Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

PubMed

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

Modeling of the Nonlinear Interface in Reinforced Concrete

NASA Astrophysics Data System (ADS)

Curiel Sosa, J. L.

2010-04-01

This article presents a novel scheme for modeling of reinforced concrete. The strategy takes into account the nonlinear behavior of the concrete as well as the debonding in the interface. The proposed technique solves the kinematic and kinetic jump in the interface by performing sub-cycles over the constituents-reinforcing bar and concrete-jointly with an innovative interface constitutive law. Application to pull-out problems is performed to show the capabilities of the proposed methodology by means of comparison with available experimental data.

A prospectus on kinetic heliophysics

NASA Astrophysics Data System (ADS)

Howes, Gregory G.

2017-05-01

Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic turbulence, collisionless magnetic reconnection, particle acceleration, and kinetic instabilities are four poorly understood, grand-challenge problems that lie at the new frontier of kinetic heliophysics. The increasing availability of high cadence and high phase-space resolution measurements of particle velocity distributions by current and upcoming spacecraft missions and of massively parallel nonlinear kinetic simulations of weakly collisional heliospheric plasmas provides the opportunity to transform our understanding of these kinetic mechanisms through the full utilization of the information contained in the particle velocity distributions. Several major considerations for future investigations of kinetic heliophysics are examined. Turbulent dissipation followed by particle heating is highlighted as an inherently two-step process in weakly collisional plasmas, distinct from the more familiar case in fluid theory. Concerted efforts must be made to tackle the big-data challenge of visualizing the high-dimensional (3D-3V) phase space of kinetic plasma theory through physics-based reductions. Furthermore, the development of innovative analysis methods that utilize full velocity-space measurements, such as the field-particle correlation technique, will enable us to gain deeper insight into these four grand-challenge problems of kinetic heliophysics. A systems approach to tackle the multi-scale problem of heliophysics through a rigorous connection between the kinetic physics at microscales and the self-consistent evolution of the heliosphere at macroscales will propel the field of kinetic heliophysics into the future.

A prospectus on kinetic heliophysics

PubMed Central

2017-01-01

Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic turbulence, collisionless magnetic reconnection, particle acceleration, and kinetic instabilities are four poorly understood, grand-challenge problems that lie at the new frontier of kinetic heliophysics. The increasing availability of high cadence and high phase-space resolution measurements of particle velocity distributions by current and upcoming spacecraft missions and of massively parallel nonlinear kinetic simulations of weakly collisional heliospheric plasmas provides the opportunity to transform our understanding of these kinetic mechanisms through the full utilization of the information contained in the particle velocity distributions. Several major considerations for future investigations of kinetic heliophysics are examined. Turbulent dissipation followed by particle heating is highlighted as an inherently two-step process in weakly collisional plasmas, distinct from the more familiar case in fluid theory. Concerted efforts must be made to tackle the big-data challenge of visualizing the high-dimensional (3D-3V) phase space of kinetic plasma theory through physics-based reductions. Furthermore, the development of innovative analysis methods that utilize full velocity-space measurements, such as the field-particle correlation technique, will enable us to gain deeper insight into these four grand-challenge problems of kinetic heliophysics. A systems approach to tackle the multi-scale problem of heliophysics through a rigorous connection between the kinetic physics at microscales and the self-consistent evolution of the heliosphere at macroscales will propel the field of kinetic heliophysics into the future. PMID:29104421

Pseudo-second order models for the adsorption of safranin onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth

2007-04-02

Kinetic experiments were carried out for the sorption of safranin onto activated carbon particles. The kinetic data were fitted to pseudo-second order model of Ho, Sobkowsk and Czerwinski, Blanchard et al. and Ritchie by linear and non-linear regression methods. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo-second order models were the same. Non-linear regression analysis showed that both Blanchard et al. and Ho have similar ideas on the pseudo-second order model but with different assumptions. The best fit of experimental data in Ho's pseudo-second order expression by linear and non-linear regression method showed that Ho pseudo-second order model was a better kinetic expression when compared to other pseudo-second order kinetic expressions.

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

NASA Technical Reports Server (NTRS)

Barth, Timothy; Charrier, Pierre; Mansour, Nagi N. (Technical Monitor)

2001-01-01

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Nonlinear Analyte Concentration Gradients for One-Step Kinetic Analysis Employing Optical Microring Resonators

PubMed Central

Marty, Michael T.; Kuhnline Sloan, Courtney D.; Bailey, Ryan C.; Sligar, Stephen G.

2012-01-01

Conventional methods to probe the binding kinetics of macromolecules at biosensor surfaces employ a stepwise titration of analyte concentrations and measure the association and dissociation to the immobilized ligand at each concentration level. It has previously been shown that kinetic rates can be measured in a single step by monitoring binding as the analyte concentration increases over time in a linear gradient. We report here the application of nonlinear analyte concentration gradients for determining kinetic rates and equilibrium binding affinities in a single experiment. A versatile nonlinear gradient maker is presented, which is easily applied to microfluidic systems. Simulations validate that accurate kinetic rates can be extracted for a wide range of association and dissociation rates, gradient slopes and curvatures, and with models for mass transport. The nonlinear analyte gradient method is demonstrated with a silicon photonic microring resonator platform to measure prostate specific antigen-antibody binding kinetics. PMID:22686186

Nonlinear analyte concentration gradients for one-step kinetic analysis employing optical microring resonators.

PubMed

Marty, Michael T; Sloan, Courtney D Kuhnline; Bailey, Ryan C; Sligar, Stephen G

2012-07-03

Conventional methods to probe the binding kinetics of macromolecules at biosensor surfaces employ a stepwise titration of analyte concentrations and measure the association and dissociation to the immobilized ligand at each concentration level. It has previously been shown that kinetic rates can be measured in a single step by monitoring binding as the analyte concentration increases over time in a linear gradient. We report here the application of nonlinear analyte concentration gradients for determining kinetic rates and equilibrium binding affinities in a single experiment. A versatile nonlinear gradient maker is presented, which is easily applied to microfluidic systems. Simulations validate that accurate kinetic rates can be extracted for a wide range of association and dissociation rates, gradient slopes, and curvatures, and with models for mass transport. The nonlinear analyte gradient method is demonstrated with a silicon photonic microring resonator platform to measure prostate specific antigen-antibody binding kinetics.

Effect of nonlinearity in hybrid kinetic Monte Carlo-continuum models.

PubMed

Balter, Ariel; Lin, Guang; Tartakovsky, Alexandre M

2012-01-01

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: comparison of linear and non-linear regression methods.

PubMed

Kumar, K Vasanth; Sivanesan, S

2006-08-25

Pseudo second order kinetic expressions of Ho, Sobkowsk and Czerwinski, Blanachard et al. and Ritchie were fitted to the experimental kinetic data of malachite green onto activated carbon by non-linear and linear method. Non-linear method was found to be a better way of obtaining the parameters involved in the second order rate kinetic expressions. Both linear and non-linear regression showed that the Sobkowsk and Czerwinski and Ritchie's pseudo second order model were the same. Non-linear regression analysis showed that both Blanachard et al. and Ho have similar ideas on the pseudo second order model but with different assumptions. The best fit of experimental data in Ho's pseudo second order expression by linear and non-linear regression method showed that Ho pseudo second order model was a better kinetic expression when compared to other pseudo second order kinetic expressions. The amount of dye adsorbed at equilibrium, q(e), was predicted from Ho pseudo second order expression and were fitted to the Langmuir, Freundlich and Redlich Peterson expressions by both linear and non-linear method to obtain the pseudo isotherms. The best fitting pseudo isotherm was found to be the Langmuir and Redlich Peterson isotherm. Redlich Peterson is a special case of Langmuir when the constant g equals unity.

Linear and non-linear regression analysis for the sorption kinetics of methylene blue onto activated carbon.

PubMed

Kumar, K Vasanth

2006-10-11

Batch kinetic experiments were carried out for the sorption of methylene blue onto activated carbon. The experimental kinetics were fitted to the pseudo first-order and pseudo second-order kinetics by linear and a non-linear method. The five different types of Ho pseudo second-order expression have been discussed. A comparison of linear least-squares method and a trial and error non-linear method of estimating the pseudo second-order rate kinetic parameters were examined. The sorption process was found to follow a both pseudo first-order kinetic and pseudo second-order kinetic model. Present investigation showed that it is inappropriate to use a type 1 and type pseudo second-order expressions as proposed by Ho and Blanachard et al. respectively for predicting the kinetic rate constants and the initial sorption rate for the studied system. Three correct possible alternate linear expressions (type 2 to type 4) to better predict the initial sorption rate and kinetic rate constants for the studied system (methylene blue/activated carbon) was proposed. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Non-linear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, G., E-mail: gchen@lanl.gov; Chacón, L.; Leibs, C.A.

2014-02-01

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solvemore » is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.« less

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

NASA Astrophysics Data System (ADS)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

Simulation of 2D rarefied gas flows based on the numerical solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

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

2017-10-01

There are various methods for calculating rarefied gas flows, in particular, statistical methods and deterministic methods based on the finite-difference solutions of the Boltzmann nonlinear kinetic equation and on the solutions of model kinetic equations. There is no universal method; each has its disadvantages in terms of efficiency or accuracy. The choice of the method depends on the problem to be solved and on parameters of calculated flows. Qualitative theoretical arguments help to determine the range of parameters of effectively solved problems for each method; however, it is advisable to perform comparative tests of calculations of the classical problems performed by different methods and with different parameters to have quantitative confirmation of this reasoning. The paper provides the results of the calculations performed by the authors with the help of the Direct Simulation Monte Carlo method and finite-difference methods of solving the Boltzmann equation and model kinetic equations. Based on this comparison, conclusions are made on selecting a particular method for flow simulations in various ranges of flow parameters.

Implicit Plasma Kinetic Simulation Using The Jacobian-Free Newton-Krylov Method

NASA Astrophysics Data System (ADS)

Taitano, William; Knoll, Dana; Chacon, Luis

2009-11-01

The use of fully implicit time integration methods in kinetic simulation is still area of algorithmic research. A brute-force approach to simultaneously including the field equations and the particle distribution function would result in an intractable linear algebra problem. A number of algorithms have been put forward which rely on an extrapolation in time. They can be thought of as linearly implicit methods or one-step Newton methods. However, issues related to time accuracy of these methods still remain. We are pursuing a route to implicit plasma kinetic simulation which eliminates extrapolation, eliminates phase-space from the linear algebra problem, and converges the entire nonlinear system within a time step. We accomplish all this using the Jacobian-Free Newton-Krylov algorithm. The original research along these lines considered particle methods to advance the distribution function [1]. In the current research we are advancing the Vlasov equations on a grid. Results will be presented which highlight algorithmic details for single species electrostatic problems and coupled ion-electron electrostatic problems. [4pt] [1] H. J. Kim, L. Chac'on, G. Lapenta, ``Fully implicit particle in cell algorithm,'' 47th Annual Meeting of the Division of Plasma Physics, Oct. 24-28, 2005, Denver, CO

Nonlinear Acoustical Assessment of Precipitate Nucleation

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Yost, William T.

2004-01-01

The purpose of the present work is to show that measurements of the acoustic nonlinearity parameter in heat treatable alloys as a function of heat treatment time can provide quantitative information about the kinetics of precipitate nucleation and growth in such alloys. Generally, information on the kinetics of phase transformations is obtained from time-sequenced electron microscopical examination and differential scanning microcalorimetry. The present nonlinear acoustical assessment of precipitation kinetics is based on the development of a multiparameter analytical model of the effects on the nonlinearity parameter of precipitate nucleation and growth in the alloy system. A nonlinear curve fit of the model equation to the experimental data is then used to extract the kinetic parameters related to the nucleation and growth of the targeted precipitate. The analytical model and curve fit is applied to the assessment of S' precipitation in aluminum alloy 2024 during artificial aging from the T4 to the T6 temper.

Wave kinetics of random fibre lasers

PubMed Central

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

2015-01-01

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

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

PubMed

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

2013-01-01

Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis-Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Hybrid genetic algorithm with an adaptive penalty function for fitting multimodal experimental data: application to exchange-coupled non-Kramers binuclear iron active sites.

PubMed

Beaser, Eric; Schwartz, Jennifer K; Bell, Caleb B; Solomon, Edward I

2011-09-26

A Genetic Algorithm (GA) is a stochastic optimization technique based on the mechanisms of biological evolution. These algorithms have been successfully applied in many fields to solve a variety of complex nonlinear problems. While they have been used with some success in chemical problems such as fitting spectroscopic and kinetic data, many have avoided their use due to the unconstrained nature of the fitting process. In engineering, this problem is now being addressed through incorporation of adaptive penalty functions, but their transfer to other fields has been slow. This study updates the Nanakorrn Adaptive Penalty function theory, expanding its validity beyond maximization problems to minimization as well. The expanded theory, using a hybrid genetic algorithm with an adaptive penalty function, was applied to analyze variable temperature variable field magnetic circular dichroism (VTVH MCD) spectroscopic data collected on exchange coupled Fe(II)Fe(II) enzyme active sites. The data obtained are described by a complex nonlinear multimodal solution space with at least 6 to 13 interdependent variables and are costly to search efficiently. The use of the hybrid GA is shown to improve the probability of detecting the global optimum. It also provides large gains in computational and user efficiency. This method allows a full search of a multimodal solution space, greatly improving the quality and confidence in the final solution obtained, and can be applied to other complex systems such as fitting of other spectroscopic or kinetics data.

Recent advances in nonlinear implicit, electrostatic particle-in-cell (PIC) algorithms

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; Barnes, Daniel

2012-10-01

An implicit 1D electrostatic PIC algorithmfootnotetextChen, Chac'on, Barnes, J. Comput. Phys. 230 (2011) has been developed that satisfies exact energy and charge conservation. The algorithm employs a kinetic-enslaved Jacobian-free Newton-Krylov methodfootnotetextIbid. that ensures nonlinear convergence while taking timesteps comparable to the dynamical timescale of interest. Here we present two main improvements of the algorithm. The first is the formulation of a preconditioner based on linearized fluid equations, which are closed using available particle information. The computational benefit is that solving the fluid system is much cheaper than the kinetic one. The effectiveness of the preconditioner in accelerating nonlinear iterations on challenging problems will be demonstrated. A second improvement is the generalization of Ref. 1 to curvilinear meshes,footnotetextChac'on, Chen, Barnes, J. Comput. Phys. submitted (2012) with a hybrid particle update of positions and velocities in logical and physical space respectively.footnotetextSwift, J. Comp. Phys., 126 (1996) The curvilinear algorithm remains exactly charge and energy-conserving, and can be extended to multiple dimensions. We demonstrate the accuracy and efficiency of the algorithm with a 1D ion-acoustic shock wave simulation.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Aspects of effective supersymmetric theories

NASA Astrophysics Data System (ADS)

Tziveloglou, Panteleimon

This work consists of two parts. In the first part we construct the complete extension of the Minimal Supersymmetric Standard Model by higher dimensional effective operators and then study its phenomenology. These operators encapsulate the effects on LHC physics of any kind of new degrees of freedom at the multiTeV scale. The effective analysis includes the case where the multiTeV physics is the supersymmetry breaking sector itself. In that case the appropriate framework is nonlinear supersymmetry. We choose to realize the nonlinear symmetry by the method of constrained superfields. Beyond the new effective couplings, the analysis suggests an interpretation of the 'little hierarchy problem' as an indication of new physics at multiTeV scale. In the second part we explore the power of constrained superfields in extended supersymmetry. It is known that in N = 2 supersymmetry the gauge kinetic function cannot depend on hypermultiplet scalars. However, it is also known that the low energy effective action of a D-brane in an N = 2 supersymmetric bulk includes the DBI action, where the gauge kinetic function does depend on the dilaton. We show how the nonlinearization of the second SUSY (imposed by the presence of the D-brane) opens this possibility, by constructing the global N = 1 linear + 1 nonlinear invariant coupling of a hypermultiplet with a gauge multiplet. The constructed theory enjoys interesting features, including a novel super-Higgs mechanism without gravity.

Combined genetic algorithm and multiple linear regression (GA-MLR) optimizer: Application to multi-exponential fluorescence decay surface.

PubMed

Fisz, Jacek J

2006-12-07

The optimization approach based on the genetic algorithm (GA) combined with multiple linear regression (MLR) method, is discussed. The GA-MLR optimizer is designed for the nonlinear least-squares problems in which the model functions are linear combinations of nonlinear functions. GA optimizes the nonlinear parameters, and the linear parameters are calculated from MLR. GA-MLR is an intuitive optimization approach and it exploits all advantages of the genetic algorithm technique. This optimization method results from an appropriate combination of two well-known optimization methods. The MLR method is embedded in the GA optimizer and linear and nonlinear model parameters are optimized in parallel. The MLR method is the only one strictly mathematical "tool" involved in GA-MLR. The GA-MLR approach simplifies and accelerates considerably the optimization process because the linear parameters are not the fitted ones. Its properties are exemplified by the analysis of the kinetic biexponential fluorescence decay surface corresponding to a two-excited-state interconversion process. A short discussion of the variable projection (VP) algorithm, designed for the same class of the optimization problems, is presented. VP is a very advanced mathematical formalism that involves the methods of nonlinear functionals, algebra of linear projectors, and the formalism of Fréchet derivatives and pseudo-inverses. Additional explanatory comments are added on the application of recently introduced the GA-NR optimizer to simultaneous recovery of linear and weakly nonlinear parameters occurring in the same optimization problem together with nonlinear parameters. The GA-NR optimizer combines the GA method with the NR method, in which the minimum-value condition for the quadratic approximation to chi(2), obtained from the Taylor series expansion of chi(2), is recovered by means of the Newton-Raphson algorithm. The application of the GA-NR optimizer to model functions which are multi-linear combinations of nonlinear functions, is indicated. The VP algorithm does not distinguish the weakly nonlinear parameters from the nonlinear ones and it does not apply to the model functions which are multi-linear combinations of nonlinear functions.

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

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, nevertheless, the present GKUAs for kinetic model Boltzmann equations in conjunction with current available high-performance parallel computer power can provide a vital engineering tool for analyzing rarefied gas flows covering the whole range of flow regimes in aerospace engineering applications.

A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

NASA Technical Reports Server (NTRS)

Stern, Boris E.; Svensson, Roland; Begelman, Mitchell C.; Sikora, Marek

1995-01-01

High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

Application of dynamic recurrent neural networks in nonlinear system identification

NASA Astrophysics Data System (ADS)

Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang

2006-11-01

An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.

Energetic and optical consequences in isotropic curved space and time.

PubMed

Ben-Abdallah, P

2001-10-20

In numerous media (nonlinear material, moving dielectrics, superfluids, Bose-Einstein condensates, and others) and different in vacuo states (nontrivial quantum electrodynamics in vacuo) matter or vacuum fluctuations modify light propagation in the same way that an effective gravitational field does. This nonlinear optical behavior affects not only the energy paths but also the form of the energetic invariant. However, such a function plays a key role when we try to develop a phenomenological kinetic theory for participating media. I analyze how modification of light propagation transforms the energetic invariant and modifies its transport inside a participating medium. A semianalytical method is presented to solve the radiative transfer equation for any spherically symmetric problems.

Alfvénic wave packets collision in a kinetic plasma

NASA Astrophysics Data System (ADS)

Pezzi, Oreste; Parashar, Tulasi N.; Servidio, Sergio; Valentini, Francesco; Malara, Francesco; Matthaeus, William H.; Veltri, Pierluigi

2016-04-01

The problem of two colliding and counter-propagating Alfvénic wave packets has been investigated in detail since the late Seventies. In particular Moffatt [1] and Parker [2] showed that, in the framework of the incompressible magnetohydrodynamics (MHD), nonlinear interactions can develop only during the overlapping of the two packets. Here we describe a similar problem in the framework of the kinetic physics. The collision of two quasi-Alfvénic packets has been analyzed by means of MHD, Hall-MHD and kinetic simulations performed with two different hybrid codes: a PIC code [3] and a Vlasov-Maxwell code [4]. Due to the huge computational cost, only a 2D-3V phase space is allowed (two dimensions in the physical space, three dimensions in the velocity space). Preliminary results suggest that, as well as in the MHD case, the most relevant nonlinear effects occur during the overlapping of the two packets. For both the PIC and Vlasov cases, strong temperature anisotropies are present during the evolution of the wave packets. Moreover, due to the absence of numerical noise, Vlasov simulations show that the collision of the counter-propagating solitary waves produces a significant beam in the velocity distribution functions [5], which, instead, cannot be appreciated in PIC simulations. We remark that, beyond the interest of studying a well-known MHD problem in the realm of the kinetic physics, our results allows also to compare different numerical codes. [1] H.K. Moffatt, Field generation in electrically conducting fluids (Cambridge University Press, 1978). [2] E.N. Parker, Cosmical magnetic fields: their origin and their activity (Oxford University Press, 1979). [3] T.N. Parashar, M.A. Shay, P.A. Cassak and W.H. Matthaeus, Physics of Plasmas 16, 032310 (2009). [4] F. Valentini, P. Trávníček, F. Califano, P. Hellinger & A. Mangeney, Journal of Computational Physics 225, 753-770 (2007). [5] J. He, C. Tu, E. Marsch, C.H. Chen, L. Wang, Z. Pei, L. Zhang, C.S. Salem and S.D. Bale, The Astrophysical Journal Letters 813, L30 (2015).

Collisions of two Alfvénic wave packets in a kinetic plasma

NASA Astrophysics Data System (ADS)

Pezzi, O.; Servidio, S.; Valentini, F.; Parashar, T.; Malara, F.; Matthaeus, W. H.; Veltri, P.

2016-12-01

The problem of two colliding and counter-propagating Alfvénic wave packets has been investigated in detail since the late Seventies. In particular Moffatt [1] and Parker [2] showed that, in the framework of the incompressible magnetohydrodynamics (MHD), nonlinear interactions can develop only during the overlapping of the two packets. Here we describe a similar problem in the framework of the kinetic physics. The collision of two quasi-Alfvénic packets has been analyzed by means of MHD, Hall-MHD and kinetic simulations performed with two different hybrid codes: a PIC code [3] and a Vlasov-Maxwell code [4]. Due to the huge computational cost, only a 2D-3V phase space is allowed (two dimensions in the physical space, three dimensions in the velocity space). Preliminary results suggest that, as well as in the MHD case, the most relevant nonlinear effects occur during the overlapping of the two packets. For both the PIC and Vlasov cases, strong temperature anisotropies are present during the evolution of the wave packets. Moreover, due to the absence of numerical noise, Vlasov simulations show that the collision of the counter-propagating solitary waves produces a significant beam in the velocity distribution functions [5], which, instead, cannot be appreciated in PIC simulations. We remark that, beyond the interest of studying a well-known MHD problem in the realm of the kinetic physics, our results allows also to compare different numerical codes. [1] H.K. Moffatt, Field generation in electrically conducting fluids (Cambridge University Press, 1978). [2] E.N. Parker, Cosmical magnetic fields: their origin and their activity (Oxford University Press, 1979). [3] T.N. Parashar, M.A. Shay, P.A. Cassak and W.H. Matthaeus, Physics of Plasmas 16, 032310 (2009). [4] F. Valentini, P. Trávníček, F. Califano, P. Hellinger & A. Mangeney, Journal of Computational Physics 225, 753-770 (2007). [5] J. He, C. Tu, E. Marsch, C.H. Chen, L. Wang, Z. Pei, L. Zhang, C.S. Salem and S.D. Bale, The Astrophysical Journal Letters 813, L30 (2015).

A modified variational method for nonlinear vibration analysis of rotating beams including Coriolis effects

NASA Astrophysics Data System (ADS)

Tian, Jiajin; Su, Jinpeng; Zhou, Kai; Hua, Hongxing

2018-07-01

This paper presents a general formulation for nonlinear vibration analysis of rotating beams. A modified variational method combined with a multi-segment partitioning technique is employed to derive the free and transient vibration behaviors of the rotating beams. The strain energy and kinetic energy functional are formulated based on the order truncation principle of the fully geometrically nonlinear beam theory. The Coriolis effects as well as nonlinear effects due to the coupling of bending-stretching, bending-twist and twist-stretching are taken into account. The present method relaxes the need to explicitly meet the requirements of the boundary conditions for the admissible functions, and allows the use of any linearly independent, complete basis functions as admissible functions for rotating beams. Moreover, the method is readily used to deal with the nonlinear transient vibration problems for rotating beams subjected to dynamic loads. The accuracy, convergence and efficiency of the proposed method are examined by numerical examples. The influences of Coriolis and centrifugal forces on the vibration behaviors of the beams with various hub radiuses and slenderness ratios and rotating at different angular velocities are also investigated.

Spectral study of wintertime kinetic energy of the Northern Hemisphere in the troposphere

NASA Technical Reports Server (NTRS)

Lee, H. N.; Zhao, Z.; Kao, S. K.

1983-01-01

Characteristics of the kinetic energy of wind fields at various pressure levels were analyzed, and significant wavenumbers in the wavenumber-frequency domain were identified. The nonlinear interaction terms of the kinetic energy equation were examined, and the distribution of the kinetic energy at the 850 mb, 500 mb, and 200 mb levels was calculated. A 5 deg latitude-longitude square grid was used, with NMC data for the 1975-1976 winter in the 20-60 deg N at 500 mb and 20-85 deg N for the 200 mb and 850 mb levels. The kinetic energy distribution was determined to be geography-dependent, with wavenumbers 6-9 westerly waves in the midfrequency range contributing significantly to kinetic energy maxima over the North Pacific and the east coast of North America. The contribution of the nonlinear interactions of these waves, which correspond to the longitudinal convergence of the kinetic energy flux, was found to be larger than the meridional convergence of the kinetic energy flux, and to occur mainly between 30-50 deg N. The nonlinear interactions were a negative contribution over the North Pacific at the 200 mb level.

Parameterization of annealing kinetics in pharmaceutical glasses.

PubMed

Hodge, Ian M

2013-07-01

Numerical simulations indicate that neglecting the canonical nonlinearity of glassy-state annealing kinetics in pharmaceutical (and other) glasses leads to good KWW fits to the dependence of enthalpy on annealing time, but with spurious KWW parameters that are affected by nonlinearity. A simplified treatment of nonlinearity that uses the Struik shift factor is found to be a useful approximation for these analyses, and can account for previously reported differences between linear and nonlinear KWW parameters (Kawakami K, Pikal MJ. 2005. J Pharm Sci 94:948-965). Copyright © 2013 Wiley Periodicals, Inc.

Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Whitaker, Ann F. (Technical Monitor)

2001-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account.

Nonlinear amplitude dynamics in flagellar beating

NASA Astrophysics Data System (ADS)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear amplitude dynamics in flagellar beating.

PubMed

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear amplitude dynamics in flagellar beating

PubMed Central

Casademunt, Jaume

2017-01-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating. PMID:28405357

A new hybrid code (CHIEF) implementing the inertial electron fluid equation without approximation

NASA Astrophysics Data System (ADS)

Muñoz, P. A.; Jain, N.; Kilian, P.; Büchner, J.

2018-03-01

We present a new hybrid algorithm implemented in the code CHIEF (Code Hybrid with Inertial Electron Fluid) for simulations of electron-ion plasmas. The algorithm treats the ions kinetically, modeled by the Particle-in-Cell (PiC) method, and electrons as an inertial fluid, modeled by electron fluid equations without any of the approximations used in most of the other hybrid codes with an inertial electron fluid. This kind of code is appropriate to model a large variety of quasineutral plasma phenomena where the electron inertia and/or ion kinetic effects are relevant. We present here the governing equations of the model, how these are discretized and implemented numerically, as well as six test problems to validate our numerical approach. Our chosen test problems, where the electron inertia and ion kinetic effects play the essential role, are: 0) Excitation of parallel eigenmodes to check numerical convergence and stability, 1) parallel (to a background magnetic field) propagating electromagnetic waves, 2) perpendicular propagating electrostatic waves (ion Bernstein modes), 3) ion beam right-hand instability (resonant and non-resonant), 4) ion Landau damping, 5) ion firehose instability, and 6) 2D oblique ion firehose instability. Our results reproduce successfully the predictions of linear and non-linear theory for all these problems, validating our code. All properties of this hybrid code make it ideal to study multi-scale phenomena between electron and ion scales such as collisionless shocks, magnetic reconnection and kinetic plasma turbulence in the dissipation range above the electron scales.

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

An inclusive SUSY approach to position dependent mass systems

NASA Astrophysics Data System (ADS)

Karthiga, S.; Chithiika Ruby, V.; Senthilvelan, M.

2018-06-01

The supersymmetry (SUSY) formalism for a position dependent mass problem with a more general ordering is yet to be formulated. In this paper, we present an unified SUSY approach for PDM problems of any ordering. Highlighting all non-Hermitian Hamiltonians of PDM problems are of quasi-Hermitian nature, the SUSY operators of these problems are constructed using similarity transformation. The methodology that we propose here is applicable for even more general cases where the kinetic energy term is represented by linear combination of infinite number of possible orderings. We illustrate the method with an example, namely Mathews-Lakshmanan (ML) oscillator. Our results show that the latter system is shape invariant for all possible orderings. We derive eigenvalues and eigenvectors of this nonlinear oscillator for all possible orderings including Hermitian and non-Hermitian ones.

Optimal blood glucose level control using dynamic programming based on minimal Bergman model

NASA Astrophysics Data System (ADS)

Rettian Anggita Sari, Maria; Hartono

2018-03-01

The purpose of this article is to simulate the glucose dynamic and the insulin kinetic of diabetic patient. The model used in this research is a non-linear Minimal Bergman model. Optimal control theory is then applied to formulate the problem in order to determine the optimal dose of insulin in the treatment of diabetes mellitus such that the glucose level is in the normal range for some specific time range. The optimization problem is solved using dynamic programming. The result shows that dynamic programming is quite reliable to represent the interaction between glucose and insulin levels in diabetes mellitus patient.

Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves

NASA Technical Reports Server (NTRS)

Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.

1992-01-01

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.

DOE Office of Scientific and Technical Information (OSTI.GOV)

J.A. Krommes

Fusion physics poses an extremely challenging, practically complex problem that does not yield readily to simple paradigms. Nevertheless, various of the theoretical tools and conceptual advances emphasized at the KaufmanFest 2007 have motivated and/or found application to the development of fusion-related plasma turbulence theory. A brief historical commentary is given on some aspects of that specialty, with emphasis on the role (and limitations) of Hamiltonian/symplectic approaches, variational methods, oscillation-center theory, and nonlinear dynamics. It is shown how to extract a renormalized ponderomotive force from the statistical equations of plasma turbulence, and the possibility of a renormalized K-χ theorem is discussed.more » An unusual application of quasilinear theory to the problem of plasma equilibria in the presence of stochastic magnetic fields is described. The modern problem of zonal-flow dynamics illustrates a confluence of several techniques, including (i) the application of nonlinear-dynamics methods, especially center-manifold theory, to the problem of the transition to plasma turbulence in the face of self-generated zonal flows; and (ii) the use of Hamiltonian formalism to determine the appropriate (Casimir) invariant to be used in a novel wave-kinetic analysis of systems of interacting zonal flows and drift waves. Recent progress in the theory of intermittent chaotic statistics and the generation of coherent structures from turbulence is mentioned, and an appeal is made for some new tools to cope with these interesting and difficult problems in nonlinear plasma physics. Finally, the important influence of the intellectually stimulating research environment fostered by Prof. Allan Kaufman on the author's thinking and teaching methodology is described.« less

Effect of Fourier transform on the streaming in quantum lattice gas algorithms

NASA Astrophysics Data System (ADS)

Oganesov, Armen; Vahala, George; Vahala, Linda; Soe, Min

2018-04-01

All our previous quantum lattice gas algorithms for nonlinear physics have approximated the kinetic energy operator by streaming sequences to neighboring lattice sites. Here, the kinetic energy can be treated to all orders by Fourier transforming the kinetic energy operator with interlaced Dirac-based unitary collision operators. Benchmarking against exact solutions for the 1D nonlinear Schrodinger equation shows an extended range of parameters (soliton speeds and amplitudes) over the Dirac-based near-lattice-site streaming quantum algorithm.

Application of separable parameter space techniques to multi-tracer PET compartment modeling.

PubMed

Zhang, Jeff L; Michael Morey, A; Kadrmas, Dan J

2016-02-07

Multi-tracer positron emission tomography (PET) can image two or more tracers in a single scan, characterizing multiple aspects of biological functions to provide new insights into many diseases. The technique uses dynamic imaging, resulting in time-activity curves that contain contributions from each tracer present. The process of separating and recovering separate images and/or imaging measures for each tracer requires the application of kinetic constraints, which are most commonly applied by fitting parallel compartment models for all tracers. Such multi-tracer compartment modeling presents challenging nonlinear fits in multiple dimensions. This work extends separable parameter space kinetic modeling techniques, previously developed for fitting single-tracer compartment models, to fitting multi-tracer compartment models. The multi-tracer compartment model solution equations were reformulated to maximally separate the linear and nonlinear aspects of the fitting problem, and separable least-squares techniques were applied to effectively reduce the dimensionality of the nonlinear fit. The benefits of the approach are then explored through a number of illustrative examples, including characterization of separable parameter space multi-tracer objective functions and demonstration of exhaustive search fits which guarantee the true global minimum to within arbitrary search precision. Iterative gradient-descent algorithms using Levenberg-Marquardt were also tested, demonstrating improved fitting speed and robustness as compared to corresponding fits using conventional model formulations. The proposed technique overcomes many of the challenges in fitting simultaneous multi-tracer PET compartment models.

Application of separable parameter space techniques to multi-tracer PET compartment modeling

NASA Astrophysics Data System (ADS)

Zhang, Jeff L.; Morey, A. Michael; Kadrmas, Dan J.

2016-02-01

Multi-tracer positron emission tomography (PET) can image two or more tracers in a single scan, characterizing multiple aspects of biological functions to provide new insights into many diseases. The technique uses dynamic imaging, resulting in time-activity curves that contain contributions from each tracer present. The process of separating and recovering separate images and/or imaging measures for each tracer requires the application of kinetic constraints, which are most commonly applied by fitting parallel compartment models for all tracers. Such multi-tracer compartment modeling presents challenging nonlinear fits in multiple dimensions. This work extends separable parameter space kinetic modeling techniques, previously developed for fitting single-tracer compartment models, to fitting multi-tracer compartment models. The multi-tracer compartment model solution equations were reformulated to maximally separate the linear and nonlinear aspects of the fitting problem, and separable least-squares techniques were applied to effectively reduce the dimensionality of the nonlinear fit. The benefits of the approach are then explored through a number of illustrative examples, including characterization of separable parameter space multi-tracer objective functions and demonstration of exhaustive search fits which guarantee the true global minimum to within arbitrary search precision. Iterative gradient-descent algorithms using Levenberg-Marquardt were also tested, demonstrating improved fitting speed and robustness as compared to corresponding fits using conventional model formulations. The proposed technique overcomes many of the challenges in fitting simultaneous multi-tracer PET compartment models.

Multidimensional radiative transfer with multilevel atoms. II. The non-linear multigrid method.

NASA Astrophysics Data System (ADS)

Fabiani Bendicho, P.; Trujillo Bueno, J.; Auer, L.

1997-08-01

A new iterative method for solving non-LTE multilevel radiative transfer (RT) problems in 1D, 2D or 3D geometries is presented. The scheme obtains the self-consistent solution of the kinetic and RT equations at the cost of only a few (<10) formal solutions of the RT equation. It combines, for the first time, non-linear multigrid iteration (Brandt, 1977, Math. Comp. 31, 333; Hackbush, 1985, Multi-Grid Methods and Applications, springer-Verlag, Berlin), an efficient multilevel RT scheme based on Gauss-Seidel iterations (cf. Trujillo Bueno & Fabiani Bendicho, 1995ApJ...455..646T), and accurate short-characteristics formal solution techniques. By combining a valid stopping criterion with a nested-grid strategy a converged solution with the desired true error is automatically guaranteed. Contrary to the current operator splitting methods the very high convergence speed of the new RT method does not deteriorate when the grid spatial resolution is increased. With this non-linear multigrid method non-LTE problems discretized on N grid points are solved in O(N) operations. The nested multigrid RT method presented here is, thus, particularly attractive in complicated multilevel transfer problems where small grid-sizes are required. The properties of the method are analyzed both analytically and with illustrative multilevel calculations for Ca II in 1D and 2D schematic model atmospheres.

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.

General Methods for Analysis of Sequential “n-step” Kinetic Mechanisms: Application to Single Turnover Kinetics of Helicase-Catalyzed DNA Unwinding

PubMed Central

Lucius, Aaron L.; Maluf, Nasib K.; Fischer, Christopher J.; Lohman, Timothy M.

2003-01-01

Helicase-catalyzed DNA unwinding is often studied using “all or none” assays that detect only the final product of fully unwound DNA. Even using these assays, quantitative analysis of DNA unwinding time courses for DNA duplexes of different lengths, L, using “n-step” sequential mechanisms, can reveal information about the number of intermediates in the unwinding reaction and the “kinetic step size”, m, defined as the average number of basepairs unwound between two successive rate limiting steps in the unwinding cycle. Simultaneous nonlinear least-squares analysis using “n-step” sequential mechanisms has previously been limited by an inability to float the number of “unwinding steps”, n, and m, in the fitting algorithm. Here we discuss the behavior of single turnover DNA unwinding time courses and describe novel methods for nonlinear least-squares analysis that overcome these problems. Analytic expressions for the time courses, fss(t), when obtainable, can be written using gamma and incomplete gamma functions. When analytic expressions are not obtainable, the numerical solution of the inverse Laplace transform can be used to obtain fss(t). Both methods allow n and m to be continuous fitting parameters. These approaches are generally applicable to enzymes that translocate along a lattice or require repetition of a series of steps before product formation. PMID:14507688

General methods for analysis of sequential "n-step" kinetic mechanisms: application to single turnover kinetics of helicase-catalyzed DNA unwinding.

PubMed

Lucius, Aaron L; Maluf, Nasib K; Fischer, Christopher J; Lohman, Timothy M

2003-10-01

Helicase-catalyzed DNA unwinding is often studied using "all or none" assays that detect only the final product of fully unwound DNA. Even using these assays, quantitative analysis of DNA unwinding time courses for DNA duplexes of different lengths, L, using "n-step" sequential mechanisms, can reveal information about the number of intermediates in the unwinding reaction and the "kinetic step size", m, defined as the average number of basepairs unwound between two successive rate limiting steps in the unwinding cycle. Simultaneous nonlinear least-squares analysis using "n-step" sequential mechanisms has previously been limited by an inability to float the number of "unwinding steps", n, and m, in the fitting algorithm. Here we discuss the behavior of single turnover DNA unwinding time courses and describe novel methods for nonlinear least-squares analysis that overcome these problems. Analytic expressions for the time courses, f(ss)(t), when obtainable, can be written using gamma and incomplete gamma functions. When analytic expressions are not obtainable, the numerical solution of the inverse Laplace transform can be used to obtain f(ss)(t). Both methods allow n and m to be continuous fitting parameters. These approaches are generally applicable to enzymes that translocate along a lattice or require repetition of a series of steps before product formation.

Book review: Modern Plasma Physics, Vol. I: Physical Kinetics of Turbulent Plasmas, by Patrick H. Diamond, Sanae-I. Itoh and Kimitaka Itoh, Cambridge University Press, Cambridge (UK), 2010, IX, 417 p., ISBN 978-0-521-86920-1 (Hardback)

NASA Astrophysics Data System (ADS)

Somov, B. V.

If you want to learn not only the most fundamental things about the physics of turbulent plasmas but also the current state of the problem including the most recent results in theoretical and experimental investigations - and certainly many physicists and astrophysicists do - this series of three excellent monographs is just for you. The first volume "Physical Kinetics of Turbulent Plasmas" develops the kinetic theory of turbulence through a focus on quasi-particle models and dynamics. It discusses the concepts and theoretical methods for describing weak and strong fluid and phase space turbulence in plasma systems far from equilibrium. The core material includes fluctuation theory, self-similar cascades and transport, mean field theory, resonance broadening and nonlinear wave-particle interaction, wave-wave interaction and wave turbulence, strong turbulence theory and renormalization. The book gives readers a deep understanding of the fields under consideration and builds a foundation for future applications to multi-scale processes of self-organization in tokamaks and other confined plasmas. In spite of a short pedagogical introduction, the book is addressed mainly to well prepared readers with a serious background in plasma physics, to researchers and advanced graduate students in nonlinear plasma physics, controlled fusions and related fields such as cosmic plasma physics

Nonlinear Drift-Kinetic Equation in the Presence of a Circularly Polarized Wave

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Krivorutsky, E. N.; Six, N. Frank (Technical Monitor)

2002-01-01

Equations of the single particle motion and nonlinear kinetic equation for plasma in the presence of a circularly polarized wave of arbitrary frequency in the drift approximation are presented. The nonstationarity and inhomogeneity of the plasma-wave system are taken into account. The time dependent part of the ponderomotive force is discussed.

The mechanism distinguishability problem in biochemical kinetics: the single-enzyme, single-substrate reaction as a case study.

PubMed

Schnell, Santiago; Chappell, Michael J; Evans, Neil D; Roussel, Marc R

2006-01-01

A theoretical analysis of the distinguishability problem of two rival models of the single enzyme-single substrate reaction, the Michaelis-Menten and Henri mechanisms, is presented. We also outline a general approach for analysing the structural indistinguishability between two mechanisms. The approach involves constructing, if possible, a smooth mapping between the two candidate models. Evans et al. [N.D. Evans, M.J. Chappell, M.J. Chapman, K.R. Godfrey, Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems, Automatica 40 (2004) 1947-1953] have shown that if, in addition, either of the mechanisms satisfies a particular criterion then such a transformation always exists when the models are indistinguishable from their experimentally observable outputs. The approach is applied to the single enzyme-single substrate reaction mechanism. In principle, mechanisms can be distinguished using this analysis, but we show that our ability to distinguish mechanistic models depends both on the precise measurements made, and on our knowledge of the system prior to performing the kinetics experiments.

Percolation, phase separation, and gelation in fluids and mixtures of spheres and rods

NASA Astrophysics Data System (ADS)

Jadrich, Ryan; Schweizer, Kenneth S.

2011-12-01

The relationship between kinetic arrest, connectivity percolation, structure and phase separation in protein, nanoparticle, and colloidal suspensions is a rich and complex problem. Using a combination of integral equation theory, connectivity percolation methods, naïve mode coupling theory, and the activated dynamics nonlinear Langevin equation approach, we study this problem for isotropic one-component fluids of spheres and variable aspect ratio rigid rods, and also percolation in rod-sphere mixtures. The key control parameters are interparticle attraction strength and its (short) spatial range, total packing fraction, and mixture composition. For spherical particles, formation of a homogeneous one-phase kinetically stable and percolated physical gel is predicted to be possible, but depends on non-universal factors. On the other hand, the dynamic crossover to activated dynamics and physical bond formation, which signals discrete cluster formation below the percolation threshold, almost always occurs in the one phase region. Rods more easily gel in the homogeneous isotropic regime, but whether a percolation or kinetic arrest boundary is reached first upon increasing interparticle attraction depends sensitively on packing fraction, rod aspect ratio and attraction range. Overall, the connectivity percolation threshold is much more sensitive to attraction range than either the kinetic arrest or phase separation boundaries. Our results appear to be qualitatively consistent with recent experiments on polymer-colloid depletion systems and brush mediated attractive nanoparticle suspensions.

State of charge estimation in Ni-MH rechargeable batteries

NASA Astrophysics Data System (ADS)

Milocco, R. H.; Castro, B. E.

In this work we estimate the state of charge (SOC) of Ni-MH rechargeable batteries using the Kalman filter based on a simplified electrochemical model. First, we derive the complete electrochemical model of the battery which includes diffusional processes and kinetic reactions in both Ni and MH electrodes. The full model is further reduced in a cascade of two parts, a linear time invariant dynamical sub-model followed by a static nonlinearity. Both parts are identified using the current and potential measured at the terminals of the battery with a simple 1-D minimization procedure. The inverse of the static nonlinearity together with a Kalman filter provide the SOC estimation as a linear estimation problem. Experimental results with commercial batteries are provided to illustrate the estimation procedure and to show the performance.

Continuum kinetic methods for analyzing wave physics and distribution function dynamics in the turbulence dissipation challenge

NASA Astrophysics Data System (ADS)

Juno, J.; Hakim, A.; TenBarge, J.; Dorland, W.

2015-12-01

We present for the first time results for the turbulence dissipation challenge, with specific focus on the linear wave portion of the challenge, using a variety of continuum kinetic models: hybrid Vlasov-Maxwell, gyrokinetic, and full Vlasov-Maxwell. As one of the goals of the wave problem as it is outlined is to identify how well various models capture linear physics, we compare our results to linear Vlasov and gyrokinetic theory. Preliminary gyrokinetic results match linear theory extremely well due to the geometry of the problem, which eliminates the dominant nonlinearity. With the non-reduced models, we explore how the subdominant nonlinearities manifest and affect the evolution of the turbulence and the energy budget. We also take advantage of employing continuum methods to study the dynamics of the distribution function, with particular emphasis on the full Vlasov results where a basic collision operator has been implemented. As the community prepares for the next stage of the turbulence dissipation challenge, where we hope to do large 3D simulations to inform the next generation of observational missions such as THOR (Turbulence Heating ObserveR), we argue for the consideration of hybrid Vlasov and full Vlasov as candidate models for these critical simulations. With the use of modern numerical algorithms, we demonstrate the competitiveness of our code with traditional particle-in-cell algorithms, with a clear plan for continued improvements and optimizations to further strengthen the code's viability as an option for the next stage of the challenge.

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

TG study of the Li0.4Fe2.4Zn0.2O4 ferrite synthesis

NASA Astrophysics Data System (ADS)

Lysenko, E. N.; Nikolaev, E. V.; Surzhikov, A. P.

2016-02-01

In this paper, the kinetic analysis of Li-Zn ferrite synthesis was studied using thermogravimetry (TG) method through the simultaneous application of non-linear regression to several measurements run at different heating rates (multivariate non-linear regression). Using TG-curves obtained for the four heating rates and Netzsch Thermokinetics software package, the kinetic models with minimal adjustable parameters were selected to quantitatively describe the reaction of Li-Zn ferrite synthesis. It was shown that the experimental TG-curves clearly suggest a two-step process for the ferrite synthesis and therefore a model-fitting kinetic analysis based on multivariate non-linear regressions was conducted. The complex reaction was described by a two-step reaction scheme consisting of sequential reaction steps. It is established that the best results were obtained using the Yander three-dimensional diffusion model at the first stage and Ginstling-Bronstein model at the second step. The kinetic parameters for lithium-zinc ferrite synthesis reaction were found and discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gur, Sourav; Frantziskonis, George N.; Univ. of Arizona, Tucson, AZ

Here, we report results from a numerical study of multi-time-scale bistable dynamics for CO oxidation on a catalytic surface in a flowing, well-mixed gas stream. The problem is posed in terms of surface and gas-phase submodels that dynamically interact in the presence of stochastic perturbations, reflecting the impact of molecular-scale fluctuations on the surface and turbulence in the gas. Wavelet-based methods are used to encode and characterize the temporal dynamics produced by each submodel and detect the onset of sudden state shifts (bifurcations) caused by nonlinear kinetics. When impending state shifts are detected, a more accurate but computationally expensive integrationmore » scheme can be used. This appears to make it possible, at least in some cases, to decrease the net computational burden associated with simulating multi-time-scale, nonlinear reacting systems by limiting the amount of time in which the more expensive integration schemes are required. Critical to achieving this is being able to detect unstable temporal transitions such as the bistable shifts in the example problem considered here. Lastly, our results indicate that a unique wavelet-based algorithm based on the Lipschitz exponent is capable of making such detections, even under noisy conditions, and may find applications in critical transition detection problems beyond catalysis.« less

Reverse engineering and identification in systems biology: strategies, perspectives and challenges.

PubMed

Villaverde, Alejandro F; Banga, Julio R

2014-02-06

The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology?

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.

PubMed

Chen, Bor-Sen; Hsu, Chih-Yuan

2012-10-26

Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks.

Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

PubMed Central

2012-01-01

Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. Conclusion If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks. PMID:23101662

The Kelvin-Helmholtz instability of boundary-layer plasmas in the kinetic regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steinbusch, Benedikt, E-mail: b.steinbusch@fz-juelich.de; Gibbon, Paul, E-mail: p.gibbon@fz-juelich.de; Department of Mathematics, Centre for Mathematical Plasma Astrophysics, Katholieke Universiteit Leuven

2016-05-15

The dynamics of the Kelvin-Helmholtz instability are investigated in the kinetic, high-frequency regime with a novel, two-dimensional, mesh-free tree code. In contrast to earlier studies which focused on specially prepared equilibrium configurations in order to compare with fluid theory, a more naturally occurring plasma-vacuum boundary layer is considered here with relevance to both space plasma and linear plasma devices. Quantitative comparisons of the linear phase are made between the fluid and kinetic models. After establishing the validity of this technique via comparison to linear theory and conventional particle-in-cell simulation for classical benchmark problems, a quantitative analysis of the more complexmore » magnetized plasma-vacuum layer is presented and discussed. It is found that in this scenario, the finite Larmor orbits of the ions result in significant departures from the effective shear velocity and width underlying the instability growth, leading to generally slower development and stronger nonlinear coupling between fast growing short-wavelength modes and longer wavelengths.« less

Nanoscale Properties of Rocks and Subduction Zone Rheology: Inferences for the Mechanisms of Deep Earthquakes

NASA Astrophysics Data System (ADS)

Riedel, M. R.

2007-12-01

Grain boundaries are the key for the understanding of mineral reaction kinetics. More generally, nanometer scale processes involved in breaking and establishing bonds at reaction sites determine how and at which rate bulk rock properties change in response to external tectonic forcing and possibly feed back into various geodynamic processes. A particular problem is the effects of grain-boundary energy on the kinetics of the olivine-spinel phase transformation in subducting slabs. Slab rheology is affected in many ways by this (metastable) mineral phase change. Sluggish kinetics due to metastable hindrance is likely to cause particular difficulties, because of possible strong non-linear feedback loops between strain-rate and change of creep properties during transformation. In order to get these nanoscale properties included into thermo-mechanical models, reliable kinetic data is required. The measurement of grain-boundary energies is, however, a rather difficult problem. Conventional methods of grain boundary surface tension measurement include (a) equilibrium angles at triple junction (b) rotating ball method (c) thermal groove method, and others (Gottstein & Shvindlerman, 1999). Here I suggest a new method that allows for the derivation of grain-boundary energies for an isochemical phase transformation based on experimental (in-situ) kinetic data in combination with a corresponding dynamic scaling law (Riedel and Karato, 1997). The application of this method to the olivine-spinel phase transformation in subducting slabs provides a solution to the extrapolation problem of measured kinetic data: Any kinetic phase boundary measured at the laboratory time scale can be "scaled" to the correct critical isotherm at subduction zones, under experimentelly "forbidden" conditions (Liou et al., 2000). Consequences for the metastability hypothesis that relates deep seismicity with olivine metastability are derived and discussed. References: Gottstein G, Shvindlerman LS (1999) Grain Boundary Migration in Metals, CRC Press, 385 pp., New York. Riedel MR, Karato S (1997) Grain-Size Evolution in Subducted Oceanic Lithosphere Associated with the Olivine- Spinel Transformation and Its Effects on Rheology. EPSL 148: 27-43. Liou JG, Hacker BR, Zhang RY (2000) Into the forbidden zone. Science 287, 1215-1216.

Application of separable parameter space techniques to multi-tracer PET compartment modeling

PubMed Central

Zhang, Jeff L; Morey, A Michael; Kadrmas, Dan J

2016-01-01

Multi-tracer positron emission tomography (PET) can image two or more tracers in a single scan, characterizing multiple aspects of biological functions to provide new insights into many diseases. The technique uses dynamic imaging, resulting in time-activity curves that contain contributions from each tracer present. The process of separating and recovering separate images and/or imaging measures for each tracer requires the application of kinetic constraints, which are most commonly applied by fitting parallel compartment models for all tracers. Such multi-tracer compartment modeling presents challenging nonlinear fits in multiple dimensions. This work extends separable parameter space kinetic modeling techniques, previously developed for fitting single-tracer compartment models, to fitting multi-tracer compartment models. The multi-tracer compartment model solution equations were reformulated to maximally separate the linear and nonlinear aspects of the fitting problem, and separable least-squares techniques were applied to effectively reduce the dimensionality of the nonlinear fit. The benefits of the approach are then explored through a number of illustrative examples, including characterization of separable parameter space multi-tracer objective functions and demonstration of exhaustive search fits which guarantee the true global minimum to within arbitrary search precision. Iterative gradient-descent algorithms using Levenberg–Marquardt were also tested, demonstrating improved fitting speed and robustness as compared to corresponding fits using conventional model formulations. The proposed technique overcomes many of the challenges in fitting simultaneous multi-tracer PET compartment models. PMID:26788888

Updated Chemical Kinetics and Sensitivity Analysis Code

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan

2005-01-01

An updated version of the General Chemical Kinetics and Sensitivity Analysis (LSENS) computer code has become available. A prior version of LSENS was described in "Program Helps to Determine Chemical-Reaction Mechanisms" (LEW-15758), NASA Tech Briefs, Vol. 19, No. 5 (May 1995), page 66. To recapitulate: LSENS solves complex, homogeneous, gas-phase, chemical-kinetics problems (e.g., combustion of fuels) that are represented by sets of many coupled, nonlinear, first-order ordinary differential equations. LSENS has been designed for flexibility, convenience, and computational efficiency. The present version of LSENS incorporates mathematical models for (1) a static system; (2) steady, one-dimensional inviscid flow; (3) reaction behind an incident shock wave, including boundary layer correction; (4) a perfectly stirred reactor; and (5) a perfectly stirred reactor followed by a plug-flow reactor. In addition, LSENS can compute equilibrium properties for the following assigned states: enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. For static and one-dimensional-flow problems, including those behind an incident shock wave and following a perfectly stirred reactor calculation, LSENS can compute sensitivity coefficients of dependent variables and their derivatives, with respect to the initial values of dependent variables and/or the rate-coefficient parameters of the chemical reactions.

Photoplasma of optically excited metal vapors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bezuglov, N.N.; Llyucharev, A.N.; Stacewicz, T.

1994-09-01

A wide range of questions associated with various aspects of photoplasma physics is considered. A comprehensive analysis of processes of optical excitation and de-excitation depending on optical characteristics of an absorbing gas medium is given. Analytical methods used for determining the excitation degree of photoresonance plasma in conditions of resonance radiation transfer are described. The accuracy of the Biberman approximation for effective lifetimes in population kinetics of resonance plasma states is analyzed for many experimental conditions. A detailed discussion of primary ionization mechanisms in photoplasma is given; the kinetics of ionization processes is discussed; and systematization of various types ofmore » photoresonance plasma is presented. Basis aspects of the LIBORS model, which is widely used for studying ionization kinetics of laser photoresonance plasma, and its limitations are considered. An ingenious method used to analytically solve a class of decay-type nonlinear problems, which arise for the capture equation in the case of noticeable saturation of a resonance transition by a short laser pulse, is described. A reliable quantitative description of fluorescence decay curve peculiarities that are associated with the bleaching of gases at resonance line frequencies can be obtained by this method. Some possible applications of photoplasma in problems of optics and spectroscopy are considered. 75 refs., 24 figs., 1 tab.« less

Development of a Grid-Based Gyro-Kinetic Simulation Code

NASA Astrophysics Data System (ADS)

Lapillonne, Xavier; Brunetti, Maura; Tran, Trach-Minh; Brunner, Stephan

2006-10-01

A grid-based semi-Lagrangian code using cubic spline interpolation is being developed at CRPP, for solving the electrostatic drift-kinetic equations [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)] in a cylindrical system. This 4-dim code, CYGNE, is part of a project with long term aim of studying microturbulence in toroidal fusion devices, in the more general frame of gyro-kinetic equations. Towards their non-linear phase, the simulations from this code are subject to significant overshoot problems, reflected by the development of negative value regions of the distribution function, which leads to bad energy conservation. This has motivated the study of alternative schemes. On the one hand, new time integration algorithms are considered in the semi-Lagrangian frame. On the other hand, fully Eulerian schemes, which separate time and space discretisation (method of lines), are investigated. In particular, the Essentially Non Oscillatory (ENO) approach, constructed so as to minimize the overshoot problem, has been considered. All these methods have first been tested in the simpler case of the 2-dim guiding-center model for the Kelvin-Helmholtz instability, which enables to address the specific issue of the E xB drift also met in the more complex gyrokinetic-type equations. Based on these preliminary studies, the most promising methods are being implemented and tested in CYGNE.

Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence

NASA Astrophysics Data System (ADS)

Schekochihin, A. A.; Parker, J. T.; Highcock, E. G.; Dellar, P. J.; Dorland, W.; Hammett, G. W.

2016-04-01

> A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g. drift-wave turbulence driven by ion temperature gradients) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. It is found that it is possible to construct a consistent theory in which very little free energy leaks into high velocity moments of the distribution function, rendering the turbulent cascade in the energetically relevant part of the wavenumber space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also in contrast with the linear problem, in which it occurs at the finite rate equal to the Landau damping rate). The ability of the free energy to stay in the low velocity moments of the distribution function is facilitated by the `anti-phase-mixing' effect, whose presence in the nonlinear system is due to the stochastic version of the plasma echo (the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wavenumber space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins its competition with nonlinear advection is governed by the `critical balance' between linear and nonlinear time scales (which for high Hermite moments splits into two thresholds, one demarcating the wavenumber region where phase mixing predominates, the other where plasma echo does).

An alternative explicit model expression equivalent to the integrated michaelis-menten equation and its application to nonlinear saturation pharmacokinetics.

PubMed

Goličnik, Marko

2011-06-01

Many pharmacodynamic processes can be described by the nonlinear saturation kinetics that are most frequently based on the hyperbolic Michaelis-Menten equation. Thus, various time-dependent solutions for drugs obeying such kinetics can be expressed in terms of the Lambert W(x)-omega function. However, unfortunately, computer programs that can perform the calculations for W(x) are not widely available. To avoid this problem, the replacement of the integrated Michaelis-Menten equation with an empiric integrated 1--exp alternative model equation was proposed recently by Keller et al. (Ther Drug Monit. 2009;31:783-785), although, as shown here, it was not necessary. Simulated concentrations of model drugs obeying Michaelis-Menten elimination kinetics were generated by two approaches: 1) calculation of time-course data based on an approximation equation W2*(x) performed using Microsoft Excel; and 2) calculation of reference time-course data based on an exact W(x) function built in to the Wolfram Mathematica. I show here that the W2*(x) function approximates the actual W(x) accurately. W2*(x) is expressed in terms of elementary mathematical functions and, consequently, it can be easily implemented using any of the widely available software. Hence, with the example of a hypothetical drug, I demonstrate here that an equation based on this approximation is far better, because it is nearly equivalent to the original solution, whereas the same characteristics cannot be fully confirmed for the 1--exp model equation. The W2*(x) equation proposed here might have an important role as a useful shortcut in optional software to estimate kinetic parameters from experimental data for drugs, and it might represent an easy and universal analytical tool for simulating and designing dosing regimens.

Pair correlation function and nonlinear kinetic equation for a spatially uniform polarizable nonideal plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belyi, V.V.; Kukharenko, Y.A.; Wallenborn, J.

Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. {copyright} {ital 1996 The American Physical Society.}

Nonlinear theory of diffusive acceleration of particles by shock waves

NASA Astrophysics Data System (ADS)

Malkov, M. A.; Drury, L. O'C.

2001-04-01

Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data.

Wave-Kinetic Simulations of the Nonlinear Generation of Electromagnetic VLF Waves through Velocity Ring Instabilities

NASA Astrophysics Data System (ADS)

Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.

2014-12-01

Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].

Nonlinear magnetoacoustic wave propagation with chemical reactions

NASA Astrophysics Data System (ADS)

Margulies, Timothy Scott

2002-11-01

The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.

Strongly nonlinear theory of rapid solidification near absolute stability

NASA Astrophysics Data System (ADS)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the morphological number, as well as the amplitude. The critical amplitude, at which solutions loose periodicity, depends on a single combination of parameters independent of the morphological number that indicate that non-periodic growth is most commonly present for moderate disequilibrium parameters. The spatial distribution of the interface develops deepening roots at late times. Similar spatial distributions are also seen in the limit in which both the cellular and oscillatory modes are close to absolute stability, and the roots deepen with larger departures from the two absolute stability boundaries.

Spectral solver for multi-scale plasma physics simulations with dynamically adaptive number of moments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vencels, Juris; Delzanno, Gian Luca; Johnson, Alec

2015-06-01

A spectral method for kinetic plasma simulations based on the expansion of the velocity distribution function in a variable number of Hermite polynomials is presented. The method is based on a set of non-linear equations that is solved to determine the coefficients of the Hermite expansion satisfying the Vlasov and Poisson equations. In this paper, we first show that this technique combines the fluid and kinetic approaches into one framework. Second, we present an adaptive strategy to increase and decrease the number of Hermite functions dynamically during the simulation. The technique is applied to the Landau damping and two-stream instabilitymore » test problems. Performance results show 21% and 47% saving of total simulation time in the Landau and two-stream instability test cases, respectively.« less

Neurobiologically Inspired Approaches to Nonlinear Process Control and Modeling

DTIC Science & Technology

1999-12-31

incorporates second messenger reaction kinetics and calcium dynamics to represent the nonlinear dynamics and the crucial role of neuromodulation in local...reflex). The dynamic neuromodulation as a mechanism for the nonlinear attenuation is the novel result of this study. Ear- lier simulations have shown

Equilibrium, kinetics and process design of acid yellow 132 adsorption onto red pine sawdust.

PubMed

Can, Mustafa

2015-01-01

Linear and non-linear regression procedures have been applied to the Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, and Redlich-Peterson isotherms for adsorption of acid yellow 132 (AY132) dye onto red pine (Pinus resinosa) sawdust. The effects of parameters such as particle size, stirring rate, contact time, dye concentration, adsorption dose, pH, and temperature were investigated, and interaction was characterized by Fourier transform infrared spectroscopy and field emission scanning electron microscope. The non-linear method of the Langmuir isotherm equation was found to be the best fitting model to the equilibrium data. The maximum monolayer adsorption capacity was found as 79.5 mg/g. The calculated thermodynamic results suggested that AY132 adsorption onto red pine sawdust was an exothermic, physisorption, and spontaneous process. Kinetics was analyzed by four different kinetic equations using non-linear regression analysis. The pseudo-second-order equation provides the best fit with experimental data.

Symmetry breaking patterns for inflation

NASA Astrophysics Data System (ADS)

Klein, Remko; Roest, Diederik; Stefanyszyn, David

2018-06-01

We study inflationary models where the kinetic sector of the theory has a non-linearly realised symmetry which is broken by the inflationary potential. We distinguish between kinetic symmetries which non-linearly realise an internal or space-time group, and which yield a flat or curved scalar manifold. This classification leads to well-known inflationary models such as monomial inflation and α-attractors, as well as a new model based on fixed couplings between a dilaton and many axions which non-linearly realises higher-dimensional conformal symmetries. In this model, inflation can be realised along the dilatonic direction, leading to a tensor-to-scalar ratio r ˜ 0 .01 and a spectral index n s ˜ 0 .975. We refer to the new model as ambient inflation since inflation proceeds along an isometry of an anti-de Sitter ambient space-time, which fully determines the kinetic sector.

Reverse engineering and identification in systems biology: strategies, perspectives and challenges

PubMed Central

Villaverde, Alejandro F.; Banga, Julio R.

2014-01-01

The interplay of mathematical modelling with experiments is one of the central elements in systems biology. The aim of reverse engineering is to infer, analyse and understand, through this interplay, the functional and regulatory mechanisms of biological systems. Reverse engineering is not exclusive of systems biology and has been studied in different areas, such as inverse problem theory, machine learning, nonlinear physics, (bio)chemical kinetics, control theory and optimization, among others. However, it seems that many of these areas have been relatively closed to outsiders. In this contribution, we aim to compare and highlight the different perspectives and contributions from these fields, with emphasis on two key questions: (i) why are reverse engineering problems so hard to solve, and (ii) what methods are available for the particular problems arising from systems biology? PMID:24307566

On the equilibrium between proton kappa distribution and compressible kinetic Alfvenic fluctuations

NASA Astrophysics Data System (ADS)

Yoon, P. H.

2017-12-01

Protons with a quasi inverse power law energetic population featuring the property f v-α, with α close to 5, are pervasively observed in the heliosphere. While many theoretical attempts have been made in order to describe such a feature, the so-called pump acceleration mechanism put forth by Fisk & Gloeckler is one of the most prominent theories. Their mechanism involves the low-frequency compressional fluctuations accelerating the protons. This presentation aims to reformulate the problem from the perspective of the steady state solution of the self-consistent plasma kinetic theory involving compressible kinetic Alfvenic fluctuations. By considering the steady state proton particle kinetic equation and quasi-linear wave kinetic for the kinetic Alfvenic turbulence we seek to obtain concomitant solutions for both proton velocity distribution function and the spectral intensity for kinetic Alfvenic fluctuation. It is found that the kappa distribution for the protons is a legitimate, if not unique, solution. The steady state spectrum of kinetic Alfvenic fluctuation is also obtained. The present investigation demonstrates that the kappa distribution for the protons featuring energetic tail population characterized by f v-2κ-2, where κ is the parameter for kappa distribution, may represent the background population of the protons in the heliosphere. However, it is speculated that in order to uniquely determine the value of κ, which must be close to 1.5 for asymptotic behavior of f v-5, one must have an additional constraint that involves the balance of nonlinear mode coupling terms in the wave kinetic equation.

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.

Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

NASA Astrophysics Data System (ADS)

Artemyev, Anton V.; Neishtadt, Anatoly I.; Vasiliev, Alexei A.

2018-04-01

Accurately modelling and forecasting of the dynamics of the Earth's radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave-particle resonant interaction. Energetic electron acceleration or scattering into the Earth's atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave-particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

A Census of Plasma Waves and Structures Associated With an Injection Front in the Inner Magnetosphere

NASA Astrophysics Data System (ADS)

Malaspina, David M.; Ukhorskiy, Aleksandr; Chu, Xiangning; Wygant, John

2018-04-01

Now that observations have conclusively established that the inner magnetosphere is abundantly populated with kinetic electric field structures and nonlinear waves, attention has turned to quantifying the ability of these structures and waves to scatter and accelerate inner magnetospheric plasma populations. A necessary step in that quantification is determining the distribution of observed structure and wave properties (e.g., occurrence rates, amplitudes, and spatial scales). Kinetic structures and nonlinear waves have broadband signatures in frequency space, and consequently, high-resolution time domain electric and magnetic field data are required to uniquely identify such structures and waves as well as determine their properties. However, most high-resolution fields data are collected with a strong bias toward high-amplitude signals in a preselected frequency range, strongly biasing observations of structure and wave properties. In this study, an ˜45 min unbroken interval of 16,384 samples/s field burst data, encompassing an electron injection event, is examined. This data set enables an unbiased census of the kinetic structures and nonlinear waves driven by this electron injection, as well as determination of their "typical" properties. It is found that the properties determined using this unbiased burst data are considerably different than those inferred from amplitude-biased burst data, with significant implications for wave-particle interactions due to kinetic structures and nonlinear waves in the inner magnetosphere.

Application of Wavelet-Based Methods for Accelerating Multi-Time-Scale Simulation of Bistable Heterogeneous Catalysis

DOE PAGES

Gur, Sourav; Frantziskonis, George N.; Univ. of Arizona, Tucson, AZ; ...

2017-02-16

Here, we report results from a numerical study of multi-time-scale bistable dynamics for CO oxidation on a catalytic surface in a flowing, well-mixed gas stream. The problem is posed in terms of surface and gas-phase submodels that dynamically interact in the presence of stochastic perturbations, reflecting the impact of molecular-scale fluctuations on the surface and turbulence in the gas. Wavelet-based methods are used to encode and characterize the temporal dynamics produced by each submodel and detect the onset of sudden state shifts (bifurcations) caused by nonlinear kinetics. When impending state shifts are detected, a more accurate but computationally expensive integrationmore » scheme can be used. This appears to make it possible, at least in some cases, to decrease the net computational burden associated with simulating multi-time-scale, nonlinear reacting systems by limiting the amount of time in which the more expensive integration schemes are required. Critical to achieving this is being able to detect unstable temporal transitions such as the bistable shifts in the example problem considered here. Lastly, our results indicate that a unique wavelet-based algorithm based on the Lipschitz exponent is capable of making such detections, even under noisy conditions, and may find applications in critical transition detection problems beyond catalysis.« less

Collisional effects on the numerical recurrence in Vlasov-Poisson simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pezzi, Oreste; Valentini, Francesco; Camporeale, Enrico

The initial state recurrence in numerical simulations of the Vlasov-Poisson system is a well-known phenomenon. Here, we study the effect on recurrence of artificial collisions modeled through the Lenard-Bernstein operator [A. Lenard and I. B. Bernstein, Phys. Rev. 112, 1456–1459 (1958)]. By decomposing the linear Vlasov-Poisson system in the Fourier-Hermite space, the recurrence problem is investigated in the linear regime of the damping of a Langmuir wave and of the onset of the bump-on-tail instability. The analysis is then confirmed and extended to the nonlinear regime through an Eulerian collisional Vlasov-Poisson code. It is found that, despite being routinely used,more » an artificial collisionality is not a viable way of preventing recurrence in numerical simulations without compromising the kinetic nature of the solution. Moreover, it is shown how numerical effects associated to the generation of fine velocity scales can modify the physical features of the system evolution even in nonlinear regime. This means that filamentation-like phenomena, usually associated with low amplitude fluctuations contexts, can play a role even in nonlinear regime.« less

Effect of Nonlinearity in Hybrid Kinetic Monte Carlo-Continuum Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balter, Ariel I.; Lin, Guang; Tartakovsky, Alexandre M.

2012-04-23

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a KMC model for a surface to a finite difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and also show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition/dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition/dissolution model including competitive adsorption, which leadsmore » to a nonlinear rate, and show that, in this case, the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.« less

Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guangye; Chacon, Luis; Knoll, Dana Alan

2015-07-31

A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ω peΔt >>1, and Δx >> λ D), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylovmore » (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary.« less

A Comprehensive Enzyme Kinetic Exercise for Biochemistry

ERIC Educational Resources Information Center

Barton, Janice S.

2011-01-01

This article describes a comprehensive treatment of experimental enzyme kinetics strongly coupled to electronic data acquisition and use of spreadsheets to organize data and perform linear and nonlinear least-squares analyses, all in a manner that promotes development of important reasoning skills. Kinetic parameters are obtained for the stable…

Simulating energy cascade of shock wave formation process in a resonator by gas kinetic scheme

NASA Astrophysics Data System (ADS)

Qu, Chengwu; Zhang, Xiaoqing; Feng, Heying

2017-12-01

The temporal-spatial evolution of gas oscillation was simulated by gas kinetic scheme (GKS) in a cylindrical resonator, driven by a piston at one end and rigidly closed at the other end. Periodic shock waves propagating back and forth were observed in the resonator under finite amplitude of gas oscillation. The studied results demonstrated that the acoustic pressure is a saw-tooth waveform and the oscillatory velocity is a square waveform at the central position of the resonant tube. Moreover, it was found by harmonic analysis that there was no presence of obvious feature for pressure node in such a typical standing wave resonator, and the distribution of acoustic fields displayed a one-dimensional feature for the acoustic pressure while a quasi-one-dimensional form for oscillatory velocity, which demonstrated the nonlinear effects. The simulation results for axial distribution of acoustic intensity showed a good consistency with the published experimental data in the open literature domain, which provides a verification for the effectiveness of the GKS model proposed. The influence of displacement amplitude of the driving piston on the formation of shock wave was numerically investigated, and the simulated results revealed the cascade process of harmonic wave energy from the fundamental wave to higher harmonics. In addition, this study found that the acoustic intensity at the driving end of the resonant tube would increase linearly with the displacement amplitude of the piston due to nonlinear effects, rather than the exponential variation by linear theory. This research demonstrates that the GKS model is strongly capable of simulating nonlinear acoustic problems.

Nonlinear interaction of kinetic Alfven wave and whistler: Turbulent spectra and anisotropic scaling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kumar Dwivedi, Navin; Sharma, R. P.

2013-04-15

In this work, we are presenting the excitation of oblique propagating whistler wave as a consequence of nonlinear interaction between whistler wave and kinetic Alfven wave (KAW) in intermediate beta plasmas. Numerical simulation has been done to study the transient evolution of magnetic field structures of KAW when the nonlinearity arises due to ponderomotive effects by taking the adiabatic response of the background density. Weak oblique propagating whistler signals in these nonlinear plasma density filaments (produced by KAW localization) get amplified. The spectral indices of the power spectrum at different times are calculated with given initial conditions of the simulations.more » Anisotropic scaling laws for KAW and whistlers are presented. The relevance of the present investigation to solar wind turbulence and its acceleration is also pointed out.« less

Model coupling intraparticle diffusion/sorption, nonlinear sorption, and biodegradation processes

USGS Publications Warehouse

Karapanagioti, Hrissi K.; Gossard, Chris M.; Strevett, Keith A.; Kolar, Randall L.; Sabatini, David A.

2001-01-01

Diffusion, sorption and biodegradation are key processes impacting the efficiency of natural attenuation. While each process has been studied individually, limited information exists on the kinetic coupling of these processes. In this paper, a model is presented that couples nonlinear and nonequilibrium sorption (intraparticle diffusion) with biodegradation kinetics. Initially, these processes are studied independently (i.e., intraparticle diffusion, nonlinear sorption and biodegradation), with appropriate parameters determined from these independent studies. Then, the coupled processes are studied, with an initial data set used to determine biodegradation constants that were subsequently used to successfully predict the behavior of a second data set. The validated model is then used to conduct a sensitivity analysis, which reveals conditions where biodegradation becomes desorption rate-limited. If the chemical is not pre-equilibrated with the soil prior to the onset of biodegradation, then fast sorption will reduce aqueous concentrations and thus biodegradation rates. Another sensitivity analysis demonstrates the importance of including nonlinear sorption in a coupled diffusion/sorption and biodegradation model. While predictions based on linear sorption isotherms agree well with solution concentrations, for the conditions evaluated this approach overestimates the percentage of contaminant biodegraded by as much as 50%. This research demonstrates that nonlinear sorption should be coupled with diffusion/sorption and biodegradation models in order to accurately predict bioremediation and natural attenuation processes. To our knowledge this study is unique in studying nonlinear sorption coupled with intraparticle diffusion and biodegradation kinetics with natural media.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Inverse problem analysis for identification of reaction kinetics constants in microreactors for biodiesel synthesis

NASA Astrophysics Data System (ADS)

Pontes, P. C.; Naveira-Cotta, C. P.

2016-09-01

The theoretical analysis for the design of microreactors in biodiesel production is a complicated task due to the complex liquid-liquid flow and mass transfer processes, and the transesterification reaction that takes place within these microsystems. Thus, computational simulation is an important tool that aids in understanding the physical-chemical phenomenon and, consequently, in determining the suitable conditions that maximize the conversion of triglycerides during the biodiesel synthesis. A diffusive-convective-reactive coupled nonlinear mathematical model, that governs the mass transfer process during the transesterification reaction in parallel plates microreactors, under isothermal conditions, is here described. A hybrid numerical-analytical solution via the Generalized Integral Transform Technique (GITT) for this partial differential system is developed and the eigenfunction expansions convergence rates are extensively analyzed and illustrated. The heuristic method of Particle Swarm Optimization (PSO) is applied in the inverse analysis of the proposed direct problem, to estimate the reaction kinetics constants, which is a critical step in the design of such microsystems. The results present a good agreement with the limited experimental data in the literature, but indicate that the GITT methodology combined with the PSO approach provide a reliable computational algorithm for direct-inverse analysis in such reactive mass transfer problems.

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization. PMID:27243005

Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohandas, Gopakumar; Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk

The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of themore » Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearing box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.« less

Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.

Non-isothermal elastoviscoplastic analysis of planar curved beams

NASA Technical Reports Server (NTRS)

Simitses, G. J.; Carlson, R. L.; Riff, R.

1988-01-01

The development of a general mathematical model and solution methodologies, to examine the behavior of thin structural elements such as beams, rings, and arches, subjected to large nonisothermal elastoviscoplastic deformations is presented. Thus, geometric as well as material type nonlinearities of higher order are present in the analysis. For this purpose a complete true abinito rate theory of kinematics and kinetics for thin bodies, without any restriction on the magnitude of the transformation is presented. A previously formulated elasto-thermo-viscoplastic material constitutive law is employed in the analysis. The methodology is demonstrated through three different straight and curved beams problems.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Solute-defect interactions in Al-Mg alloys from diffusive variational Gaussian calculations

NASA Astrophysics Data System (ADS)

Dontsova, E.; Rottler, J.; Sinclair, C. W.

2014-11-01

Resolving atomic-scale defect topologies and energetics with accurate atomistic interaction models provides access to the nonlinear phenomena inherent at atomic length and time scales. Coarse graining the dynamics of such simulations to look at the migration of, e.g., solute atoms, while retaining the rich atomic-scale detail required to properly describe defects, is a particular challenge. In this paper, we present an adaptation of the recently developed "diffusive molecular dynamics" model to describe the energetics and kinetics of binary alloys on diffusive time scales. The potential of the technique is illustrated by applying it to the classic problems of solute segregation to a planar boundary (stacking fault) and edge dislocation in the Al-Mg system. Our approach provides fully dynamical solutions in situations with an evolving energy landscape in a computationally efficient way, where atomistic kinetic Monte Carlo simulations are difficult or impractical to perform.

Protein Crystallization: Specific Phenomena and General Insights on Crystallization Kinetics

NASA Technical Reports Server (NTRS)

Rosenberger, F.

1998-01-01

Experimental and simulation studies of the nucleation and growth kinetics of proteins have revealed phenomena that are specific for macromolecular crystallization, and others that provide a more detailed understanding of solution crystallization in general. The more specific phenomena, which include metastable liquid-liquid phase separations and gelation prior to solid nucleation, are due to the small ratio of the intermolecular interaction-range to the size of molecules involved. The apparently more generally applicable mechanisms include the cascade-like formation of macrosteps, as an intrinsic morphological instability that roots in the coupled bulk transport and nonlinear interface kinetics in systems with mixed growth rate control. Analyses of this nonlinear response provide (a) criteria for the choice of bulk transport conditions to minimize structural defect formation, and (b) indications that the "slow" protein crystallization kinetics stems from the mutual retardation of growth steps.

Isothermal Ice Crystallization Kinetics in the Gas-Diffusion Layer of a Proton-Exchange-Membrane Fuel Cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dursch, Thomas J.; Ciontea, Monica A.; Radke, Clayton J.

2011-12-01

Nucleation and growth of ice in the fibrous gas-diffusion layer (GDL) of a proton-exchange membrane fuel cell (PEMFC) are studied using isothermal differential scanning calorimetry (DSC). Isothermal crystallization rates and pseudo-steady-state nucleation rates are obtained as a function of subcooling from heat-flow and induction-time measurements. Kinetics of ice nucleation and growth are studied at two polytetrafluoroethylene (PTFE) loadings (0 and 10 wt %) in a commercial GDL for temperatures between 240 and 273 K. A nonlinear ice-crystallization rate expression is developed using Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory, in which the heat-transfer-limited growth rate is determined from the moving-boundary Stefan problem. Induction timesmore » follow a Poisson distribution and increase upon addition of PTFE, indicating that nucleation occurs more slowly on a hydrophobic fiber than on a hydrophilic fiber. The determined nucleation rates and induction times follow expected trends from classical nucleation theory. Finally, a validated rate expression is now available for predicting ice-crystallization kinetics in GDLs.« less

A dynamical model of plasma turbulence in the solar wind

PubMed Central

Howes, G. G.

2015-01-01

A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature. PMID:25848075

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

PubMed

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

2015-01-01

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

Physiologically based pharmacokinetic model for ethyl tertiary‐butyl ether and tertiary‐butyl alcohol in rats: Contribution of binding to α2u–globulin in male rats and high‐exposure nonlinear kinetics to toxicity and cancer outcomes

PubMed Central

Ring, Caroline; Banton, Marcy I.; Leavens, Teresa L.

2016-01-01

Abstract In cancer bioassays, inhalation, but not drinking water exposure to ethyl tertiary‐butyl ether (ETBE), caused liver tumors in male rats, while tertiary‐butyl alcohol (TBA), an ETBE metabolite, caused kidney tumors in male rats following exposure via drinking water. To understand the contribution of ETBE and TBA kinetics under varying exposure scenarios to these tumor responses, a physiologically based pharmacokinetic model was developed based on a previously published model for methyl tertiary‐butyl ether, a structurally similar chemical, and verified against the literature and study report data. The model included ETBE and TBA binding to the male rat‐specific protein α2u–globulin, which plays a role in the ETBE and TBA kidney response observed in male rats. Metabolism of ETBE and TBA was described as a single, saturable pathway in the liver. The model predicted similar kidney AUC0–∞ for TBA for various exposure scenarios from ETBE and TBA cancer bioassays, supporting a male‐rat‐specific mode of action for TBA‐induced kidney tumors. The model also predicted nonlinear kinetics at ETBE inhalation exposure concentrations above ~2000 ppm, based on blood AUC0–∞ for ETBE and TBA. The shift from linear to nonlinear kinetics at exposure concentrations below the concentration associated with liver tumors in rats (5000 ppm) suggests the mode of action for liver tumors operates under nonlinear kinetics following chronic exposure and is not relevant for assessing human risk. Copyright © 2016 The Authors Journal of Applied Toxicology Published by John Wiley & Sons Ltd PMID:27885692

Physiologically based pharmacokinetic model for ethyl tertiary-butyl ether and tertiary-butyl alcohol in rats: Contribution of binding to α2u-globulin in male rats and high-exposure nonlinear kinetics to toxicity and cancer outcomes.

PubMed

Borghoff, Susan J; Ring, Caroline; Banton, Marcy I; Leavens, Teresa L

2017-05-01

In cancer bioassays, inhalation, but not drinking water exposure to ethyl tertiary-butyl ether (ETBE), caused liver tumors in male rats, while tertiary-butyl alcohol (TBA), an ETBE metabolite, caused kidney tumors in male rats following exposure via drinking water. To understand the contribution of ETBE and TBA kinetics under varying exposure scenarios to these tumor responses, a physiologically based pharmacokinetic model was developed based on a previously published model for methyl tertiary-butyl ether, a structurally similar chemical, and verified against the literature and study report data. The model included ETBE and TBA binding to the male rat-specific protein α2u-globulin, which plays a role in the ETBE and TBA kidney response observed in male rats. Metabolism of ETBE and TBA was described as a single, saturable pathway in the liver. The model predicted similar kidney AUC 0-∞ for TBA for various exposure scenarios from ETBE and TBA cancer bioassays, supporting a male-rat-specific mode of action for TBA-induced kidney tumors. The model also predicted nonlinear kinetics at ETBE inhalation exposure concentrations above ~2000 ppm, based on blood AUC 0-∞ for ETBE and TBA. The shift from linear to nonlinear kinetics at exposure concentrations below the concentration associated with liver tumors in rats (5000 ppm) suggests the mode of action for liver tumors operates under nonlinear kinetics following chronic exposure and is not relevant for assessing human risk. Copyright © 2016 The Authors Journal of Applied Toxicology Published by John Wiley & Sons Ltd. Copyright © 2016 The Authors Journal of Applied Toxicology Published by John Wiley & Sons Ltd.

Kinetic theory of turbulence for parallel propagation revisited: Low-to-intermediate frequency regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoon, Peter H., E-mail: yoonp@umd.edu; School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701

2015-09-15

A previous paper [P. H. Yoon, “Kinetic theory of turbulence for parallel propagation revisited: Formal results,” Phys. Plasmas 22, 082309 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field, in which the original work according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] was refined, following the paper by Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)]. The main finding involved the dimensional correction pertaining to discrete-particle effects in Yoon and Fang's theory. However, the final result was presented in terms of formal linear and nonlinear susceptibility response functions. Inmore » the present paper, the formal equations are explicitly written down for the case of low-to-intermediate frequency regime by making use of approximate forms for the response functions. The resulting equations are sufficiently concrete so that they can readily be solved by numerical means or analyzed by theoretical means. The derived set of equations describe nonlinear interactions of quasi-parallel modes whose frequency range covers the Alfvén wave range to ion-cyclotron mode, but is sufficiently lower than the electron cyclotron mode. The application of the present formalism may range from the nonlinear evolution of whistler anisotropy instability in the high-beta regime, and the nonlinear interaction of electrons with whistler-range turbulence.« less

Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).

Simplified path integral for supersymmetric quantum mechanics and type-A trace anomalies

NASA Astrophysics Data System (ADS)

Bastianelli, Fiorenzo; Corradini, Olindo; Iacconi, Laura

2018-05-01

Particles in a curved space are classically described by a nonlinear sigma model action that can be quantized through path integrals. The latter require a precise regularization to deal with the derivative interactions arising from the nonlinear kinetic term. Recently, for maximally symmetric spaces, simplified path integrals have been developed: they allow to trade the nonlinear kinetic term with a purely quadratic kinetic term (linear sigma model). This happens at the expense of introducing a suitable effective scalar potential, which contains the information on the curvature of the space. The simplified path integral provides a sensible gain in the efficiency of perturbative calculations. Here we extend the construction to models with N = 1 supersymmetry on the worldline, which are applicable to the first quantized description of a Dirac fermion. As an application we use the simplified worldline path integral to compute the type-A trace anomaly of a Dirac fermion in d dimensions up to d = 16.

SigrafW: An easy-to-use program for fitting enzyme kinetic data.

PubMed

Leone, Francisco Assis; Baranauskas, José Augusto; Furriel, Rosa Prazeres Melo; Borin, Ivana Aparecida

2005-11-01

SigrafW is Windows-compatible software developed using the Microsoft® Visual Basic Studio program that uses the simplified Hill equation for fitting kinetic data from allosteric and Michaelian enzymes. SigrafW uses a modified Fibonacci search to calculate maximal velocity (V), the Hill coefficient (n), and the enzyme-substrate apparent dissociation constant (K). The estimation of V, K, and the sum of the squares of residuals is performed using a Wilkinson nonlinear regression at any Hill coefficient (n). In contrast to many currently available kinetic analysis programs, SigrafW shows several advantages for the determination of kinetic parameters of both hyperbolic and nonhyperbolic saturation curves. No initial estimates of the kinetic parameters are required, a measure of the goodness-of-the-fit for each calculation performed is provided, the nonlinear regression used for calculations eliminates the statistical bias inherent in linear transformations, and the software can be used for enzyme kinetic simulations either for educational or research purposes. Persons interested in receiving a free copy of the software should contact Dr. F. A. Leone. Copyright © 2005 International Union of Biochemistry and Molecular Biology, Inc.

ITG-TEM turbulence simulation with bounce-averaged kinetic electrons in tokamak geometry

NASA Astrophysics Data System (ADS)

Kwon, Jae-Min; Qi, Lei; Yi, S.; Hahm, T. S.

2017-06-01

We develop a novel numerical scheme to simulate electrostatic turbulence with kinetic electron responses in magnetically confined toroidal plasmas. Focusing on ion gyro-radius scale turbulences with slower frequencies than the time scales for electron parallel motions, we employ and adapt the bounce-averaged kinetic equation to model trapped electrons for nonlinear turbulence simulation with Coulomb collisions. Ions are modeled by employing the gyrokinetic equation. The newly developed scheme is implemented on a global δf particle in cell code gKPSP. By performing linear and nonlinear simulations, it is demonstrated that the new scheme can reproduce key physical properties of Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) instabilities, and resulting turbulent transport. The overall computational cost of kinetic electrons using this novel scheme is limited to 200%-300% of the cost for simulations with adiabatic electrons. Therefore the new scheme allows us to perform kinetic simulations with trapped electrons very efficiently in magnetized plasmas.

Weak turbulence theory for beam-plasma interaction

NASA Astrophysics Data System (ADS)

Yoon, Peter H.

2018-01-01

The kinetic theory of weak plasma turbulence, of which Ronald C. Davidson was an important early pioneer [R. C. Davidson, Methods in Nonlinear Plasma Theory, (Academic Press, New York, 1972)], is a venerable and valid theory that may be applicable to a large number of problems in both laboratory and space plasmas. This paper applies the weak turbulence theory to the problem of gentle beam-plasma interaction and Langmuir turbulence. It is shown that the beam-plasma interaction undergoes various stages of physical processes starting from linear instability, to quasilinear saturation, to mode coupling that takes place after the quasilinear stage, followed by a state of quasi-static "turbulent equilibrium." The long term quasi-equilibrium stage is eventually perturbed by binary collisional effects in order to bring the plasma to a thermodynamic equilibrium with increased entropy.

The Dynamics of Small-Scale Turbulence Driven Flows

NASA Astrophysics Data System (ADS)

Beer, M. A.; Hammett, G. W.

1997-11-01

The dynamics of small-scale fluctuation driven flows are of great interest for micro-instability driven turbulence, since nonlinear toroidal simulations have shown that these flows play an important role in the regulation of the turbulence and transport levels. The gyrofluid treatment of these flows was shown to be accurate for times shorter than a bounce time.(Beer, M. A., Ph. D. thesis, Princeton University (1995).) Since the decorrelation times of the turbulence are generally shorter than a bounce time, our original hypothesis was that this description was adequate. Recent work(Hinton, F. L., Rosenbluth, M. N., and Waltz, R. E., International Sherwood Fusion Theory Conference (1997).) pointed out possible problems with this hypothesis, emphasizing the existence of a linearly undamped component of the flow which could build up in time and lower the final turbulence level. While our original gyrofluid model reproduces some aspects of the linear flow, there are differences between the long time gyrofluid and kinetic linear results in some cases. On the other hand, if the long time behavior of these flows is dominated by nonlinear damping (which seems reasonable), then the existing nonlinear gyrofluid simulations may be sufficiently accurate. We test these possibilities by modifying the gyrofluid description of these flows and diagnosing the flow evolution in nonlinear simulations.

Evolution of large amplitude Alfven waves in solar wind plasmas: Kinetic-fluid models

NASA Astrophysics Data System (ADS)

Nariyuki, Y.

2014-12-01

Large amplitude Alfven waves are ubiquitously observed in solar wind plasmas. Mjolhus(JPP, 1976) and Mio et al(JPSJ, 1976) found that nonlinear evolution of the uni-directional, parallel propagating Alfven waves can be described by the derivative nonlinear Schrodinger equation (DNLS). Later, the multi-dimensional extension (Mjolhus and Wyller, JPP, 1988; Passot and Sulem, POP, 1993; Gazol et al, POP, 1999) and ion kinetic modification (Mjolhus and Wyller, JPP, 1988; Spangler, POP, 1989; Medvedev and Diamond, POP, 1996; Nariyuki et al, POP, 2013) of DNLS have been reported. Recently, Nariyuki derived multi-dimensional DNLS from an expanding box model of the Hall-MHD system (Nariyuki, submitted). The set of equations including the nonlinear evolution of compressional wave modes (TDNLS) was derived by Hada(GRL, 1993). DNLS can be derived from TDNLS by rescaling of the variables (Mjolhus, Phys. Scr., 2006). Nariyuki and Hada(JPSJ, 2007) derived a kinetically modified TDNLS by using a simple Landau closure (Hammet and Perkins, PRL, 1990; Medvedev and Diamond, POP, 1996). In the present study, we revisit the ion kinetic modification of multi-dimensional TDNLS through more rigorous derivations, which is consistent with the past kinetic modification of DNLS. Although the original TDNLS was derived in the multi-dimensional form, the evolution of waves with finite propagation angles in TDNLS has not been paid much attention. Applicability of the resultant models to solar wind turbulence is discussed.

Critical Evaluation of Kinetic Method Measurements: Possible Origins of Nonlinear Effects

NASA Astrophysics Data System (ADS)

Bourgoin-Voillard, Sandrine; Afonso, Carlos; Lesage, Denis; Zins, Emilie-Laure; Tabet, Jean-Claude; Armentrout, P. B.

2013-03-01

The kinetic method is a widely used approach for the determination of thermochemical data such as proton affinities (PA) and gas-phase acidities ( ΔH° acid ). These data are easily obtained from decompositions of noncovalent heterodimers if care is taken in the choice of the method, references used, and experimental conditions. Previously, several papers have focused on theoretical considerations concerning the nature of the references. Few investigations have been devoted to conditions required to validate the quality of the experimental results. In the present work, we are interested in rationalizing the origin of nonlinear effects that can be obtained with the kinetic method. It is shown that such deviations result from intrinsic properties of the systems investigated but can also be enhanced by artifacts resulting from experimental issues. Overall, it is shown that orthogonal distance regression (ODR) analysis of kinetic method data provides the optimum way of acquiring accurate thermodynamic information.

On the dimensionally correct kinetic theory of turbulence for parallel propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Ziebell, L. F., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Yoon, P. H., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br

2015-03-15

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectivelymore » emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms.« less

Small amplitude Kinetic Alfven waves in a superthermal electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Adnan, Muhammad; Mahmood, Sahahzad; Qamar, Anisa; Tribeche, Mouloud

2016-11-01

We are investigating the propagating properties of coupled Kinetic Alfven-acoustic waves in a low beta plasma having superthermal electrons and positrons. Using the standard reductive perturbation method, a nonlinear Korteweg-de Vries (KdV) type equation is derived which describes the evolution of Kinetic Alfven waves. It is found that nonlinearity and Larmor radius effects can compromise and give rise to solitary structures. The parametric role of superthermality and positron content on the characteristics of solitary wave structures is also investigated. It is found that only sub-Alfvenic and compressive solitons are supported in the present model. The present study may find applications in a low β electron-positron-ion plasma having superthermal electrons and positrons.

Kinetic theory of turbulence for parallel propagation revisited: Formal results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoon, Peter H., E-mail: yoonp@umd.edu

2015-08-15

In a recent paper, Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. The original work was according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)], but Gaelzer et al. noted that the terms pertaining to discrete-particle effects in Yoon and Fang's theory did not enjoy proper dimensionality. The purpose of Gaelzer et al. was to restore the dimensional consistency associated with such terms. However, Gaelzer et al. was concerned only with linear wave-particle interaction terms. The present paper completes the analysis bymore » considering the dimensional correction to nonlinear wave-particle interaction terms in the wave kinetic equation.« less

Modeling of Long-Term Fate of Mobilized Fines due to Dam-Embankment Interfacial Dislocations

NASA Astrophysics Data System (ADS)

Glascoe, L. G.; Ezzedine, S. M.; Kanarska, Y.; Lomov, I.; Antoun, T. H.

2011-12-01

Transverse cracks in embankment dams can develop as a result of post-construction settlements, earthquake deformations, or anthropogenic loads such as emplaced explosives. During these dislocations, fine particles are released from the damaged zones and can create unwanted inertial erosion and piping through the transverse cracks. These processes are equally critical to the overall stability of the dam. We present numerical results related to the problem of the fluid flow, transport, and filtration of particulates from damaged zones between the concrete sections of a gravity dam and the embankment wraparound sections. The model solves simultaneously the flow, attachment, and washout of fine particles within a wraparound heterogeneous porous media. We used a state-of-the-art finite element method with adaptive mesh refinement to capture 1) the interface between water dense with fines and clear water, and 2) the non-linearity of the free surface itself. A few scenarios of sediment entrapment in the filter layers of a gravity dam were considered. Several parameterizations of the filtration model and constitutive laws of soil behavior were also investigated. Through these analyses, we concluded that the attachment kinetic isotherm is the key function of the model. More parametric studies need to be conducted to assess the sensitivity of the kinetic isotherm parameters on the overall stability of the embankment. These kinetic parameters can be obtained, for example, through numerical micro- and meso-scale studies. It is worth mentioning that the current model, for the more realistic non-linear kinetic isotherms, has predicted a self-rehabilitation of the breached core with retention of 50% of the mobilized fines using a very conservative filtration length. A more realistic value should exceed the assumed one, resulting in a retention exceeding 50%. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and funded by the U.S. Department of Homeland Security, Science and Technology Directorate.

Suppression of Phase Mixing in Drift-Kinetic Plasma Turbulence

NASA Astrophysics Data System (ADS)

Parker, J. T.; Dellar, P. J.; Schekochihin, A. A.; Highcock, E. G.

2017-12-01

The solar wind and interstellar medium are examples of strongly magnetised, weakly collisional, astrophysical plasmas. Their turbulent fluctuations are strongly anisotropic, with small amplitudes, and frequencies much lower than the Larmor frequency. This regime is described by gyrokinetic theory, a reduced five-dimensional kinetic system describing averages over Larmor orbits. A turbulent plasma may transfer free energy, a measure of fluctuation amplitudes, from injection at large scales, typically by an instability, to dissipation at small physical scales like a turbulent fluid. Alternatively, a turbulent plasma may form fine scale structures in velocity space via phase-mixing, the mechanism that leads to Landau damping in linear plasma theory. Macroscopic plasma properties like heat and momentum transport are affected by both mechanisms. While each is understood in isolation, their interaction is not. We study this interaction using a Hankel-Hermite velocity space representation of gyrokinetic theory. The Hankel transform interacts neatly with the Bessel functions that arise from averaging over Larmor orbits, so the perpendicular velocity space is decoupled for linearized problems. The Hermite transform expresses phase mixing as nearest-neighbor coupling between parallel velocity space scales represented by Hermite mode numbers. We use this representation to study transfer mechanisms in drift-kinetic plasma turbulence, the long wavelength limit of gyrokinetic theory. We show that phase space is divided into two regions, with one transfer mechanism dominating in each. Most energy is contained in the region where the fluid-like nonlinear cascade dominates. Moreover, in that region the nonlinear cascade interferes with phase mixing by exciting an "anti phase mixing" transfer of free energy from small to large velocity space scales. This cancels out the usual phase mixing, and renders the overall behavior fluid-like. These results profoundly change our understanding of free energy flow in drift-kinetic turbulence, and, moreover, explain previously observed spectra.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

A novel determination of calcite dissolution kinetics in seawater

NASA Astrophysics Data System (ADS)

Subhas, Adam V.; Rollins, Nick E.; Berelson, William M.; Dong, Sijia; Erez, Jonathan; Adkins, Jess F.

2015-12-01

We present a novel determination of the dissolution kinetics of inorganic calcite in seawater. We dissolved 13 C -labeled calcite in unlabeled seawater, and traced the evolving δ13 C composition of the fluid over time to establish dissolution rates. This method provides sensitive determinations of dissolution rate, which we couple with tight constraints on both seawater saturation state and surface area of the dissolving minerals. We have determined dissolution rates for two different abiotic calcite materials and three different grain sizes. Near-equilibrium dissolution rates are highly nonlinear, and are well normalized by geometric surface area, giving an empirical dissolution rate dependence on saturation state (Ω) of: This result substantiates the non-linear response of calcite dissolution to undersaturation. The bulk dissolution rate constant calculated here is in excellent agreement with those determined in far from equilibrium and dilute solution experiments. Plots of dissolution versus undersaturation indicates the presence of at least two dissolution mechanisms, implying a criticality in the calcite-seawater system. Finally, our new rate determination has implications for modeling of pelagic and seafloor dissolution. Nonlinear dissolution kinetics in a simple 1-D lysocline model indicate a possible transition from kinetic to diffusive control with increasing water depth, and also confirm the importance of respiration-driven dissolution in setting the shape of the calcite lysocline.

Multi-q pattern classification of polarization curves

NASA Astrophysics Data System (ADS)

Fabbri, Ricardo; Bastos, Ivan N.; Neto, Francisco D. Moura; Lopes, Francisco J. P.; Gonçalves, Wesley N.; Bruno, Odemir M.

2014-02-01

Several experimental measurements are expressed in the form of one-dimensional profiles, for which there is a scarcity of methodologies able to classify the pertinence of a given result to a specific group. The polarization curves that evaluate the corrosion kinetics of electrodes in corrosive media are applications where the behavior is chiefly analyzed from profiles. Polarization curves are indeed a classic method to determine the global kinetics of metallic electrodes, but the strong nonlinearity from different metals and alloys can overlap and the discrimination becomes a challenging problem. Moreover, even finding a typical curve from replicated tests requires subjective judgment. In this paper, we used the so-called multi-q approach based on the Tsallis statistics in a classification engine to separate the multiple polarization curve profiles of two stainless steels. We collected 48 experimental polarization curves in an aqueous chloride medium of two stainless steel types, with different resistance against localized corrosion. Multi-q pattern analysis was then carried out on a wide potential range, from cathodic up to anodic regions. An excellent classification rate was obtained, at a success rate of 90%, 80%, and 83% for low (cathodic), high (anodic), and both potential ranges, respectively, using only 2% of the original profile data. These results show the potential of the proposed approach towards efficient, robust, systematic and automatic classification of highly nonlinear profile curves.

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arefiev, A. V.; Dodin, I. Y.; Kohn, A.

Spherical tokamak plasmas are typically overdense and thus inaccessible to externally-injected microwaves in the electron cyclotron range. The electrostatic electron Bernstein wave (EBW), however, provides a method to access the plasma core for heating and diagnostic purposes. Understanding the details of the coupling process to electromagnetic waves is thus important both for the interpretation of microwave diagnostic data and for assessing the feasibility of EBW heating and current drive. While the coupling is reasonably well–understood in the linear regime, nonlinear physics arising from high input power has not been previously quantified. To tackle this problem, we have performed one- andmore » two-dimensional fully kinetic particle-in-cell simulations of the two possible coupling mechanisms, namely X-B and O-X-B mode conversion. We find that the ion dynamics has a profound effect on the field structure in the nonlinear regime, as high amplitude short-scale oscillations of the longitudinal electric field are excited in the region below the high-density cut-off prior to the arrival of the EBW. We identify this effect as the instability of the X wave with respect to resonant scattering into an EBW and a lower-hybrid wave. Finally, we calculate the instability rate analytically and find this basic theory to be in reasonable agreement with our simulation results.« less

Kinetic simulations of X-B and O-X-B mode conversion and its deterioration at high input power

DOE PAGES

Arefiev, A. V.; Dodin, I. Y.; Kohn, A.; ...

2017-08-09

Spherical tokamak plasmas are typically overdense and thus inaccessible to externally-injected microwaves in the electron cyclotron range. The electrostatic electron Bernstein wave (EBW), however, provides a method to access the plasma core for heating and diagnostic purposes. Understanding the details of the coupling process to electromagnetic waves is thus important both for the interpretation of microwave diagnostic data and for assessing the feasibility of EBW heating and current drive. While the coupling is reasonably well–understood in the linear regime, nonlinear physics arising from high input power has not been previously quantified. To tackle this problem, we have performed one- andmore » two-dimensional fully kinetic particle-in-cell simulations of the two possible coupling mechanisms, namely X-B and O-X-B mode conversion. We find that the ion dynamics has a profound effect on the field structure in the nonlinear regime, as high amplitude short-scale oscillations of the longitudinal electric field are excited in the region below the high-density cut-off prior to the arrival of the EBW. We identify this effect as the instability of the X wave with respect to resonant scattering into an EBW and a lower-hybrid wave. Finally, we calculate the instability rate analytically and find this basic theory to be in reasonable agreement with our simulation results.« less

A numerical study of biofilm growth in a microgravity environment

NASA Astrophysics Data System (ADS)

Aristotelous, A. C.; Papanicolaou, N. C.

2017-10-01

A mathematical model is proposed to investigate the effect of microgravity on biofilm growth. We examine the case of biofilm suspended in a quiescent aqueous nutrient solution contained in a rectangular tank. The bacterial colony is assumed to follow logistic growth whereas nutrient absorption is assumed to follow Monod kinetics. The problem is modeled by a coupled system of nonlinear partial differential equations in two spatial dimensions solved using the Discontinuous Galerkin Finite Element method. Nutrient and biofilm concentrations are computed in microgravity and normal gravity conditions. A preliminary quantitative relationship between the biofilm concentration and the gravity field intensity is derived.

Isotropic matrix elements of the collision integral for the Boltzmann equation

NASA Astrophysics Data System (ADS)

Ender, I. A.; Bakaleinikov, L. A.; Flegontova, E. Yu.; Gerasimenko, A. B.

2017-09-01

We have proposed an algorithm for constructing matrix elements of the collision integral for the nonlinear Boltzmann equation isotropic in velocities. These matrix elements have been used to start the recurrent procedure for calculating matrix elements of the velocity-nonisotropic collision integral described in our previous publication. In addition, isotropic matrix elements are of independent interest for calculating isotropic relaxation in a number of physical kinetics problems. It has been shown that the coefficients of expansion of isotropic matrix elements in Ω integrals are connected by the recurrent relations that make it possible to construct the procedure of their sequential determination.

An exploration of viscosity models in the realm of kinetic theory of liquids originated fluids

NASA Astrophysics Data System (ADS)

Hussain, Azad; Ghafoor, Saadia; Malik, M. Y.; Jamal, Sarmad

The preeminent perspective of this article is to study flow of an Eyring Powell fluid model past a penetrable plate. To find the effects of variable viscosity on fluid model, continuity, momentum and energy equations are elaborated. Here, viscosity is taken as function of temperature. To understand the phenomenon, Reynold and Vogel models of variable viscosity are incorporated. The highly non-linear partial differential equations are transfigured into ordinary differential equations with the help of suitable similarity transformations. The numerical solution of the problem is presented. Graphs are plotted to visualize the behavior of pertinent parameters on the velocity and temperature profiles.

Nonlinear generation of kinetic-scale waves by magnetohydrodynamic Alfvén waves and nonlocal spectral transport in the solar wind

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, J. S.; Wu, D. J.; Voitenko, Y.

We study the nonlocal nonlinear coupling and generation of kinetic Alfvén waves (KAWs) and kinetic slow waves (KSWs) by magnetohydrodynamic Alfvén waves (MHD AWs) in conditions typical for the solar wind in the inner heliosphere. This cross-scale process provides an alternative to the turbulent energy cascade passing through many intermediate scales. The nonlinearities we study are proportional to the scalar products of wave vectors and hence are called 'scalar' ones. Despite the strong Landau damping of kinetic waves, we found fast growing KAWs and KSWs at perpendicular wavelengths close to the ion gyroradius. Using the parametric decay formalism, we investigatemore » two independent decay channels for the pump AW: forward decay (involving co-propagating product waves) and backward decay (involving counter-propagating product waves). The growth rate of the forward decay is typically 0.05 but can exceed 0.1 of the pump wave frequency. The resulting spectral transport is nonlocal and anisotropic, sharply increasing perpendicular wavenumbers but not parallel ones. AWs and KAWs propagating against the pump AW grow with about the same rate and contribute to the sunward wave flux in the solar wind. Our results suggest that the nonlocal decay of MHD AWs into KAWs and KSWs is a robust mechanism for the cross-scale spectral transport of the wave energy from MHD to dissipative kinetic scales in the solar wind and similar media.« less

Frequency-tunable superconducting resonators via nonlinear kinetic inductance

NASA Astrophysics Data System (ADS)

Vissers, M. R.; Hubmayr, J.; Sandberg, M.; Chaudhuri, S.; Bockstiegel, C.; Gao, J.

2015-08-01

We have designed, fabricated, and tested a frequency-tunable high-Q superconducting resonator made from a niobium titanium nitride film. The frequency tunability is achieved by injecting a DC through a current-directing circuit into the nonlinear inductor whose kinetic inductance is current-dependent. We have demonstrated continuous tuning of the resonance frequency in a 180 MHz frequency range around 4.5 GHz while maintaining the high internal quality factor Qi > 180 000. This device may serve as a tunable filter and find applications in superconducting quantum computing and measurement. It also provides a useful tool to study the nonlinear response of a superconductor. In addition, it may be developed into techniques for measurement of the complex impedance of a superconductor at its transition temperature and for readout of transition-edge sensors.

Peptide concentration alters intermediate species in amyloid β fibrillation kinetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garvey, M., E-mail: megan.garvey@molbiotech.rwth-aachen.de; Morgado, I., E-mail: immorgado@ualg.pt

2013-04-12

Highlights: ► Aβ(1–40) aggregation in vitro has been monitored at different concentrations. ► Aβ(1–40) fibrillation does not always follow conventional kinetic mechanisms. ► We demonstrate non-linear features in the kinetics of Aβ(1–40) fibril formation. ► At high Aβ(1–40) concentrations secondary processes dictate fibrillation speed. ► Intermediate species may play significant roles on final amyloid fibril development. -- Abstract: The kinetic mechanism of amyloid aggregation remains to be fully understood. Investigations into the species present in the different kinetic phases can assist our comprehension of amyloid diseases and further our understanding of the mechanism behind amyloid β (Aβ) (1–40) peptide aggregation.more » Thioflavin T (ThT) fluorescence and transmission electron microscopy (TEM) have been used in combination to monitor Aβ(1–40) aggregation in vitro at both normal and higher than standard concentrations. The observed fibrillation behaviour deviates, in several respects, from standard concepts of the nucleation–polymerisation models and shows such features as concentration-dependent non-linear effects in the assembly mechanism. Aβ(1–40) fibrillation kinetics do not always follow conventional kinetic mechanisms and, specifically at high concentrations, intermediate structures become populated and secondary processes may further modify the fibrillation mechanism.« less

Electron plasma wave filamentation in the kinetic regime

NASA Astrophysics Data System (ADS)

Lushnikov, Pavel; Rose, Harvey; Silantyev, Denis

2016-10-01

We consider nonlinear electron plasma wave (EPW) dynamics in the kinetic wavenumber regime, 0.25 < kλD < 0.45 , which is typical for current high temperature laser-plasma interaction experiments, where k is the EPW wavenumber and λD is the electron Debye length. In this kinetic regime, EPW frequency reduction due to electron trapping may dominate the ponderomotive frequency shift. Previous 3D PIC simulations showed that the trapped electron EPW filamentation instability can saturate stimulated Raman backscatter by reducing the EPWs coherence but multidimensional Vlasov simulations [1] are needed to address that saturation in details. We performed nonlinear, non-equilibrium 2D Vlasov simulations to study the EPW filamentation. The initial conditions are created either by external forcing or by constructing the appropriate 1D travelling Bernstein-Greene-Kruskal (BGK) mode. Transverse perturbations of any of these initial conditions grow with time eventually producing strongly nonlinear filamentation followed by plasma turbulence. We compared these simulations with the theoretical results on growth rates of the transverse instability BGK mode showing the satisfactory agreement. Supported by the New Mexico Consortium and NSF DMS-1412140.

Theory and modeling of atmospheric turbulence, part 1

NASA Technical Reports Server (NTRS)

1984-01-01

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

Nonlinear Two Fluid and Kinetic ELM Simulations

NASA Astrophysics Data System (ADS)

Strauss, H. R.; Sugiyama, L.; Chang, C. S.; Ku, S.; Hientzsch, B.; Breslau, J.; Park, W.; Samtaney, R.; Adams, M.; Jardin, S.

2006-04-01

Simulations of ELMs using dissipative MHD, two fluid MHD, and neoclassical kinetic physics models are being carried out using the M3D code [1]. Resistive MHD simulations of nonlinear edge pressure and current driven instabilities have been performed, initialized with realistic DIIID equilibria. Simulations show the saturation of the modes and relaxation of equilbrium profiles. Linear simulations including two fluid effects show the stabilization of toroidal mode number n = 10 modes, when the Hall parameter H, the ratio of ion skin depth to major radius, exceeds a threshhold. Nonlinear simulations are being done including gyroviscous stabilization. Kinetic effects are incorporated by coupling with the XGC code [2], which is able to simulate the edge plasma density and pressure pedestal buildup. These profiles are being used to initialize M3D simulations of an ELM crash and pedestal relaxation. The goal is to simulate an ELM cycle. [1] Park, W., Belova, E.V., Fu, G.Y., Tang, X.Z., Strauss, H.R., Sugiyama, L.E., Phys. Plas. 6, 1796 (1999).[2] Chang, C.S., Ku, S., and Weitzner, H., Phys. Plas. 11, 2649 (2004)

Combining experimental techniques with non-linear numerical models to assess the sorption of pesticides on soils

NASA Astrophysics Data System (ADS)

Magga, Zoi; Tzovolou, Dimitra N.; Theodoropoulou, Maria A.; Tsakiroglou, Christos D.

2012-03-01

The risk assessment of groundwater pollution by pesticides may be based on pesticide sorption and biodegradation kinetic parameters estimated with inverse modeling of datasets from either batch or continuous flow soil column experiments. In the present work, a chemical non-equilibrium and non-linear 2-site sorption model is incorporated into solute transport models to invert the datasets of batch and soil column experiments, and estimate the kinetic sorption parameters for two pesticides: N-phosphonomethyl glycine (glyphosate) and 2,4-dichlorophenoxy-acetic acid (2,4-D). When coupling the 2-site sorption model with the 2-region transport model, except of the kinetic sorption parameters, the soil column datasets enable us to estimate the mass-transfer coefficients associated with solute diffusion between mobile and immobile regions. In order to improve the reliability of models and kinetic parameter values, a stepwise strategy that combines batch and continuous flow tests with adequate true-to-the mechanism analytical of numerical models, and decouples the kinetics of purely reactive steps of sorption from physical mass-transfer processes is required.

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

NASA Astrophysics Data System (ADS)

Squire, J.; Quataert, E.; Kunz, M. W.

2017-12-01

In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the `parasitic instabilities' that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Liu, Huan

2018-04-01

The Riemann-Hilbert problem for the coupled nonlinear Schrödinger equation is formulated on the basis of the corresponding 3× 3 matrix spectral problem. Using the nonlinear steepest descent method, we obtain leading-order asymptotics for the Cauchy problem of the coupled nonlinear Schrödinger equation.

Verification of nonlinear particle simulation of radio frequency waves in fusion plasmas

NASA Astrophysics Data System (ADS)

Kuley, Animesh; Bao, Jian; Lin, Zhihong

2015-11-01

Nonlinear global particle simulation model has been developed in GTC to study the nonlinear interactions of radio frequency (RF) waves with plasmas in tokamak. In this model, ions are considered as fully kinetic particles using the Vlasov equation and electrons are treated as guiding centers using the drift kinetic. Boris push scheme for the ion motion has been implemented in the toroidal geometry using magnetic coordinates and successfully verified for the ion cyclotron, ion Bernstein and lower hybrid waves. The nonlinear GTC simulation of the lower hybrid wave shows that the amplitude of the electrostatic potential is oscillatory due to the trapping of resonant electrons by the electric field of the lower hybrid wave. The nonresonant parametric decay is observed an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating with a heating rate proportional to the pump wave intensity. This work is supported by PPPL subcontract number S013849-F and US Department of Energy (DOE) SciDAC GSEP Program.

A physiology-based parametric imaging method for FDG-PET data

NASA Astrophysics Data System (ADS)

Scussolini, Mara; Garbarino, Sara; Sambuceti, Gianmario; Caviglia, Giacomo; Piana, Michele

2017-12-01

Parametric imaging is a compartmental approach that processes nuclear imaging data to estimate the spatial distribution of the kinetic parameters governing tracer flow. The present paper proposes a novel and efficient computational method for parametric imaging which is potentially applicable to several compartmental models of diverse complexity and which is effective in the determination of the parametric maps of all kinetic coefficients. We consider applications to [18 F]-fluorodeoxyglucose positron emission tomography (FDG-PET) data and analyze the two-compartment catenary model describing the standard FDG metabolization by an homogeneous tissue and the three-compartment non-catenary model representing the renal physiology. We show uniqueness theorems for both models. The proposed imaging method starts from the reconstructed FDG-PET images of tracer concentration and preliminarily applies image processing algorithms for noise reduction and image segmentation. The optimization procedure solves pixel-wise the non-linear inverse problem of determining the kinetic parameters from dynamic concentration data through a regularized Gauss-Newton iterative algorithm. The reliability of the method is validated against synthetic data, for the two-compartment system, and experimental real data of murine models, for the renal three-compartment system.

Essentially Entropic Lattice Boltzmann Model

NASA Astrophysics Data System (ADS)

Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

2017-12-01

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

Thermal radiation from optically driven Kerr (χ{sup (3)}) photonic cavities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khandekar, Chinmay; Rodriguez, Alejandro W.; Lin, Zin

2015-04-13

We describe thermal radiation from nonlinear (χ{sup (3)}) photonic cavities coupled to external channels and subject to incident monochromatic light. Our work extends related work on nonlinear mechanical oscillators to the problem of thermal radiation, demonstrating that bistability can enhance thermal radiation by orders of magnitude and result in strong lineshape alternations, including “super-narrow spectral peaks” occurring at the onset of kinetic phase transitions. We show that when the cavities are designed to exhibit perfect linear emissivity (rate matching), such thermally activated transitions can be exploited to dramatically tune the output power and radiative properties of the cavity, leading tomore » a kind of Kerr-mediated thermo-optic effect. Finally, we demonstrate that in certain parameter regimes, the output radiation exhibits Stokes and anti-Stokes side peaks whose relative magnitudes can be altered by tuning the internal temperature of the cavity relative to its surroundings, a consequence of strong correlations and interference between the emitted and reflected radiation.« less

Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials

NASA Astrophysics Data System (ADS)

Shiroky, I. B.; Gendelman, O. V.

2018-02-01

We address the problem of transition front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of the front propagation, and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to the fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its velocity, as well as the frequency and the amplitude of the oscillatory tail. Numerical results are in good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load, the next-nearest-neighbor coupling and the on-site damping. When the damping is moderate, it is possible to consider the shock propagation in the damped chain as a perturbation of the undamped dynamics. This approach yields reasonable predictions. When the damping is high, the transition front enters a completely different asymptotic regime of a subsonic kink. The gradient nonlinearity generically turns negligible, and the propagating front converges to the regime described by a simple exact solution for a continuous model with linear coupling.

Scalar discrete nonlinear multipoint boundary value problems

NASA Astrophysics Data System (ADS)

Rodriguez, Jesus; Taylor, Padraic

2007-06-01

In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].

CONSEQUENCES OF NON-LINEAR DENSITY EFFECTS ON BUOYANCY AND PLUME BEHAVIOR

EPA Science Inventory

Aquatic plumes, as turbulent streams, grow by entraining ambient water. Buoyant plumes rise and dense ones sink, but, non-linear kinetic effects can reverse the buoyant force in mid-phenomenon. The class of nascent-density plumes begin as buoyant, upwardly accelerating plumes tha...

Position-dependent mass, finite-gap systems, and supersymmetry

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Plyushchay, Mikhail S.

2016-05-01

The ordering problem in quantum systems with position-dependent mass (PDM) is treated by inclusion of the classically fictitious similarity transformation into the kinetic term. This provides a generation of supersymmetry with the first-order supercharges from the kinetic term alone, while inclusion of the potential term allows us also to generate nonlinear supersymmetry with higher-order supercharges. A broad class of finite-gap systems with PDM is obtained by different reduction procedures, and general results on supersymmetry generation are applied to them. We show that elliptic finite-gap systems of Lamé and Darboux-Treibich-Verdier types can be obtained by reduction to Seiffert's spherical spiral and Bernoulli lemniscate in the presence of Calogero-like or harmonic oscillator potentials, or by angular momentum reduction of a free motion on some AdS2 -related surfaces in the presence of Aharonov-Bohm flux. The limiting cases include the Higgs and Mathews-Lakshmanan oscillator models as well as a reflectionless model with PDM exploited recently in the discussion of cosmological inflationary scenarios.

Energy Conservation and Conversion in NIMROD Computations of Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Maddox, J. A.; Sovinec, C. R.

2017-10-01

Previous work modeling magnetic relaxation during non-inductive start-up at the Pegasus spherical tokamak indicates an order of magnitude gap between measured experimental temperature and simulated temperature in NIMROD. Potential causes of the plasma temperature gap include: insufficient transport modeling, too low modeled injector power input, and numerical loss of energy, as energy is not algorithmically conserved in NIMROD simulations. Simple 2D nonlinear MHD simulations explore numerical energy conservation discrepancies in NIMROD because understanding numerical loss of energy is fundamental to addressing the physical problems of the other potential causes of energy loss. Evolution of these configurations induces magnetic reconnection, which transfers magnetic energy to heat and kinetic energy. The kinetic energy is eventually damped so, magnetic energy loss must correspond to an increase in internal energy. Results in the 2D geometries indicate that numerical energy loss during reconnection depends on the temporal resolution of the dynamics. Work support from U.S. Department of Energy through a subcontract from the Plasma Science and Innovation Center.

Frequency-tunable superconducting resonators via nonlinear kinetic inductance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vissers, M. R.; Hubmayr, J.; Sandberg, M.

2015-08-10

We have designed, fabricated, and tested a frequency-tunable high-Q superconducting resonator made from a niobium titanium nitride film. The frequency tunability is achieved by injecting a DC through a current-directing circuit into the nonlinear inductor whose kinetic inductance is current-dependent. We have demonstrated continuous tuning of the resonance frequency in a 180 MHz frequency range around 4.5 GHz while maintaining the high internal quality factor Q{sub i} > 180 000. This device may serve as a tunable filter and find applications in superconducting quantum computing and measurement. It also provides a useful tool to study the nonlinear response of a superconductor. In addition,more » it may be developed into techniques for measurement of the complex impedance of a superconductor at its transition temperature and for readout of transition-edge sensors.« less

Subpiosecond Third Order Nonlinear Response in Polythiophene and Thiopene Based Thin Films

NASA Technical Reports Server (NTRS)

Harris, D.; Royer, E.; Dorsinville, R.

1995-01-01

Ultrafast relaxation kinetics of the third order nonlinear susceptibility of polythiophene and polycondensed thiophene-based polymer was determined by the forward degenerate four-wave mixing technique. Deep into the absorption band the nonlinear response shows only a fast component (less than 900 fs at 587 nm) while at the edge of the absorption band at 642 nm a much slower and complex decay was measured.

libSRES: a C library for stochastic ranking evolution strategy for parameter estimation.

PubMed

Ji, Xinglai; Xu, Ying

2006-01-01

Estimation of kinetic parameters in a biochemical pathway or network represents a common problem in systems studies of biological processes. We have implemented a C library, named libSRES, to facilitate a fast implementation of computer software for study of non-linear biochemical pathways. This library implements a (mu, lambda)-ES evolutionary optimization algorithm that uses stochastic ranking as the constraint handling technique. Considering the amount of computing time it might require to solve a parameter-estimation problem, an MPI version of libSRES is provided for parallel implementation, as well as a simple user interface. libSRES is freely available and could be used directly in any C program as a library function. We have extensively tested the performance of libSRES on various pathway parameter-estimation problems and found its performance to be satisfactory. The source code (in C) is free for academic users at http://csbl.bmb.uga.edu/~jix/science/libSRES/

Noise-induced modulation of the relaxation kinetics around a non-equilibrium steady state of non-linear chemical reaction networks.

PubMed

Ramaswamy, Rajesh; Sbalzarini, Ivo F; González-Segredo, Nélido

2011-01-28

Stochastic effects from correlated noise non-trivially modulate the kinetics of non-linear chemical reaction networks. This is especially important in systems where reactions are confined to small volumes and reactants are delivered in bursts. We characterise how the two noise sources confinement and burst modulate the relaxation kinetics of a non-linear reaction network around a non-equilibrium steady state. We find that the lifetimes of species change with burst input and confinement. Confinement increases the lifetimes of all species that are involved in any non-linear reaction as a reactant. Burst monotonically increases or decreases lifetimes. Competition between burst-induced and confinement-induced modulation may hence lead to a non-monotonic modulation. We quantify lifetime as the integral of the time autocorrelation function (ACF) of concentration fluctuations around a non-equilibrium steady state of the reaction network. Furthermore, we look at the first and second derivatives of the ACF, each of which is affected in opposite ways by burst and confinement. This allows discriminating between these two noise sources. We analytically derive the ACF from the linear Fokker-Planck approximation of the chemical master equation in order to establish a baseline for the burst-induced modulation at low confinement. Effects of higher confinement are then studied using a partial-propensity stochastic simulation algorithm. The results presented here may help understand the mechanisms that deviate stochastic kinetics from its deterministic counterpart. In addition, they may be instrumental when using fluorescence-lifetime imaging microscopy (FLIM) or fluorescence-correlation spectroscopy (FCS) to measure confinement and burst in systems with known reaction rates, or, alternatively, to correct for the effects of confinement and burst when experimentally measuring reaction rates.

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

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.

Nonlinear Waves, Instabilities and Singularities in Plasma and Hydrodynamics

NASA Astrophysics Data System (ADS)

Silantyev, Denis Albertovich

Nonlinear effects are present in almost every area of science as soon as one tries to go beyond the first order approximation. In particular, nonlinear waves emerge in such areas as hydrodynamics, nonlinear optics, plasma physics, quantum physics, etc. The results of this work are related to nonlinear waves in two areas, plasma physics and hydrodynamics, united by concepts of instability, singularity and advanced numerical methods used for their investigation. The first part of this work concentrates on Langmuir wave filamentation instability in the kinetic regime of plasma. In Internal Confinement Fusion Experiments (ICF) at National Ignition Facility (NIF), where attempts are made to achieve fusion by compressing a small target by many powerful lasers to extremely high temperatures and pressures, plasma is created in the first moments of the laser reaching the target and undergoes complicated dynamics. Some of the most challenging difficulties arise from various plasma instabilities that occur due to interaction of the laser beam and a plasma surrounding the target. In this work we consider one of such instabilities that describes a decay of nonlinear plasma wave, initially excited due to interaction of the laser beam with the plasma, into many filaments in direction perpendicular to the laser beam, therefore named Langmuir filamentation instability. This instability occurs in the kinetic regime of plasma, klambda D > 0.2, where k is the wavenumber and lambda D is the Debye length. The filamentation of Langmuir waves in turn leads to the saturation of the stimulated Raman scattering (SRS) in laser-plasma interaction experiments which plays an essential role in ICF experiments. The challenging part of this work was that unlike in hydrodynamics we needed to use fully kinetic description of plasma to capture the physics in question properly, meaning that we needed to consider the distribution function of charged particles and its evolution in time not only with respect to spatial coordinates but with respect to velocities as well. To study Langmuir filamentation instability in its simplest form we performed 2D+2V numerical simulations. Taking into account that the distribution function in question was 4-dimensional function, making these simulation quite challenging, we developed an efficient numerical method making these simulations possible on modern desktop computers. Using the developed numerical method we studied how Langmuir wave filamentation instability depends on the parameters of the Langmuir wave such as wave length and amplitude that are relevant to ICF experiments. We considered several types of Langmuir waves, including nonlinear Langmuir waves exited by external electric field as well as an idealized approximation of such Langmuir waves by a particular family of Bernstein-Greene-Kruskal (BGK) modes that bifurcates from the linear Langmuir wave. The results of these simulations were compared to the theoretical predictions in our recent papers. An alternative approach to overcome computational difficulty of this problem was considered by our research group in Ref. It involves reducing the number of transverse direction in the model therefore lowering computational difficulty at a cost of lesser accuracy of the model. The second part of this work concentrates on 2D free surface hydrodynamics and in particular on computing Stokes waves with high-precision using conformal maps and spectral methods. Stokes waves are fully nonlinear periodic gravity waves propagating with the constant velocity on a free surface of two-dimensional potential flow of the ideal incompressible fluid of infinite depth. The increase of the scaled wave height H/lambda, where H is the wave height and lambda is the wavelength, from H/lambda = 0 to the critical value Hmax/lambda marks the transition from almost linear wave to a strongly nonlinear limiting Stokes wave. The Stokes wave of the greatest height H = Hmax has an angle of 120° at the crest. To obtain Stokes wave fully nonlinear Euler equations describing the flow can be reformulated in terms of conformal map of the fluid domain into the complex lower half-plane, with fluid free surface mapped into the real line. This description is convenient for analysis and numerical simulations since the whole problem is then reduced to a single nonlinear equation on the real line. Having computed solutions on the real line we extend them to the rest of the complex plane to analyze the singularities above real line. The distance vc from the closest singularity in the upper half-plane to the real line goes to zero as we approach the limiting Stokes wave with maximum hight Hmax/lambda, which is the reason for the widening of the solution's Fourier spectrum. (Abstract shortened by ProQuest.).

Kinetics and Mechanisms of Phosphorus Adsorption in Soils from Diverse Ecological Zones in the Source Area of a Drinking-Water Reservoir

PubMed Central

Zhang, Liang; Loáiciga, Hugo A.; Xu, Meng; Du, Chao; Du, Yun

2015-01-01

On-site soils are increasingly used in the treatment and restoration of ecosystems to harmonize with the local landscape and minimize costs. Eight natural soils from diverse ecological zones in the source area of a drinking-water reservoir in central China are used as adsorbents for the uptake of phosphorus from aqueous solutions. The X-ray fluorescence (XRF) spectrometric and BET (Brunauer-Emmett-Teller) tests and the Scanning Electron Microscopy (SEM) and Fourier Transform Infrared (FTIR) spectral analyses are carried out to investigate the soils’ chemical properties and their potential changes with adsorbed phosphorous from aqueous solutions. The intra-particle diffusion, pseudo-first-order, and pseudo-second-order kinetic models describe the adsorption kinetic processes. Our results indicate that the adsorption processes of phosphorus in soils occurred in three stages and that the rate-controlling steps are not solely dependent on intra-particle diffusion. A quantitative comparison of two kinetics models based on their linear and non-linear representations, and using the chi-square (χ2) test and the coefficient of determination (r2), indicates that the adsorptive properties of the soils are best described by the non-linear pseudo-second-order kinetic model. The adsorption characteristics of aqueous phosphorous are determined along with the essential kinetic parameters. PMID:26569278

Hierarchic Extensions in the Static and Dynamic Analysis of Elastic Beams. Ph.D. Thesis, 1990 Final Report, May 1990

NASA Technical Reports Server (NTRS)

Watson, Robert A.

1991-01-01

Approximate solutions of static and dynamic beam problems by the p-version of the finite element method are investigated. Within a hierarchy of engineering beam idealizations, rigorous formulations of the strain and kinetic energies for straight and circular beam elements are presented. These formulations include rotating coordinate system effects and geometric nonlinearities to allow for the evaluation of vertical axis wind turbines, the motivating problem for this research. Hierarchic finite element spaces, based on extensions of the polynomial orders used to approximate the displacement variables, are constructed. The developed models are implemented into a general purpose computer program for evaluation. Quality control procedures are examined for a diverse set of sample problems. These procedures include estimating discretization errors in energy norm and natural frequencies, performing static and dynamic equilibrium checks, observing convergence for qualities of interest, and comparison with more exacting theories and experimental data. It is demonstrated that p-extensions produce exponential rates of convergence in the approximation of strain energy and natural frequencies for the class of problems investigated.

Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

2014-01-01

In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

Stability of the Tonks–Langmuir discharge pre-sheath

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tskhakaya, D. D.; Kos, L.; Tskhakaya, D.

The article formulates the stability problem of the plasma sheath in the Tonks–Langmuir discharge. Using the kinetic description of the ion gas, i.e., the stability of the potential shape in the quasi-neutral pre-sheath regarding the high and low frequency, the perturbations are investigated. The electrons are assumed to be Maxwell–Boltzmann distributed. Regarding high-frequency perturbations, the pre-sheath is shown to be stable. The stability problem regarding low-frequency perturbations can be reduced to an analysis of the “diffusion like” equation, which results in the instability of the potential distribution in the pre-sheath. By means of the Particle in Cell simulations, also themore » nonlinear stage of low frequency oscillations is investigated. Comparing the figure obtained with the figure for linear stage, one can find obvious similarity in the spatial-temporal behavior of the potential.« less

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

REVIEWS OF TOPICAL PROBLEMS: Particle kinetics in highly turbulent plasmas (renormalization and self-consistent field methods)

NASA Astrophysics Data System (ADS)

Bykov, Andrei M.; Toptygin, Igor'N.

1993-11-01

This review presents methods available for calculating transport coefficients for impurity particles in plasmas with strong long-wave MHD-type velocity and magnetic-field fluctuations, and random ensembles of strong shock fronts. The renormalization of the coefficients of the mean-field equation of turbulent dynamo theory is also considered. Particular attention is devoted to the renormalization method developed by the authors in which the renormalized transport coefficients are calculated from a nonlinear transcendental equation (or a set of such equations) and are expressed in the form of explicit functions of pair correlation tensors describing turbulence. Numerical calculations are reproduced for different turbulence spectra. Spatial transport in a magnetic field and particle acceleration by strong turbulence are investigated. The theory can be used in a wide range of practical problems in plasma physics, atmospheric physics, ocean physics, astrophysics, cosmic-ray physics, and so on.

Tampering with the turbulent energy cascade with polymer additives

NASA Astrophysics Data System (ADS)

Valente, Pedro; da Silva, Carlos; Pinho, Fernando

2014-11-01

We show that the strong depletion of the viscous dissipation in homogeneous viscoelastic turbulence reported by previous authors does not necessarily imply a depletion of the turbulent energy cascade. However, for large polymer relaxation times there is an onset of a polymer-induced kinetic energy cascade which competes with the non-linear energy cascade leading to its depletion. Remarkably, the total energy cascade flux from both cascade mechanisms remains approximately the same fraction of the kinetic energy over the turnover time as the non-linear energy cascade flux in Newtonian turbulence. The authors acknowledge the funding from COMPETE, FEDER and FCT (Grant PTDC/EME-MFE/113589/2009).

Toroidal turbulence simulations with gyro-Landau fluid models in a nonlinear ballooning mode representation

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Kerbel, G. D.

1994-05-01

The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyro-kinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro-Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel 3D nonlinear ballooning mode representation. The representation is a Fourier transform of the Cowley et al. [Phys. Fluids B 3, 2767 (1991)] field line following twisted eddy basis (kx',ky',z') with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky'=0, kx'≠0) ``radial modes'' in stabilizing the transport from the finite-n ITG ballooning modes.

Kinetic Alfvén solitary and rogue waves in superthermal plasmas

NASA Astrophysics Data System (ADS)

Bains, A. S.; Li, Bo; Xia, Li-Dong

2014-03-01

We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compressive solitons are supported. We then extend the study to examine kinetic Alfvén rogue waves by deriving a nonlinear Schrödinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.

Nonlinear responses of chiral fluids from kinetic theory

NASA Astrophysics Data System (ADS)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

On the interpretation of energy and energy fluxes of nonlinear internal waves: An example from Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.; Butman, B.

2006-01-01

A self-consistent formalism to estimate baroclinic energy densities and fluxes resulting from the propagation of internal waves of arbitrary amplitude is derived using the concept of available potential energy. The method can be applied to numerical, laboratory or field data. The total energy flux is shown to be the sum of the linear energy flux ??? u??? p??? dz (primes denote baroclinic quantities), plus contributions from the non-hydrostatic pressure anomaly and the self-advection of kinetic and available potential energy. Using highly resolved observations in Massachusetts Bay, it is shown that due to the presence of nonlinear internal waves periodically propagating in the area, ??? u??? p??? dz accounts for only half of the total flux. The same data show that equipartition of available potential and kinetic energy can be violated, especially when the nonlinear waves begin to interact with the bottom. ?? 2006 Cambridge University Press.

On the nature of kinetic electrostatic electron nonlinear (KEEN) waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dodin, I. Y.; Fisch, N. J.

2014-03-15

An analytical theory is proposed for the kinetic electrostatic electron nonlinear (KEEN) waves originally found in simulations by Afeyan et al. [arXiv:1210.8105]. We suggest that KEEN waves represent saturated states of the negative mass instability (NMI) reported recently by Dodin et al. [Phys. Rev. Lett. 110, 215006 (2013)]. Due to the NMI, trapped electrons form macroparticles that produce field oscillations at harmonics of the bounce frequency. At large enough amplitudes, these harmonics can phase-lock to the main wave and form stable nonlinear dissipationless structures that are nonstationary but otherwise similar to Bernstein-Greene-Kruskal modes. The theory explains why the formation ofmore » KEEN modes is sensitive to the excitation scenario and yields estimates that agree with the numerical results of Afeyan et al. A new type of KEEN wave may be possible at even larger amplitudes of the driving field than those used in simulations so far.« less

Moving boundary problems for a rarefied gas: Spatially one-dimensional case

NASA Astrophysics Data System (ADS)

Tsuji, Tetsuro; Aoki, Kazuo

2013-10-01

Unsteady flows of a rarefied gas in a full space caused by an oscillation of an infinitely wide plate in its normal direction are investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The paper aims at showing properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting. More specifically, the following two problems are considered: (Problem I) the plate starts a forced harmonic oscillation (forced motion); (Problem II) the plate, which is subject to an external restoring force obeying Hooke’s law, is displaced from its equilibrium position and released (free motion). The physical interest in Problem I lies in the propagation of nonlinear acoustic waves in a rarefied gas, whereas that in Problem II in the decay rate of the oscillation of the plate. An accurate numerical method, which is capable of describing singularities caused by the oscillating plate, is developed on the basis of the method of characteristics and is applied to the two problems mentioned above. As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified. Some results are also compared with those based on the existing method.

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

LSENS - GENERAL CHEMICAL KINETICS AND SENSITIVITY ANALYSIS CODE

NASA Technical Reports Server (NTRS)

Bittker, D. A.

1994-01-01

LSENS has been developed for solving complex, homogeneous, gas-phase, chemical kinetics problems. The motivation for the development of this program is the continuing interest in developing detailed chemical reaction mechanisms for complex reactions such as the combustion of fuels and pollutant formation and destruction. A reaction mechanism is the set of all elementary chemical reactions that are required to describe the process of interest. Mathematical descriptions of chemical kinetics problems constitute sets of coupled, nonlinear, first-order ordinary differential equations (ODEs). The number of ODEs can be very large because of the numerous chemical species involved in the reaction mechanism. Further complicating the situation are the many simultaneous reactions needed to describe the chemical kinetics of practical fuels. For example, the mechanism describing the oxidation of the simplest hydrocarbon fuel, methane, involves over 25 species participating in nearly 100 elementary reaction steps. Validating a chemical reaction mechanism requires repetitive solutions of the governing ODEs for a variety of reaction conditions. Analytical solutions to the systems of ODEs describing chemistry are not possible, except for the simplest cases, which are of little or no practical value. Consequently, there is a need for fast and reliable numerical solution techniques for chemical kinetics problems. In addition to solving the ODEs describing chemical kinetics, it is often necessary to know what effects variations in either initial condition values or chemical reaction mechanism parameters have on the solution. Such a need arises in the development of reaction mechanisms from experimental data. The rate coefficients are often not known with great precision and in general, the experimental data are not sufficiently detailed to accurately estimate the rate coefficient parameters. The development of a reaction mechanism is facilitated by a systematic sensitivity analysis which provides the relationships between the predictions of a kinetics model and the input parameters of the problem. LSENS provides for efficient and accurate chemical kinetics computations and includes sensitivity analysis for a variety of problems, including nonisothermal conditions. LSENS replaces the previous NASA general chemical kinetics codes GCKP and GCKP84. LSENS is designed for flexibility, convenience and computational efficiency. A variety of chemical reaction models can be considered. The models include static system, steady one-dimensional inviscid flow, reaction behind an incident shock wave including boundary layer correction, and the perfectly stirred (highly backmixed) reactor. In addition, computations of equilibrium properties can be performed for the following assigned states, enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. For static problems LSENS computes sensitivity coefficients with respect to the initial values of the dependent variables and/or the three rates coefficient parameters of each chemical reaction. To integrate the ODEs describing chemical kinetics problems, LSENS uses the packaged code LSODE, the Livermore Solver for Ordinary Differential Equations, because it has been shown to be the most efficient and accurate code for solving such problems. The sensitivity analysis computations use the decoupled direct method, as implemented by Dunker and modified by Radhakrishnan. This method has shown greater efficiency and stability with equal or better accuracy than other methods of sensitivity analysis. LSENS is written in FORTRAN 77 with the exception of the NAMELIST extensions used for input. While this makes the code fairly machine independent, execution times on IBM PC compatibles would be unacceptable to most users. LSENS has been successfully implemented on a Sun4 running SunOS and a DEC VAX running VMS. With minor modifications, it should also be easily implemented on other platforms with FORTRAN compilers which support NAMELIST input. LSENS required 4Mb of RAM under SunOS 4.1.1 and 3.4Mb of RAM under VMS 5.5.1. The standard distribution medium for LSENS is a .25 inch streaming magnetic tape cartridge (QIC-24) in UNIX tar format. It is also available on a 1600 BPI 9-track magnetic tape or a TK50 tape cartridge in DEC VAX BACKUP format. Alternate distribution media and formats are available upon request. LSENS was developed in 1992.

The relative importance of fluid and kinetic frequency shifts of an electron plasma wave

NASA Astrophysics Data System (ADS)

Winjum, B. J.; Fahlen, J.; Mori, W. B.

2007-10-01

The total nonlinear frequency shift of a plasma wave including both fluid and kinetic effects is estimated when the phase velocity of the wave is much less than the speed of light. Using a waterbag or fluid model, the nonlinear frequency shift due to harmonic generation is calculated for an arbitrary shift in the wavenumber. In the limit where the wavenumber does not shift, the result is in agreement with previously published work [R. L. Dewar and J. Lindl, Phys. Fluids 15, 820 (1972); T. P. Coffey, Phys. Fluids 14, 1402 (1971)]. This shift is compared to the kinetic shift of Morales and O'Neil [G. J. Morales and T. M. O'Neil, Phys. Rev. Lett. 28, 417 (1972)] for wave amplitudes and values of kλD of interest to Raman backscatter of a laser driver in inertial confinement fusion.

High-informative version of nonlinear transformation of Langmuir waves to electromagnetic waves

NASA Astrophysics Data System (ADS)

Erofeev, Vasily I.; Erofeev

2014-04-01

The concept of informativeness of nonlinear plasma physical scenario is discussed. Basic principles for heightening the informativeness of plasma kinetic models are explained. Former high-informative correlation analysis of plasma kinetics (Erofeev, V. 2011 High-Informative Plasma Theory, Saarbrücken: LAP) is generalized for studies of weakly turbulent plasmas that contain fields of solenoidal plasma waves apart from former potential ones. Respective machinery of plasma kinetic modeling is applied to an analysis of fusion of Langmuir waves with transformation to electromagnetic waves. It is shown that the customary version of this phenomenon (Terashima, Y. and Yajima, N. 1963 Prog. Theor. Phys. 30, 443; Akhiezer, I. A., Danelia, I. A. and Tsintsadze, N. L. 1964 Sov. Phys. JETP 19, 208; Al'tshul', L. M. and Karpman, V. I. 1965 Sov. Phys. JETP 20, 1043) substantially distorts the picture of merging of Langmuir waves with long wavelengths (λ >~ c/ωpe ).

Nonlinear machine learning and design of reconfigurable digital colloids.

PubMed

Long, Andrew W; Phillips, Carolyn L; Jankowksi, Eric; Ferguson, Andrew L

2016-09-14

Digital colloids, a cluster of freely rotating "halo" particles tethered to the surface of a central particle, were recently proposed as ultra-high density memory elements for information storage. Rational design of these digital colloids for memory storage applications requires a quantitative understanding of the thermodynamic and kinetic stability of the configurational states within which information is stored. We apply nonlinear machine learning to Brownian dynamics simulations of these digital colloids to extract the low-dimensional intrinsic manifold governing digital colloid morphology, thermodynamics, and kinetics. By modulating the relative size ratio between halo particles and central particles, we investigate the size-dependent configurational stability and transition kinetics for the 2-state tetrahedral (N = 4) and 30-state octahedral (N = 6) digital colloids. We demonstrate the use of this framework to guide the rational design of a memory storage element to hold a block of text that trades off the competing design criteria of memory addressability and volatility.

Recent advances in reduction methods for nonlinear problems. [in structural mechanics

NASA Technical Reports Server (NTRS)

Noor, A. K.

1981-01-01

Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

Multivariate moment closure techniques for stochastic kinetic models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

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.

Classical Michaelis-Menten and system theory approach to modeling metabolite formation kinetics.

PubMed

Popović, Jovan

2004-01-01

When single doses of drug are administered and kinetics are linear, techniques, which are based on the compartment approach and the linear system theory approach, in modeling the formation of the metabolite from the parent drug are proposed. Unlike the purpose-specific compartment approach, the methodical, conceptual and computational uniformity in modeling various linear biomedical systems is the dominant characteristic of the linear system approach technology. Saturation of the metabolic reaction results in nonlinear kinetics according to the Michaelis-Menten equation. The two compartment open model with Michaelis-Menten elimination kinetics is theorethicaly basic when single doses of drug are administered. To simulate data or to fit real data using this model, one must resort to numerical integration. A biomathematical model for multiple dosage regimen calculations of nonlinear metabolic systems in steady-state and a working example with phenytoin are presented. High correlation between phenytoin steady-state serum levels calculated from individual Km and Vmax values in the 15 adult epileptic outpatients and the observed levels at the third adjustment of phenytoin daily dose (r=0.961, p<0.01) were found.

Study the oxidation kinetics of uranium using XRD and Rietveld method

NASA Astrophysics Data System (ADS)

Zhang, Yanzhi; Guan, Weijun; Wang, Qinguo; Wang, Xiaolin; Lai, Xinchun; Shuai, Maobing

2010-03-01

The surface oxidation of uranium metal has been studied by X-ray diffraction (XRD) and Rietveld method in the range of 50~300°C in air. The oxidation processes are analyzed by XRD to determine the extent of surface oxidation and the oxide structure. The dynamics expression for the formation of UO2 was derived. At the beginning, the dynamic expression was nonlinear, but switched to linear subsequently for uranium in air and humid oxygen. That is, the growth kinetics of UO2 can be divided into two stages: nonlinear portion and linear portion. Using the kinetic data of linear portion, the activation energy of reaction between uranium and air was calculated about 46.0 kJ/mol. However the content of oxide as a function of time was linear in humid helium ambience. Contrast the dynamics results, it prove that the absence of oxygen would accelerate the corrosion rate of uranium in the humid gas. We can find that the XRD and Rietveld method are a useful convenient method to estimate the kinetics and thermodynamics of solid-gas reaction.

Effects of compressional magnetic perturbation on kinetic Alfven waves

NASA Astrophysics Data System (ADS)

Dong, Ge; Bhattacharjee, Amitava; Lin, Zhihong

2016-10-01

Kinetic Alfven waves play a very important role in the dynamics of fusion as well as space and astrophysical plasmas. The compressional magnetic perturbation δB|| can play important role in kinetic Alfven waves (KAW) and various instabilities at large plasma β. It could affect the nonlinear behavior of these modes significantly even at small β. In this study, we have implemented δB|| in gyrokinetic toroidal code (GTC). The perpendicular Ampere's law is solved as a force balance equation. Double gyroaveraging is incorporated in the code to treat the finite Larmor radius effects related to δB|| terms. KAW is studied in slab geometry as a benchmark case. A scan in β for the KAW dispersion relation shows that as β approaches 1 (>0.3), the effects of δB|| becomes important. Connections are made with other existing studies of KAWs in the fusion and space plasma literature. This new capability of including δB|| in GTC could be applied to nonlinear simulations of modes such as kinetic ballooning and tearing modes. This research is supported by DOE Contract No. DE-AC02-09CH11466.

Poster — Thur Eve — 44: Linearization of Compartmental Models for More Robust Estimates of Regional Hemodynamic, Metabolic and Functional Parameters using DCE-CT/PET Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blais, AR; Dekaban, M; Lee, T-Y

2014-08-15

Quantitative analysis of dynamic positron emission tomography (PET) data usually involves minimizing a cost function with nonlinear regression, wherein the choice of starting parameter values and the presence of local minima affect the bias and variability of the estimated kinetic parameters. These nonlinear methods can also require lengthy computation time, making them unsuitable for use in clinical settings. Kinetic modeling of PET aims to estimate the rate parameter k{sub 3}, which is the binding affinity of the tracer to a biological process of interest and is highly susceptible to noise inherent in PET image acquisition. We have developed linearized kineticmore » models for kinetic analysis of dynamic contrast enhanced computed tomography (DCE-CT)/PET imaging, including a 2-compartment model for DCE-CT and a 3-compartment model for PET. Use of kinetic parameters estimated from DCE-CT can stabilize the kinetic analysis of dynamic PET data, allowing for more robust estimation of k{sub 3}. Furthermore, these linearized models are solved with a non-negative least squares algorithm and together they provide other advantages including: 1) only one possible solution and they do not require a choice of starting parameter values, 2) parameter estimates are comparable in accuracy to those from nonlinear models, 3) significantly reduced computational time. Our simulated data show that when blood volume and permeability are estimated with DCE-CT, the bias of k{sub 3} estimation with our linearized model is 1.97 ± 38.5% for 1,000 runs with a signal-to-noise ratio of 10. In summary, we have developed a computationally efficient technique for accurate estimation of k{sub 3} from noisy dynamic PET data.« less

New Nonlinear Multigrid Analysis

NASA Technical Reports Server (NTRS)

Xie, Dexuan

1996-01-01

The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

Estimating the kinetic parameters of activated sludge storage using weighted non-linear least-squares and accelerating genetic algorithm.

PubMed

Fang, Fang; Ni, Bing-Jie; Yu, Han-Qing

2009-06-01

In this study, weighted non-linear least-squares analysis and accelerating genetic algorithm are integrated to estimate the kinetic parameters of substrate consumption and storage product formation of activated sludge. A storage product formation equation is developed and used to construct the objective function for the determination of its production kinetics. The weighted least-squares analysis is employed to calculate the differences in the storage product concentration between the model predictions and the experimental data as the sum of squared weighted errors. The kinetic parameters for the substrate consumption and the storage product formation are estimated to be the maximum heterotrophic growth rate of 0.121/h, the yield coefficient of 0.44 mg CODX/mg CODS (COD, chemical oxygen demand) and the substrate half saturation constant of 16.9 mg/L, respectively, by minimizing the objective function using a real-coding-based accelerating genetic algorithm. Also, the fraction of substrate electrons diverted to the storage product formation is estimated to be 0.43 mg CODSTO/mg CODS. The validity of our approach is confirmed by the results of independent tests and the kinetic parameter values reported in literature, suggesting that this approach could be useful to evaluate the product formation kinetics of mixed cultures like activated sludge. More importantly, as this integrated approach could estimate the kinetic parameters rapidly and accurately, it could be applied to other biological processes.

Validation of Bayesian analysis of compartmental kinetic models in medical imaging.

PubMed

Sitek, Arkadiusz; Li, Quanzheng; El Fakhri, Georges; Alpert, Nathaniel M

2016-10-01

Kinetic compartmental analysis is frequently used to compute physiologically relevant quantitative values from time series of images. In this paper, a new approach based on Bayesian analysis to obtain information about these parameters is presented and validated. The closed-form of the posterior distribution of kinetic parameters is derived with a hierarchical prior to model the standard deviation of normally distributed noise. Markov chain Monte Carlo methods are used for numerical estimation of the posterior distribution. Computer simulations of the kinetics of F18-fluorodeoxyglucose (FDG) are used to demonstrate drawing statistical inferences about kinetic parameters and to validate the theory and implementation. Additionally, point estimates of kinetic parameters and covariance of those estimates are determined using the classical non-linear least squares approach. Posteriors obtained using methods proposed in this work are accurate as no significant deviation from the expected shape of the posterior was found (one-sided P>0.08). It is demonstrated that the results obtained by the standard non-linear least-square methods fail to provide accurate estimation of uncertainty for the same data set (P<0.0001). The results of this work validate new methods for a computer simulations of FDG kinetics. Results show that in situations where the classical approach fails in accurate estimation of uncertainty, Bayesian estimation provides an accurate information about the uncertainties in the parameters. Although a particular example of FDG kinetics was used in the paper, the methods can be extended for different pharmaceuticals and imaging modalities. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

One-dimensional kinetic description of nonlinear traveling-pulse and traveling-wave disturbances in long coasting charged particle beams

DOE PAGES

Davidson, Ronald C.; Qin, Hong

2015-09-21

This study makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r w. The average axial electric field is expressed as < E z >=-(∂/∂z)=-e bg 0∂λ b/∂z-e bg 2r 2 w∂ 3λ b/∂z 3, where g 0 and g 2 are constant geometric factors, λ b(z,t)=∫dp zF b(z,p z,t) is the line density of beam particles, and F b(z,p z,t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for amore » wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where F b=const in a bounded region of p z-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field < E z >.« less

One-dimensional kinetic description of nonlinear traveling-pulse and traveling-wave disturbances in long coasting charged particle beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidson, Ronald C.; Qin, Hong

This study makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius r w. The average axial electric field is expressed as < E z >=-(∂/∂z)=-e bg 0∂λ b/∂z-e bg 2r 2 w∂ 3λ b/∂z 3, where g 0 and g 2 are constant geometric factors, λ b(z,t)=∫dp zF b(z,p z,t) is the line density of beam particles, and F b(z,p z,t) satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (soliton) solutions with time-stationary waveform are examined for amore » wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (i) the nonlinear waterbag distribution, where F b=const in a bounded region of p z-space; and (ii) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field < E z >.« less

A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints

NASA Technical Reports Server (NTRS)

Hanson, R. J.; Krogh, Fred T.

1992-01-01

A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.

Variational algorithms for nonlinear smoothing applications

NASA Technical Reports Server (NTRS)

Bach, R. E., Jr.

1977-01-01

A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.

The role of zonal flows in reactive fluid closures

NASA Astrophysics Data System (ADS)

Jan, WEILAND

2018-07-01

We will give an overview of results obtained by our reactive fluid model. It is characterised as a fluid model where all moments with sources in the experiment are kept. Furthermore, full account is taken for the highest moments appearing in unexpanded denominators also including full toroidicity. It has been demonstrated that the strength of zonal flows is dramatically larger in reactive fluid closures than in those which involve dissipation. This gives a direct connection between the fluid closure and the level of excitation of turbulence. This is because zonal flows are needed to absorb the inverse cascade in quasi 2D turbulence. This also explains the similarity in structure of the transport coefficients in our model with a reactive closure in the energy equation and models which have a reactive closure because of zero ion temperature such as the Hasegawa–Wakatani model. Our exact reactive closure unifies several well-known features of tokamak experiments such as the L–H transition, internal transport barriers and the nonlinear Dimits upshift of the critical gradient for onset of transport. It also gives transport of the same level as that in nonlinear gyrokinetic codes. Since these include the kinetic resonance this confirms the validity of the thermodynamic properties of our model. Furthermore, we can show that while a strongly nonlinear model is needed in kinetic theory a quasilinear model is sufficient in the fluid description. Thus our quasilinear fluid model will be adequate for treating all relevant problems in bulk transport. This is finally confirmed by the reproduction by the model of the experimental power scaling of the confinement time τ E ∼ P ‑2/3. This confirms the validity of our reactive fluid model. This also gives credibility to our ITER simulations including the H-mode barrier. A new result is here, that alpha heating strongly reduces the slope of the H-mode barrier. This should significantly reduce the effects of ELM’s.

Turbulent Heating and Fluctuation Characteristics in Alfvenic Turbulence

NASA Astrophysics Data System (ADS)

Dorland, William

2005-10-01

Alfve'n waves are ubiquitous in natural and laboratory plasmas. In this talk, the main focus is on astrophysical plasmas that are turbulent, magnetized, hot and diffuse. The dynamically important characteristics of these plasmas are often well- described by magnetohydrodynamics [see e.g., Ref. 1]. However, much of what we actually observe is critically affected by how much of the turbulent energy is absorbed by (highly radiative) electrons [2], the amplitude of density fluctuations [3], and the spectral indices of turbulent, Alfve'nic cascades. These questions each have essentially kinetic aspects. In this talk, we present detailed simulations and analyses of of the cascade of shear Alfve'n waves, to and through scales comparable to the ion Larmor radius in the direction perpendicular to the magnetic field. We demonstrate analytically and numerically that the nonlinear gyrokinetic equations, originally developed for fusion applications, are perfectly suited to these astrophysical problems. We present extensive linear and nonlinear gyrokinetic simulation results from the GS2 code. We demonstrate accurate resolution of the damping of kinetic Alfve'n waves in plasmas with beta small, large and comparable to unity, for a wide range of electron-to-ion temperature ratios, in linear and nonlinear contexts. We have used the GS2 code to calculate the turbulent energy absorption, density fluctuation characteristics, and spectral indices for plasmas with parameters taken from hot accretion flows and from the interstellar plasma. These results will be compared with theoretical predictions [2] and to observations. Co-authors: S. C. Cowley (UCLA), G. W. Hammett (PPPL), E. Quataert and G. Howes (UC-Berkeley), and A. Scheckochihin (Cambridge) 1. S. Balbus and J. Hawley, Rev Mod Phys, Vol. 70, p. 1. 2. E. Quataert and A. Gruzinov, Ap J, Vol. 520, p. 248; E. Quataert, Ap J, Vol. 500, p. 978.3. Y. Lithwick and P. Goldreich, Ap J, Vol. 562, p. 279.4. P. Goldreich and Sridhar, Ap J, Vol. 438, p. 763; P. Goldreich and Sridhar, Ap J, Vol. 485, p. 680.

Extended MHD modeling of nonlinear instabilities in fusion and space plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Germaschewski, Kai

A number of different sub-projects where pursued within this DOE early career project. The primary focus was on using fully nonlinear, curvilinear, extended MHD simulations of instabilities with applications to fusion and space plasmas. In particular, we performed comprehensive studies of the dynamics of the double tearing mode in different regimes and confi gurations, using Cartesian and cyclindrical geometry and investigating both linear and non-linear dynamics. In addition to traditional extended MHD involving Hall term and electron pressure gradient, we also employed a new multi-fluid moment model, which shows great promise to incorporate kinetic effects, in particular off-diagonal elements ofmore » the pressure tensor, in a fluid model, which is naturally computationally much cheaper than fully kinetic particle or Vlasov simulations. We used our Vlasov code for detailed studies of how weak collisions effect plasma echos. In addition, we have played an important supporting role working with the PPPL theory group around Will Fox and Amitava Bhattacharjee on providing simulation support for HED plasma experiments performed at high-powered laser facilities like OMEGA-EP in Rochester, NY. This project has support a great number of computational advances in our fluid and kinetic plasma models, and has been crucial to winning multiple INCITE computer time awards that supported our computational modeling.« less

Recent Advances in the Development and Application of Power Plate Transducers in Dense Gas Extraction and Aerosol Agglomeration Processes

NASA Astrophysics Data System (ADS)

Riera, E.; Cardoni, A.; Gallego-Juárez, J. A.; Acosta, V. M.; Blanco, A.; Rodríguez, G.; Blasco, M.; Herranz, L. E.

Power ultrasound (PU) is an emerging, innovative, energy saving and environmental friendly technology that is generating a great interest in sectors such as food and pharmaceutical industries, green chemistry, environmental pollution, and other processes, where sustainable and energy efficient methods are required to improve and/or produce specific effects. Two typical effects of PU are the enhancement of mass transfer in gases and liquids, and the induction of particle agglomeration in aerosols. These effects are activated by a variety of mechanisms associated to the nonlinear propagation of high amplitude ultrasonic waves such as diffusion, agitation, entrainment, turbulence, etc. During the last years a great effort has been jointly made by the Spanish National Research Council (CSIC) and the company Pusonics towards introducing novel processes into the market based on airborne ultrasonic plate transducers. This technology was specifically developed for the treatment of gas and multiphasic media characterized by low specific acoustic impedance and high acoustic absorption. Different strategies have been developed to mitigate the effects of the nonlinear dynamic behavior of such ultrasonic piezoelectric transducers in order to enhance and stabilize their response at operational power conditions. This work deals with the latter advances in the mitigation of nonlinear problems found in power transducers; besides it describes two applications assisted by ultrasound developed at semi-industrial and laboratory scales and consisting in extraction via dense gases and particle agglomeration. Dense Gas Extraction (DGE) assisted by PU is a new process with a potential to enhance the extraction kinetics with supercritical CO2. Acoustic agglomeration of fine aerosol particles has a great potential for the treatment of air pollution problems generated by particulate materials. Experimental and numerical results in both processes will be shown and discussed.

Hydrodynamics beyond Navier-Stokes: exact solution to the lattice Boltzmann hierarchy.

PubMed

Ansumali, S; Karlin, I V; Arcidiacono, S; Abbas, A; Prasianakis, N I

2007-03-23

The exact solution to the hierarchy of nonlinear lattice Boltzmann (LB) kinetic equations in the stationary planar Couette flow is found at nonvanishing Knudsen numbers. A new method of solving LB kinetic equations which combines the method of moments with boundary conditions for populations enables us to derive closed-form solutions for all higher-order moments. A convergence of results suggests that the LB hierarchy with larger velocity sets is the novel way to approximate kinetic theory.

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

Science and Technology Review April/May 2011

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nikolic, R J

2011-03-03

At Lawrence Livermore National Laboratory, the focus is on science and technology research to ensure the nation's security. That expertise is also applied to solve other important national problems in energy, bioscience, and the environment. Science & Technology Review is published eight time a year to communicate, to a broad audience, the Laboratory's scientific and technological accomplishments in fulfilling its primary missions. The publication's goal is to help readers understand these accomplishments and appreciate their value to the individual citizen, the nation, and the world. In this issue for April/May 2011, the features are 'Dealing with the Nonlinear Battlefield' andmore » 'From Video to Knowledge.' Research highlights are 'Kinetic Models Predict Biofuel Efficiency,' Going Deep with MEGa-Rays' and 'Energy on Demand.'« less

Spatially Localized Particle Energization by Landau Damping in Current Sheets

NASA Astrophysics Data System (ADS)

Howes, G. G.; Klein, K. G.; McCubbin, A. J.

2017-12-01

Understanding the mechanisms of particle energization through the removal of energy from turbulent fluctuations in heliospheric plasmas is a grand challenge problem in heliophysics. Under the weakly collisional conditions typical of heliospheric plasma, kinetic mechanisms must be responsible for this energization, but the nature of those mechanisms remains elusive. In recent years, the spatial localization of plasma heating near current sheets in the solar wind and numerical simulations has gained much attention. Here we show, using the innovative and new field-particle correlation technique, that the spatially localized particle energization occurring in a nonlinear gyrokinetic simulation has the velocity space signature of Landau damping, suggesting that this well-known collisionless damping mechanism indeed actively leads to spatially localized heating in the vicinity of current sheets.

A study of the extended-range forecasting problem blocking

NASA Technical Reports Server (NTRS)

Chen, T. C.; Marshall, H. G.; Shukla, J.

1981-01-01

Wavenumber frequency spectral analysis of a 90 day winter (Jan. 15 - April 14) wind field simulated by a climate experiment of the GLAS atmospheric circulation model is made using the space time Fourier analysis which is modified with Tukey's numerical spectral analysis. Computations are also made to examine how the model wave disturbances in the wavenumber frequency domain are maintained by nonlinear interactions. Results are compared with observation. It is found that equatorial easterlies do not show up in this climate experiment at 200 mb. The zonal kinetic energy and momentum transport of stationary waves are too small in the model's Northern Hemisphere. The wavenumber and frequency spectra of the model are generally in good agreement with observation. However, some distinct features of the model's spectra are revealed. The wavenumber spectra of kinetic energy show that the eastward moving waves of low wavenumbers have stronger zonal motion while the eastward moving waves of intermediate wavenumbers have larger meridional motion compared with observation. Furthermore, the eastward moving waves show a band of large spectral value in the medium frequency regime.

Kinetic modelling of passive transport and active efflux of a fluoroquinolone across Caco-2 cells using a compartmental approach in NONMEM.

PubMed

González-Alvarez, I; Fernández-Teruel, C; Garrigues, T M; Casabo, V G; Ruiz-García, A; Bermejo, M

2005-12-01

The purpose was to develop a general mathematical model for estimating passive permeability and efflux transport parameters from in vitro cell culture experiments. The procedure is applicable for linear and non-linear transport of drug with time, <10 or >10% of drug transport, negligible or relevant back flow, and would allow the adequate correction in the case of relevant mass balance problems. A compartmental kinetic approach was used and the transport barriers were described quantitatively in terms of apical and basolateral clearances. The method can be applied when sink conditions are not achieved and it allows the evaluation of the location of the transporter and its binding site. In this work it was possible to demonstrate, from a functional point of view, the higher efflux capacity of the TC7 clone and to identify the apical membrane as the main resistance for the xenobiotic transport. This methodology can be extremely useful as a complementary tool for molecular biology approaches in order to establish meaningful hypotheses about transport mechanisms.

Experimental quantification of nonlinear time scales in inertial wave rotating turbulence

NASA Astrophysics Data System (ADS)

Yarom, Ehud; Salhov, Alon; Sharon, Eran

2017-12-01

We study nonlinearities of inertial waves in rotating turbulence. At small Rossby numbers the kinetic energy in the system is contained in helical inertial waves with time dependence amplitudes. In this regime the amplitude variations time scales are slow compared to wave periods, and the spectrum is concentrated along the dispersion relation of the waves. A nonlinear time scale was extracted from the width of the spectrum, which reflects the intensity of nonlinear wave interactions. This nonlinear time scale is found to be proportional to (U.k ) -1, where k is the wave vector and U is the root-mean-square horizontal velocity, which is dominated by large scales. This correlation, which indicates the existence of turbulence in which inertial waves undergo weak nonlinear interactions, persists only for small Rossby numbers.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems

NASA Astrophysics Data System (ADS)

Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao

Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.

Eddy-driven low-frequency variability: physics and observability through altimetry

NASA Astrophysics Data System (ADS)

Penduff, Thierry; Sérazin, Guillaume; Arbic, Brian; Mueller, Malte; Richman, James G.; Shriver, Jay F.; Morten, Andrew J.; Scott, Robert B.

2015-04-01

Model studies have revealed the propensity of the eddying ocean circulation to generate strong low-frequency variability (LFV) intrinsically, i.e. without low-frequency atmospheric variability. In the present study, gridded satellite altimeter products, idealized quasi-geostrophic (QG) turbulent simulations, and realistic high-resolution global ocean simulations are used to study the spontaneous tendency of mesoscale (relatively high frequency and high wavenumber) kinetic energy to non-linearly cascade towards larger time and space scales. The QG model reveals that large-scale variability, arising from the well-known spatial inverse cascade, is associated with low frequencies. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing (by large-scale shear) and friction playing secondary roles. In realistic simulations, nonlinearities also generally drive kinetic energy to low frequencies and low wavenumbers. In some, but not all, regions of the gridded altimeter product, surface kinetic energy is also found to cascade toward low frequencies. Exercises conducted with the realistic model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies seen in some regions between the direction of frequency cascade in models versus gridded altimeter maps. Finally, the range of frequencies that are highly energized and engaged these cascades appears much greater than the range of highly energized and engaged wavenumbers. Global eddying simulations, performed in the context of the CHAOCEAN project in collaboration with the CAREER project, provide estimates of the range of timescales that these oceanic nonlinearities are likely to feed without external variability.

Nonlinear vortex dynamics in open nonequilibrium systems with bulk mass loss and a generation mechanism for tornadoes and typhoons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pashitskii, E. A., E-mail: pashitsk@iop.kiev.u

2010-06-15

Based on a general model of nonlinear vortex dynamics in open thermodynamically nonequilibrium systems with bulk or surface mass losses, an analysis is presented of the mechanism of generation of violent atmospheric vortices (tornadoes, typhoons, cyclones) associated with the formation of deep cloud systems by intense condensation of water vapor from moist air cooled below the dew point. Simple particular solutions to the Navier-Stokes equations are found that describe both axisymmetric and nonaxisymmetric incompressible vortex motions involving radial and vertical flows with viscous dissipation vanishing identically everywhere except for a thin shear layer at the boundary of the condensation region.more » It is shown that the nonlinear convective and local Coriolis forces generated by radial inflow in the presence of a background vorticity due to a global Coriolis force (the Earth's rotation) accelerate the solid-body rotation in the vortex core either exponentially or in a nonlinear regime of finite-time blow-up. Due to updrafts, such a vortex is characterized by a strong helicity. This mechanism explains a number of observed properties and characteristics of the structure and evolution of tornadoes and typhoons. Upper estimates are found for the kinetic energies of violent atmospheric vortices. It is shown that increase in rotational kinetic energy of atmospheric vortices with constant vortex-core radii is consistent with energy and momentum conservation, because radial inflow continually supplies the required amount of rotational kinetic energy drawn from the ambient atmosphere to an open system.« less

Finite elements of nonlinear continua.

NASA Technical Reports Server (NTRS)

Oden, J. T.

1972-01-01

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

An efficient variable projection formulation for separable nonlinear least squares problems.

PubMed

Gan, Min; Li, Han-Xiong

2014-05-01

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

A Genetic Algorithm Approach to Nonlinear Least Squares Estimation

ERIC Educational Resources Information Center

Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.

2004-01-01

A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…

Structure and Dynamics of Replication-Mutation Systems

NASA Astrophysics Data System (ADS)

Schuster, Peter

1987-03-01

The kinetic equations of polynucleotide replication can be brought into fairly simple form provided certain environmental conditions are fulfilled. Two flow reactors, the continuously stirred tank reactor (CSTR) and a special dialysis reactor are particularly suitable for the analysis of replication kinetics. An experimental setup to study the chemical reaction network of RNA synthesis was derived from the bacteriophage Qβ. It consists of a virus specific RNA polymerase, Qβ replicase, the activated ribonucleosides GTP, ATP, CTP and UTP as well as a template suitable for replication. The ordinary differential equations for replication and mutation under the conditions of the flow reactors were analysed by the qualitative methods of bifurcation theory as well as by numerical integration. The various kinetic equations are classified according to their dynamical properties: we distinguish "quasilinear systems" which have uniquely stable point attractors and "nonlinear systems" with inherent nonlinearities which lead to multiple steady states, Hopf bifuractions, Feigenbaum-like sequences and chaotic dynamics for certain parameter ranges. Some examples which are relevant in molecular evolution and population genetics are discussed in detail.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

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

Nonlinear transport for a dilute gas in steady Couette flow

NASA Astrophysics Data System (ADS)

Garzó, V.; López de Haro, M.

1997-03-01

Transport properties of a dilute gas subjected to arbitrarily large velocity and temperature gradients (steady planar Couette flow) are determined. The results are obtained from the so-called ellipsoidal statistical (ES) kinetic model, which is an extension of the well-known BGK kinetic model to account for the correct Prandtl number. At a hydrodynamic level, the solution is characterized by constant pressure, and linear velocity and parabolic temperature profiles with respect to a scaled variable. The transport coefficients are explicitly evaluated as nonlinear functions of the shear rate. A comparison with previous results derived from a perturbative solution of the Boltzmann equation as well as from other kinetic models is carried out. Such a comparison shows that the ES predictions are in better agreement with the Boltzmann results than those of the other approximations. In addition, the velocity distribution function is also computed. Although the shear rates required for observing non-Newtonian effects are experimentally unrealizable, the conclusions obtained here may be relevant for analyzing computer results.

Nonlinear behavior during NO2 hydrogenation on a nanosized Pt-Rh catalyst sample

NASA Astrophysics Data System (ADS)

Barroo, Cédric; De Decker, Yannick; Jacobs, Luc; de Bocarmé, Thierry Visart

2017-08-01

Automotive pollution control crucially relies on the reactivity of metal alloy catalysts. Understanding how the chemistry of an alloy compares with that of pure metals forms a decisive step towards the rational development of applied formulations of such catalysts. In this context, we studied the hydrogenation of NO2 on Pt-Rh catalysts at the nanoscale with field emission microscopy (FEM). Previous studies have shown the presence of complex reaction kinetics at the surface of Pt for this reaction, including periodic oscillations at 390 K. As we briefly show here, similar kinetics can also be observed on Rh at higher temperatures. The alloy samples (Pt-17.4 at.%Rh) show signs of important reactivity and associated nonlinear dynamics in an intermediate temperature range. In particular, at 425 K isothermal oscillations are observed on this specific alloy catalyst. The role of the alloy composition on the window of reactivity is explained with a simple theoretical model for the kinetics of the reaction.

Nonlinear Constitutive Relations for High Temperature Applications

NASA Technical Reports Server (NTRS)

1983-01-01

The topics of discussion addressed were material behavior, design analysis, deformation kinetics, metallurgical characterization, mechanical subelement models, stress analysis, fracture mechanics, viscoplasticity, and thermal loading.

Frustration of resonant preheating by exotic kinetic terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rahmati, Shohreh; Seahra, Sanjeev S., E-mail: srahmati@unb.ca, E-mail: sseahra@unb.ca

2014-10-01

We study the effects of exotic kinetic terms on parametric resonance during the preheating epoch of the early universe. Specifically, we consider modifications to the action of ordinary matter fields motivated by generalized uncertainty principles, polymer quantization, as well as Dirac-Born-Infeld and k-essence models. To leading order in an ''exotic physics'' scale, the equations of motion derived from each of these models have the same algebraic form involving a nonlinear self-interaction in the matter sector. Neglecting spatial dependence, we show that the nonlinearity effectively shuts down the parametric resonance after a finite time period. We find numeric evidence that themore » frustration of parametric resonance persists to spatially inhomogenous matter in (1+1)-dimensions.« less

Electromagnetic nonlinear gyrokinetics with polarization drift

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duthoit, F.-X.; Hahm, T. S., E-mail: tshahm@snu.ac.kr; Wang, Lu

2014-08-15

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen,more » Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.« less

Electromagnetic nonlinear gyrokinetics with polarization drift

NASA Astrophysics Data System (ADS)

Duthoit, F.-X.; Hahm, T. S.; Wang, Lu

2014-08-01

A set of new nonlinear electromagnetic gyrokinetic Vlasov equation with polarization drift and gyrokinetic Maxwell equations is systematically derived by using the Lie-transform perturbation method in toroidal geometry. For the first time, we recover the drift-kinetic expression for parallel acceleration [R. M. Kulsrud, in Basic Plasma Physics, edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam, 1983)] from the nonlinear gyrokinetic equations, thereby bridging a gap between the two formulations. This formalism should be useful in addressing nonlinear ion Compton scattering of intermediate-mode-number toroidal Alfvén eigenmodes for which the polarization current nonlinearity [T. S. Hahm and L. Chen, Phys. Rev. Lett. 74, 266 (1995)] and the usual finite Larmor radius effects should compete.

An approximation theory for the identification of nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

Spline approximations for nonlinear hereditary control systems

NASA Technical Reports Server (NTRS)

Daniel, P. L.

1982-01-01

A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.

Solving intuitionistic fuzzy multi-objective nonlinear programming problem

NASA Astrophysics Data System (ADS)

Anuradha, D.; Sobana, V. E.

2017-11-01

This paper presents intuitionistic fuzzy multi-objective nonlinear programming problem (IFMONLPP). All the coefficients of the multi-objective nonlinear programming problem (MONLPP) and the constraints are taken to be intuitionistic fuzzy numbers (IFN). The IFMONLPP has been transformed into crisp one and solved by using Kuhn-Tucker condition. Numerical example is provided to illustrate the approach.

Inflation Rates, Car Devaluation, and Chemical Kinetics.

ERIC Educational Resources Information Center

Pogliani, Lionello; Berberan-Santos, Mario N.

1996-01-01

Describes the inflation rate problem and offers an interesting analogy with chemical kinetics. Presents and solves the car devaluation problem as a normal chemical kinetic problem where the order of the rate law and the value of the rate constant are derived. (JRH)

New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

NASA Astrophysics Data System (ADS)

Rahman, Md. Saifur; Lee, Yiu-Yin

2017-10-01

In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

NASA Technical Reports Server (NTRS)

Cerro, J. A.; Scotti, S. J.

1991-01-01

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

NASA Technical Reports Server (NTRS)

Winget, J. M.; Hughes, T. J. R.

1985-01-01

The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

NASA Astrophysics Data System (ADS)

Li, Guang

2017-01-01

This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

Nonlinear Monte Carlo model of superdiffusive shock acceleration with magnetic field amplification

NASA Astrophysics Data System (ADS)

Bykov, Andrei M.; Ellison, Donald C.; Osipov, Sergei M.

2017-03-01

Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplification (MFA) generated by the anisotropic distribution of accelerated particles. This anisotropy is determined by fast particle transport, making the problem strongly nonlinear and multiscale. Here, we present a nonlinear Monte Carlo model of collisionless shock structure with superdiffusive propagation of high-energy Fermi accelerated particles coupled to particle acceleration and MFA, which affords a consistent description of strong shocks. A distinctive feature of the Monte Carlo technique is that it includes the full angular anisotropy of the particle distribution at all precursor positions. The model reveals that the superdiffusive transport of energetic particles (i.e., Lévy-walk propagation) generates a strong quadruple anisotropy in the precursor particle distribution. The resultant pressure anisotropy of the high-energy particles produces a nonresonant mirror-type instability that amplifies compressible wave modes with wavelengths longer than the gyroradii of the highest-energy protons produced by the shock.

Gyrokinetic turbulence: between idealized estimates and a detailed analysis of nonlinear energy transfers

NASA Astrophysics Data System (ADS)

Teaca, Bogdan; Jenko, Frank; Told, Daniel

2017-04-01

Using large resolution numerical simulations of gyrokinetic (GK) turbulence, spanning an interval ranging from the end of the fluid scales to the electron gyroradius, we study the energy transfers in the perpendicular direction for a proton-electron plasma in a slab equilibrium magnetic geometry. The plasma parameters employed here are relevant to kinetic Alfvén wave turbulence in solar wind conditions. In addition, we use an idealized test representation for the energy transfers between two scales, to aid our understanding of the diagnostics applicable to the nonlinear cascade in an infinite inertial range. For GK turbulence, a detailed analysis of nonlinear energy transfers that account for the separation of energy exchanging scales is performed. Starting from the study of the energy cascade and the scale locality problem, we show that the general nonlocal nature of GK turbulence, captured via locality functions, contains a subset of interactions that are deemed local, are scale invariant (i.e. a sign of asymptotic locality) and possess a locality exponent that can be recovered directly from measurements on the energy cascade. It is the first time that GK turbulence is shown to possess an asymptotic local component, even if the overall locality of interactions is nonlocal. The results presented here and their implications are discussed from the perspective of previous findings reported in the literature and the idea of universality of GK turbulence.

State-Dependent Riccati Equation Regulation of Systems with State and Control Nonlinearities

NASA Technical Reports Server (NTRS)

Beeler, Scott C.; Cox, David E. (Technical Monitor)

2004-01-01

The state-dependent Riccati equations (SDRE) is the basis of a technique for suboptimal feedback control of a nonlinear quadratic regulator (NQR) problem. It is an extension of the Riccati equation used for feedback control of linear problems, with the addition of nonlinearities in the state dynamics of the system resulting in a state-dependent gain matrix as the solution of the equation. In this paper several variations on the SDRE-based method will be considered for the feedback control problem with control nonlinearities. The control nonlinearities may result in complications in the numerical implementation of the control, which the different versions of the SDRE method must try to overcome. The control methods will be applied to three test problems and their resulting performance analyzed.

Comments on the present state and future directions of PDF methods

NASA Technical Reports Server (NTRS)

Obrien, E. E.

1992-01-01

The one point probability density function (PDF) method is examined in light of its use in actual engineering problems. The PDF method, although relatively complicated, appears to be the only format available to handle the nonlinear stochastic difficulties caused by typical reaction kinetics. Turbulence modeling, if it is to play a central role in combustion modeling, has to be integrated with the chemistry in a way which produces accurate numerical solutions to combustion problems. It is questionable whether the development of turbulent models in isolation from the peculiar statistics of reactant concentrations is a fruitful line of development as far as propulsion is concerned. There are three issues for which additional viewgraphs are prepared: the one point pdf method; the amplitude mapping closure; and a hybrid strategy for replacing a full two point pdf treatment of reacting flows by a single point pdf and correlation functions. An appeal is made for the establishment of an adequate data base for compressible flow with reactions for Mach numbers of unity or higher.

TURBULENCE AND PROTON–ELECTRON HEATING IN KINETIC PLASMA

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matthaeus, William H; Parashar, Tulasi N; Wu, P.

2016-08-10

Analysis of particle-in-cell simulations of kinetic plasma turbulence reveals a connection between the strength of cascade, the total heating rate, and the partitioning of dissipated energy into proton heating and electron heating. A von Karman scaling of the cascade rate explains the total heating across several families of simulations. The proton to electron heating ratio increases in proportion to total heating. We argue that the ratio of gyroperiod to nonlinear turnover time at the ion kinetic scales controls the ratio of proton and electron heating. The proposed scaling is consistent with simulations.

A multiscale numerical study into the cascade of kinetic energy leading to severe local storms

NASA Technical Reports Server (NTRS)

Paine, D. A.; Kaplan, M. L.

1977-01-01

The cascade of kinetic energy from macro- through mesoscales is studied on the basis of a nested grid system used to solve a set of nonlinear differential equations. The kinetic energy cascade and the concentration of vorticity through the hydrodynamic spectrum provide a means for predicting the location and intensity of severe weather from large-scale data sets. A mechanism described by the surface pressure tendency equation proves to be important in explaining how initial middle-tropospheric mass-momentum imbalances alter the low-level pressure field.

Nonlinear Cascades of Surface Oceanic Geostrophic Kinetic Energy in the Frequency Domain

DTIC Science & Technology

2012-09-01

kinetic energy in wavenumber k space for surface ocean geostrophic flows have been computed from sat - ellite altimetry data of sea surface height (Scott...5 0.65kN, where kN corresponds to the Nyquist scale. The filter is applied to bq 1 and bq 2 , the Fourier transforms of q1 and q2, at every time step

Electrodiffusion kinetics of ionic transport in a simple membrane channel.

PubMed

Valent, Ivan; Petrovič, Pavol; Neogrády, Pavel; Schreiber, Igor; Marek, Miloš

2013-11-21

We employ numerical techniques for solving time-dependent full Poisson-Nernst-Planck (PNP) equations in 2D to analyze transient behavior of a simple ion channel subject to a sudden electric potential jump across the membrane (voltage clamp). Calculated spatiotemporal profiles of the ionic concentrations and electric potential show that two principal exponential processes can be distinguished in the electrodiffusion kinetics, in agreement with original Planck's predictions. The initial fast process corresponds to the dielectric relaxation, while the steady state is approached in a second slower exponential process attributed to the nonlinear ionic redistribution. Effects of the model parameters such as the channel length, height of the potential step, boundary concentrations, permittivity of the channel interior, and ionic mobilities on electrodiffusion kinetics are studied. Numerical solutions are used to determine spatiotemporal profiles of the electric field, ionic fluxes, and both the conductive and displacement currents. We demonstrate that the displacement current is a significant transient component of the total electric current through the channel. The presented results provide additional information about the classical voltage-clamp problem and offer further physical insights into the mechanism of electrodiffusion. The used numerical approach can be readily extended to multi-ionic models with a more structured domain geometry in 2D or 3D, and it is directly applicable to other systems, such as synthetic nanopores, nanofluidic channels, and nanopipettes.

Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

NASA Astrophysics Data System (ADS)

Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

2017-03-01

Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Wonjung; Kovacic, Gregor; Cai, David

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distributionmore » is in excellent agreement with the simulation of the full wave system in equilibrium.« less

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

NASA Astrophysics Data System (ADS)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

Analysis and gyrokinetic simulation of MHD Alfven wave interactions

NASA Astrophysics Data System (ADS)

Nielson, Kevin Derek

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfven waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfven waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfven waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvenic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfven waves by reproducing laboratory Alfven dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfven eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥rho i << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ rhoi ≳ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfven wave turbulence.

The internal gravity wave spectrum in two high-resolution global ocean models

NASA Astrophysics Data System (ADS)

Arbic, B. K.; Ansong, J. K.; Buijsman, M. C.; Kunze, E. L.; Menemenlis, D.; Müller, M.; Richman, J. G.; Savage, A.; Shriver, J. F.; Wallcraft, A. J.; Zamudio, L.

2016-02-01

We examine the internal gravity wave (IGW) spectrum in two sets of high-resolution global ocean simulations that are forced concurrently by atmospheric fields and the astronomical tidal potential. We analyze global 1/12th and 1/25th degree HYCOM simulations, and global 1/12th, 1/24th, and 1/48th degree simulations of the MITgcm. We are motivated by the central role that IGWs play in ocean mixing, by operational considerations of the US Navy, which runs HYCOM as an ocean forecast model, and by the impact of the IGW continuum on the sea surface height (SSH) measurements that will be taken by the planned NASA/CNES SWOT wide-swath altimeter mission. We (1) compute the IGW horizontal wavenumber-frequency spectrum of kinetic energy, and interpret the results with linear dispersion relations computed from the IGW Sturm-Liouville problem, (2) compute and similarly interpret nonlinear spectral kinetic energy transfers in the IGW band, (3) compute and similarly interpret IGW contributions to SSH variance, (4) perform comparisons of modeled IGW kinetic energy frequency spectra with moored current meter observations, and (5) perform comparisons of modeled IGW kinetic energy vertical wavenumber-frequency spectra with moored observations. This presentation builds upon our work in Muller et al. (2015, GRL), who performed tasks (1), (2), and (4) in 1/12th and 1/25th degree HYCOM simulations, for one region of the North Pacific. New for this presentation are tasks (3) and (5), the inclusion of MITgcm solutions, and the analysis of additional ocean regions.

Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

NASA Astrophysics Data System (ADS)

Zhang, Yue; Zhu, Lianhua; Wang, Ruijie; Guo, Zhaoli

2018-05-01

Recently a discrete unified gas kinetic scheme (DUGKS) in a finite-volume formulation based on the Boltzmann model equation has been developed for gas flows in all flow regimes. The original DUGKS is designed for flows of single-species gases. In this work, we extend the DUGKS to flows of binary gas mixtures of Maxwell molecules based on the Andries-Aoki-Perthame kinetic model [P. Andries et al., J. Stat. Phys. 106, 993 (2002), 10.1023/A:1014033703134. A particular feature of the method is that the flux at each cell interface is evaluated based on the characteristic solution of the kinetic equation itself; thus the numerical dissipation is low in comparison with that using direct reconstruction. Furthermore, the implicit treatment of the collision term enables the time step to be free from the restriction of the relaxation time. Unlike the DUGKS for single-species flows, a nonlinear system must be solved to determine the interaction parameters appearing in the equilibrium distribution function, which can be obtained analytically for Maxwell molecules. Several tests are performed to validate the scheme, including the shock structure problem under different Mach numbers and molar concentrations, the channel flow driven by a small gradient of pressure, temperature, or concentration, the plane Couette flow, and the shear driven cavity flow under different mass ratios and molar concentrations. The results are compared with those from other reliable numerical methods. The results show that the proposed scheme is an effective and reliable method for binary gas mixtures in all flow regimes.

Combining in silico evolution and nonlinear dimensionality reduction to redesign responses of signaling networks

NASA Astrophysics Data System (ADS)

Prescott, Aaron M.; Abel, Steven M.

2016-12-01

The rational design of network behavior is a central goal of synthetic biology. Here, we combine in silico evolution with nonlinear dimensionality reduction to redesign the responses of fixed-topology signaling networks and to characterize sets of kinetic parameters that underlie various input-output relations. We first consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm (EA) to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 orders of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. We also consider a network with both positive and negative feedback and use the EA to evolve oscillatory responses with different periods in response to a change in input. For each targeted input-output relation, we conduct many independent runs of the EA and use nonlinear dimensionality reduction to embed the resulting data for each network in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the cases considered, the network topologies exhibit significant flexibility in generating alternative responses, with distinct patterns of kinetic rates emerging for different targeted responses.

Parameter estimation in large-scale systems biology models: a parallel and self-adaptive cooperative strategy.

PubMed

Penas, David R; González, Patricia; Egea, Jose A; Doallo, Ramón; Banga, Julio R

2017-01-21

The development of large-scale kinetic models is one of the current key issues in computational systems biology and bioinformatics. Here we consider the problem of parameter estimation in nonlinear dynamic models. Global optimization methods can be used to solve this type of problems but the associated computational cost is very large. Moreover, many of these methods need the tuning of a number of adjustable search parameters, requiring a number of initial exploratory runs and therefore further increasing the computation times. Here we present a novel parallel method, self-adaptive cooperative enhanced scatter search (saCeSS), to accelerate the solution of this class of problems. The method is based on the scatter search optimization metaheuristic and incorporates several key new mechanisms: (i) asynchronous cooperation between parallel processes, (ii) coarse and fine-grained parallelism, and (iii) self-tuning strategies. The performance and robustness of saCeSS is illustrated by solving a set of challenging parameter estimation problems, including medium and large-scale kinetic models of the bacterium E. coli, bakerés yeast S. cerevisiae, the vinegar fly D. melanogaster, Chinese Hamster Ovary cells, and a generic signal transduction network. The results consistently show that saCeSS is a robust and efficient method, allowing very significant reduction of computation times with respect to several previous state of the art methods (from days to minutes, in several cases) even when only a small number of processors is used. The new parallel cooperative method presented here allows the solution of medium and large scale parameter estimation problems in reasonable computation times and with small hardware requirements. Further, the method includes self-tuning mechanisms which facilitate its use by non-experts. We believe that this new method can play a key role in the development of large-scale and even whole-cell dynamic models.

Enhanced charging kinetics of porous electrodes: surface conduction as a short-circuit mechanism.

PubMed

Mirzadeh, Mohammad; Gibou, Frederic; Squires, Todd M

2014-08-29

We use direct numerical simulations of the Poisson-Nernst-Planck equations to study the charging kinetics of porous electrodes and to evaluate the predictive capabilities of effective circuit models, both linear and nonlinear. The classic transmission line theory of de Levie holds for general electrode morphologies, but only at low applied potentials. Charging dynamics are slowed appreciably at high potentials, yet not as significantly as predicted by the nonlinear transmission line model of Biesheuvel and Bazant. We identify surface conduction as a mechanism which can effectively "short circuit" the high-resistance electrolyte in the bulk of the pores, thus accelerating the charging dynamics and boosting power densities. Notably, the boost in power density holds only for electrode morphologies with continuous conducting surfaces in the charging direction.

Modelling the influence of ionic and fluid transport on rebars corrosion in unsaturated cement systems

NASA Astrophysics Data System (ADS)

Dridi, W.; Dangla, P.; Foct, F.; Petre-Lazar, I.

2006-11-01

This paper deals with numerical modelling of rebar corrosion kinetics in unsaturated concrete structures. The corrosion kinetics is investigated in terms of mechanistic coupling between reaction rates at the steel surface and the ionic transport processes in the concrete pore system. The ionic and mass transport model consists of time-dependent equations for the concentration of dissolved species, the liquid pressure and the electrical potential. The complete set of nonlinear equations is solved using the finite-volume method. The nonlinear boundary conditions dealing with corrosion are introduced at the steel-concrete interface where they are implicitly coupled with the mass transport model in the concrete structure. Both the case of free corrosion and potentiostatic polarisation are discussed in a one dimensional model.

A Hamiltonian Model of Dissipative Wave-particle Interactions and the Negative-mass Effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

A. Zhmoginov

2011-02-07

The effect of radiation friction is included in the Hamiltonian treatment of wave-particle interactions with autoresonant phase-locking, yielding a generalized canonical approach to the problem of dissipative dynamics near a nonlinear resonance. As an example, the negativemass eff ect exhibited by a charged particle in a pump wave and a static magnetic field is studied in the presence of the friction force due to cyclotron radiation. Particles with negative parallel masses m! are shown to transfer their kinetic energy to the pump wave, thus amplifying it. Counterintuitively, such particles also undergo stable dynamics, decreasing their transverse energy monotonically due tomore » cyclotron cooling, whereas some of those with positive m! undergo cyclotron heating instead, extracting energy from the pump wave.« less

Solutions for a Kirchhoff equation with critical Caffarelli–Kohn–Nirenberg growth and discontinuous nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, Gelson G.; Figueiredo, Giovany M.

2018-06-01

In this paper, we study the existence of nonegative solutions to a class of nonlinear boundary value problems of the Kirchhoff type. We prove existence results when the problem has discontinuous nonlinearity and critical Caffarelli-Kohn-Nirenberg growth.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bai, Zhaojun; Yang, Chao

What is common among electronic structure calculation, design of MEMS devices, vibrational analysis of high speed railways, and simulation of the electromagnetic field of a particle accelerator? The answer: they all require solving large scale nonlinear eigenvalue problems. In fact, these are just a handful of examples in which solving nonlinear eigenvalue problems accurately and efficiently is becoming increasingly important. Recognizing the importance of this class of problems, an invited minisymposium dedicated to nonlinear eigenvalue problems was held at the 2005 SIAM Annual Meeting. The purpose of the minisymposium was to bring together numerical analysts and application scientists to showcasemore » some of the cutting edge results from both communities and to discuss the challenges they are still facing. The minisymposium consisted of eight talks divided into two sessions. The first three talks focused on a type of nonlinear eigenvalue problem arising from electronic structure calculations. In this type of problem, the matrix Hamiltonian H depends, in a non-trivial way, on the set of eigenvectors X to be computed. The invariant subspace spanned by these eigenvectors also minimizes a total energy function that is highly nonlinear with respect to X on a manifold defined by a set of orthonormality constraints. In other applications, the nonlinearity of the matrix eigenvalue problem is restricted to the dependency of the matrix on the eigenvalues to be computed. These problems are often called polynomial or rational eigenvalue problems In the second session, Christian Mehl from Technical University of Berlin described numerical techniques for solving a special type of polynomial eigenvalue problem arising from vibration analysis of rail tracks excited by high-speed trains.« less

A family of approximate solutions and explicit error estimates for the nonlinear stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Karel, S.

1975-01-01

An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.

A computational algorithm for spacecraft control and momentum management

NASA Technical Reports Server (NTRS)

Dzielski, John; Bergmann, Edward; Paradiso, Joseph

1990-01-01

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl-von Kármán equation: energy decomposition analysis and energy budget.

PubMed

Yokoyama, Naoto; Takaoka, Masanori

2014-12-01

A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

Nonlinear friction dynamics on polymer surface under accelerated movement

NASA Astrophysics Data System (ADS)

Aita, Yuuki; Asanuma, Natsumi; Takahashi, Akira; Mayama, Hiroyuki; Nonomura, Yoshimune

2017-04-01

Nonlinear phenomena on the soft material surface are one of the most exciting topics of chemical physics. However, only a few reports exist on the friction phenomena under accelerated movement, because friction between two solid surfaces is considered a linear phenomenon in many cases. We aim to investigate how nonlinear accelerated motion affects friction on solid surfaces. In the present study, we evaluate the frictional forces between two polytetrafluoroethylene (PTFE) resins using an advanced friction evaluation system. On PTFE surfaces, the normalized delay time δ, which is the time lag in the response of the friction force to the accelerated movement, is observed in the pre-sliding friction process. Under high-velocity conditions, kinetic friction increases with velocity. Based on these experimental results, we propose a two-phase nonlinear model including a pre-sliding process (from the beginning of sliding of a contact probe to the establishment of static friction) and a kinetic friction process. The present model consists of several factors including velocity, acceleration, stiffness, viscosity, and vertical force. The findings reflecting the viscoelastic properties of soft material is useful for various fields such as in the fabrication of clothes, cosmetics, automotive materials, and virtual reality systems as well as for understanding friction phenomena on soft material surfaces.

Kinetics of Molybdenum Adsorption and Desorption in Soils.

PubMed

Sun, Wenguang; Selim, H Magdi

2018-05-01

Much uncertainty exists in mechanisms and kinetics controlling the adsorption and desorption of molybdenum (Mo) in the soil environment. To investigate the characteristics of Mo adsorption and desorption and predict Mo behavior in the vadose zone, kinetic batch experiments were performed using three soils: Webster loam, Windsor sand and Mahan sand. Adsorption isotherms for Mo were strongly nonlinear for all three soils. Strong kinetic adsorption of Mo by all soils was also observed, where the rate of retention was rapid initially and was followed by slow retention behavior with time. The time-dependent Mo sorption rate was not influenced when constant pH was maintained. Desorption or release results indicated that there were significant fractions of Mo that appeared to be irreversible or slowly reversibly sorbed by Windsor and Mahan. X-ray absorption near edge structure (XANES) analysis for Windsor and Mahan soils indicated that most of Mo had been bound to kaolinite, whereas Webster had similar XANES features to those of Mo sorbed to montmorillonite. A sequential extraction procedure provided evidence that a significant amount of Mo was irreversibly sorbed. A multireaction model (MRM) with nonlinear equilibrium and kinetic sorption parameters was used to describe the adsorption-desorption kinetics of Mo on soils. Our results demonstrated that a formulation of MRM with two sorption sites (equilibrium and reversible) successfully described Mo adsorption-desorption data for Webster loam, and an additional irreversible reaction phase was recommended to describe Mo desorption or release with time for Windsor and Mahan soils. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse

NASA Astrophysics Data System (ADS)

Grishkov, V. E.; Uryupin, S. A.

2017-03-01

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron-ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grishkov, V. E.; Uryupin, S. A., E-mail: uryupin@sci.lebedev.ru

Excitation of plasma waves by nonlinear currents induced by a high-frequency electromagnetic pulse is analyzed within the kinetic approach. It is shown that the most efficient source of plasma waves is the nonlinear current arising due to the gradient of the energy density of the high-frequency field. Generation of plasma waves by the drag current is usually less efficient but not negligibly small at relatively high frequencies of electron–ion collisions. The influence of electron collisions on the excitation of plasma waves by pulses of different duration is described quantitatively.

Trapped-Particle Instability Leading to Bursting in Stimulated Raman Scattering Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

S. Brunner; E. Valeo

2001-11-08

Nonlinear, kinetic simulations of Stimulated Raman Scattering (SRS) for laser-fusion-relevant conditions present a bursting behavior. Different explanations for this regime has been given in previous studies: Saturation of SRS by increased nonlinear Landau damping [K. Estabrook et al., Phys. Fluids B 1 (1989) 1282] and detuning due to the nonlinear frequency shift of the plasma wave [H.X. Vu et al., Phys. Rev. Lett. 86 (2001) 4306]. Another mechanism, also assigning a key role to the trapped electrons, is proposed here: The break-up of the plasma wave through the trapped-particle instability.

A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

2017-07-01

We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

A linear framework for time-scale separation in nonlinear biochemical systems.

PubMed

Gunawardena, Jeremy

2012-01-01

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.

Study of solar wind spectra by nonlinear waves interaction

NASA Astrophysics Data System (ADS)

Dwivedi, Navin; Sharma, Rampal; Narita, Yasuhito

2014-05-01

The nature of small-scale turbulent fluctuations in the solar wind (SW) turbulence is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations predict the evidence of the dominance of kinetic Alfvén waves (KAW) at sub-ion scales with frequency below than ion cyclotron frequency, while other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode is more relevant. In the present work, nonlinear interaction of kinetic Alfvén wave with whistler wave is considered as one of the possible cause responsible for the solar wind turbulence. A set of coupled dimensionless equations are derived for the intermediate beta plasmas and the nonlinear interaction between these two wave modes has been studied. As a consequence of ponderomotive nonlinearity, the pump KAW becomes filamented when its power exceeds the threshold for the filamentation instability. Whistler is considered to be weak and thus doesn't have enough intensity to initiate its own localization. It gets localized while propagating through the density channel created by KAW localization. In addition, spectral scales of power spectra of KAW and whistler are also calculated. The steeper spectra are found with scaling greater than -5/3. This type of nonlinear interaction between different wave modes and steeper spectra is one of the reasons for the solar wind turbulence and particles acceleration. This work is partially supported by DST (India) and FP7/STORM (313038)

State estimation with incomplete nonlinear constraint

NASA Astrophysics Data System (ADS)

Huang, Yuan; Wang, Xueying; An, Wei

2017-10-01

A problem of state estimation with a new constraints named incomplete nonlinear constraint is considered. The targets are often move in the curve road, if the width of road is neglected, the road can be considered as the constraint, and the position of sensors, e.g., radar, is known in advance, this info can be used to enhance the performance of the tracking filter. The problem of how to incorporate the priori knowledge is considered. In this paper, a second-order sate constraint is considered. A fitting algorithm of ellipse is adopted to incorporate the priori knowledge by estimating the radius of the trajectory. The fitting problem is transformed to the nonlinear estimation problem. The estimated ellipse function is used to approximate the nonlinear constraint. Then, the typical nonlinear constraint methods proposed in recent works can be used to constrain the target state. Monte-Carlo simulation results are presented to illustrate the effectiveness proposed method in state estimation with incomplete constraint.

Pitch Angle Scattering of Energetic Electrons by Plasmaspheric Hiss Emissions

NASA Astrophysics Data System (ADS)

Tobita, M.; Omura, Y.; Summers, D.

2017-12-01

We study scattering of energetic electrons in pitch angles and kinetic energies through their resonance with plasmaspheric hiss emissions consisting of many coherent discrete whistler-mode wave packets with rising and falling frequencies [1,2,3]. Using test particle simulations, we evaluate the efficiency of scattering, which depends on the inhomogeneity ratio S of whistler mode wave-particle interaction [4]. The value of S is determined by the wave amplitude, frequency sweep rate, and the gradient of the background magnetic field. We first modulate those parameters and observe variations of pitch angles and kinetic energies of electrons with a single wave under various S values so as to obtain basic understanding. We then include many waves into the system to simulate plasmaspheric hiss emissions. As the wave packets propagate away from the magnetic equator, the nonlinear trapping potential at the resonance velocity is deformed, making a channel of gyrophase for untrapped electrons to cross the resonance velocity, and causing modulations in their pitch angles and kinetic energies. We find efficient scattering of pitch angles and kinetic energies because of coherent nonlinear wave-particle interaction, resulting in electron precipitations into the polar atmosphere. We compare the results with the bounce averaged pitch angle diffusion coefficient based on quasi-linear theory, and show that the nonlinear wave model with many coherent packets can cause scattering of resonant electrons much faster than the quasi-linear diffusion process. [1] Summers, D., Omura, Y., Nakamura, S., and C. A. Kletzing (2014), Fine structure of plasmaspheric hiss, J. Geophys. Res., 119, 9134-9149. [2] Omura, Y., Y. Miyashita, M. Yoshikawa, D. Summers, M. Hikishima, Y. Ebihara, and Y. Kubota (2015), Formation process of relativistic electron flux through interaction with chorus emissions in the Earth's inner magnetosphere, J. Geophys. Res. Space Physics, 120, 9545-9562. [3] Nakamura, S., Y. Omura, D. Summers, and C. A. Kletzing (2016), Observational evidence of the nonlinear wave growth theory of plasmaspheric hiss, Geophys. Res. Lett., 43, 10,040-10,049. [4] Omura, Y., Katoh, Y., and Summers, D., Theory and simulation of the generation of whistler-mode chorus (2008), J. Geophys. Res., 113, A04223.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

A Unified Approach for Solving Nonlinear Regular Perturbation Problems

ERIC Educational Resources Information Center

Khuri, S. A.

2008-01-01

This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

NASA Astrophysics Data System (ADS)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the method of disturbed observations, we conclude that it practically should be still entirely acceptable to adequately describe the orbital uncertainty since, from a geometrical point of view, the efficiency of the method directly depends only on the nonflatness of the estimation subspace and it gets higher as the nonflatness decreases.

A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles.

PubMed

Kitayama, Tomoya; Kinoshita, Ayako; Sugimoto, Masahiro; Nakayama, Yoichi; Tomita, Masaru

2006-07-17

In order to improve understanding of metabolic systems there have been attempts to construct S-system models from time courses. Conventionally, non-linear curve-fitting algorithms have been used for modelling, because of the non-linear properties of parameter estimation from time series. However, the huge iterative calculations required have hindered the development of large-scale metabolic pathway models. To solve this problem we propose a novel method involving power-law modelling of metabolic pathways from the Jacobian of the targeted system and the steady-state flux profiles by linearization of S-systems. The results of two case studies modelling a straight and a branched pathway, respectively, showed that our method reduced the number of unknown parameters needing to be estimated. The time-courses simulated by conventional kinetic models and those described by our method behaved similarly under a wide range of perturbations of metabolite concentrations. The proposed method reduces calculation complexity and facilitates the construction of large-scale S-system models of metabolic pathways, realizing a practical application of reverse engineering of dynamic simulation models from the Jacobian of the targeted system and steady-state flux profiles.

Unsteady Crystal Growth Due to Step-Bunch Cascading

NASA Technical Reports Server (NTRS)

Vekilov, Peter G.; Lin, Hong; Rosenberger, Franz

1997-01-01

Based on our experimental findings of growth rate fluctuations during the crystallization of the protein lysozym, we have developed a numerical model that combines diffusion in the bulk of a solution with diffusive transport to microscopic growth steps that propagate on a finite crystal facet. Nonlinearities in layer growth kinetics arising from step interaction by bulk and surface diffusion, and from step generation by surface nucleation, are taken into account. On evaluation of the model with properties characteristic for the solute transport, and the generation and propagation of steps in the lysozyme system, growth rate fluctuations of the same magnitude and characteristic time, as in the experiments, are obtained. The fluctuation time scale is large compared to that of step generation. Variations of the governing parameters of the model reveal that both the nonlinearity in step kinetics and mixed transport-kinetics control of the crystallization process are necessary conditions for the fluctuations. On a microscopic scale, the fluctuations are associated with a morphological instability of the vicinal face, in which a step bunch triggers a cascade of new step bunches through the microscopic interfacial supersaturation distribution.

A Well-Posed, Objective and Dynamic Two-Fluid Model

NASA Astrophysics Data System (ADS)

Chetty, Krishna; Vaidheeswaran, Avinash; Sharma, Subash; Clausse, Alejandro; Lopez de Bertodano, Martin

The transition from dispersed to clustered bubbly flows due to wake entrainment is analyzed with a well-posed and objective one-dimensional (1-D) Two-Fluid Model, derived from variational principles. Modeling the wake entrainment force using the variational technique requires formulation of the inertial coupling coefficient, which defines the kinetic coupling between the phases. The kinetic coupling between a pair of bubbles and the liquid is obtained from potential flow over two-spheres and the results are validated by comparing the virtual mass coefficients with existing literature. The two-body interaction kinetic coupling is then extended to a lumped parameter model for viscous flow over two cylindrical bubbles, to get the Two-Fluid Model for wake entrainment. Linear stability analyses comprising the characteristics and the dispersion relation and non-linear numerical simulations are performed with the 1-D variational Two-Fluid Model to demonstrate the wake entrainment instability leading to clustering of bubbles. Finally, the wavelengths, amplitudes and propagation velocities of the void waves from non-linear simulations are compared with the experimental data.

Kinetic mechanism of V-shaped twinning in 3C/4H-SiC heteroepitaxy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xin, Bin; Zhang, Yu-Ming; Jia, Ren-Xu, E-mail: rxjia@mail.xidian.edu.cn

The authors investigated the kinetic mechanism of V-shaped twinning in 3C/4H-SiC heteroepitaxy. A fourfold V-shaped twinning complex was found, and its interface was measured with high-resolution transmission electron microscopy (HRTEM). Two linear coherent boundaries and a nonlinear incoherent boundary (also called the double-position boundary) were observed. On the basis of the HRTEM results, the authors proposed an adatom migration growth model, in which the activation barrier at the coherent boundary is much lower than that at the incoherent boundary. From a kinetic perspective, adatoms are prone to migrate to the side of the boundary with the lower potential energy ifmore » they have sufficient thermal energy to overcome the activation barrier. In the case of a coherent boundary, the growth rates of the domains either side of the boundary can be balanced through the intermigration of adatoms, leading to a linear boundary. Conversely, it is difficult for adatoms to migrate across an incoherent boundary, which results in asynchronous growth rates and a nonlinear boundary.« less

Middle School Students' Reasoning in Nonlinear Proportional Problems in Geometry

ERIC Educational Resources Information Center

Ayan, Rukiye; Isiksal Bostan, Mine

2018-01-01

In this study, we investigate sixth, seventh, and eighth grade students' achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students' solution strategies for the problems and obstacles that prevent students from answering the problems correctly by…

Chemical kinetics as a contract sport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolb, C.E.

1990-01-01

Earlier in this century chemical kinetics was a basic physical chemistry research topic widely pursued in leading academic chemistry departments. Chemical kinetics now appears to be a discipline practiced chiefly for its applications to societal problems. The chemical kinetics activities directed by D.M. Golden at SRI International are strikingly successful in generating data for key applied problems while at the same time advancing our understanding of chemical kinetics as a scientific discipline. In this talk, the author will contrast the chemical kinetics activities in two contract R D laboratories, one on the right side of the U.S. (ARI) and themore » other on the left (SRI). Their approach to common applied problems ranging from stratospheric heterogeneous kinetics to plasma etching systems for semiconductor processing will be compared and contrasted. Empirically discovered Golden Rules for the pursuit of quality chemical kinetics research in a contract R D environment will be presented and discussed.« less

Multidimensional electron beam-plasma instabilities in the relativistic regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bret, A.; Gremillet, L.; Dieckmann, M. E.

2010-12-15

The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, themore » basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell-Juettner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.« less

Multi-equilibrium property of metabolic networks: SSI module.

PubMed

Lei, Hong-Bo; Zhang, Ji-Feng; Chen, Luonan

2011-06-20

Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI) metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module.

Multi-equilibrium property of metabolic networks: SSI module

PubMed Central

2011-01-01

Background Revealing the multi-equilibrium property of a metabolic network is a fundamental and important topic in systems biology. Due to the complexity of the metabolic network, it is generally a difficult task to study the problem as a whole from both analytical and numerical viewpoint. On the other hand, the structure-oriented modularization idea is a good choice to overcome such a difficulty, i.e. decomposing the network into several basic building blocks and then studying the whole network through investigating the dynamical characteristics of the basic building blocks and their interactions. Single substrate and single product with inhibition (SSI) metabolic module is one type of the basic building blocks of metabolic networks, and its multi-equilibrium property has important influence on that of the whole metabolic networks. Results In this paper, we describe what the SSI metabolic module is, characterize the rates of the metabolic reactions by Hill kinetics and give a unified model for SSI modules by using a set of nonlinear ordinary differential equations with multi-variables. Specifically, a sufficient and necessary condition is first given to describe the injectivity of a class of nonlinear systems, and then, the sufficient condition is used to study the multi-equilibrium property of SSI modules. As a main theoretical result, for the SSI modules in which each reaction has no more than one inhibitor, a sufficient condition is derived to rule out multiple equilibria, i.e. the Jacobian matrix of its rate function is nonsingular everywhere. Conclusions In summary, we describe SSI modules and give a general modeling framework based on Hill kinetics, and provide a sufficient condition for ruling out multiple equilibria of a key type of SSI module. PMID:21689474

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graf, Peter; Dykes, Katherine; Scott, George

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Binding kinetics of five drugs to beta2-adrenoceptor using peak profiling method and nonlinear chromatography.

PubMed

Liang, Yuan; Wang, Jing; Fei, Fuhuan; Sun, Huanmei; Liu, Ting; Li, Qian; Zhao, Xinfeng; Zheng, Xiaohui

2018-02-23

Investigations of drug-protein interactions have advanced our knowledge of ways to design more rational drugs. In addition to extensive thermodynamic studies, ongoing works are needed to enhance the exploration of drug-protein binding kinetics. In this work, the beta2-adrenoceptor (β 2 -AR) was immobilized on N, N'-carbonyldiimidazole activated amino polystyrene microspheres to prepare an affinity column (4.6 mm × 5.0 cm, 8 μm). The β 2 -AR column was utilized to determine the binding kinetics of five drugs to the receptor. Introducing peak profiling method into this receptor chromatographic analysis, we determined the dissociation rate constants (k d ) of salbutamol, terbutaline, methoxyphenamine, isoprenaline hydrochloride and ephedrine hydrochloride to β 2 -AR to be 15 (±1), 22 (±1), 3.3 (±0.2), 2.3 (±0.2) and 2.1 (±0.1) s -1 , respectively. The employment of nonlinear chromatography (NLC) in this case exhibited the same rank order of k d values for the five drugs bound to β 2 -AR. We confirmed that both the peak profiling method and NLC were capable of routine measurement of receptor-drug binding kinetics. Compared with the peak profiling method, NLC was advantageous in the simultaneous assessment of the kinetic and apparent thermodynamic parameters. It will become a powerful method for high throughput drug-receptor interaction analysis. Copyright © 2018 Elsevier B.V. All rights reserved.

Effects of Convective Transport of Solute and Impurities on Defect-Causing Kinetics Instabilities in Protein Crystallization

NASA Technical Reports Server (NTRS)

Vekilov, Peter G.

2002-01-01

The objective of the proposed research is to obtain further insight into the onset and development of the defect-causing instabilities that anise due to the coupling of the bulk transport and nonlinear-interfacial kinetics during growth in the mixed regime, utilizing the reduction of the convective contribution to the bulk transport under microgravity. These studies will build upon the data on the effects of quantitative variations of the forced convection velocity on the averaged and time-dependent kinetic behavior of protein crystal growth systems that have recently been obtained in our laboratory.

Multivariate curve resolution-alternating least squares and kinetic modeling applied to near-infrared data from curing reactions of epoxy resins: mechanistic approach and estimation of kinetic rate constants.

PubMed

Garrido, M; Larrechi, M S; Rius, F X

2006-02-01

This study describes the combination of multivariate curve resolution-alternating least squares with a kinetic modeling strategy for obtaining the kinetic rate constants of a curing reaction of epoxy resins. The reaction between phenyl glycidyl ether and aniline is monitored by near-infrared spectroscopy under isothermal conditions for several initial molar ratios of the reagents. The data for all experiments, arranged in a column-wise augmented data matrix, are analyzed using multivariate curve resolution-alternating least squares. The concentration profiles recovered are fitted to a chemical model proposed for the reaction. The selection of the kinetic model is assisted by the information contained in the recovered concentration profiles. The nonlinear fitting provides the kinetic rate constants. The optimized rate constants are in agreement with values reported in the literature.

Full PIC simulations of solar radio emission

NASA Astrophysics Data System (ADS)

Sgattoni, A.; Henri, P.; Briand, C.; Amiranoff, F.; Riconda, C.

2017-12-01

Solar radio emissions are electromagnetic (EM) waves emitted in the solar wind plasma as a consequence of electron beams accelerated during solar flares or interplanetary shocks such as ICMEs. To describe their origin, a multi-stage model has been proposed in the 60s which considers a succession of non-linear three-wave interaction processes. A good understanding of the process would allow to infer the kinetic energy transfered from the electron beam to EM waves, so that the radio waves recorded by spacecraft can be used as a diagnostic for the electron beam.Even if the electrostatic problem has been extensively studied, full electromagnetic simulations were attempted only recently. Our large scale 2D-3V electromagnetic PIC simulations allow to identify the generation of both electrostatic and EM waves originated by the succession of plasma instabilities. We tested several configurations varying the electron beam density and velocity considering a background plasma of uniform density. For all the tested configurations approximately 105 of the electron-beam kinetic energy is transfered into EM waves emitted in all direction nearly isotropically. With this work we aim to design experiments of laboratory astrophysics to reproduce the electromagnetic emission process and test its efficiency.

Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions

NASA Astrophysics Data System (ADS)

Lorenzi, Juan M.; Stecher, Thomas; Reuter, Karsten; Matera, Sebastian

2017-10-01

Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.

Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions.

PubMed

Lorenzi, Juan M; Stecher, Thomas; Reuter, Karsten; Matera, Sebastian

2017-10-28

Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.

Applying constraints on model-based methods: Estimation of rate constants in a second order consecutive reaction

NASA Astrophysics Data System (ADS)

Kompany-Zareh, Mohsen; Khoshkam, Maryam

2013-02-01

This paper describes estimation of reaction rate constants and pure ultraviolet/visible (UV-vis) spectra of the component involved in a second order consecutive reaction between Ortho-Amino benzoeic acid (o-ABA) and Diazoniom ions (DIAZO), with one intermediate. In the described system, o-ABA was not absorbing in the visible region of interest and thus, closure rank deficiency problem did not exist. Concentration profiles were determined by solving differential equations of the corresponding kinetic model. In that sense, three types of model-based procedures were applied to estimate the rate constants of the kinetic system, according to Levenberg/Marquardt (NGL/M) algorithm. Original data-based, Score-based and concentration-based objective functions were included in these nonlinear fitting procedures. Results showed that when there is error in initial concentrations, accuracy of estimated rate constants strongly depends on the type of applied objective function in fitting procedure. Moreover, flexibility in application of different constraints and optimization of the initial concentrations estimation during the fitting procedure were investigated. Results showed a considerable decrease in ambiguity of obtained parameters by applying appropriate constraints and adjustable initial concentrations of reagents.

Pupils' over-reliance on linearity: a scholastic effect?

PubMed

Van Dooren, Wim; De Bock, Dirk; Janssens, Dirk; Verschaffel, Lieven

2007-06-01

From upper elementary education on, children develop a tendency to over-use linearity. Particularly, it is found that many pupils assume that if a figure enlarges k times, the area enlarges k times too. However, most research was conducted with traditional, school-like word problems. This study examines whether pupils also over-use linearity if non-linear problems are embedded in meaningful, authentic performance tasks instead of traditional, school-like word problems, and whether this experience influences later behaviour. Ninety-three sixth graders from two primary schools in Flanders, Belgium. Pupils received a pre-test with traditional word problems. Those who made a linear error on the non-linear area problem were subjected to individual interviews. They received one new non-linear problem, in the S-condition (again a traditional, scholastic word problem), D-condition (the same word problem with a drawing) or P-condition (a meaningful performance-based task). Shortly afterwards, pupils received a post-test, containing again a non-linear word problem. Most pupils from the S-condition displayed linear reasoning during the interview. Offering drawings (D-condition) had a positive effect, but presenting the problem as a performance task (P-condition) was more beneficial. Linear reasoning was nearly absent in the P-condition. Remarkably, at the post-test, most pupils from all three groups again applied linear strategies. Pupils' over-reliance on linearity seems partly elicited by the school-like word problem format of test items. Pupils perform much better if non-linear problems are offered as performance tasks. However, a single experience does not change performances on a comparable word problem test afterwards.

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

The Nonlinear Spring and Energy Conservation.

ERIC Educational Resources Information Center

Sherfinski, John

1989-01-01

Describes an air track experiment demonstrating the transfer of mechanical energy from elastic potential to kinetic. Discusses four methods for calculating energy stored in the spring. Included are pictures, typical data, and graphs. (YP)

Optimization strategies based on sequential quadratic programming applied for a fermentation process for butanol production.

PubMed

Pinto Mariano, Adriano; Bastos Borba Costa, Caliane; de Franceschi de Angelis, Dejanira; Maugeri Filho, Francisco; Pires Atala, Daniel Ibraim; Wolf Maciel, Maria Regina; Maciel Filho, Rubens

2009-11-01

In this work, the mathematical optimization of a continuous flash fermentation process for the production of biobutanol was studied. The process consists of three interconnected units, as follows: fermentor, cell-retention system (tangential microfiltration), and vacuum flash vessel (responsible for the continuous recovery of butanol from the broth). The objective of the optimization was to maximize butanol productivity for a desired substrate conversion. Two strategies were compared for the optimization of the process. In one of them, the process was represented by a deterministic model with kinetic parameters determined experimentally and, in the other, by a statistical model obtained using the factorial design technique combined with simulation. For both strategies, the problem was written as a nonlinear programming problem and was solved with the sequential quadratic programming technique. The results showed that despite the very similar solutions obtained with both strategies, the problems found with the strategy using the deterministic model, such as lack of convergence and high computational time, make the use of the optimization strategy with the statistical model, which showed to be robust and fast, more suitable for the flash fermentation process, being recommended for real-time applications coupling optimization and control.

Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

DOE PAGES

Willert, Jeffrey; Park, H.; Taitano, William

2015-11-01

High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.

Evidence for cluster shape effects on the kinetic energy spectrum in thermionic emission.

PubMed

Calvo, F; Lépine, F; Baguenard, B; Pagliarulo, F; Concina, B; Bordas, C; Parneix, P

2007-11-28

Experimental kinetic energy release distributions obtained for the thermionic emission from C(n) (-) clusters, 10< or =n< or =20, exhibit significant non-Boltzmann variations. Using phase space theory, these different features are analyzed and interpreted as the consequence of contrasting shapes in the daughter clusters; linear and nonlinear isomers have clearly distinct signatures. These results provide a novel indirect structural probe for atomic clusters associated with their thermionic emission spectra.

Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code

NASA Technical Reports Server (NTRS)

Hou, Gene

2000-01-01

The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.

A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

NASA Astrophysics Data System (ADS)

Mamehrashi, K.; Yousefi, S. A.

2017-02-01

This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-08-01

This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. Themore » notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.« less

Development of a fully-consistent reduced order model to study instabilities in boiling water reactors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dykin, V.; Demaziere, C.

2012-07-01

A simple nonlinear Reduced Order Model to study global, regional and local instabilities in Boiling Water Reactors is described. The ROM consists of three submodels: neutron-kinetic, thermal-hydraulic and heat-transfer models. The neutron-kinetic model allows representing the time evolution of the three first neutron kinetic modes: the fundamental, the first and the second azimuthal modes. The thermal-hydraulic model describes four heated channels in order to correctly simulate out-of-phase behavior. The coupling between the different submodels is performed via both void and Doppler feedback mechanisms. After proper spatial homogenization, the governing equations are discretized in the time-domain. Several modifications, compared to othermore » existing ROMs, have been implemented, and are reported in this paper. One novelty of the ROM is the inclusion of both azimuthal modes, which allows to study combined instabilities (in-phase and out-of-phase), as well as to investigate the corresponding interference effects between them. The second modification concerns the precise estimation of so-called reactivity coefficients or C{sub mn}{sup *V,D} - coefficients by using direct cross-section data from SIMULATE-3 combined with the CORE SIM core simulator in order to calculate Eigenmodes. Furthermore, a non-uniform two-step axial power profile is introduced to simulate the separate heat production in the single and two-phase regions, respectively. An iterative procedure was developed to calculate the solution to the coupled neutron-kinetic/thermal-hydraulic static problem prior to solving the time-dependent problem. Besides, the possibility of taking into account the effect of local instabilities is demonstrated in a simplified manner. The present ROM is applied to the investigation of an actual instability that occurred at the Swedish Forsmark-1 BWR in 1996/1997. The results generated by the ROM are compared with real power plant measurements performed during stability tests and show a good qualitative agreement. The present study provides some insight in a deeper understanding of the physical principles which drive both core-wide and local instabilities. (authors)« less

On some control problems of dynamic of reactor

NASA Astrophysics Data System (ADS)

Baskakov, A. V.; Volkov, N. P.

2017-12-01

The paper analyzes controllability of the transient processes in some problems of nuclear reactor dynamics. In this case, the mathematical model of nuclear reactor dynamics is described by a system of integro-differential equations consisting of the non-stationary anisotropic multi-velocity kinetic equation of neutron transport and the balance equation of delayed neutrons. The paper defines the formulation of the linear problem on control of transient processes in nuclear reactors with application of spatially distributed actions on internal neutron sources, and the formulation of the nonlinear problems on control of transient processes with application of spatially distributed actions on the neutron absorption coefficient and the neutron scattering indicatrix. The required control actions depend on the spatial and velocity coordinates. The theorems on existence and uniqueness of these control actions are proved in the paper. To do this, the control problems mentioned above are reduced to equivalent systems of integral equations. Existence and uniqueness of the solution for this system of integral equations is proved by the method of successive approximations, which makes it possible to construct an iterative scheme for numerical analyses of transient processes in a given nuclear reactor with application of the developed mathematical model. Sufficient conditions for controllability of transient processes are also obtained. In conclusion, a connection is made between the control problems and the observation problems, which, by to the given information, allow us to reconstruct either the function of internal neutron sources, or the neutron absorption coefficient, or the neutron scattering indicatrix....

Kinetic modeling of the photocatalytic degradation of clofibric acid in a slurry reactor.

PubMed

Manassero, Agustina; Satuf, María Lucila; Alfano, Orlando Mario

2015-01-01

A kinetic study of the photocatalytic degradation of the pharmaceutical clofibric acid is presented. Experiments were carried out under UV radiation employing titanium dioxide in water suspension. The main reaction intermediates were identified and quantified. Intrinsic expressions to represent the kinetics of clofibric acid and the main intermediates were derived. The modeling of the radiation field in the reactor was carried out by Monte Carlo simulation. Experimental runs were performed by varying the catalyst concentration and the incident radiation. Kinetic parameters were estimated from the experiments by applying a non-linear regression procedure. Good agreement was obtained between model predictions and experimental data, with an error of 5.9 % in the estimations of the primary pollutant concentration.

Direct Estimation of Kinetic Parametric Images for Dynamic PET

PubMed Central

Wang, Guobao; Qi, Jinyi

2013-01-01

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed. PMID:24396500

Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

NASA Astrophysics Data System (ADS)

Sumin, M. I.

2015-06-01

A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.

Development of a Two-Dimensional Hybrid-Kinetic Code for Simulations of Low-Altitude Auroral Flux-Tubes

NASA Astrophysics Data System (ADS)

Sydorenko, D.; Rankin, R.; Kabin, K.

2009-12-01

This paper presents initial results based on kinetic extensions of a nonlinear two-dimensional (2D) multi-fluid (three ion species and fluid electrons) MHD model that is designed to study propagation of shear Alfven waves in low-altitude auroral flux tubes. It is intended to use the model for scientific support of the “enhanced polar outflow probe” e-POP/CASSIOPE spacecraft mission (launch scheduled in 2010). Effects of gravity, thermal pressure, and geomagnetic field curvature are included, while the parallel electric field along geomagnetic field lines is calculated under the assumption of plasma quasineutrality. The model has been used successfully to study excitation of eigenmodes of the ionospheric Alfven resonator (IAR) by an Alfven wave packet injected from the magnetospheric end of the simulated plasma region. The formation of density cavities due to the ponderomotive force of standing oscillations in the IAR [Sydorenko, Rankin, and Kabin, 2008], and excitation of double layers and ion-acoustic wave packets, has been demonstrated. The kinetic extension of the multi-fluid code involves replacing the fluid electron model with a kinetic module that solves the simplified drift-kinetic Vlasov equation for the electron velocity distribution function (EVDF). To avoid undue complexity, it is assumed that (i) the electrons move only along geomagnetic field lines and (ii) the electron magnetic moment is conserved. As a result, the evolution of the EVDF is reduced to the problem of advection in 2D phase space “distance along the field line - velocity along the field line”. This problem is solved using a semi-Lagrangian algorithm [Staniforth and Cote, 1991]. The kinetic simulation starts from the initial equilibrium state similar to [Ergun et al., 2000]. The equilibrium assumes that the plasma consists of two electron populations: cold electrons with isotropic EVDF originating from the ionosphere, and hot anisotropic electrons with a loss-cone EVDF coming from the high-altitude end. The loss-cone distribution is prone to strong numerical dispersion, which is compensated by tracing the interface of the EVDF in the coordinate-velocity phase space. Ergun R. E., C. W. Carlson, J. P. McFadden, F. S. Mozer, and R. J. Strangeway (2000), Geophys. Res. Lett., 27, 4053-4056. Staniforth A. and J. Cote (1991), Mon. Wea. Rev., 119, 2206-2223 Sydorenko, D., R. Rankin, and K. Kabin (2008), J. Geophys. Res., 113, A10206, doi:10.1029/2008JA013579.

The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavlenko, V N; Potapov, D K

2015-09-30

This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions. Bibliography: 32 titles.

Wind Farm Turbine Type and Placement Optimization

NASA Astrophysics Data System (ADS)

Graf, Peter; Dykes, Katherine; Scott, George; Fields, Jason; Lunacek, Monte; Quick, Julian; Rethore, Pierre-Elouan

2016-09-01

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. This document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Wind farm turbine type and placement optimization

DOE PAGES

Graf, Peter; Dykes, Katherine; Scott, George; ...

2016-10-03

The layout of turbines in a wind farm is already a challenging nonlinear, nonconvex, nonlinearly constrained continuous global optimization problem. Here we begin to address the next generation of wind farm optimization problems by adding the complexity that there is more than one turbine type to choose from. The optimization becomes a nonlinear constrained mixed integer problem, which is a very difficult class of problems to solve. Furthermore, this document briefly summarizes the algorithm and code we have developed, the code validation steps we have performed, and the initial results for multi-turbine type and placement optimization (TTP_OPT) we have run.

Nonlinear Waves.

DTIC Science & Technology

1988-02-01

in Multi- dimensions II, P.M. Santini and A.S. Fokas, preprint INS#67, 1986. The Recursion Operator of the Kadomtsev - Petviashvili Equation and the...solitons, multidimensional inverse problems, Painleve equations , direct linearizations of certain nonlinear wave equations , DBAR problems, Riemann...the Navy is (a) the recent discovery that many of the equations describing ship hydrodynamics in channels of finite depth obey nonlinear equations

Nonlinear functional approximation with networks using adaptive neurons

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1992-01-01

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Multigrid approaches to non-linear diffusion problems on unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

2001-01-01

The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Division by zero, pseudo-division by zero, Zhang dynamics method and Zhang-gradient method about control singularity conquering

NASA Astrophysics Data System (ADS)

Zhang, Yunong; Zhang, Yinyan; Chen, Dechao; Xiao, Zhengli; Yan, Xiaogang

2017-01-01

In this paper, the division-by-zero (DBO) problem in the field of nonlinear control, which is traditionally termed the control singularity problem (or specifically, controller singularity problem), is investigated by the Zhang dynamics (ZD) method and the Zhang-gradient (ZG) method. According to the impact of the DBO problem on the state variables of the controlled nonlinear system, the concepts of the pseudo-DBO problem and the true-DBO problem are proposed in this paper, which provide a new perspective for the researchers on the DBO problems as well as nonlinear control systems. Besides, the two classes of DBO problems are solved under the framework of the ZG method. Specific examples are shown and investigated in this paper to illustrate the two proposed concepts and the efficacy of the ZG method in conquering pseudo-DBO and true-DBO problems. The application of the ZG method to the tracking control of a two-wheeled mobile robot further substantiates the effectiveness of the ZG method. In addition, the ZG method is successfully applied to the tracking control of a pure-feedback nonlinear system.

Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm

NASA Astrophysics Data System (ADS)

Kania, Adhe; Sidarto, Kuntjoro Adji

2016-02-01

Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

Complexity in Nature and Society: Complexity Management in the Age of Globalization

NASA Astrophysics Data System (ADS)

Mainzer, Klaus

The theory of nonlinear complex systems has become a proven problem-solving approach in the natural sciences from cosmic and quantum systems to cellular organisms and the brain. Even in modern engineering science self-organizing systems are developed to manage complex networks and processes. It is now recognized that many of our ecological, social, economic, and political problems are also of a global, complex, and nonlinear nature. What are the laws of sociodynamics? Is there a socio-engineering of nonlinear problem solving? What can we learn from nonlinear dynamics for complexity management in social, economic, financial and political systems? Is self-organization an acceptable strategy to handle the challenges of complexity in firms, institutions and other organizations? It is a main thesis of the talk that nature and society are basically governed by nonlinear and complex information dynamics. How computational is sociodynamics? What can we hope for social, economic and political problem solving in the age of globalization?.

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, George V.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is very well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

Global Simulation of Electromagnetic Ion Cyclotron Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K.; Gallagher, D. L.; Kozyra, J. U.

2007-01-01

It is well known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wave-normal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and particles. Such a self-consistent model is being progressively developed by Khazanov et al. [2002 - 2007]. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. We will discuss the recent progress in understanding EMIC waves formation mechanisms in the inner magnetosphere. This problem remains unsettled in spite of many years of experimental and theoretical studies. Modern satellite observations by CRRES, Polar and Cluster still do not reveal the whole picture experimentally since they do not stay long enough in the generation region to give a full account of all the spatio-temporal structure of EMIC waves. The complete self-consistent theory taking into account all factors significant for EMIC waves generation remains to be developed. Several mechanisms are discussed with respect to formation of EMIC waves, among them are nonlinear modification of the ionospheric reflection by precipitating energetic protons, modulation of ion-cyclotron instability by long-period (Pc3/4) pulsations, reflection of waves from layers of heavy-ion gyroresonances, and nonlinearities of wave generation process. We show that each of these mechanisms have their attractive features and explains certain part experimental data but any of them, if taken alone, meets some difficulties when compared to observations. We conclude that development of a refined nonlinear theory and further correlated analysis of modern satellite and ground-based data is needed to solve this very intriguing problem.

Kinetic effects on turbulence driven by the magnetorotational instability in black hole accretion

NASA Astrophysics Data System (ADS)

Sharma, Prateek

Many astrophysical objects (e.g., spiral galaxies, the solar system, Saturn's rings, and luminous disks around compact objects) occur in the form of a disk. One of the important astrophysical problems is to understand how rotationally supported disks lose angular momentum, and accrete towards the bottom of the gravitational potential, converting gravitational energy into thermal (and radiation) energy. The magnetorotational instability (MRI), an instability causing turbulent transport in ionized accretion disks, is studied in the kinetic regime. Kinetic effects are important because radiatively inefficient accretion flows (RIAFs), like the one around the supermassive black hole in the center of our Galaxy, are collisionless. The ion Larmor radius is tiny compared to the scale of MHD turbulence so that the drift kinetic equation (DKE), obtained by averaging the Vlasov equation over the fast gyromotion, is appropriate for evolving the distribution function. The kinetic MHD formalism, based on the moments of the DKE, is used for linear and nonlinear studies. A Landau fluid closure for parallel heat flux, which models kinetic effects like collisionless damping, is used to close the moment hierarchy. We show, that the kinetic MHD and drift kinetic formalisms give the same set of linear modes for a Keplerian disk. The BGK collision operator is used to study the transition of the MRI from kinetic to the MHD regime. The ZEUS MHD code is modified to include the key kinetic MHD terms: anisotropy, pressure tensor and anisotropic thermal conduction. The modified code is used to simulate the collisionless MRI in a local shearing box. As magnetic field is amplified by the MRI, pressure anisotropy ( p [perpendicular] > p || ) is created because of the adiabatic invariance (m 0( p [perpendicular] / B ). Larmor radius scale instabilities---mirror, ion-cyclotron, and firehose---are excited even at small pressure anisotropies (D p/p ~ 1/b). Pressure isotropization due to pitch angle scattering by these instabilities is included as a subgrid model. A key result of the kinetic MHD simulations is that the anisotropy stress can be as large as the Maxwell stress. It is shown, with the help of simple tests, that the centered differencing of anisotropic thermal conduction can cause the heat to flow from lower to higher temperatures, giving negative temperatures in regions with large temperature gradients. A new method, based on limiting the transverse temperature gradient, allows heat to flow only from higher to lower temperatures. Several tests and convergence studies are presented to compare the different methods.

Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

NASA Astrophysics Data System (ADS)

Kakhktsyan, V. M.; Khachatryan, A. Kh.

2013-07-01

A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

The initial value problem in Lagrangian drift kinetic theory

NASA Astrophysics Data System (ADS)

Burby, J. W.

2016-06-01

> Existing high-order variational drift kinetic theories contain unphysical rapidly varying modes that are not seen at low orders. These unphysical modes, which may be rapidly oscillating, damped or growing, are ushered in by a failure of conventional high-order drift kinetic theory to preserve the structure of its parent model's initial value problem. In short, the (infinite dimensional) system phase space is unphysically enlarged in conventional high-order variational drift kinetic theory. I present an alternative, `renormalized' variational approach to drift kinetic theory that manifestly respects the parent model's initial value problem. The basic philosophy underlying this alternate approach is that high-order drift kinetic theory ought to be derived by truncating the all-orders system phase-space Lagrangian instead of the usual `field particle' Lagrangian. For the sake of clarity, this story is told first through the lens of a finite-dimensional toy model of high-order variational drift kinetics; the analogous full-on drift kinetic story is discussed subsequently. The renormalized drift kinetic system, while variational and just as formally accurate as conventional formulations, does not support the troublesome rapidly varying modes.

Third-order nonlinear optical properties of methylammonium lead halide perovskite films

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Justin C.; Li, Zhen; Ndione, Paul F.

2016-01-01

We report third-order nonlinear coefficient values and decay time kinetics vs. halide composition (CH3NH3PbBr3 and CH3NH3PbBr2I), temperature, and excitation wavelength. The maximum values of the third-order nonlinear susceptibility X(3) (-1.6 x 10-6 esu) are similar to or larger than many common third-order materials. The source of the nonlinearity is shown to be primarily excitonic in the tribromide film by virtue of its strong enhancement near the exciton resonance. Nonresonant excitation reduces the nonlinearity significantly, as does increasing the temperature. Substitution of one I for one Br also reduces the nonlinearity by at least one order of magnitude, presumably due tomore » the lack of strong exciton resonance in the substituted form. The thin films are stable, highly homogenous (lacking significant light scattering), and simple and inexpensive to fabricate, making them potentially useful in a variety of optoelectronic applications in which wavelength selectivity is important.« less

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

The Control Based on Internal Average Kinetic Energy in Complex Environment for Multi-robot System

NASA Astrophysics Data System (ADS)

Yang, Mao; Tian, Yantao; Yin, Xianghua

In this paper, reference trajectory is designed according to minimum energy consumed for multi-robot system, which nonlinear programming and cubic spline interpolation are adopted. The control strategy is composed of two levels, which lower-level is simple PD control and the upper-level is based on the internal average kinetic energy for multi-robot system in the complex environment with velocity damping. Simulation tests verify the effectiveness of this control strategy.

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

PubMed

Fan, Quan-Yong; Yang, Guang-Hong

2017-01-01

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Kinetic analysis of hyperpolarized data with minimum a priori knowledge: Hybrid maximum entropy and nonlinear least squares method (MEM/NLS).

PubMed

Mariotti, Erika; Veronese, Mattia; Dunn, Joel T; Southworth, Richard; Eykyn, Thomas R

2015-06-01

To assess the feasibility of using a hybrid Maximum-Entropy/Nonlinear Least Squares (MEM/NLS) method for analyzing the kinetics of hyperpolarized dynamic data with minimum a priori knowledge. A continuous distribution of rates obtained through the Laplace inversion of the data is used as a constraint on the NLS fitting to derive a discrete spectrum of rates. Performance of the MEM/NLS algorithm was assessed through Monte Carlo simulations and validated by fitting the longitudinal relaxation time curves of hyperpolarized [1-(13) C] pyruvate acquired at 9.4 Tesla and at three different flip angles. The method was further used to assess the kinetics of hyperpolarized pyruvate-lactate exchange acquired in vitro in whole blood and to re-analyze the previously published in vitro reaction of hyperpolarized (15) N choline with choline kinase. The MEM/NLS method was found to be adequate for the kinetic characterization of hyperpolarized in vitro time-series. Additional insights were obtained from experimental data in blood as well as from previously published (15) N choline experimental data. The proposed method informs on the compartmental model that best approximate the biological system observed using hyperpolarized (13) C MR especially when the metabolic pathway assessed is complex or a new hyperpolarized probe is used. © 2014 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc.

Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2006-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Efficient numerical method for analyzing optical bistability in photonic crystal microcavities.

PubMed

Yuan, Lijun; Lu, Ya Yan

2013-05-20

Nonlinear optical effects can be enhanced by photonic crystal microcavities and be used to develop practical ultra-compact optical devices with low power requirements. The finite-difference time-domain method is the standard numerical method for simulating nonlinear optical devices, but it has limitations in terms of accuracy and efficiency. In this paper, a rigorous and efficient frequency-domain numerical method is developed for analyzing nonlinear optical devices where the nonlinear effect is concentrated in the microcavities. The method replaces the linear problem outside the microcavities by a rigorous and numerically computed boundary condition, then solves the nonlinear problem iteratively in a small region around the microcavities. Convergence of the iterative method is much easier to achieve since the size of the problem is significantly reduced. The method is presented for a specific two-dimensional photonic crystal waveguide-cavity system with a Kerr nonlinearity, using numerical methods that can take advantage of the geometric features of the structure. The method is able to calculate multiple solutions exhibiting the optical bistability phenomenon in the strongly nonlinear regime.

Optimal control in adaptive optics modeling of nonlinear systems

NASA Astrophysics Data System (ADS)

Herrmann, J.

The problem of using an adaptive optics system to correct for nonlinear effects like thermal blooming is addressed using a model containing nonlinear lenses through which Gaussian beams are propagated. The best correction of this nonlinear system can be formulated as a deterministic open loop optimal control problem. This treatment gives a limit for the best possible correction. Aspects of adaptive control and servo systems are not included at this stage. An attempt is made to determine that control in the transmitter plane which minimizes the time averaged area or maximizes the fluence in the target plane. The standard minimization procedure leads to a two-point-boundary-value problem, which is ill-conditioned in the case. The optimal control problem was solved using an iterative gradient technique. An instantaneous correction is introduced and compared with the optimal correction. The results of the calculations show that for short times or weak nonlinearities the instantaneous correction is close to the optimal correction, but that for long times and strong nonlinearities a large difference develops between the two types of correction. For these cases the steady state correction becomes better than the instantaneous correction and approaches the optimum correction.

A new energy transfer model for turbulent free shear flow

NASA Technical Reports Server (NTRS)

Liou, William W.-W.

1992-01-01

A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.

KEEN Wave Simulations: Comparing various PIC to various fixed grid Vlasov to Phase-Space Adaptive Sparse Tiling & Effective Lagrangian (PASTEL) Techniques

NASA Astrophysics Data System (ADS)

Afeyan, Bedros; Larson, David; Shadwick, Bradley; Sydora, Richard

2017-10-01

We compare various ways of solving the Vlasov-Poisson and Vlasov-Maxwell equations on rather demanding nonlinear kinetic phenomena associated with KEEN and KEEPN waves. KEEN stands for Kinetic, Electrostatic, Electron Nonlinear, and KEEPN, for electron-positron or pair plasmas analogs. Because these self-organized phase space structures are not steady-state, or single mode, or fluid or low order moment equation limited, typical techniques with low resolution or too much noise will distort the answer too much, too soon, and fail. This will be shown via Penrose criteria triggers for instability at the formation stage as well as particle orbit statistics in fully formed KEEN waves and KEEN-KEEN and KEEN-EPW interacting states. We will argue that PASTEL is a viable alternative to traditional methods with reasonable chances of success in higher dimensions. Work supported by a Grant from AFOSR PEEP.

Nonlinear Full-f Edge Gyrokinetic Turbulence Simulations

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Dimits, A. M.; Umansky, M. V.

2008-11-01

TEMPEST is a nonlinear full-f 5D electrostatic gyrokinetic code for simulations of neoclassical and turbulent transport for tokamak plasmas. Given an initial density perturbation, 4D TEMPEST simulations show that the kinetic GAM exists in the edge in the form of outgoing waves [1], its radial scale is set by plasma profiles, and the ion temperature inhomogeneity is necessary for GAM radial propagation. From an initial Maxwellian distribution with uniform poloidal profiles on flux surfaces, the 5D TEMPEST simulations in a flux coordinates with Boltzmann electron model in a circular geometry show the development of neoclassical equilibrium, the generation of the neoclassical electric field due to neoclassical polarization, and followed by a growth of instability due to the spatial gradients. 5D TEMPEST simulations of kinetic GAM turbulent generation, radial propagation, and its impact on transport will be reported. [1] X. Q. Xu, Phys. Rev. E., 78 (2008).

Saturation mechanisms of backward stimulated Raman scattering in a one-dimensional geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friou, A.; Bénisti, D.; Gremillet, L.

2013-10-15

In this paper, we investigate the saturation mechanisms of backward stimulated Raman scattering (BSRS) induced by nonlinear kinetic effects. In particular, we stress the importance of accounting for both the nonlinear frequency shift of the electron plasma wave and the growth of sidebands, in order to understand what stops the coherent growth of Raman scattering. Using a Bernstein-Greene-Kruskal approach, we provide an estimate for the maximum amplitude reached by a BSRS-driven plasma wave after the phase of monotonic growth. This estimate is in very good agreement with the results from kinetic simulations of stimulated Raman scattering using both a Vlasovmore » and a Particle in Cell code. Our analysis, which may be generalized to a multidimensional geometry, should provide a means to estimate the limits of backward Raman amplification or the effectiveness of strategies that aim at strongly reducing Raman reflectivity in a fusion plasma.« less

Learning the inverse kinetics of an octopus-like manipulator in three-dimensional space.

PubMed

Giorelli, M; Renda, F; Calisti, M; Arienti, A; Ferri, G; Laschi, C

2015-05-13

This work addresses the inverse kinematics problem of a bioinspired octopus-like manipulator moving in three-dimensional space. The bioinspired manipulator has a conical soft structure that confers the ability of twirling around objects as a real octopus arm does. Despite the simple design, the soft conical shape manipulator driven by cables is described by nonlinear differential equations, which are difficult to solve analytically. Since exact solutions of the equations are not available, the Jacobian matrix cannot be calculated analytically and the classical iterative methods cannot be used. To overcome the intrinsic problems of methods based on the Jacobian matrix, this paper proposes a neural network learning the inverse kinematics of a soft octopus-like manipulator driven by cables. After the learning phase, a feed-forward neural network is able to represent the relation between manipulator tip positions and forces applied to the cables. Experimental results show that a desired tip position can be achieved in a short time, since heavy computations are avoided, with a degree of accuracy of 8% relative average error with respect to the total arm length.

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

PubMed Central

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

NASA Astrophysics Data System (ADS)

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

ISS method for coordination control of nonlinear dynamical agents under directed topology.

PubMed

Wang, Xiangke; Qin, Jiahu; Yu, Changbin

2014-10-01

The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.

Nonlinear Response of Layer Growth Dynamics in the Mixed Kinetics-Bulk-Transport Regime

NASA Technical Reports Server (NTRS)

Vekilov, Peter G.; Alexander, J. Iwan D.; Rosenberger, Franz

1996-01-01

In situ high-resolution interferometry on horizontal facets of the protein lysozyme reveal that the local growth rate R, vicinal slope p, and tangential (step) velocity v fluctuate by up to 80% of their average values. The time scale of these fluctuations, which occur under steady bulk transport conditions through the formation and decay of step bunches (macrosteps), is of the order of 10 min. The fluctuation amplitude of R increases with growth rate (supersaturation) and crystal size, while the amplitude of the v and p fluctuations changes relatively little. Based on a stability analysis for equidistant step trains in the mixed transport-interface-kinetics regime, we argue that the fluctuations originate from the coupling of bulk transport with nonlinear interface kinetics. Furthermore, step bunches moving across the interface in the direction of or opposite to the buoyancy-driven convective flow increase or decrease in height, respectively. This is in agreement with analytical treatments of the interaction of moving steps with solution flow. Major excursions in growth rate are associated with the formation of lattice defects (striations). We show that, in general, the system-dependent kinetic Peclet number, Pe(sub k) , i.e., the relative weight of bulk transport and interface kinetics in the control of the growth process, governs the step bunching dynamics. Since Pe(sub k) can be modified by either forced solution flow or suppression of buoyancy-driven convection under reduced gravity, this model provides a rationale for the choice of specific transport conditions to minimize the formation of compositional inhomogeneities under steady bulk nutrient crystallization conditions.

Kinetic theory for the ion humps at the foot of the Earth's bow shock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jovanovic, D.; Krasnoselskikh, V. V.

2009-10-15

The nonlinear kinetic theory is presented for the ion acoustic perturbations at the foot of the Earth's quasiperpendicular bow shock, that is characterized by weakly magnetized electrons and unmagnetized ions. The streaming ions, due to the reflection of the solar wind ions from the shock, provide the free energy source for the linear instability of the acoustic wave. In the fully nonlinear regime, a coherent localized solution is found in the form of a stationary ion hump, which is traveling with the velocity close to the phase velocity of the linear mode. The structure is supported by the nonlinearities comingmore » from the increased population of the resonant beam ions, trapped in the self-consistent potential. As their size in the direction perpendicular to the local magnetic field is somewhat smaller that the electron Larmor radius and much larger that the Debye length, their spatial properties are determined by the effects of the magnetic field on weakly magnetized electrons. These coherent structures provide a theoretical explanation for the bipolar electric pulses, observed upstream of the shock by Polar and Cluster satellite missions.« less

Mammalian cell culture process for monoclonal antibody production: nonlinear modelling and parameter estimation.

PubMed

Selişteanu, Dan; Șendrescu, Dorin; Georgeanu, Vlad; Roman, Monica

2015-01-01

Monoclonal antibodies (mAbs) are at present one of the fastest growing products of pharmaceutical industry, with widespread applications in biochemistry, biology, and medicine. The operation of mAbs production processes is predominantly based on empirical knowledge, the improvements being achieved by using trial-and-error experiments and precedent practices. The nonlinearity of these processes and the absence of suitable instrumentation require an enhanced modelling effort and modern kinetic parameter estimation strategies. The present work is dedicated to nonlinear dynamic modelling and parameter estimation for a mammalian cell culture process used for mAb production. By using a dynamical model of such kind of processes, an optimization-based technique for estimation of kinetic parameters in the model of mammalian cell culture process is developed. The estimation is achieved as a result of minimizing an error function by a particle swarm optimization (PSO) algorithm. The proposed estimation approach is analyzed in this work by using a particular model of mammalian cell culture, as a case study, but is generic for this class of bioprocesses. The presented case study shows that the proposed parameter estimation technique provides a more accurate simulation of the experimentally observed process behaviour than reported in previous studies.

Nonlinear effects in subthreshold virtual electrode polarization.

PubMed

Sambelashvili, Aleksandre T; Nikolski, Vladimir P; Efimov, Igor R

2003-06-01

Introduction of the virtual electrode polarization (VEP) theory suggested solutions to several century-old puzzles of heart electrophysiology including explanation of the mechanisms of stimulation and defibrillation. Bidomain theory predicts that VEPs should exist at any stimulus strength. Although the presence of VEPs for strong suprathreshold pulses has been well documented, their existence at subthreshold strengths during diastole remains controversial. We studied cardiac membrane polarization produced by subthreshold stimuli in 1) rabbit ventricular muscle using high-resolution fluorescent imaging with the voltage-sensitive dye pyridinium 4-[2-[6-(dibutylamino)-2-naphthalenyl]-ethenyl]-1-(3-sulfopropyl)hydroxide (di-4-ANEPPS) and 2) an active bidomain model with Luo-Rudy ion channel kinetics. Both in vitro and in numero models show that the common dog-bone-shaped VEP is present at any stimulus strength during both systole and diastole. Diastolic subthreshold VEPs exhibited nonlinear properties that were expressed in time-dependent asymmetric reversal of membrane polarization with respect to stimulus polarity. The bidomain model reveals that this asymmetry is due to nonlinear properties of the inward rectifier potassium current. Our results suggest that active ion channel kinetics modulate the transmembrane polarization pattern that is predicted by the linear bidomain model of cardiac syncytium.

Kinetic Monte Carlo simulations of excitation density dependent scintillation in CsI and CsI(Tl)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Zhiguo; Williams, Richard; Grim, Joel

2013-08-15

Nonlinear quenching of electron-hole pairs in the denser regions of ionization tracks created by γ-ray and high-energy electrons is a likely cause of the light yield nonproportionality of many inorganic scintillators. Therefore, kinetic Monte Carlo (KMC) simulations were carried out to investigate the scintillation properties of pure and thallium-doped CsI as a function of electron-hole pair density. The availability of recent experimental data on the excitation density dependence of the light yield of CsI following ultraviolet excitation allowed for an improved parameterization of the interactions between self-trapped excitons (STE) in the KMC model via dipole-dipole Förster transfer. The KMC simulationsmore » reveal that nonlinear quenching occurs very rapidly (within a few picoseconds) in the early stages of the scintillation process. In addition, the simulations predict that the concentration of thallium activators can affect the extent of nonlinear quenching as it has a direct influence on the STE density through STE dissociation and electron scavenging. This improved model will enable more realistic simulations of the nonproportional γ-ray and electron response of inorganic scintillators.« less

The interplay between the kinetic nonlinear frequency shift and the flowing gradient in stimulated Brillouin scattering

NASA Astrophysics Data System (ADS)

Wang, Q.; Y Zheng, C.; Liu, Z. J.; Xiao, C. Z.; Feng, Q. S.; Zhang, H. C.; He, X. T.

2018-02-01

The effect of the kinetic nonlinear frequency shift (KNFS) on backward stimulated Brillouin scattering (SBS) in homogeneous plasmas and inhomogeneous flowing plasmas is investigated by three-wave coupled-mode equations. When the positive contribution to the KNFS from electrons as well as the negative contribution from ions is included, the net KNFS can become positive at a large electron-ion temperature ratio {{ZT}}e/{T}i. In homogeneous plasmas, KNFS can greatly reduce the SBS reflectivity at low or large {{ZT}}e/{T}i but has a weak effect on SBS at {{ZT}}e/{T}i where the positive frequency shifts from electrons almost cancels out the negative shifts from ions. In inhomogeneous plasmas, the net negative frequency shift can enhance the backward SBS reflectivity for the negative gradient of the plasma flowing, and can suppress the reflectivity for the positive case. On the contrary, the net positive frequency can suppress the reflectivity for the negative case of the flowing gradient and enhance the reflectivity for the positive case. This indicates that the SBS in inhomogeneous flowing plasmas can be controlled by changing the sign of the nonlinear frequency shift.

Modulation of kinetic Alfvén waves in an intermediate low-beta magnetoplasma

NASA Astrophysics Data System (ADS)

Chatterjee, Debjani; Misra, A. P.

2018-05-01

We study the amplitude modulation of nonlinear kinetic Alfvén waves (KAWs) in an intermediate low-beta magnetoplasma. Starting from a set of fluid equations coupled to the Maxwell's equations, we derive a coupled set of nonlinear partial differential equations (PDEs) which govern the evolution of KAW envelopes in the plasma. The modulational instability (MI) of such KAW envelopes is then studied by a nonlinear Schrödinger equation derived from the coupled PDEs. It is shown that the KAWs can evolve into bright envelope solitons or can undergo damping depending on whether the characteristic ratio ( α ) of the Alfvén to ion-acoustic speeds remains above or below a critical value. The parameter α is also found to shift the MI domains around the k x k z plane, where k x ( k z ) is the KAW number perpendicular (parallel) to the external magnetic field. The growth rate of MI, as well as the frequency shift and the energy transfer rate, are obtained and analyzed. The results can be useful for understanding the existence and formation of bright and dark envelope solitons, or damping of KAW envelopes in space plasmas, e.g., interplanetary space, solar winds, etc.

Toroidal gyro-Landau fluid model turbulence simulations in a nonlinear ballooning mode representation with radial modes

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Kerbel, G. D.; Milovich, J.

1994-07-01

The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyrokinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro-Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel three-dimensional (3-D) nonlinear ballooning mode representation. The representation is a Fourier transform of a field line following basis (ky',kx',z') with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky' = 0, kx' ≠ 0) ``radial modes'' in stabilizing the transport from the finite-n ITG ballooning modes. Detailing the parametric dependence of toroidal ITG turbulence is a key result.

Mammalian Cell Culture Process for Monoclonal Antibody Production: Nonlinear Modelling and Parameter Estimation

PubMed Central

Selişteanu, Dan; Șendrescu, Dorin; Georgeanu, Vlad

2015-01-01

Monoclonal antibodies (mAbs) are at present one of the fastest growing products of pharmaceutical industry, with widespread applications in biochemistry, biology, and medicine. The operation of mAbs production processes is predominantly based on empirical knowledge, the improvements being achieved by using trial-and-error experiments and precedent practices. The nonlinearity of these processes and the absence of suitable instrumentation require an enhanced modelling effort and modern kinetic parameter estimation strategies. The present work is dedicated to nonlinear dynamic modelling and parameter estimation for a mammalian cell culture process used for mAb production. By using a dynamical model of such kind of processes, an optimization-based technique for estimation of kinetic parameters in the model of mammalian cell culture process is developed. The estimation is achieved as a result of minimizing an error function by a particle swarm optimization (PSO) algorithm. The proposed estimation approach is analyzed in this work by using a particular model of mammalian cell culture, as a case study, but is generic for this class of bioprocesses. The presented case study shows that the proposed parameter estimation technique provides a more accurate simulation of the experimentally observed process behaviour than reported in previous studies. PMID:25685797

Linear and nonlinear analysis of kinetic Alfven waves in quantum magneto-plasmas with arbitrary temperature degeneracy

NASA Astrophysics Data System (ADS)

Sadiq, Nauman; Ahmad, Mushtaq; Farooq, M.; Jan, Qasim

2018-06-01

Linear and nonlinear kinetic Alfven waves (KAWs) are studied in collisionless, non-relativistic two fluid quantum magneto-plasmas by considering arbitrary temperature degeneracy. A general coupling parameter is applied to discuss the range of validity of the proposed model in nearly degenerate and nearly non-degenerate plasma limits. Linear analysis of KAWs shows an increase (decrease) in frequency with the increase in parameter ζ ( δ ) for the nearly non-degenerate (nearly degenerate) plasma limit. The energy integral equation in the form of Sagdeev potential is obtained by using the approach of the Lorentz transformation. The analysis reveals that the amplitude of the Sagdeev potential curves and soliton structures remains the same, but the potential depth and width of soliton structure change for both the limiting cases. It is further observed that only density hump structures are formed in the sub-alfvenic region for value Kz 2 > 1 . The effects of parameters ζ, δ on the nonlinear properties of KAWs are shown in graphical plots. New results for comparison with earlier work have also been highlighted. The significance of this work to astrophysical plasmas is also emphasized.

The troposphere-to-stratosphere transition in kinetic energy spectra and nonlinear spectral fluxes as seen in ECMWF analyses

NASA Astrophysics Data System (ADS)

Burgess, A. B. H.; Erler, A. R.; Shepherd, T. G.

2012-04-01

We present spectra, nonlinear interaction terms, and fluxes computed for horizontal wind fields from high-resolution meteorological analyses made available by ECMWF for the International Polar Year. Total kinetic energy spectra clearly show two spectral regimes: a steep spectrum at large scales and a shallow spectrum in the mesoscale. The spectral shallowing appears at ~200 hPa, and is due to decreasing rotational power with height, which results in the shallower divergent spectrum dominating in the mesoscale. The spectra we find are steeper than those observed in aircraft data and GCM simulations. Though the analyses resolve total spherical harmonic wavenumbers up to n = 721, effects of dissipation on the fluxes and spectra are visible starting at about n = 200. We find a weak forward energy cascade and a downscale enstrophy cascade in the mesoscale. Eddy-eddy nonlinear kinetic energy transfers reach maximum amplitudes at the tropopause, and decrease with height thereafter; zonal mean-eddy transfers dominate in the stratosphere. In addition, zonal anisotropy reaches a minimum at the tropopause. Combined with strong eddy-eddy interactions, this suggests flow in the tropopause region is very active and bears the greatest resemblance to isotropic turbulence. We find constant enstrophy flux over a broad range of wavenumbers around the tropopause and in the upper stratosphere. A relatively constant spectral enstrophy flux at the tropopause suggests a turbulent inertial range, and that the enstrophy flux is resolved. A main result of our work is its implications for explaining the shallow mesoscale spectrum observed in aircraft wind measurements, GCM studies, and now meteorological analyses. The strong divergent component in the shallow mesoscale spectrum indicates unbalanced flow, and nonlinear transfers decreasing quickly with height are characteristic of waves, not turbulence. Together with the downscale flux of energ y through the shallow spectral range, these findings add further evidence that the shallow mesoscale spectrum is not generated by balanced two-dimensional turbulence.

Non-linear dynamics of stable carbon and hydrogen isotope signatures based on a biological kinetic model of aerobic enzymatic methane oxidation.

PubMed

Vavilin, Vasily A; Rytov, Sergey V; Shim, Natalia; Vogt, Carsten

2016-06-01

The non-linear dynamics of stable carbon and hydrogen isotope signatures during methane oxidation by the methanotrophic bacteria Methylosinus sporium strain 5 (NCIMB 11126) and Methylocaldum gracile strain 14 L (NCIMB 11912) under copper-rich (8.9 µM Cu(2+)), copper-limited (0.3 µM Cu(2+)) or copper-regular (1.1 µM Cu(2+)) conditions has been described mathematically. The model was calibrated by experimental data of methane quantities and carbon and hydrogen isotope signatures of methane measured previously in laboratory microcosms reported by Feisthauer et al. [ 1 ] M. gracile initially oxidizes methane by a particulate methane monooxygenase and assimilates formaldehyde via the ribulose monophosphate pathway, whereas M. sporium expresses a soluble methane monooxygenase under copper-limited conditions and uses the serine pathway for carbon assimilation. The model shows that during methane solubilization dominant carbon and hydrogen isotope fractionation occurs. An increase of biomass due to growth of methanotrophs causes an increase of particulate or soluble monooxygenase that, in turn, decreases soluble methane concentration intensifying methane solubilization. The specific maximum rate of methane oxidation υm was proved to be equal to 4.0 and 1.3 mM mM(-1) h(-1) for M. sporium under copper-rich and copper-limited conditions, respectively, and 0.5 mM mM(-1) h(-1) for M. gracile. The model shows that methane oxidation cannot be described by traditional first-order kinetics. The kinetic isotope fractionation ceases when methane concentrations decrease close to the threshold value. Applicability of the non-linear model was confirmed by dynamics of carbon isotope signature for carbon dioxide that was depleted and later enriched in (13)C. Contrasting to the common Rayleigh linear graph, the dynamic curves allow identifying inappropriate isotope data due to inaccurate substrate concentration analyses. The non-linear model pretty adequately described experimental data presented in the two-dimensional plot of hydrogen versus carbon stable isotope signatures.

Numerical method for solving the nonlinear four-point boundary value problems

NASA Astrophysics Data System (ADS)

Lin, Yingzhen; Lin, Jinnan

2010-12-01

In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Shultz, Louis A.

1994-01-01

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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 usemore » 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)« less

Cross-Diffusion Driven Instability for a Lotka-Volterra Competitive Reaction-Diffusion System

NASA Astrophysics Data System (ADS)

Gambino, G.; Lombardo, M. C.; Sammartino, M.

2008-04-01

In this work we investigate the possibility of the pattern formation for a reaction-diffusion system with nonlinear diffusion terms. Through a linear stability analysis we find the conditions which allow a homogeneous steady state (stable for the kinetics) to become unstable through a Turing mechanism. In particular, we show how cross-diffusion effects are responsible for the initiation of spatial patterns. Finally, we find a Fisher amplitude equation which describes the weakly nonlinear dynamics of the system near the marginal stability.

FAST TRACK COMMUNICATION: The nonlinear fragmentation equation

NASA Astrophysics Data System (ADS)

Ernst, Matthieu H.; Pagonabarraga, Ignacio

2007-04-01

We study the kinetics of nonlinear irreversible fragmentation. Here, fragmentation is induced by interactions/collisions between pairs of particles and modelled by general classes of interaction kernels, for several types of breakage models. We construct initial value and scaling solutions of the fragmentation equations, and apply the 'non-vanishing mass flux' criterion for the occurrence of shattering transitions. These properties enable us to determine the phase diagram for the occurrence of shattering states and of scaling states in the phase space of model parameters.

Paralinear Oxidation of Silicon Nitride in a Water Vapor/Oxygen Environment

NASA Technical Reports Server (NTRS)

Fox, Dennis S.; Opila, Elizabeth J.; Nguyen, QuynhGiao; Humphrey, Donald L.; Lewton, Susan M.; Gray, Hugh R. (Technical Monitor)

2002-01-01

Three silicon nitride materials were exposed to dry oxygen flowing at 0.44 cm/s at temperatures between 1200 and 1400 C. Reaction kinetics were measured with a continuously recording microbalance. Parabolic kinetics were observed. When the same materials were exposed to a 50% H2O - 50% O2 gas mixture flowing at 4.4 cm/s, all three types exhibited paralinear kinetics. The material is oxidized by water vapor to form solid silica. The protective silica is in turn volatilized by water vapor to form primarily gaseous Si(OH)4. Nonlinear least squares analysis and a paralinear kinetic model were used to determine both parabolic and linear rate constants from the kinetic data. Volatilization of the protective silica scale can result in accelerated consumption of Si3N4. Recession rates under conditions more representative of actual combustors are compared to the furnace data.

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 3: Illustrative test problems

NASA Technical Reports Server (NTRS)

Bittker, David A.; Radhakrishnan, Krishnan

1994-01-01

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 3 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 3 explains the kinetics and kinetics-plus-sensitivity analysis problems supplied with LSENS and presents sample results. These problems illustrate the various capabilities of, and reaction models that can be solved by, the code and may provide a convenient starting point for the user to construct the problem data file required to execute LSENS. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems

NASA Technical Reports Server (NTRS)

Padovan, Joe; Krishna, Lala

1986-01-01

To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

On the interaction of small-scale linear waves with nonlinear solitary waves

NASA Astrophysics Data System (ADS)

Xu, Chengzhu; Stastna, Marek

2017-04-01

In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow interaction in a fully nonlinear framework.

Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

NASA Technical Reports Server (NTRS)

Costiner, Sorin; Taasan, Shlomo

1994-01-01

This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.

Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

NASA Astrophysics Data System (ADS)

Kharibegashvili, S. S.; Jokhadze, O. M.

2014-04-01

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles.

Finite element analysis of structural engineering problems using a viscoplastic model incorporating two back stresses

NASA Technical Reports Server (NTRS)

Arya, Vinod K.; Halford, Gary R.

1993-01-01

The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. To demonstrate suitability for nonlinear structural analyses, the model is implemented into a finite element program and analyses for several uniaxial and multiaxial problems are performed. Good agreement is shown between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.

Nonlinear interaction and wave breaking with a submerged porous structure

NASA Astrophysics Data System (ADS)

Hsieh, Chih-Min; Sau, Amalendu; Hwang, Robert R.; Yang, W. C.

2016-12-01

Numerical simulations are performed to investigate interactive velocity, streamline, turbulent kinetic energy, and vorticity perturbations in the near-field of a submerged offshore porous triangular structure, as Stokes waves of different heights pass through. The wave-structure interaction and free-surface breaking for the investigated flow situations are established based on solutions of 2D Reynolds Averaged Navier-Stokes equations in a Cartesian grid in combination with K-ɛ turbulent closure and the volume of fluid methodology. The accuracy and stability of the adopted model are ascertained by extensive comparisons of computed data with the existing experimental and theoretical findings and through efficient predictions of the internal physical kinetics. Simulations unfold "clockwise" and "anticlockwise" rotation of fluid below the trough and the crest of the viscous waves, and the penetrated wave energy creates systematic flow perturbation in the porous body. The interfacial growths of the turbulent kinetic energy and the vorticity appear phenomenal, around the apex of the immersed structure, and enhanced significantly following wave breaking. Different values of porosity parameter and two non-porous cases have been examined in combination with varied incident wave height to reveal/analyze the nonlinear flow behavior in regard to local spectral amplification and phase-plane signatures. The evolution of leading harmonics of the undulating free-surface and the vertical velocity exhibits dominating roles of the first and the second modes in inducing the nonlinearity in the post-breaking near-field that penetrates well below the surface layer. The study further suggests the existence of a critical porosity that can substantially enhance the wave-shoaling and interface breaking.

Neon diffusion kinetics and implications for cosmogenic neon paleothermometry in feldspars

NASA Astrophysics Data System (ADS)

Tremblay, Marissa M.; Shuster, David L.; Balco, Greg; Cassata, William S.

2017-05-01

Observations of cosmogenic neon concentrations in feldspars can potentially be used to constrain the surface exposure duration or surface temperature history of geologic samples. The applicability of cosmogenic neon to either application depends on the temperature-dependent diffusivity of neon isotopes. In this work, we investigate the kinetics of neon diffusion in feldspars of different compositions and geologic origins through stepwise degassing experiments on single, proton-irradiated crystals. To understand the potential causes of complex diffusion behavior that is sometimes manifest as nonlinearity in Arrhenius plots, we compare our results to argon stepwise degassing experiments previously conducted on the same feldspars. Many of the feldspars we studied exhibit linear Arrhenius behavior for neon whereas argon degassing from the same feldspars did not. This suggests that nonlinear behavior in argon experiments is an artifact of structural changes during laboratory heating. However, other feldspars that we examined exhibit nonlinear Arrhenius behavior for neon diffusion at temperatures far below any known structural changes, which suggests that some preexisting material property is responsible for the complex behavior. In general, neon diffusion kinetics vary widely across the different feldspars studied, with estimated activation energies (Ea) ranging from 83.3 to 110.7 kJ/mol and apparent pre-exponential factors (D0) spanning three orders of magnitude from 2.4 × 10-3 to 8.9 × 10-1 cm2 s-1. As a consequence of this variability, the ability to reconstruct temperatures or exposure durations from cosmogenic neon abundances will depend on both the specific feldspar and the surface temperature conditions at the geologic site of interest.

Kinetic treatment of nonlinear ion-acoustic waves in multi-ion plasma

NASA Astrophysics Data System (ADS)

Ahmad, Zulfiqar; Ahmad, Mushtaq; Qamar, A.

2017-09-01

By applying the kinetic theory of the Valsove-Poisson model and the reductive perturbation technique, a Korteweg-de Vries (KdV) equation is derived for small but finite amplitude ion acoustic waves in multi-ion plasma composed of positive and negative ions along with the fraction of electrons. A correspondent equation is also derived from the basic set of fluid equations of adiabatic ions and isothermal electrons. Both kinetic and fluid KdV equations are stationary solved with different nature of coefficients. Their differences are discussed both analytically and numerically. The criteria of the fluid approach as a limiting case of kinetic theory are also discussed. The presence of negative ion makes some modification in the solitary structure that has also been discussed with its implication at the laboratory level.

Filamentary and hierarchical pictures - Kinetic energy criterion

NASA Technical Reports Server (NTRS)

Klypin, Anatoly A.; Melott, Adrian L.

1992-01-01

We present a new criterion for formation of second-generation filaments. The criterion called the kinetic energy ratio, KR, is based on comparison of peculiar velocities at different scales. We suggest that the clumpiness of the distribution in some cases might be less important than the 'coldness' or 'hotness' of the flow for formation of coherent structures. The kinetic energy ratio is analogous to the Mach number except for one essential difference. If at some scale KR is greater than 1, as estimated at the linear stage, then when fluctuations of this scale reach nonlinearity, the objects they produce must be anisotropic ('filamentary'). In the case of power-law initial spectra the kinetic ratio criterion suggests that the border line is the power-spectrum with the slope n = -1.

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

Performance bounds for nonlinear systems with a nonlinear ℒ2-gain property

NASA Astrophysics Data System (ADS)

Zhang, Huan; Dower, Peter M.

2012-09-01

Nonlinear ℒ2-gain is a finite gain concept that generalises the notion of conventional (linear) finite ℒ2-gain to admit the application of ℒ2-gain analysis tools of a broader class of nonlinear systems. The computation of tight comparison function bounds for this nonlinear ℒ2-gain property is important in applications such as small gain design. This article presents an approximation framework for these comparison function bounds through the formulation and solution of an optimal control problem. Key to the solution of this problem is the lifting of an ℒ2-norm input constraint, which is facilitated via the introduction of an energy saturation operator. This admits the solution of the optimal control problem of interest via dynamic programming and associated numerical methods, leading to the computation of the proposed bounds. Two examples are presented to demonstrate this approach.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

PubMed

Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

2017-09-01

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Nonlinear Waves and Inverse Scattering

DTIC Science & Technology

1990-09-18

to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

USING METHANOL-WATER SYSTEMS TO INVESTIGATE PHENANTHRENE SORPTION-DESORPTION ON SEDIMENT

EPA Science Inventory

Sorption isotherm nonlinearity, sorption-desorption hysteresis, slow desorption kinetics, and other nonideal phenomena have been attributed to the differing sorptive characteristics of the natural organic matter (NOM) polymers associated with soils and sediments. A conceptualizat...

Nucleation and convection effects in protein crystal growth

NASA Technical Reports Server (NTRS)

Rosenberger, Franz (Principal Investigator)

1996-01-01

The following activities are reported on: repartitioning of NaCl and protein impurities in lysozyme crystallization; dependence of lysozyme growth kinetics on step sources and impurities; facet morphology response to nonuniformities in nutrient and impurity supply; interactions in undersaturated and supersaturated lysozyme solutions; heterogeneity determination and purification of commercial hen egg white lysozyme; nonlinear response of layer growth dynamics in the mixed kinetics-bulk transport regime; development of a simultaneous multiangle light scattering technique; and x-ray topography of tetragonal lysozyme grown by the temperature-control technique.

Convective cell generation by kinetic Alfven wave turbulence in the auroral ionosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, J. S.; Wu, D. J.; Yu, M. Y.

2012-06-15

Modulation of convective cells by kinetic Alfven wave (KAW) turbulence is investigated. The interaction is governed by a nonlinear dispersion relation for the convective cells. It is shown that KAW turbulence is disrupted by excitation of the large-scale convective motion through a resonant instability. Application of the results to the auroral ionosphere shows that cross-scale coupling of the KAW turbulence and convective cells plays an important role in the evolution of ionospheric plasma turbulence.

Direct application of Padé approximant for solving nonlinear differential equations.

PubMed

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes with a nonlinear conjugate gradient method.

PubMed

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho

2008-12-01

Geometrical optics analysis of the structural imperfection of retroreflection corner cubes is described. In the analysis, a geometrical optics model of six-beam reflection patterns generated by an imperfect retroreflection corner cube is developed, and its structural error extraction is formulated as a nonlinear optimization problem. The nonlinear conjugate gradient method is employed for solving the nonlinear optimization problem, and its detailed implementation is described. The proposed method of analysis is a mathematical basis for the nondestructive optical inspection of imperfectly fabricated retroreflection corner cubes.

Numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains.

PubMed

Li, Hongwei; Guo, Yue

2017-12-01

The numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains is considered by applying the artificial boundary method in this paper. In order to design the local absorbing boundary conditions for the coupled nonlinear Schrödinger equations, we generalize the unified approach previously proposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709]. Based on the methodology underlying the unified approach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-way operator to approximate the linear term to make the wave out-going, and finally we combine the one-way operator with the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original problem into an initial boundary value problem on the bounded domain, which can be solved by the finite difference method. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Ample numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

Nonlinear Analysis of Two-phase Circumferential Motion in the Ablation Circumstance

NASA Astrophysics Data System (ADS)

Xiao-liang, Xu; Hai-ming, Huang; Zi-mao, Zhang

2010-05-01

In aerospace craft reentry and solid rocket propellant nozzle, thermal chemistry ablation is a complex process coupling with convection, heat transfer, mass transfer and chemical reaction. Based on discrete vortex method (DVM), thermal chemical ablation model and particle kinetic model, a computational module dealing with the two-phase circumferential motion in ablation circumstance is designed, the ablation velocity and circumferential field can be thus calculated. The calculated nonlinear time series are analyzed in chaotic identification method: relative chaotic characters such as correlation dimension and the maximum Lyapunov exponent are calculated, fractal dimension of vortex bulbs and particles distributions are also obtained, thus the nonlinear ablation process can be judged as a spatiotemporal chaotic process.

Nonlinear dielectric response and transient current: An effective potential for ferroelectric domain wall displacement

NASA Astrophysics Data System (ADS)

Placeres Jiménez, Rolando; Pedro Rino, José; Marino Gonçalves, André; Antonio Eiras, José

2013-09-01

Ferroelectric domain walls are modeled as rigid bodies moving under the action of a potential field in a dissipative medium. Assuming that the dielectric permittivity follows the dependence ɛ '∝1/(α+βE2), it obtained the exact expression for the effective potential. Simulations of polarization current correctly predict a power law. Such results could be valuable in the study of domain wall kinetic and ultrafast polarization processes. The model is extended to poled samples allowing the study of nonlinear dielectric permittivity under subswitching electric fields. Experimental nonlinear data from PZT 20/80 thin films and Fe+3 doped PZT 40/60 ceramic are reproduced.

Nonlinear dynamics of toroidal Alfvén eigenmodes in presence of tearing modes

NASA Astrophysics Data System (ADS)

Zhu, Jia; Ma, Zhiwei; Wang, Sheng; Zhang, Wei

2016-10-01

A new hybrid kinetic-MHD code CLT-K is developed to study nonlinear dynamics of n =1 toroidal Alfvén eigenmodes (TAEs) with the m/n =2/1 tearing mode. It is found that the n =1 TAE is first excited by isotropic energetic particles in the earlier stage and reaches the steady state due to wave-particle interaction. After the saturation of the n =1 TAE, the tearing mode intervenes and triggers the second growth of the mode. The modes goes into the second steady state due to multiple tearing mode-mode nonlinear coupling. Both wave-particle and wave-wave interactions are observed in our hybrid simulation.

Universal linear and nonlinear electrodynamics of a Dirac fluid

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, Dmitry N.; Fogler, Michael M.

2018-03-01

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential, or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory.

A synergic simulation-optimization approach for analyzing biomolecular dynamics in living organisms.

PubMed

Sadegh Zadeh, Kouroush

2011-01-01

A synergic duo simulation-optimization approach was developed and implemented to study protein-substrate dynamics and binding kinetics in living organisms. The forward problem is a system of several coupled nonlinear partial differential equations which, with a given set of kinetics and diffusion parameters, can provide not only the commonly used bleached area-averaged time series in fluorescence microscopy experiments but more informative full biomolecular/drug space-time series and can be successfully used to study dynamics of both Dirac and Gaussian fluorescence-labeled biomacromolecules in vivo. The incomplete Cholesky preconditioner was coupled with the finite difference discretization scheme and an adaptive time-stepping strategy to solve the forward problem. The proposed approach was validated with analytical as well as reference solutions and used to simulate dynamics of GFP-tagged glucocorticoid receptor (GFP-GR) in mouse cancer cell during a fluorescence recovery after photobleaching experiment. Model analysis indicates that the commonly practiced bleach spot-averaged time series is not an efficient approach to extract physiological information from the fluorescence microscopy protocols. It was recommended that experimental biophysicists should use full space-time series, resulting from experimental protocols, to study dynamics of biomacromolecules and drugs in living organisms. It was also concluded that in parameterization of biological mass transfer processes, setting the norm of the gradient of the penalty function at the solution to zero is not an efficient stopping rule to end the inverse algorithm. Theoreticians should use multi-criteria stopping rules to quantify model parameters by optimization. Copyright © 2010 Elsevier Ltd. All rights reserved.

Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

NASA Astrophysics Data System (ADS)

Costiner, Sorin; Ta'asan, Shlomo

1995-07-01

Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

Nonlinear optical conductivity and subharmonic instabilities of graphene in a strong electromagnetic field

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Basov, Dimitri; Fogler, Michael

We study theoretically the second-order nonlinear optical conductivity σ (2) of graphene as a function of frequency and momentum. We distinguish two regimes. At frequencies ω higher than the temperature-dependent electron-electron collision rate γee- 1 , the conductivity σ (2) can be derived from the semiclassical kinetic equation. The calculation requires taking into account the photon drag (Lorentz force) due to the ac magnetic field. In the low-frequency hydrodynamic regime ω <<γee- 1 , the nonlinear conductivity has a different form and the photon drag effect is suppressed. As a consequence of the nonlinearity, a strong enough photoexcitation can cause spontaneous generation of collective modes in a graphene strip: plasmons in the high-frequency regime and energy waves (demons) in the hydrodynamic one. The dominant instability occurs at frequency ω / 2 .

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Photochemical numerics for global-scale modeling: Fidelity and GCM testing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elliott, S.; Jim Kao, Chih-Yue; Zhao, X.

1995-03-01

Atmospheric photochemistry lies at the heart of global-scale pollution problems, but it is a nonlinear system embedded in nonlinear transport and so must be modeled in three dimensions. Total earth grids are massive and kinetics require dozens of interacting tracers, taxing supercomputers to their limits in global calculations. A matrix-free and noniterative family scheme is described that permits chemical step sizes an order of magnitude or more larger than time constants for molecular groupings, in the 1-h range used for transport. Families are partitioned through linearized implicit integrations that produce stabilizing species concentrations for a mass-conserving forward solver. The kineticsmore » are also parallelized by moving geographic loops innermost and changes in the continuity equations are automated through list reading. The combination of speed, parallelization and automation renders the programs naturally modular. Accuracy lies within 1% for all species in week-long fidelity tests. A 50-species, 150-reaction stratospheric module tested in a spectral GCM benchmarks at 10 min CPU time per day and agrees with lower-dimensionality simulations. Tropospheric nonmethane hydrocarbon chemistry will soon be added, and inherently three-dimensional phenomena will be investigated both decoupled from dynamics and in a complete chemical GCM. 225 refs., 11 figs., 2 tabs.« less

User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

NASA Technical Reports Server (NTRS)

Whitcomb, J. D.; Dattaguru, B.

1984-01-01

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.

Nonlinear oscillatory rarefied gas flow inside a rectangular cavity

NASA Astrophysics Data System (ADS)

Wang, Peng; Zhu, Lianhua; Su, Wei; Wu, Lei; Zhang, Yonghao

2018-04-01

The nonlinear oscillation of rarefied gas flow inside a two-dimensional rectangular cavity is investigated on the basis of the Shakhov kinetic equation. The gas dynamics, heat transfer, and damping force are studied numerically via the discrete unified gas-kinetic scheme for a wide range of parameters, including gas rarefaction, cavity aspect ratio, and oscillation frequency. Contrary to the linear oscillation where the velocity, temperature, and heat flux are symmetrical and oscillate with the same frequency as the oscillating lid, flow properties in nonlinear oscillatory cases turn out to be asymmetrical, and second-harmonic oscillation of the temperature field is observed. As a consequence, the amplitude of the shear stress near the top-right corner of the cavity could be several times larger than that at the top-left corner, while the temperature at the top-right corner could be significantly higher than the wall temperature in nearly the whole oscillation period. For the linear oscillation with the frequency over a critical value, and for the nonlinear oscillation, the heat transfer from the hot to cold region dominates inside the cavity, which is contrary to the anti-Fourier heat transfer in a low-speed rarefied lid-driven cavity flow. The damping force exerted on the oscillating lid is studied in detail, and the scaling laws are developed to describe the dependency of the resonance and antiresonance frequencies (corresponding to the damping force at a local maximum and minimum, respectively) on the reciprocal aspect ratio from the near hydrodynamic to highly rarefied regimes. These findings could be useful in the design of the micro-electro-mechanical devices operating in the nonlinear-flow regime.

A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.

1991-01-01

The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.

Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators

NASA Astrophysics Data System (ADS)

Cho, Yumi

2018-05-01

We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.

Thermally induced rarefied gas flow in a three-dimensional enclosure with square cross-section

NASA Astrophysics Data System (ADS)

Zhu, Lianhua; Yang, Xiaofan; Guo, Zhaoli

2017-12-01

Rarefied gas flow in a three-dimensional enclosure induced by nonuniform temperature distribution is numerically investigated. The enclosure has a square channel-like geometry with alternatively heated closed ends and lateral walls with a linear temperature distribution. A recently proposed implicit discrete velocity method with a memory reduction technique is used to numerically simulate the problem based on the nonlinear Shakhov kinetic equation. The Knudsen number dependencies of the vortices pattern, slip velocity at the planar walls and edges, and heat transfer are investigated. The influences of the temperature ratio imposed at the ends of the enclosure and the geometric aspect ratio are also evaluated. The overall flow pattern shows similarities with those observed in two-dimensional configurations in literature. However, features due to the three-dimensionality are observed with vortices that are not identified in previous studies on similar two-dimensional enclosures at high Knudsen and small aspect ratios.

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

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

NASA Astrophysics Data System (ADS)

Schmidt, Eldon; Lazareth, Otto; Ludewig, Hans

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.

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

System design optimization for a Mars-roving vehicle and perturbed-optimal solutions in nonlinear programming

NASA Technical Reports Server (NTRS)

Pavarini, C.

1974-01-01

Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.

Program for the solution of multipoint boundary value problems of quasilinear differential equations

NASA Technical Reports Server (NTRS)

1973-01-01

Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

From nonlinear optimization to convex optimization through firefly algorithm and indirect approach with applications to CAD/CAM.

PubMed

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

PubMed Central

Gálvez, Akemi; Iglesias, Andrés

2013-01-01

Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor's method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently. PMID:24376380

An enhanced lumped element electrical model of a double barrier memristive device

NASA Astrophysics Data System (ADS)

Solan, Enver; Dirkmann, Sven; Hansen, Mirko; Schroeder, Dietmar; Kohlstedt, Hermann; Ziegler, Martin; Mussenbrock, Thomas; Ochs, Karlheinz

2017-05-01

The massive parallel approach of neuromorphic circuits leads to effective methods for solving complex problems. It has turned out that resistive switching devices with a continuous resistance range are potential candidates for such applications. These devices are memristive systems—nonlinear resistors with memory. They are fabricated in nanotechnology and hence parameter spread during fabrication may aggravate reproducible analyses. This issue makes simulation models of memristive devices worthwhile. Kinetic Monte-Carlo simulations based on a distributed model of the device can be used to understand the underlying physical and chemical phenomena. However, such simulations are very time-consuming and neither convenient for investigations of whole circuits nor for real-time applications, e.g. emulation purposes. Instead, a concentrated model of the device can be used for both fast simulations and real-time applications, respectively. We introduce an enhanced electrical model of a valence change mechanism (VCM) based double barrier memristive device (DBMD) with a continuous resistance range. This device consists of an ultra-thin memristive layer sandwiched between a tunnel barrier and a Schottky-contact. The introduced model leads to very fast simulations by using usual circuit simulation tools while maintaining physically meaningful parameters. Kinetic Monte-Carlo simulations based on a distributed model and experimental data have been utilized as references to verify the concentrated model.

Kinetic electron and ion instability of the lunar wake simulated at physical mass ratio

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haakonsen, Christian Bernt, E-mail: chaako@mit.edu; Hutchinson, Ian H., E-mail: ihutch@mit.edu; Zhou, Chuteng, E-mail: ctzhou@mit.edu

2015-03-15

The solar wind wake behind the moon is studied with 1D electrostatic particle-in-cell (PIC) simulations using a physical ion to electron mass ratio (unlike prior investigations); the simulations also apply more generally to supersonic flow of dense magnetized plasma past non-magnetic objects. A hybrid electrostatic Boltzmann electron treatment is first used to investigate the ion stability in the absence of kinetic electron effects, showing that the ions are two-stream unstable for downstream wake distances (in lunar radii) greater than about three times the solar wind Mach number. Simulations with PIC electrons are then used to show that kinetic electron effectsmore » can lead to disruption of the ion beams at least three times closer to the moon than in the hybrid simulations. This disruption occurs as the result of a novel wake phenomenon: the non-linear growth of electron holes spawned from a narrow dimple in the electron velocity distribution. Most of the holes arising from the dimple are small and quickly leave the wake, approximately following the unperturbed electron phase-space trajectories, but some holes originating near the center of the wake remain and grow large enough to trigger disruption of the ion beams. Non-linear kinetic-electron effects are therefore essential to a comprehensive understanding of the 1D electrostatic stability of such wakes, and possible observational signatures in ARTEMIS data from the lunar wake are discussed.« less

A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

NASA Astrophysics Data System (ADS)

Li, Jinquan; Feng, Shuang; Mi, Honghai

In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

Kinetics of DSB rejoining and formation of simple chromosome exchange aberrations

NASA Technical Reports Server (NTRS)

Cucinotta, F. A.; Nikjoo, H.; O'Neill, P.; Goodhead, D. T.

2000-01-01

PURPOSE: To investigate the role of kinetics in the processing of DNA double strand breaks (DSB), and the formation of simple chromosome exchange aberrations following X-ray exposures to mammalian cells based on an enzymatic approach. METHODS: Using computer simulations based on a biochemical approach, rate-equations that describe the processing of DSB through the formation of a DNA-enzyme complex were formulated. A second model that allows for competition between two processing pathways was also formulated. The formation of simple exchange aberrations was modelled as misrepair during the recombination of single DSB with undamaged DNA. Non-linear coupled differential equations corresponding to biochemical pathways were solved numerically by fitting to experimental data. RESULTS: When mediated by a DSB repair enzyme complex, the processing of single DSB showed a complex behaviour that gives the appearance of fast and slow components of rejoining. This is due to the time-delay caused by the action time of enzymes in biomolecular reactions. It is shown that the kinetic- and dose-responses of simple chromosome exchange aberrations are well described by a recombination model of DSB interacting with undamaged DNA when aberration formation increases with linear dose-dependence. Competition between two or more recombination processes is shown to lead to the formation of simple exchange aberrations with a dose-dependence similar to that of a linear quadratic model. CONCLUSIONS: Using a minimal number of assumptions, the kinetics and dose response observed experimentally for DSB rejoining and the formation of simple chromosome exchange aberrations are shown to be consistent with kinetic models based on enzymatic reaction approaches. A non-linear dose response for simple exchange aberrations is possible in a model of recombination of DNA containing a DSB with undamaged DNA when two or more pathways compete for DSB repair.

LSENS, a general chemical kinetics and sensitivity analysis code for homogeneous gas-phase reactions. 2: Code description and usage

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan; Bittker, David A.

1994-01-01

LSENS, the Lewis General Chemical Kinetics Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 2 of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part 2 describes the code, how to modify it, and its usage, including preparation of the problem data file required to execute LSENS. Code usage is illustrated by several example problems, which further explain preparation of the problem data file and show how to obtain desired accuracy in the computed results. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions. Part 1 (NASA RP-1328) derives the governing equations describes the numerical solution procedures for the types of problems that can be solved by lSENS. Part 3 (NASA RP-1330) explains the kinetics and kinetics-plus-sensitivity-analysis problems supplied with LSENS and presents sample results.

Nonlinearization and waves in bounded media: old wine in a new bottle

NASA Astrophysics Data System (ADS)

Mortell, Michael P.; Seymour, Brian R.

2017-02-01

We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.

Portfolios with nonlinear constraints and spin glasses

NASA Astrophysics Data System (ADS)

Gábor, Adrienn; Kondor, I.

1999-12-01

In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.

COPS: Large-scale nonlinearly constrained optimization problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bondarenko, A.S.; Bortz, D.M.; More, J.J.

2000-02-10

The authors have started the development of COPS, a collection of large-scale nonlinearly Constrained Optimization Problems. The primary purpose of this collection is to provide difficult test cases for optimization software. Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, and optimal control. For each problem they provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers. They currently have results for DONLP2, LANCELOT, MINOS, SNOPT, and LOQO.

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

NASA Astrophysics Data System (ADS)

Li, Hong; Zhang, Li; Jiao, Yong-Chang

2016-07-01

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

Adaptive Neural Networks Decentralized FTC Design for Nonstrict-Feedback Nonlinear Interconnected Large-Scale Systems Against Actuator Faults.

PubMed

Li, Yongming; Tong, Shaocheng

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Unified Models of Turbulence and Nonlinear Wave Evolution in the Extended Solar Corona and Solar Wind

NASA Technical Reports Server (NTRS)

Cranmer, Steven R.; Wagner, William (Technical Monitor)

2003-01-01

The PI (Cranmer) and Co-I (A. van Ballegooijen) made significant progress toward the goal of building a "unified model" of the dominant physical processes responsible for the acceleration of the solar wind. The approach outlined in the original proposal comprised two complementary pieces: (1) to further investigate individual physical processes under realistic coronal and solar wind conditions, and (2) to extract the dominant physical effects from simulations and apply them to a one-dimensional and time-independent model of plasma heating and acceleration. The accomplishments in the report period are thus divided into these two categories: 1a. Focused Study of Kinetic MHD Turbulence. We have developed a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. A turbulent cascade is one possible way of generating small-scale fluctuations (easy to dissipate/heat) from a pre-existing population of low-frequency Alfven waves (difficult to dissipate/heat). We modeled the cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, though, there is insufficient power to heat protons and heavy ions. The dominant oblique waves undergo Landau damping, which implies strong parallel electron heating. We thus investigated the nonlinear evolution of the electron velocity distributions (VDFs) into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere) which are an alternate means of heating protons via stochastic interactions similar to particle-particle collisions. 1b. Focused Study of the Multi-Mode Detailed Balance Formalism. The PI began to explore the feasibility of using the "weak turbulence," or detailed-balance theory of Tsytovich, Melrose, and others to encompass the relevant physics of the solar wind. This study did not go far, however, because if the "strong" MHD turbulence discussed above is a dominant player in the wind's acceleration region, this formalism is inherently not applicable to the corona. We will continue to study the various published approaches to the weak turbulence formalism, especially with an eye on ways to parameterize nonlinear wave reflection rates. 2. Building the Unified Model Code Architecture. We have begun developing the computational model of a time-steady open flux tube in the extended corona. The model will be "unified" in the sense that it will include (simultaneously for the first time) as many of the various proposed physical processes as possible, all on equal footing. To retain this generality, we have formulated the problem in two interconnected parts: a completely kinetic model for the particles, using the Monte Carlo approach, and a finite-difference approach for the self-consistent fluctuation spectra. The two codes are run sequentially and iteratively until complete consistency is achieved. The current version of the Monte Carlo code incorporates gravity, the zero-current electric field, magnetic mirroring, and collisions. The fluctuation code incorporates WKJ3 wave action conservation and the cascade/dissipation processes discussed above. The codes are being run for various test problems with known solutions. Planned additions to the codes include prescriptions for nonlinear wave steepening, kinetic velocity-space diffusion, and multi-mode coupling (including reflection and refraction).

Continuous theory of active matter systems with metric-free interactions.

PubMed

Peshkov, Anton; Ngo, Sandrine; Bertin, Eric; Chaté, Hugues; Ginelli, Francesco

2012-08-31

We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones-a situation advocated recently to be relevant for bird flocks, fish schools, and crowds-we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that the density-independent collision rate per particle characteristic of topological interactions suppresses the linear instability of the homogeneous ordered phase and the nonlinear density segregation generically present near threshold in metric models, in agreement with microscopic simulations.

A Critical, Nonlinear Threshold Dictates Bacterial Invasion and Initial Kinetics During Influenza

NASA Astrophysics Data System (ADS)

Smith, Amber M.; Smith, Amanda P.

2016-12-01

Secondary bacterial infections increase morbidity and mortality of influenza A virus (IAV) infections. Bacteria are able to invade due to virus-induced depletion of alveolar macrophages (AMs), but this is not the only contributing factor. By analyzing a kinetic model, we uncovered a nonlinear initial dose threshold that is dependent on the amount of virus-induced AM depletion. The threshold separates the growth and clearance phenotypes such that bacteria decline for dose-AM depletion combinations below the threshold, stay constant near the threshold, and increase above the threshold. In addition, the distance from the threshold correlates to the growth rate. Because AM depletion changes throughout an IAV infection, the dose requirement for bacterial invasion also changes accordingly. Using the threshold, we found that the dose requirement drops dramatically during the first 7d of IAV infection. We then validated these analytical predictions by infecting mice with doses below or above the predicted threshold over the course of IAV infection. These results identify the nonlinear way in which two independent factors work together to support successful post-influenza bacterial invasion. They provide insight into coinfection timing, the heterogeneity in outcome, the probability of acquiring a coinfection, and the use of new therapeutic strategies to combat viral-bacterial coinfections.

Fully Nonlinear Edge Gyrokinetic Simulations of Kinetic Geodesic-Acoustic Modes and Boundary Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xu, X Q; Belli, E; Bodi, K

We present edge gyrokinetic neoclassical simulations of tokamak plasmas using the fully nonlinear (full-f) continuum code TEMPEST. A nonlinear Boltzmann model is used for the electrons. The electric field is obtained by solving the 2D gyrokinetic Poisson Equation. We demonstrate the following: (1) High harmonic resonances (n > 2) significantly enhance geodesic-acoustic mode (GAM) damping at high-q (tokamak safety factor), and are necessary to explain both the damping observed in our TEMPEST q-scans and experimental measurements of the scaling of the GAM amplitude with edge q{sub 95} in the absence of obvious evidence that there is a strong q dependencemore » of the turbulent drive and damping of the GAM. (2) The kinetic GAM exists in the edge for steep density and temperature gradients in the form of outgoing waves, its radial scale is set by the ion temperature profile, and ion temperature inhomogeneity is necessary for GAM radial propagation. (3) The development of the neoclassical electric field evolves through different phases of relaxation, including GAMs, their radial propagation, and their long-time collisional decay. (4) Natural consequences of orbits in the pedestal and scrape-off layer region in divertor geometry are substantial non-Maxwellian ion distributions and flow characteristics qualitatively like those observed in experiments.« less

A Critical, Nonlinear Threshold Dictates Bacterial Invasion and Initial Kinetics During Influenza.

PubMed

Smith, Amber M; Smith, Amanda P

2016-12-15

Secondary bacterial infections increase morbidity and mortality of influenza A virus (IAV) infections. Bacteria are able to invade due to virus-induced depletion of alveolar macrophages (AMs), but this is not the only contributing factor. By analyzing a kinetic model, we uncovered a nonlinear initial dose threshold that is dependent on the amount of virus-induced AM depletion. The threshold separates the growth and clearance phenotypes such that bacteria decline for dose-AM depletion combinations below the threshold, stay constant near the threshold, and increase above the threshold. In addition, the distance from the threshold correlates to the growth rate. Because AM depletion changes throughout an IAV infection, the dose requirement for bacterial invasion also changes accordingly. Using the threshold, we found that the dose requirement drops dramatically during the first 7d of IAV infection. We then validated these analytical predictions by infecting mice with doses below or above the predicted threshold over the course of IAV infection. These results identify the nonlinear way in which two independent factors work together to support successful post-influenza bacterial invasion. They provide insight into coinfection timing, the heterogeneity in outcome, the probability of acquiring a coinfection, and the use of new therapeutic strategies to combat viral-bacterial coinfections.

Neon diffusion kinetics and implications for cosmogenic neon paleothermometry in feldspars

DOE PAGES

Tremblay, Marissa M.; Shuster, David L.; Balco, Greg; ...

2017-02-20

Observations of cosmogenic neon concentrations in feldspars can potentially be used to constrain the surface exposure duration or surface temperature history of geologic samples. The applicability of cosmogenic neon to either application depends on the temperature-dependent diffusivity of neon isotopes. Here in this work, we investigate the kinetics of neon diffusion in feldspars of different compositions and geologic origins through stepwise degassing experiments on single, proton-irradiated crystals. To understand the potential causes of complex diffusion behavior that is sometimes manifest as nonlinearity in Arrhenius plots, we compare our results to argon stepwise degassing experiments previously conducted on the same feldspars.more » Many of the feldspars we studied exhibit linear Arrhenius behavior for neon whereas argon degassing from the same feldspars did not. This suggests that nonlinear behavior in argon experiments is an artifact of structural changes during laboratory heating. However, other feldspars that we examined exhibit nonlinear Arrhenius behavior for neon diffusion at temperatures far below any known structural changes, which suggests that some preexisting material property is responsible for the complex behavior. In general, neon diffusion kinetics vary widely across the different feldspars studied, with estimated activation energies (E a) ranging from 83.3 to 110.7 kJ/mol and apparent pre-exponential factors (D 0) spanning three orders of magnitude from 2.4 ×10 -3 to 8.9 × 10 -1 cm 2 s -1. Finally, as a consequence of this variability, the ability to reconstruct temperatures or exposure durations from cosmogenic neon abundances will depend on both the specific feldspar and the surface temperature conditions at the geologic site of interest.« less

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1985-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Bounding solutions of geometrically nonlinear viscoelastic problems

NASA Technical Reports Server (NTRS)

Stubstad, J. M.; Simitses, G. J.

1986-01-01

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.

PubMed

Petrov, E Yu; Kudrin, A V

2010-05-14

The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.

Presenting a new kinetic model for methanol to light olefins reactions over a hierarchical SAPO-34 catalyst using the Langmuir-Hinshelwood-Hougen-Watson mechanism

NASA Astrophysics Data System (ADS)

Javad Azarhoosh, Mohammad; Halladj, Rouein; Askari, Sima

2017-10-01

In this study, a new kinetic model for methanol to light olefins (MTO) reactions over a hierarchical SAPO-34 catalyst using the Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism was presented and the kinetic parameters was obtained using a genetic algorithm (GA) and genetic programming (GP). Several kinetic models for the MTO reactions have been presented. However, due to the complexity of the reactions, most reactions are considered lumped and elementary, which cannot be deemed a completely accurate kinetic model of the process. Therefore, in this study, the LHHW mechanism is presented as kinetic models of MTO reactions. Because of the non-linearity of the kinetic models and existence of many local optimal points, evolutionary algorithms (GA and GP) are used in this study to estimate the kinetic parameters in the rate equations. Via the simultaneous connection of the code related to modelling the reactor and the GA and GP codes in the MATLAB R2013a software, optimization of the kinetic models parameters was performed such that the least difference between the results from the kinetic models and experiential results was obtained and the best kinetic parameters of MTO process reactions were achieved. A comparison of the results from the model with experiential results showed that the present model possesses good accuracy.

Nonlinear second order evolution inclusions with noncoercive viscosity term

NASA Astrophysics Data System (ADS)

Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.

2018-04-01

In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.

Implementing Nonlinear Feedback Controllers Using DNA Strand Displacement Reactions.

PubMed

Sawlekar, Rucha; Montefusco, Francesco; Kulkarni, Vishwesh V; Bates, Declan G

2016-07-01

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs.

Neural networks for feedback feedforward nonlinear control systems.

PubMed

Parisini, T; Zoppoli, R

1994-01-01

This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

Nonlinear dynamics of a two-dimensional Wigner solid on superfluid helium

NASA Astrophysics Data System (ADS)

Monarkha, Yu. P.

2018-04-01

Nonlinear dynamics and transport properties of a 2D Wigner solid (WS) on the free surface of superfluid helium are theoretically studied. The analysis is nonperturbative in the amplitude of the WS velocity. An anomalous nonlinear response of the liquid helium surface to the oscillating motion of the WS is shown to appear when the driving frequency is close to subharmonics of the frequency of a capillary wave (ripplon) whose wave vector coincides with a reciprocal-lattice vector. As a result, the effective mass of surface dimples formed under electrons and the kinetic friction acquire sharp anomalies in the low-frequency range, which affects the mobility and magnetoconductivity of the WS. The results obtained here explain a variety of experimental observations reported previously.

A nonlinear dynamics for the scalar field in Randers spacetime

NASA Astrophysics Data System (ADS)

Silva, J. E. G.; Maluf, R. V.; Almeida, C. A. S.

2017-03-01

We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order.

Investigation of the dynamics of a nonlinear optical response in glassy chalcogenide semiconductors by the pump–probe method

NASA Astrophysics Data System (ADS)

Romanova, E. A.; Kuzyutkina, Yu S.; Shiryaev, V. S.; Guizard, S.

2018-03-01

An analysis of the results of measurements by using the pump–probe method with a femtosecond resolution in time and computer simulation of the charge carrier kinetics have revealed two types of a nonlinear optical response in samples of chalcogenide glasses belonging to the As – S – Se system, irradiated by 50-fs laser pulses with a wavelength of 0.79 μm. The difference in the nonlinear dynamics is due to the difference in the photoexcitation character, because laser radiation can be absorbed either through bound states in the band gap or without their participation, depending on the ratio of the pump photon energy to the bandgap energy.

Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Killingsworth, W. R., Jr.

1972-01-01

The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

NASA Technical Reports Server (NTRS)

Stein, M.; Stein, P. A.

1978-01-01

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Finite difference time domain calculation of transients in antennas with nonlinear loads

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent

1991-01-01

Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

On a variational approach to some parameter estimation problems

NASA Technical Reports Server (NTRS)

Banks, H. T.

1985-01-01

Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

Onsager's variational principle in soft matter.

PubMed

Doi, Masao

2011-07-20

In the celebrated paper on the reciprocal relation for the kinetic coefficients in irreversible processes, Onsager (1931 Phys. Rev. 37 405) extended Rayleigh's principle of the least energy dissipation to general irreversible processes. In this paper, I shall show that this variational principle gives us a very convenient framework for deriving many established equations which describe the nonlinear and non-equilibrium phenomena in soft matter, such as phase separation kinetics in solutions, gel dynamics, molecular modeling for viscoelasticity nemato-hydrodynamics, etc. Onsager's variational principle can therefore be regarded as a solid general basis for soft matter physics.

Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.

PubMed

Wang, Xinghu; Hong, Yiguang; Ji, Haibo

2016-07-01

The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jones, J E; Vassilevski, P S; Woodward, C S

This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities inmore » the principal part of the elliptic operator.« less

Overdetermined elliptic problems in topological disks

NASA Astrophysics Data System (ADS)

Mira, Pablo

2018-06-01

We introduce a method, based on the Poincaré-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems.

Quasilinear saturation of the aperiodic ordinary mode streaming instability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stockem Novo, A., E-mail: anne@tp4.rub.de; Schlickeiser, R.; Yoon, P. H.

2015-09-15

In collisionless plasmas, only kinetic instabilities and fluctuations are effective in reducing the free energy and scatter plasma particles, preventing an increase of their anisotropy. Solar energetic outflows into the interplanetary plasma give rise to important thermal anisotropies and counterstreaming motions of plasma shells, and the resulting instabilities are expected to regulate the expansion of the solar wind. The present paper combines quasilinear theory and kinetic particle-in-cell simulations in order to study the weakly nonlinear saturation of the ordinary mode in hot counter-streaming plasmas with a temperature anisotropy as a follow-up of the paper by Seough et al. [Phys. Plasmasmore » 22, 082122 (2015)]. This instability provides a plausible mechanism for the origin of dominating, two-dimensional spectrum of transverse magnetic fluctuations observed in the solar wind. Stimulated by the differential motion of electron counterstreams the O mode instability may convert their free large-scale energy by nonlinear collisionless dissipation on plasma particles.« less

WAKES: Wavelet Adaptive Kinetic Evolution Solvers

NASA Astrophysics Data System (ADS)

Mardirian, Marine; Afeyan, Bedros; Larson, David

2016-10-01

We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.

Theory of multiwave mixing within the superconducting kinetic-inductance traveling-wave amplifier

NASA Astrophysics Data System (ADS)

Erickson, R. P.; Pappas, D. P.

2017-03-01

We present a theory of parametric mixing within the coplanar waveguide (CPW) of a superconducting nonlinear kinetic-inductance traveling-wave (KIT) amplifier engineered with periodic dispersion loadings. This is done by first developing a metamaterial band theory of the dispersion-engineered KIT using a Floquet-Bloch construction and then applying it to the description of mixing of the nonlinear RF traveling waves. Our theory allows us to calculate signal gain versus signal frequency in the presence of a frequency stop gap, based solely on loading design. We present results for both three-wave mixing (3WM), with applied dc bias, and four-wave mixing (4WM), without dc. Our theory predicts an intrinsic and deterministic origin to undulations of 4WM signal gain with signal frequency, apart from extrinsic sources, such as impedance mismatch, and shows that such undulations are absent from 3WM signal gain achievable with dc. Our theory is extensible to amplifiers based on Josephson junctions in a lumped LC-ladder transmission line (TWPA).

The effect of the polymer relaxation time on the nonlinear energy cas- cade and dissipation of statistically steady and decaying homogeneous isotropic turbulence

NASA Astrophysics Data System (ADS)

Valente, Pedro C.; da Silva, Carlos B.; Pinho, Fernando T.

2013-11-01

We report a numerical study of statistically steady and decaying turbulence of FENE-P fluids for varying polymer relaxation times ranging from the Kolmogorov dissipation time-scale to the eddy turnover time. The total turbulent kinetic energy dissipation is shown to increase with the polymer relaxation time in both steady and decaying turbulence, implying a ``drag increase.'' If the total power input in the statistically steady case is kept equal in the Newtonian and the viscoelastic simulations the increase in the turbulence-polymer energy transfer naturally lead to the previously reported depletion of the Newtonian, but not the overall, kinetic energy dissipation. The modifications to the nonlinear energy cascade with varying Deborah/Weissenberg numbers are quantified and their origins investigated. The authors acknowledge the financial support from Fundação para a Ciência e a Tecnologia under grant PTDC/EME-MFE/113589/2009.

Biodrying of sewage sludge: kinetics of volatile solids degradation under different initial moisture contents and air-flow rates.

PubMed

Villegas, Manuel; Huiliñir, Cesar

2014-12-01

This study focuses on the kinetics of the biodegradation of volatile solids (VS) of sewage sludge for biodrying under different initial moisture contents (Mc) and air-flow rates (AFR). For the study, a 3(2) factorial design, whose factors were AFR (1, 2 or 3L/minkgTS) and initial Mc (59%, 68% and 78% w.b.), was used. Using seven kinetic models and a nonlinear regression method, kinetic parameters were estimated and the models were analyzed with two statistical indicators. Initial Mc of around 68% increases the temperature matrix and VS consumption, with higher moisture removal at lower initial Mc values. Lower AFRs gave higher matrix temperatures and VS consumption, while higher AFRs increased water removal. The kinetic models proposed successfully simulate VS biodegradation, with root mean square error (RMSE) between 0.007929 and 0.02744, and they can be used as a tool for satisfactory prediction of VS in biodrying. Copyright © 2014 Elsevier Ltd. All rights reserved.

LSENS, A General Chemical Kinetics and Sensitivity Analysis Code for Homogeneous Gas-Phase Reactions. Part 2; Code Description and Usage

NASA Technical Reports Server (NTRS)

Radhakrishnan, Krishnan; Bittker, David A.

1994-01-01

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part II of a series of three reference publications that describe LSENS, provide a detailed guide to its usage, and present many example problems. Part II describes the code, how to modify it, and its usage, including preparation of the problem data file required to execute LSENS. Code usage is illustrated by several example problems, which further explain preparation of the problem data file and show how to obtain desired accuracy in the computed results. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions. Part I (NASA RP-1328) derives the governing equations and describes the numerical solution procedures for the types of problems that can be solved by LSENS. Part III (NASA RP-1330) explains the kinetics and kinetics-plus-sensitivity-analysis problems supplied with LSENS and presents sample results.

FRF decoupling of nonlinear systems

NASA Astrophysics Data System (ADS)

Kalaycıoğlu, Taner; Özgüven, H. Nevzat

2018-03-01

Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition

NASA Astrophysics Data System (ADS)

Umezu, Kenichiro

In this paper, we consider a semilinear elliptic boundary value problem in a smooth bounded domain, having the so-called logistic nonlinearity that originates from population dynamics, with a nonlinear boundary condition. Although the logistic nonlinearity has an absorption effect in the problem, the nonlinear boundary condition is induced by the homogeneous incoming flux on the boundary. The objective of our study is to analyze the existence of a bifurcation component of positive solutions from trivial solutions and its asymptotic behavior and stability. We perform this analysis using the method developed by Lyapunov and Schmidt, based on a scaling argument.

Nonlinear multivariable design by total synthesis. [of gas turbine engine control systems

NASA Technical Reports Server (NTRS)

Sain, M. K.; Peczkowski, J. L.

1982-01-01

The Nominal Design Problem (NDP) is extended to nonlinear cases, and a new case study of robust feedback synthesis for gas turbine control design is presented. The discussion of NDP extends and builds on earlier Total Synthesis Problem theory and ideas. Some mathematical preliminaries are given in which a bijection from a set S onto a set T is considered, with T admitting the structure of an F-vector space. NDP is then discussed for a nonlinear plant, and nonlinear nominal design is defined and characterized. The design of local controllers for a turbojet and the scheduling of these controls into a global control are addressed.

Toward Effective Shell Modeling of Wrinkled Thin-Film Membranes Exhibiting Stress Concentrations

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sleight, David W.

2004-01-01

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns. An element-level, strain-energy density criterion is suggested for facilitating automated, adaptive mesh refinements specifically aimed at the modeling of thin-film membranes undergoing wrinkling deformations.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Analysis and control of hourglass instabilities in underintegrated linear and nonlinear elasticity

NASA Technical Reports Server (NTRS)

Jacquotte, Olivier P.; Oden, J. Tinsley

1994-01-01

Methods are described to identify and correct a bad finite element approximation of the governing operator obtained when under-integration is used in numerical code for several model problems: the Poisson problem, the linear elasticity problem, and for problems in the nonlinear theory of elasticity. For each of these problems, the reason for the occurrence of instabilities is given, a way to control or eliminate them is presented, and theorems of existence, uniqueness, and convergence for the given methods are established. Finally, numerical results are included which illustrate the theory.

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

NASA Technical Reports Server (NTRS)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Metabolic control analysis using transient metabolite concentrations. Determination of metabolite concentration control coefficients.

PubMed Central

Delgado, J; Liao, J C

1992-01-01

The methodology previously developed for determining the Flux Control Coefficients [Delgado & Liao (1992) Biochem. J. 282, 919-927] is extended to the calculation of metabolite Concentration Control Coefficients. It is shown that the transient metabolite concentrations are related by a few algebraic equations, attributed to mass balance, stoichiometric constraints, quasi-equilibrium or quasi-steady states, and kinetic regulations. The coefficients in these relations can be estimated using linear regression, and can be used to calculate the Control Coefficients. The theoretical basis and two examples are discussed. Although the methodology is derived based on the linear approximation of enzyme kinetics, it yields reasonably good estimates of the Control Coefficients for systems with non-linear kinetics. PMID:1497632

Kinetic Equations for Describing the Liquid-Glass Transition in Polymers

NASA Astrophysics Data System (ADS)

Aksenov, V. L.; Tropin, T. V.; Schmelzer, J. V. P.

2018-01-01

We present a theoretical approach based on nonequilibrium thermodynamics and used to describe the kinetics of the transition from the liquid to the glassy state (glass transition). In the framework of this approach, we construct kinetic equations describing the time and temperature evolution of the structural parameter. We discuss modifications of the equations required for taking the nonexponential, nonlinear character of the relaxation in the vitrification region into account. To describe the formation of polymer glasses, we present modified expressions for the system relaxation time. We compare the obtained results with experimental data, measurements of the polystyrene glass transition for different cooling rates using the method of differential scanning calorimetry. We discuss prospects for developing a method for describing the polymer glass transition.

Supercritical nonlinear parametric dynamics of Timoshenko microbeams

NASA Astrophysics Data System (ADS)

Farokhi, Hamed; Ghayesh, Mergen H.

2018-06-01

The nonlinear supercritical parametric dynamics of a Timoshenko microbeam subject to an axial harmonic excitation force is examined theoretically, by means of different numerical techniques, and employing a high-dimensional analysis. The time-variant axial load is assumed to consist of a mean value along with harmonic fluctuations. In terms of modelling, a continuous expression for the elastic potential energy of the system is developed based on the modified couple stress theory, taking into account small-size effects; the kinetic energy of the system is also modelled as a continuous function of the displacement field. Hamilton's principle is employed to balance the energies and to obtain the continuous model of the system. Employing the Galerkin scheme along with an assumed-mode technique, the energy terms are reduced, yielding a second-order reduced-order model with finite number of degrees of freedom. A transformation is carried out to convert the second-order reduced-order model into a double-dimensional first order one. A bifurcation analysis is performed for the system in the absence of the axial load fluctuations. Moreover, a mean value for the axial load is selected in the supercritical range, and the principal parametric resonant response, due to the time-variant component of the axial load, is obtained - as opposed to transversely excited systems, for parametrically excited system (such as our problem here), the nonlinear resonance occurs in the vicinity of twice any natural frequency of the linear system; this is accomplished via use of the pseudo-arclength continuation technique, a direct time integration, an eigenvalue analysis, and the Floquet theory for stability. The natural frequencies of the system prior to and beyond buckling are also determined. Moreover, the effect of different system parameters on the nonlinear supercritical parametric dynamics of the system is analysed, with special consideration to the effect of the length-scale parameter.

Kinetic filtering of [18F]Fluorothymidine in positron emission tomography studies

NASA Astrophysics Data System (ADS)

Gray, Katherine R.; Contractor, Kaiyumars B.; Kenny, Laura M.; Al-Nahhas, Adil; Shousha, Sami; Stebbing, Justin; Wasan, Harpreet S.; Coombes, R. Charles; Aboagye, Eric O.; Turkheimer, Federico E.; Rosso, Lula

2010-02-01

[18F]Fluorothymidine (FLT) is a cell proliferation marker that undergoes predominantly hepatic metabolism and therefore shows a high level of accumulation in the liver, as well as in rapidly proliferating tumours. Furthermore, the tracer's uptake is substantial in other organs including the heart. We present a nonlinear kinetic filtering technique which enhances the visualization of tumours imaged with FLT positron emission tomography (FLT-PET). A classification algorithm to isolate cancerous tissue from healthy organs was developed and validated using 29 scan data from patients with locally advanced or metastatic breast cancer. A large reduction in signal from the liver and heart of 80% was observed following application of the kinetic filter, whilst the majority of signal from both primary tumours and metastases was retained. A scan acquisition time of 60 min has been shown to be sufficient to obtain the necessary kinetic data. The algorithm extends utility of FLT-PET imaging in oncology research.

Disproportionation of rosin on an industrial Pd/C catalyst: reaction pathway and kinetic model discrimination.

PubMed

Souto, Juan Carlos; Yustos, Pedro; Ladero, Miguel; Garcia-Ochoa, Felix

2011-02-01

In this work, a phenomenological study of the isomerisation and disproportionation of rosin acids using an industrial 5% Pd on charcoal catalyst from 200 to 240°C is carried out. Medium composition is determined by elemental microanalysis, GC-MS and GC-FID. Dehydrogenated and hydrogenated acid species molar amounts in the final product show that dehydrogenation is the main reaction. Moreover, both hydrogen and non-hydrogen concentration considering kinetic models are fitted to experimental data using a multivariable non-linear technique. Statistical discrimination among the proposed kinetic models lead to the conclusion hydrogen considering models fit much better to experimental results. The final kinetic model involves first-order isomerisation reactions of neoabietic and palustric acids to abietic acid, first-order dehydrogenation and hydrogenation of this latter acid, and hydrogenation of pimaric acids. Hydrogenation reactions are partial first-order regarding the acid and hydrogen. Copyright © 2010 Elsevier Ltd. All rights reserved.

Kinetic modeling of sporulation and product formation in stationary phase by Bacillus coagulans RK-02 vis-à-vis other Bacilli.

PubMed

Das, Subhasish; Sen, Ramkrishna

2011-10-01

A logistic kinetic model was derived and validated to characterize the dynamics of a sporogenous bacterium in stationary phase with respect to sporulation and product formation. The kinetic constants as determined using this model are particularly important for describing intrinsic properties of a sporogenous bacterial culture in stationary phase. Non-linear curve fitting of the experimental data into the mathematical model showed very good correlation with the predicted values for sporulation and lipase production by Bacillus coagulans RK-02 culture in minimal media. Model fitting of literature data of sporulation and product (protease and amylase) formation in the stationary phase by some other Bacilli and comparison of the results of model fitting with those of Bacillus coagulans helped validate the significance and robustness of the developed kinetic model. Copyright © 2011 Elsevier Ltd. All rights reserved.

Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

ERIC Educational Resources Information Center

Fulcher, Lewis P.

1979-01-01

Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

NASA Technical Reports Server (NTRS)

Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium.

PubMed

Es'kin, V A; Kudrin, A V; Petrov, E Yu

2011-06-01

The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.

Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

PubMed Central

Kaikina, Elena I.

2013-01-01

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time. PMID:24204185

On Some Separated Algorithms for Separable Nonlinear Least Squares Problems.

PubMed

Gan, Min; Chen, C L Philip; Chen, Guang-Yong; Chen, Long

2017-10-03

For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.

Numerical solution of special ultra-relativistic Euler equations using central upwind scheme

NASA Astrophysics Data System (ADS)

Ghaffar, Tayabia; Yousaf, Muhammad; Qamar, Shamsul

2018-06-01

This article is concerned with the numerical approximation of one and two-dimensional special ultra-relativistic Euler equations. The governing equations are coupled first-order nonlinear hyperbolic partial differential equations. These equations describe perfect fluid flow in terms of the particle density, the four-velocity and the pressure. A high-resolution shock-capturing central upwind scheme is employed to solve the model equations. To avoid excessive numerical diffusion, the considered scheme avails the specific information of local propagation speeds. By using Runge-Kutta time stepping method and MUSCL-type initial reconstruction, we have obtained 2nd order accuracy of the proposed scheme. After discussing the model equations and the numerical technique, several 1D and 2D test problems are investigated. For all the numerical test cases, our proposed scheme demonstrates very good agreement with the results obtained by well-established algorithms, even in the case of highly relativistic 2D test problems. For validation and comparison, the staggered central scheme and the kinetic flux-vector splitting (KFVS) method are also implemented to the same model. The robustness and efficiency of central upwind scheme is demonstrated by the numerical results.

Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

NASA Technical Reports Server (NTRS)

Acikmese, Ahmet Behcet; Martin, Corless

2004-01-01

We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

Adaptive Fuzzy Output Feedback Control for Switched Nonlinear Systems With Unmodeled Dynamics.

PubMed

Tong, Shaocheng; Li, Yongming

2017-02-01

This paper investigates a robust adaptive fuzzy control stabilization problem for a class of uncertain nonlinear systems with arbitrary switching signals that use an observer-based output feedback scheme. The considered switched nonlinear systems possess the unstructured uncertainties, unmodeled dynamics, and without requiring the states being available for measurement. A state observer which is independent of switching signals is designed to solve the problem of unmeasured states. Fuzzy logic systems are used to identify unknown lumped nonlinear functions so that the problem of unstructured uncertainties can be solved. By combining adaptive backstepping design principle and small-gain approach, a novel robust adaptive fuzzy output feedback stabilization control approach is developed. The stability of the closed-loop system is proved via the common Lyapunov function theory and small-gain theorem. Finally, the simulation results are given to demonstrate the validity and performance of the proposed control strategy.

The estimation of nonlinearity in problems of the building of initial confidence regions for small bodies motion. (Russian Title: Оценивание нелинейности в задачах построения начальных доверительных областей движения малых тел)

NASA Astrophysics Data System (ADS)

Syusina, O. M.; Chernitsov, A. M.; Tamarov, V. A.

2011-07-01

Simple and mathematically rigorous methods for calculating of nonlinearity coefficients are proposed. These coefficients allow us to make classification for the least squares problem as strongly or weakly nonlinear one. The advices are given on how to reduce a concrete estimation problem to weakly nonlinear one where a more efficient linear approach can be used.

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

The Impacts of Dry Dynamic Cores on Asymmetric Hurricane Intensification

NASA Technical Reports Server (NTRS)

Guimond, Stephen R.; Reisner, Jon M.; Marras, Simone; Giraldo, Francis X.

2016-01-01

The fundamental pathways for tropical cyclone (TC) intensification are explored by considering axisymmetric and asymmetric impulsive thermal perturbations to balanced, TC-like vortices using the dynamic cores of three different nonlinear numerical models. Attempts at reproducing the results of previous work, which used the community WRF Model, revealed a discrepancy with the impacts of purely asymmetric thermal forcing. The current study finds that thermal asymmetries can have an important, largely positive role on the vortex intensification, whereas other studies find that asymmetric impacts are negligible. Analysis of the spectral energetics of each numerical model indicates that the vortex response to asymmetric thermal perturbations is significantly damped in WRF relative to the other models. Spectral kinetic energy budgets show that this anomalous damping is primarily due to the increased removal of kinetic energy from the vertical divergence of the vertical pressure flux, which is related to the flux of inertia-gravity wave energy. The increased kinetic energy in the other two models is shown to originate around the scales of the heating and propagate upscale with time from nonlinear effects. For very large thermal amplitudes (50 K), the anomalous removal of kinetic energy due to inertia-gravity wave activity is much smaller, resulting in good agreement between models. The results of this paper indicate that the numerical treatment of small-scale processes that project strongly onto inertia-gravity wave energy can lead to significant differences in asymmetric TC intensification. Sensitivity tests with different time integration schemes suggest that diffusion entering into the implicit solution procedure is partly responsible for the anomalous damping of energy.

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.

Program Helps To Determine Chemical-Reaction Mechanisms

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Radhakrishnan, K.

1995-01-01

General Chemical Kinetics and Sensitivity Analysis (LSENS) computer code developed for use in solving complex, homogeneous, gas-phase, chemical-kinetics problems. Provides for efficient and accurate chemical-kinetics computations and provides for sensitivity analysis for variety of problems, including problems involving honisothermal conditions. Incorporates mathematical models for static system, steady one-dimensional inviscid flow, reaction behind incident shock wave (with boundary-layer correction), and perfectly stirred reactor. Computations of equilibrium properties performed for following assigned states: enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. Written in FORTRAN 77 with exception of NAMELIST extensions used for input.

Alternative kinetic energy metrics for Lagrangian systems

NASA Astrophysics Data System (ADS)

Sarlet, W.; Prince, G.

2010-11-01

We examine Lagrangian systems on \\ {R}^n with standard kinetic energy terms for the possibility of additional, alternative Lagrangians with kinetic energy metrics different to the Euclidean one. Using the techniques of the inverse problem in the calculus of variations we find necessary and sufficient conditions for the existence of such Lagrangians. We illustrate the problem in two and three dimensions with quadratic and cubic potentials. As an aside we show that the well-known anomalous Lagrangians for the Coulomb problem can be removed by switching on a magnetic field, providing an appealing resolution of the ambiguous quantizations of the hydrogen atom.

Numerical solutions of acoustic wave propagation problems using Euler computations

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1984-01-01

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

NASA Astrophysics Data System (ADS)

Vasant, Pandian

2011-06-01

Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models

USGS Publications Warehouse

Cooley, R.L.; Hill, M.C.

1992-01-01

Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.

Documentation of computer program VS2D to solve the equations of fluid flow in variably saturated porous media

USGS Publications Warehouse

Lappala, E.G.; Healy, R.W.; Weeks, E.P.

1987-01-01

This report documents FORTRAN computer code for solving problems involving variably saturated single-phase flow in porous media. The flow equation is written with total hydraulic potential as the dependent variable, which allows straightforward treatment of both saturated and unsaturated conditions. The spatial derivatives in the flow equation are approximated by central differences, and time derivatives are approximated either by a fully implicit backward or by a centered-difference scheme. Nonlinear conductance and storage terms may be linearized using either an explicit method or an implicit Newton-Raphson method. Relative hydraulic conductivity is evaluated at cell boundaries by using either full upstream weighting, the arithmetic mean, or the geometric mean of values from adjacent cells. Nonlinear boundary conditions treated by the code include infiltration, evaporation, and seepage faces. Extraction by plant roots that is caused by atmospheric demand is included as a nonlinear sink term. These nonlinear boundary and sink terms are linearized implicitly. The code has been verified for several one-dimensional linear problems for which analytical solutions exist and against two nonlinear problems that have been simulated with other numerical models. A complete listing of data-entry requirements and data entry and results for three example problems are provided. (USGS)

Straightening of a wavy strip: An elastic-plastic contact problem including snap-through

NASA Technical Reports Server (NTRS)

Fischer, D. F.; Rammerstorfer, F. G.

1980-01-01

The nonlinear behavior of a wave like deformed metal strip during the levelling process were calculated. Elastic-plastic material behavior as well as nonlinearities due to large deformations were considered. The considered problem lead to a combined stability and contact problem. It is shown that, despite the initially concentrated loading, neglecting the change of loading conditions due to altered contact domains may lead to a significant error in the evaluation of the nonlinear behavior and particularly to an underestimation of the stability limit load. The stability was examined by considering the load deflection path and the behavior of a load-dependent current stiffness parameter in combination with the determinant of the current stiffness matrix.

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Gyrofluid turbulence models with kinetic effects

NASA Astrophysics Data System (ADS)

Dorland, W.; Hammett, G. W.

1993-03-01

Nonlinear gyrofluid equations are derived by taking moments of the nonlinear, electrostatic gyrokinetic equation. The principal model presented includes evolution equations for the guiding center n, u∥, T∥, and T⊥ along with an equation expressing the quasineutrality constraint. Additional evolution equations for higher moments are derived that may be used if greater accuracy is desired. The moment hierarchy is closed with a Landau damping model [G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)], which is equivalent to a multipole approximation to the plasma dispersion function, extended to include finite Larmor radius effects (FLR). In particular, new dissipative, nonlinear terms are found that model the perpendicular phase mixing of the distribution function along contours of constant electrostatic potential. These ``FLR phase-mixing'' terms introduce a hyperviscositylike damping ∝k⊥2‖Φkk×k'‖, which should provide a physics-based damping mechanism at high k⊥ρ which is potentially as important as the usual polarization drift nonlinearity. The moments are taken in guiding center space to pick up the correct nonlinear FLR terms and the gyroaveraging of the shear. The equations are solved with a nonlinear, three-dimensional initial value code. Linear results are presented, showing excellent agreement with linear gyrokinetic theory.

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

NASA Astrophysics Data System (ADS)

Faghih Shojaei, Mostafa; Yavari, Arash

2018-05-01

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

Accelerated Simulation of Kinetic Transport Using Variational Principles and Sparsity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caflisch, Russel

This project is centered on the development and application of techniques of sparsity and compressed sensing for variational principles, PDEs and physics problems, in particular for kinetic transport. This included derivation of sparse modes for elliptic and parabolic problems coming from variational principles. The research results of this project are on methods for sparsity in differential equations and their applications and on application of sparsity ideas to kinetic transport of plasmas.

Investigation on the effect of nonlinear processes on similarity law in high-pressure argon discharges

NASA Astrophysics Data System (ADS)

Fu, Yangyang; Parsey, Guy M.; Verboncoeur, John P.; Christlieb, Andrew J.

2017-11-01

In this paper, the effect of nonlinear processes (such as three-body collisions and stepwise ionizations) on the similarity law in high-pressure argon discharges has been studied by the use of the Kinetic Global Model framework. In the discharge model, the ground state argon atoms (Ar), electrons (e), atom ions (Ar+), molecular ions (Ar2+), and fourteen argon excited levels Ar*(4s and 4p) are considered. The steady-state electron and ion densities are obtained with nonlinear processes included and excluded in the designed models, respectively. It is found that in similar gas gaps, keeping the product of gas pressure and linear dimension unchanged, with the nonlinear processes included, the normalized density relations deviate from the similarity relations gradually as the scale-up factor decreases. Without the nonlinear processes, the parameter relations are in good agreement with the similarity law predictions. Furthermore, the pressure and the dimension effects are also investigated separately with and without the nonlinear processes. It is shown that the gas pressure effect on the results is less obvious than the dimension effect. Without the nonlinear processes, the pressure and the dimension effects could be estimated from one to the other based on the similarity relations.

Nonlinearity measure and internal model control based linearization in anti-windup design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perev, Kamen

2013-12-18

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequencymore » ranges.« less

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

Nonlinear stability of Taylor's vortex array

NASA Technical Reports Server (NTRS)

Lin, S. P.; Tobak, M.

1987-01-01

It is proved that the two-dimensional Taylor vortex array, which is an exact unsteady solution of the Navier-Stokes equation, is globally and asymptotically stable in the mean with respect to three-dimensional periodic disturbances. A time-dependent bound on the decay rate of the kinetic energy of disturbances is obtained.

Advances in electron kinetics and theory of gas discharges

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolobov, Vladimir I.; The University of Alabama in Huntsville, Huntsville, Alabama 35899

2013-10-15

“Electrons, like people, are fertile and infertile: high-energy electrons are fertile and able to reproduce.”—Lev TsendinModern physics of gas discharges increasingly uses physical kinetics for analysis of non-equilibrium plasmas. The description of underlying physics at the kinetic level appears to be important for plasma applications in modern technologies. In this paper, we attempt to grasp the legacy of Professor Lev Tsendin, who advocated the use of the kinetic approach for understanding fundamental problems of gas discharges. We outline the fundamentals of electron kinetics in low-temperature plasmas, describe elements of the modern kinetic theory of gas discharges, and show examples ofmore » the theoretical approach to gas discharge problems used by Lev Tsendin. Important connections between electron kinetics in gas discharges and semiconductors are also discussed. Using several examples, we illustrate how Tsendin's ideas and methods are currently being developed for the implementation of next generation computational tools for adaptive kinetic-fluid simulations of gas discharges used in modern technologies.« less

Advanced Numerical Methods for Computing Statistical Quantities of Interest from Solutions of SPDES

DTIC Science & Technology

2012-01-19

and related optimization problems; developing numerical methods for option pricing problems in the presence of random arbitrage return. 1. Novel...equations (BSDEs) are connected to nonlinear partial differen- tial equations and non-linear semigroups, to the theory of hedging and pricing of contingent...the presence of random arbitrage return [3] We consider option pricing problems when we relax the condition of no arbitrage in the Black- Scholes

Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

NASA Astrophysics Data System (ADS)

Yamagishi, Osamu; Sugama, Hideo

2016-03-01

Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamagishi, Osamu, E-mail: yamagisi@nifs.ac.jp; Sugama, Hideo

Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

Inversion of Robin coefficient by a spectral stochastic finite element approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Numerical methods for stiff systems of two-point boundary value problems

NASA Technical Reports Server (NTRS)

Flaherty, J. E.; Omalley, R. E., Jr.

1983-01-01

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma

NASA Astrophysics Data System (ADS)

Shukla, P. K.; Mirza, Arshad M.; Faria, R. T.

1998-03-01

By using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson's equation as well as Ampère's law, a system of nonlinear equations for low-frequency (in comparison with the electron gyrofrequency) long-(short-) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvén-like electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas.

Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

NASA Technical Reports Server (NTRS)

Banks, H. T.; Reich, Simeon; Rosen, I. G.

1988-01-01

An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions

USGS Publications Warehouse

Rubin, Jacob

1983-01-01

Examples involving six broad reaction classes show that the nature of transport-affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass-balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport-equation system (e.g., whether it involves algebraic, partial-differential, or integro-partial-differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical-relation (i.e., equilibrium or rate) equations.

Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

PubMed

Goto, Hayato; Lin, Zhirong; Nakamura, Yasunobu

2018-05-08

A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.

A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal

NASA Astrophysics Data System (ADS)

Coudeyras, N.; Sinou, J.-J.; Nacivet, S.

2009-01-01

Brake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system. The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm. Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping.