed with values of 158 (111, 235) (median [interquartile range]) mL/min and 15.6 (11.4, 22.8) L, respectively. K(M) was independent of dialysate potassium concentration (P > 0.2), but V(pre) was lower at higher dialysate potassium concentration (R = -0.188, P < 0.001). For patients with dialysate potassium concentration between 1.6 and 2.5 mEq/L (N = 437), multiple linear regression of K(M) and V(pre) demonstrated positive association with predialysis body weight and negative association with predialysis serum potassium concentration. Potassium kinetics during hemodialysis can be described using a pseudo one-compartment model.
Terefe, Netsanet Shiferaw; Nhan, Minh Tri; Vallejo, David; Van Loey, Ann; Hendrickx, Marc
2004-01-01
The applicability of the William, Landel, and Ferry (WLF) equation with a modification to take into account the effect of melt-dilution and an empirical log-logistic equation were evaluated to model the kinetics of diffusion-controlled reactions in frozen systems. Kinetic data for the pectin methylesterase catalyzed hydrolysis of pectin in four model systems with different glass transition temperatures: sucrose, maltodextrin (DE = 16.5-19.5), carboxymethylcellulose (CMC) and fructose in a temperature range of -24 to 0 degrees C were used. The modified WLF equation was evaluated with a concentration-dependent glass transition temperature (T(g)) as well as the glass transition temperature of the maximally freeze-concentrated matrix (T(g)') as reference temperatures. The equation with temperature-dependent T(g) described the reaction kinetics reasonably well in all the model systems studied. However the kinetics was better described by a linear relationship between log(V(0)/V(0ref)) and (T - T(ref)) in all cases except CMC. The log-logistic equation also described the kinetics reasonably well. The effect of melt-dilution on reactant concentration was found to be minimal in all cases.
NASA Astrophysics Data System (ADS)
Taff, L. G.; Brennan, T. A.
1989-06-01
Intrigued by the recent advances in research on solving Kepler's equation, we have attacked the problem too. Our contributions emphasize the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques in both mean anomaly/eccentricity space and eccentric anomaly/eccentricity space, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions. The very close second is Broucke's bounds coupled with Newton's second-order scheme.
Makkonen, Lasse
2016-04-01
Young's construction for a contact angle at a three-phase intersection forms the basis of all fields of science that involve wetting and capillary action. We find compelling evidence from recent experimental results on the deformation of a soft solid at the contact line, and displacement of an elastic wire immersed in a liquid, that Young's equation can only be interpreted by surface energies, and not as a balance of surface tensions. It follows that the a priori variable in finding equilibrium is not the position of the contact line, but the contact angle. This finding provides the explanation for the pinning of a contact line. PMID:26940644
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.
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.
Kinetics of interstitial segregation in Cottrell atmospheres and grain boundaries
NASA Astrophysics Data System (ADS)
Svoboda, J.; Zickler, G. A.; Kozeschnik, E.; Fischer, F. D.
2015-09-01
Trapping of interstitial (e.g. carbon) atoms is driven by the reduction in energy in the system. Diffusion of interstitials, together with their trapping in dislocation cores and/or grain boundaries, is studied by the thermodynamic extremal principle. In addition to the total Gibbs energy, a well-established formulation of the total dissipation is applied. Dimension-free evolution equations are derived, whose solution is well approximated by an easy to handle kinetic equation. Cottrell's power law can be verified in the initial stage.
A semiclassical kinetic theory of Dirac particles and Thomas precession
NASA Astrophysics Data System (ADS)
Dayi, Ömer F.; Kilinçarslan, Eda
2015-10-01
Kinetic theory of Dirac fermions is studied within the matrix valued differential forms method. It is based on the symplectic form derived by employing the semiclassical wave packet build of the positive energy solutions of the Dirac equation. A satisfactory definition of the distribution matrix elements imposes to work in the basis where the helicity is diagonal which is also needed to attain the massless limit. We show that the kinematic Thomas precession correction can be studied straightforwardly within this approach. It contributes on an equal footing with the Berry gauge fields. In fact in equations of motion it eliminates the terms arising from the Berry gauge fields.
The Gaussian radial basis function method for plasma kinetic theory
NASA Astrophysics Data System (ADS)
Hirvijoki, E.; Candy, J.; Belli, E.; Embréus, O.
2015-10-01
Description of a magnetized plasma involves the Vlasov equation supplemented with the non-linear Fokker-Planck collision operator. For non-Maxwellian distributions, the collision operator, however, is difficult to compute. In this Letter, we introduce Gaussian Radial Basis Functions (RBFs) to discretize the velocity space of the entire kinetic system, and give the corresponding analytical expressions for the Vlasov and collision operator. Outlining the general theory, we also highlight the connection to plasma fluid theories, and give 2D and 3D numerical solutions of the non-linear Fokker-Planck equation. Applications are anticipated in both astrophysical and laboratory plasmas.
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.
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.
Conservational PDF Equations of Turbulence
NASA Technical Reports Server (NTRS)
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Solitons and nonlinear wave equations
Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.
1982-01-01
A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.
Kinetic modeling of Nernst effect in magnetized hohlraums.
Joglekar, A S; Ridgers, C P; Kingham, R J; Thomas, A G R
2016-04-01
We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic fields. In addition to showing the prevalence of nonlocal behavior, we demonstrate that effects such as anomalous heat flow are induced by inverse bremsstrahlung heating. We show magnetic field amplification up to a factor of 3 from Nernst compression into the hohlraum wall. The magnetic field is also expelled towards the hohlraum axis due to Nernst advection faster than frozen-in flux would suggest. Nonlocality contributes to the heat flow towards the hohlraum axis and results in an augmented Nernst advection mechanism that is included self-consistently through kinetic modeling.
Kinetic modeling of Nernst effect in magnetized hohlraums.
Joglekar, A S; Ridgers, C P; Kingham, R J; Thomas, A G R
2016-04-01
We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic fields. In addition to showing the prevalence of nonlocal behavior, we demonstrate that effects such as anomalous heat flow are induced by inverse bremsstrahlung heating. We show magnetic field amplification up to a factor of 3 from Nernst compression into the hohlraum wall. The magnetic field is also expelled towards the hohlraum axis due to Nernst advection faster than frozen-in flux would suggest. Nonlocality contributes to the heat flow towards the hohlraum axis and results in an augmented Nernst advection mechanism that is included self-consistently through kinetic modeling. PMID:27176417
Kinetic Method for Hydrogen-Deuterium-Tritium Mixture Distillation Simulation
Sazonov, A.B.; Kagramanov, Z.G.; Magomedbekov, E.P.
2005-07-15
Simulation of hydrogen distillation plants requires mathematical procedures suitable for multicomponent systems. In most of the present-day simulation methods a distillation column is assumed to be composed of theoretical stages, or plates. However, in the case of a multicomponent mixture theoretical plate does not exist.An alternative kinetic method of simulation is depicted in the work. According to this method a system of mass-transfer differential equations is solved numerically. Mass-transfer coefficients are estimated with using experimental results and empirical equations.Developed method allows calculating the steady state of a distillation column as well as its any non-steady state when initial conditions are given. The results for steady states are compared with ones obtained via Thiele-Geddes theoretical stage technique and the necessity of using kinetic method is demonstrated. Examples of a column startup period and periodic distillation simulations are shown as well.
Kinetic Description of Vacuum Creation of Massive Vector Bosons
Blaschke, D.B.; Prozorkevich, A.V.; Smolyansky, S.A.; Reichel, A.V.
2005-06-01
In the simple model of massive vector field in a flat spacetime, we derive the kinetic equation of non-Markovian type describing the vacuum pair creation under action of external fields of different nature. We use for this aim the nonperturbative methods of kinetic theory in combination with a new element when the transition of the instantaneous quasiparticle representation is realized within the oscillator (holomorphic) representation. We study in detail the process of vacuum creation of vector bosons generated by a time-dependent boson mass in accordance with the framework of a conformal-invariant scalar-tensor gravitational theory and its cosmological application. It is indicated that the choice of the equation of state allows one to obtain a number density of vector bosons that is sufficient to explain the observed number density of photons in the cosmic microwave background radiation.
Kinetic modeling of Nernst effect in magnetized hohlraums
NASA Astrophysics Data System (ADS)
Joglekar, A. S.; Ridgers, C. P.; Kingham, R. J.; Thomas, A. G. R.
2016-04-01
We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic fields. In addition to showing the prevalence of nonlocal behavior, we demonstrate that effects such as anomalous heat flow are induced by inverse bremsstrahlung heating. We show magnetic field amplification up to a factor of 3 from Nernst compression into the hohlraum wall. The magnetic field is also expelled towards the hohlraum axis due to Nernst advection faster than frozen-in flux would suggest. Nonlocality contributes to the heat flow towards the hohlraum axis and results in an augmented Nernst advection mechanism that is included self-consistently through kinetic modeling.
Propagation of radiation in fluctuating multiscale plasmas. II. Kinetic simulations
Pal Singh, Kunwar; Robinson, P. A.; Cairns, Iver H.; Tyshetskiy, Yu.
2012-11-15
A numerical algorithm is developed and tested that implements the kinetic treatment of electromagnetic radiation propagating through plasmas whose properties have small scale fluctuations, which was developed in a companion paper. This method incorporates the effects of refraction, damping, mode structure, and other aspects of large-scale propagation of electromagnetic waves on the distribution function of quanta in position and wave vector, with small-scale effects of nonuniformities, including scattering and mode conversion approximated as causing drift and diffusion in wave vector. Numerical solution of the kinetic equation yields the distribution function of radiation quanta in space, time, and wave vector. Simulations verify the convergence, accuracy, and speed of the methods used to treat each term in the equation. The simulations also illustrate the main physical effects and place the results in a form that can be used in future applications.
Reproducing Phenomenology of Peroxidation Kinetics via Model Optimization
NASA Astrophysics Data System (ADS)
Ruslanov, Anatole D.; Bashylau, Anton V.
2010-06-01
We studied mathematical modeling of lipid peroxidation using a biochemical model system of iron (II)-ascorbate-dependent lipid peroxidation of rat hepatocyte mitochondrial fractions. We found that antioxidants extracted from plants demonstrate a high intensity of peroxidation inhibition. We simplified the system of differential equations that describes the kinetics of the mathematical model to a first order equation, which can be solved analytically. Moreover, we endeavor to algorithmically and heuristically recreate the processes and construct an environment that closely resembles the corresponding natural system. Our results demonstrate that it is possible to theoretically predict both the kinetics of oxidation and the intensity of inhibition without resorting to analytical and biochemical research, which is important for cost-effective discovery and development of medical agents with antioxidant action from the medicinal plants.
Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C; Brooks, Scott C; Pace, Molly N; Kim, Young-Jin; Jardine, Philip M; Watson, David B
2007-06-16
This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.
``Riemann equations'' in bidifferential calculus
NASA Astrophysics Data System (ADS)
Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.
2015-10-01
We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.
Fluid flow and chemical reaction kinetics in metamorphic systems
Lasaga, A.C.; Rye, D.M. )
1993-05-01
The treatment and effects of chemical reaction kinetics during metamorphism are developed along with the incorporation of fluid flow, diffusion, and thermal evolution. The interplay of fluid flow and surface reaction rates, the distinction between steady state and equilibrium, and the possible overstepping of metamorphic reactions are discussed using a simple analytic model. This model serves as an introduction to the second part of the paper, which develops a reaction model that solves the coupled temperature-fluid flow-chemical composition differential equations relevant to metamorphic processes. Consideration of stable isotopic evidence requires that such a kinetic model be considered for the chemical evolution of a metamorphic aureole. A general numerical scheme is discussed to handle the solution of the model. The results of this kinetic model allow us to reach several important conclusions regarding the factors controlling the chemical evolution of mineral assemblages during a metamorphic event. 41 refs., 19 figs., 5 tabs.
Kinetic electrons in global electromagnetic gyrokinetic particle simulations
NASA Astrophysics Data System (ADS)
Nishimura, Y.; Wang, W.
2005-10-01
Employing an electromagnetic gyrokinetic simulation model,ootnotetextZ. Lin and L. Chen, Phys. Plasmas 8, 1447 (2001). kinetic electron dynamics in global tokamak geometry is investigated. The massless fluid electron model is developed as a base. We further evolve gyrokinetic equations for non-adiabatic kinetic electrons. To obtain the magnetic perturbation, the fluid-kinetic hybrid electron model^1 employs the inverse of the Faraday's law. Instead, the Ampere's law is used as a closure relation to avoid uncertainties in estimating ue|, the moment of the electron velocities. The physics goal is to investigate the finite beta effects on the turbulent transport, as well as α particle driven turbulence.ootnotetextI. Holod, Z. Lin, et al., this conference. This work is supported by Department of Energy (DOE) Cooperative Agreement No. DE-FC02-03ER54695 (UCI), DOE Contract No. DE-AC02-76CH03073 (PPPL).
Fast algorithm for calculating chemical kinetics in turbulent reacting flow
NASA Technical Reports Server (NTRS)
Radhakrishnan, K.; Pratt, D. T.
1986-01-01
This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.
SABIO-RK--database for biochemical reaction kinetics.
Wittig, Ulrike; Kania, Renate; Golebiewski, Martin; Rey, Maja; Shi, Lei; Jong, Lenneke; Algaa, Enkhjargal; Weidemann, Andreas; Sauer-Danzwith, Heidrun; Mir, Saqib; Krebs, Olga; Bittkowski, Meik; Wetsch, Elina; Rojas, Isabel; Müller, Wolfgang
2012-01-01
SABIO-RK (http://sabio.h-its.org/) is a web-accessible database storing comprehensive information about biochemical reactions and their kinetic properties. SABIO-RK offers standardized data manually extracted from the literature and data directly submitted from lab experiments. The database content includes kinetic parameters in relation to biochemical reactions and their biological sources with no restriction on any particular set of organisms. Additionally, kinetic rate laws and corresponding equations as well as experimental conditions are represented. All the data are manually curated and annotated by biological experts, supported by automated consistency checks. SABIO-RK can be accessed via web-based user interfaces or automatically via web services that allow direct data access by other tools. Both interfaces support the export of the data together with its annotations in SBML (Systems Biology Markup Language), e.g. for import in modelling tools.
Modified Enskog kinetic theory for strongly coupled plasmas.
Baalrud, Scott D; Daligault, Jérôme
2015-06-01
Concepts underlying the Enskog kinetic theory of hard-spheres are applied to include short-range correlation effects in a model for transport coefficients of strongly coupled plasmas. The approach is based on an extension of the effective potential transport theory [S. D. Baalrud and J. Daligault, Phys. Rev. Lett. 110, 235001 (2013)] to include an exclusion radius surrounding individual charged particles that is associated with Coulomb repulsion. This is obtained by analogy with the finite size of hard spheres in Enskog's theory. Predictions for the self-diffusion and shear viscosity coefficients of the one-component plasma are tested against molecular dynamics simulations. The theory is found to accurately capture the kinetic contributions to the transport coefficients, but not the potential contributions that arise at very strong coupling (Γ≳30). Considerations related to a first-principles generalization of Enskog's kinetic equation to continuous potentials are also discussed.
Landau-Lifshitz-Gilbert equation with symmetric coefficients of the dissipative function II
NASA Astrophysics Data System (ADS)
Salazar, M.; Pérez Alcazar, G. A.
2016-07-01
In a previous study (Salazar and Perez Alcazar, 2015) we obtained the modified Landau-Lifshitz-Gilbert equation. The modification consisted in proposing a method to convert to symmetrical the kinetic coefficients of this equation. In the present study we find the solution to the proposed equation. This solution shows that the Mx and My components of the magnetization have damped oscillations. We find the expressions for the damping coefficient and the frequency of the oscillations and show their graphs. Finally, we compare these graphs with those that correspond to the frequency of oscillations for the magnetization in the Landau-Lifshitz-Gilbert equation.
Seery, D.J.; Freihaut, J.D.; Proscia, W.M. ); Howard, J.B.; Peters, W.; Hsu, J.; Hajaligol, M.; Sarofim, A. ); Jenkins, R.; Mallin, J.; Espindola-Merin, B. ); Essenhigh, R.; Misra, M.K. )
1989-07-01
This report contains results of a coordinated, multi-laboratory investigation of coal devolatilization. Data is reported pertaining to the devolatilization for bituminous coals over three orders of magnitude in apparent heating rate (100 to 100,000 + {degree}C/sec), over two orders of magnitude in particle size (20 to 700 microns), final particle temperatures from 400 to 1600{degree}C, heat transfer modes ranging from convection to radiative, ambient pressure ranging from near vacuum to one atmosphere pressure. The heat transfer characteristics of the reactors are reported in detail. It is assumed the experimental results are to form the basis of a devolatilization data base. Empirical rate expressions are developed for each phase of devolatilization which, when coupled to an awareness of the heat transfer rate potential of a particular devolatilization reactor, indicate the kinetics emphasized by a particular system reactor plus coal sample. The analysis indicates the particular phase of devolatilization that will be emphasized by a particular reactor type and, thereby, the kinetic expressions appropriate to that devolatilization system. Engineering rate expressions are developed from the empirical rate expressions in the context of a fundamental understanding of coal devolatilization developed in the course of the investigation. 164 refs., 223 figs., 44 tabs.
Delayed uncoupled continuous-time random walks do not provide a model for the telegraph equation.
Rukolaine, S A; Samsonov, A M
2012-02-01
It has been alleged in several papers that the so-called delayed continuous-time random walks (DCTRWs) provide a model for the one-dimensional telegraph equation at microscopic level. This conclusion, being widespread now, is strange, since the telegraph equation describes phenomena with finite propagation speed, while the velocity of the motion of particles in the DCTRWs is infinite. In this paper we investigate the accuracy of the approximations to the DCTRWs provided by the telegraph equation. We show that the diffusion equation, being the correct limit of the DCTRWs, gives better approximations in L(2) norm to the DCTRWs than the telegraph equation. We conclude, therefore, that first, the DCTRWs do not provide any correct microscopic interpretation of the one-dimensional telegraph equation, and second, the kinetic (exact) model of the telegraph equation is different from the model based on the DCTRWs.
Solving Nonlinear Coupled Differential Equations
NASA Technical Reports Server (NTRS)
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
Successfully Transitioning to Linear Equations
ERIC Educational Resources Information Center
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…