Master Equation Analysis of Thermal and Nonthermal Microwave Effects.

PubMed

Ma, Jianyi

2016-10-11

Master equation is a successful model to describe the conventional heating reaction, it is expanded to capture the "microwave effect" in this work. The work equation of "microwave effect" included master equation presents the direct heating, indirect heating, and nonthermal effect about the microwave field. The modified master equation provides a clear physics picture to the nonthermal microwave effect: (1) The absorption and the emission of the microwave, which is dominated by the transition dipole moment between two corresponding states and the intensity of the microwave field, provides a new path to change the reaction rate constants. (2) In the strong microwave field, the distribution of internal states of the molecules will deviate from the equilibrium distribution, and the system temperature defined in the conventional heating reaction is no longer available. According to the general form of "microwave effect" included master equation, a two states model for unimolecular dissociation is proposed and is used to discuss the microwave nonthermal effect particularly. The average rate constants can be increased up to 2400 times for some given cases without the temperature changed in the two states model. Additionally, the simulation of a model system was executed using our State Specified Master Equation package. Three important conclusions can be obtained in present work: (1) A reasonable definition of the nonthermal microwave effect is given in the work equation of "microwave effect" included master equation. (2) Nonthermal microwave effect possibly exists theoretically. (3) The reaction rate constants perhaps can be changed obviously by the microwave field for the non-RRKM and the mode-specified reactions.

APPLE - An aeroelastic analysis system for turbomachines and propfans

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, Milind A.; Srivastava, R.; Mehmed, Oral

1992-01-01

This paper reviews aeroelastic analysis methods for propulsion elements (advanced propellers, compressors and turbines) being developed and used at NASA Lewis Research Center. These aeroelastic models include both structural and aerodynamic components. The structural models include the typical section model, the beam model with and without disk flexibility, and the finite element blade model with plate bending elements. The aerodynamic models are based on the solution of equations ranging from the two-dimensional linear potential equation for a cascade to the three-dimensional Euler equations for multi-blade configurations. Typical results are presented for each aeroelastic model. Suggestions for further research are indicated. All the available aeroelastic models and analysis methods are being incorporated into a unified computer program named APPLE (Aeroelasticity Program for Propulsion at LEwis).

An Evaluation of Three Approximate Item Response Theory Models for Equating Test Scores.

ERIC Educational Resources Information Center

Marco, Gary L.; And Others

Three item response models were evaluated for estimating item parameters and equating test scores. The models, which approximated the traditional three-parameter model, included: (1) the Rasch one-parameter model, operationalized in the BICAL computer program; (2) an approximate three-parameter logistic model based on coarse group data divided…

A Review of Recent Aeroelastic Analysis Methods for Propulsion at NASA Lewis Research Center

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Bakhle, Milind A.; Srivastava, R.; Mehmed, Oral; Stefko, George L.

1993-01-01

This report reviews aeroelastic analyses for propulsion components (propfans, compressors and turbines) being developed and used at NASA LeRC. These aeroelastic analyses include both structural and aerodynamic models. The structural models include a typical section, a beam (with and without disk flexibility), and a finite-element blade model (with plate bending elements). The aerodynamic models are based on the solution of equations ranging from the two-dimensional linear potential equation to the three-dimensional Euler equations for multibladed configurations. Typical calculated results are presented for each aeroelastic model. Suggestions for further research are made. Many of the currently available aeroelastic models and analysis methods are being incorporated in a unified computer program, APPLE (Aeroelasticity Program for Propulsion at LEwis).

Mathematical Model of Two Phase Flow in Natural Draft Wet-Cooling Tower Including Flue Gas Injection

NASA Astrophysics Data System (ADS)

Hyhlík, Tomáš

2016-03-01

The previously developed model of natural draft wet-cooling tower flow, heat and mass transfer is extended to be able to take into account the flow of supersaturated moist air. The two phase flow model is based on void fraction of gas phase which is included in the governing equations. Homogeneous equilibrium model, where the two phases are well mixed and have the same velocity, is used. The effect of flue gas injection is included into the developed mathematical model by using source terms in governing equations and by using momentum flux coefficient and kinetic energy flux coefficient. Heat and mass transfer in the fill zone is described by the system of ordinary differential equations, where the mass transfer is represented by measured fill Merkel number and heat transfer is calculated using prescribed Lewis factor.

Turbulence modeling for hypersonic flows

NASA Technical Reports Server (NTRS)

Marvin, J. G.; Coakley, T. J.

1989-01-01

Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed.

A 4-cylinder Stirling engine computer program with dynamic energy equations

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Lorenzo, C. F.

1983-01-01

A computer program for simulating the steady state and transient performance of a four cylinder Stirling engine is presented. The thermodynamic model includes both continuity and energy equations and linear momentum terms (flow resistance). Each working space between the pistons is broken into seven control volumes. Drive dynamics and vehicle load effects are included. The model contains 70 state variables. Also included in the model are piston rod seal leakage effects. The computer program includes a model of a hydrogen supply system, from which hydrogen may be added to the system to accelerate the engine. Flow charts are provided.

Development of a One-Equation Transition/Turbulence Model

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

EDWARDS,JACK R.; ROY,CHRISTOPHER J.; BLOTTNER,FREDERICK G.

2000-09-26

This paper reports on the development of a unified one-equation model for the prediction of transitional and turbulent flows. An eddy viscosity - transport equation for non-turbulent fluctuation growth based on that proposed by Warren and Hassan (Journal of Aircraft, Vol. 35, No. 5) is combined with the Spalart-Allmaras one-equation model for turbulent fluctuation growth. Blending of the two equations is accomplished through a multidimensional intermittence function based on the work of Dhawan and Narasimha (Journal of Fluid Mechanics, Vol. 3, No. 4). The model predicts both the onset and extent of transition. Low-speed test cases include transitional flow overmore » a flat plate, a single element airfoil, and a multi-element airfoil in landing configuration. High-speed test cases include transitional Mach 3.5 flow over a 5{degree} cone and Mach 6 flow over a flared-cone configuration. Results are compared with experimental data, and the spatial accuracy of selected predictions is analyzed.« less

Deriving Differential Equations from Process Algebra Models in Reagent-Centric Style

NASA Astrophysics Data System (ADS)

Hillston, Jane; Duguid, Adam

The reagent-centric style of modeling allows stochastic process algebra models of biochemical signaling pathways to be developed in an intuitive way. Furthermore, once constructed, the models are amenable to analysis by a number of different mathematical approaches including both stochastic simulation and coupled ordinary differential equations. In this chapter, we give a tutorial introduction to the reagent-centric style, in PEPA and Bio-PEPA, and the way in which such models can be used to generate systems of ordinary differential equations.

A lumped model of venting during thermal runaway in a cylindrical Lithium Cobalt Oxide lithium-ion cell

NASA Astrophysics Data System (ADS)

Coman, Paul T.; Rayman, Sean; White, Ralph E.

2016-03-01

This paper presents a mathematical model built for analyzing the intricate thermal behavior of a 18650 LCO (Lithium Cobalt Oxide) battery cell during thermal runaway when venting of the electrolyte and contents of the jelly roll (ejecta) is considered. The model consists of different ODEs (Ordinary Differential Equations) describing reaction rates and electrochemical reactions, as well as the isentropic flow equations for describing electrolyte venting. The results are validated against experimental findings from Golubkov et al. [1] [Andrey W. Golubkov, David Fuchs, Julian Wagner, Helmar Wiltsche, Christoph Stangl, Gisela Fauler, Gernot Voitice Alexander Thaler and Viktor Hacker, RSC Advances, 4:3633-3642, 2014] for two cases - with flow and without flow. The results show that if the isentropic flow equations are not included in the model, the thermal runaway is triggered prematurely at the point where venting should occur. This shows that the heat dissipation due to ejection of electrolyte and jelly roll contents has a significant contribution. When the flow equations are included, the model shows good agreement with the experiment and therefore proving the importance of including venting.

A mathematical model for Vertical Attitude Takeoff and Landing (VATOL) aircraft simulation. Volume 2: Model equations and base aircraft data

NASA Technical Reports Server (NTRS)

Fortenbaugh, R. L.

1980-01-01

Equations incorporated in a VATOL six degree of freedom off-line digital simulation program and data for the Vought SF-121 VATOL aircraft concept which served as the baseline for the development of this program are presented. The equations and data are intended to facilitate the development of a piloted VATOL simulation. The equation presentation format is to state the equations which define a particular model segment. Listings of constants required to quantify the model segment, input variables required to exercise the model segment, and output variables required by other model segments are included. In several instances a series of input or output variables are followed by a section number in parentheses which identifies the model segment of origination or termination of those variables.

A two-phase micromorphic model for compressible granular materials

NASA Astrophysics Data System (ADS)

Paolucci, Samuel; Li, Weiming; Powers, Joseph

2009-11-01

We introduce a new two-phase continuum model for compressible granular material based on micromorphic theory and treat it as a two-phase mixture with inner structure. By taking an appropriate number of moments of the local micro scale balance equations, the average phase balance equations result from a systematic averaging procedure. In addition to equations for mass, momentum and energy, the balance equations also include evolution equations for microinertia and microspin tensors. The latter equations combine to yield a general form of a compaction equation when the material is assumed to be isotropic. When non-linear and inertial effects are neglected, the generalized compaction equation reduces to that originally proposed by Bear and Nunziato. We use the generalized compaction equation to numerically model a mixture of granular high explosive and interstitial gas. One-dimensional shock tube and piston-driven solutions are presented and compared with experimental results and other known solutions.

Development of Semi-Empirical Damping Equation for Baffled Tank with Oblate Spheroidal Dome

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeff; Brodnick, Jacob; Eberhart, Chad

2016-01-01

Propellant slosh is a potential source of disturbance that can significantly impact the stability of space vehicles. The slosh dynamics are typically represented by a mechanical model of a spring-mass-damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control analysis. The typical parameters required by the mechanical model include natural frequency of the slosh, slosh mass, slosh mass center location, and the critical damping ratio. A fundamental study has been undertaken at NASA MSFC to understand the fluid damping physics from a ring baffle in the barrel section of a propellant tank. An asymptotic damping equation and CFD blended equation have been derived by NASA MSFC team to complement the popularly used Miles equation at different flow regimes. The new development has found success in providing a nonlinear damping model for the Space Launch System. The purpose of this study is to further extend the semi-empirical damping equations into the oblate spheroidal dome section of the propellant tanks. First, previous experimental data from the spherical baffled tank are collected and analyzed. Several methods of taking the dome curvature effect, including a generalized Miles equation, area projection method, and equalized fill height method, are assessed. CFD simulation is used to shed light on the interaction of vorticity around the baffle with the locally curved wall and liquid-gas interface. The final damping equation will be validated by a recent subscale test with an oblate spheroidal dome conducted at NASA MSFC.

A mathematical simulation model of a 1985-era tilt-rotor passenger aircraft

NASA Technical Reports Server (NTRS)

Mcveigh, M. A.; Widdison, C. A.

1976-01-01

A mathematical model for use in real-time piloted simulation of a 1985-era tilt rotor passenger aircraft is presented. The model comprises the basic six degrees-of-freedom equations of motion, and a large angle of attack representation of the airframe and rotor aerodynamics, together with equations and functions used to model turbine engine performance, aircraft control system and stability augmentation system. A complete derivation of the primary equations is given together with a description of the modeling techniques used. Data for the model is included in an appendix.

A Comparison between Multiple Regression Models and CUN-BAE Equation to Predict Body Fat in Adults

PubMed Central

Fuster-Parra, Pilar; Bennasar-Veny, Miquel; Tauler, Pedro; Yañez, Aina; López-González, Angel A.; Aguiló, Antoni

2015-01-01

Background Because the accurate measure of body fat (BF) is difficult, several prediction equations have been proposed. The aim of this study was to compare different multiple regression models to predict BF, including the recently reported CUN-BAE equation. Methods Multi regression models using body mass index (BMI) and body adiposity index (BAI) as predictors of BF will be compared. These models will be also compared with the CUN-BAE equation. For all the analysis a sample including all the participants and another one including only the overweight and obese subjects will be considered. The BF reference measure was made using Bioelectrical Impedance Analysis. Results The simplest models including only BMI or BAI as independent variables showed that BAI is a better predictor of BF. However, adding the variable sex to both models made BMI a better predictor than the BAI. For both the whole group of participants and the group of overweight and obese participants, using simple models (BMI, age and sex as variables) allowed obtaining similar correlations with BF as when the more complex CUN-BAE was used (ρ = 0:87 vs. ρ = 0:86 for the whole sample and ρ = 0:88 vs. ρ = 0:89 for overweight and obese subjects, being the second value the one for CUN-BAE). Conclusions There are simpler models than CUN-BAE equation that fits BF as well as CUN-BAE does. Therefore, it could be considered that CUN-BAE overfits. Using a simple linear regression model, the BAI, as the only variable, predicts BF better than BMI. However, when the sex variable is introduced, BMI becomes the indicator of choice to predict BF. PMID:25821960

A comparison between multiple regression models and CUN-BAE equation to predict body fat in adults.

PubMed

Fuster-Parra, Pilar; Bennasar-Veny, Miquel; Tauler, Pedro; Yañez, Aina; López-González, Angel A; Aguiló, Antoni

2015-01-01

Because the accurate measure of body fat (BF) is difficult, several prediction equations have been proposed. The aim of this study was to compare different multiple regression models to predict BF, including the recently reported CUN-BAE equation. Multi regression models using body mass index (BMI) and body adiposity index (BAI) as predictors of BF will be compared. These models will be also compared with the CUN-BAE equation. For all the analysis a sample including all the participants and another one including only the overweight and obese subjects will be considered. The BF reference measure was made using Bioelectrical Impedance Analysis. The simplest models including only BMI or BAI as independent variables showed that BAI is a better predictor of BF. However, adding the variable sex to both models made BMI a better predictor than the BAI. For both the whole group of participants and the group of overweight and obese participants, using simple models (BMI, age and sex as variables) allowed obtaining similar correlations with BF as when the more complex CUN-BAE was used (ρ = 0:87 vs. ρ = 0:86 for the whole sample and ρ = 0:88 vs. ρ = 0:89 for overweight and obese subjects, being the second value the one for CUN-BAE). There are simpler models than CUN-BAE equation that fits BF as well as CUN-BAE does. Therefore, it could be considered that CUN-BAE overfits. Using a simple linear regression model, the BAI, as the only variable, predicts BF better than BMI. However, when the sex variable is introduced, BMI becomes the indicator of choice to predict BF.

An assessment and application of turbulence models for hypersonic flows

NASA Technical Reports Server (NTRS)

Coakley, T. J.; Viegas, J. R.; Huang, P. G.; Rubesin, M. W.

1990-01-01

The current approach to the Accurate Computation of Complex high-speed flows is to solve the Reynolds averaged Navier-Stokes equations using finite difference methods. An integral part of this approach consists of development and applications of mathematical turbulence models which are necessary in predicting the aerothermodynamic loads on the vehicle and the performance of the propulsion plant. Computations of several high speed turbulent flows using various turbulence models are described and the models are evaluated by comparing computations with the results of experimental measurements. The cases investigated include flows over insulated and cooled flat plates with Mach numbers ranging from 2 to 8 and wall temperature ratios ranging from 0.2 to 1.0. The turbulence models investigated include zero-equation, two-equation, and Reynolds-stress transport models.

Modeling unsteady sound refraction by coherent structures in a high-speed jet

NASA Astrophysics Data System (ADS)

Kan, Pinqing; Lewalle, Jacques

2011-11-01

We construct a visual model for the unsteady refraction of sound waves from point sources in a Ma = 0.6 jet. The mass and inviscid momentum equations give an equation governing acoustic fluctuations, including anisotropic propagation, attenuation and sources; differences with Lighthill's equation will be discussed. On this basis, the theory of characteristics gives canonical equations for the acoustic paths from any source into the far field. We model a steady mean flow in the near-jet region including the potential core and the mixing region downstream of its collapse, and model the convection of coherent structures as traveling wave perturbations of this mean flow. For a regular distribution of point sources in this region, we present a visual rendition of fluctuating distortion, lensing and deaf spots from the viewpoint of a far-field observer. Supported in part by AFOSR Grant FA-9550-10-1-0536 and by a Syracuse University Graduate Fellowship.

A simplified rotor system mathematical model for piloted flight dynamics simulation

NASA Technical Reports Server (NTRS)

Chen, R. T. N.

1979-01-01

The model was developed for real-time pilot-in-the-loop investigation of helicopter flying qualities. The mathematical model included the tip-path plane dynamics and several primary rotor design parameters, such as flapping hinge restraint, flapping hinge offset, blade Lock number, and pitch-flap coupling. The model was used in several exploratory studies of the flying qualities of helicopters with a variety of rotor systems. The basic assumptions used and the major steps involved in the development of the set of equations listed are described. The equations consisted of the tip-path plane dynamic equation, the equations for the main rotor forces and moments, and the equation for control phasing required to achieve decoupling in pitch and roll due to cyclic inputs.

Bayesian Semiparametric Structural Equation Models with Latent Variables

ERIC Educational Resources Information Center

Yang, Mingan; Dunson, David B.

2010-01-01

Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In…

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.; Ochs, Harry T., III

1988-01-01

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian

NASA Astrophysics Data System (ADS)

Zabrodin, A.; Zotov, A.

2018-02-01

We discuss a self-dual form or the Bäcklund transformations for the continuous (in time variable) glN Ruijsenaars-Schneider model. It is based on the first order equations in N + M complex variables which include N positions of particles and M dual variables. The latter satisfy equations of motion of the glM Ruijsenaars-Schneider model. In the elliptic case it holds M = N while for the rational and trigonometric models M is not necessarily equal to N. Our consideration is similar to the previously obtained results for the Calogero-Moser models which are recovered in the non-relativistic limit. We also show that the self-dual description of the Ruijsenaars-Schneider models can be derived from complexified intermediate long wave equation with discrete Laplacian by means of the simple pole ansatz likewise the Calogero-Moser models arise from ordinary intermediate long wave and Benjamin-Ono equations.

Deriving Biomass Estimation Equations for Seven Plantation Hardwood Species

Treesearch

Bryce E. Schlaegel; Harvey E. Kennedy

1986-01-01

Trees of seven species sampled from a plantation over 7 years were used to derive weight equations to predict primary tree components. The seven species required the use of five different model forms to insure the greatest precision. Regardless of model form, all equations include variables for tree diameter, tree height, age, and number of trees planted. The most...

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.

The influence of a wind tunnel on helicopter rotational noise: Formulation of analysis

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

An analytical model is discussed that can be used to examine the effects of wind tunnel walls on helicopter rotational noise. A complete physical model of an acoustic source in a wind tunnel is described and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. The simplified physical model is then modeled as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. Details of generating a suitable Green's function and integral equation are included and the equation is discussed and also given for a two-dimensional case.

Effect of liquid droplets on turbulence in a round gaseous jet

NASA Technical Reports Server (NTRS)

Mostafa, A. A.; Elghobashi, S. E.

1986-01-01

The main objective of this investigation is to develop a two-equation turbulence model for dilute vaporizing sprays or in general for dispersed two-phase flows including the effects of phase changes. The model that accounts for the interaction between the two phases is based on rigorously derived equations for turbulence kinetic energy (K) and its dissipation rate epsilon of the carrier phase using the momentum equation of that phase. Closure is achieved by modeling the turbulent correlations, up to third order, in the equations of the mean motion, concentration of the vapor in the carrier phase, and the kinetic energy of turbulence and its dissipation rate for the carrier phase. The governing equations are presented in both the exact and the modeled formes. The governing equations are solved numerically using a finite-difference procedure to test the presented model for the flow of a turbulent axisymmetric gaseous jet laden with either evaporating liquid droplets or solid particles. The predictions include the distribution of the mean velocity, volume fractions of the different phases, concentration of the evaporated material in the carrier phase, turbulence intensity and shear stress of the carrier phase, droplet diameter distribution, and the jet spreading rate. The predictions are in good agreement with the experimental data.

Multiplicity Control in Structural Equation Modeling: Incorporating Parameter Dependencies

ERIC Educational Resources Information Center

Smith, Carrie E.; Cribbie, Robert A.

2013-01-01

When structural equation modeling (SEM) analyses are conducted, significance tests for all important model relationships (parameters including factor loadings, covariances, etc.) are typically conducted at a specified nominal Type I error rate ([alpha]). Despite the fact that many significance tests are often conducted in SEM, rarely is…

A Structural Equation Model of Expertise in College Physics

ERIC Educational Resources Information Center

Taasoobshirazi, Gita; Carr, Martha

2009-01-01

A model of expertise in physics was tested on a sample of 374 college students in 2 different level physics courses. Structural equation modeling was used to test hypothesized relationships among variables linked to expert performance in physics including strategy use, pictorial representation, categorization skills, and motivation, and these…

A Structural Equation Model of Conceptual Change in Physics

ERIC Educational Resources Information Center

Taasoobshirazi, Gita; Sinatra, Gale M.

2011-01-01

A model of conceptual change in physics was tested on introductory-level, college physics students. Structural equation modeling was used to test hypothesized relationships among variables linked to conceptual change in physics including an approach goal orientation, need for cognition, motivation, and course grade. Conceptual change in physics…

Electron-Impact Excitation Cross Sections for Modeling Non-Equilibrium Gas

NASA Technical Reports Server (NTRS)

Huo, Winifred M.; Liu, Yen; Panesi, Marco; Munafo, Alessandro; Wray, Alan; Carbon, Duane F.

2015-01-01

In order to provide a database for modeling hypersonic entry in a partially ionized gas under non-equilibrium, the electron-impact excitation cross sections of atoms have been calculated using perturbation theory. The energy levels covered in the calculation are retrieved from the level list in the HyperRad code. The downstream flow-field is determined by solving a set of continuity equations for each component. The individual structure of each energy level is included. These equations are then complemented by the Euler system of equations. Finally, the radiation field is modeled by solving the radiative transfer equation.

Gyro-Landau fluid models for toroidal geometry

NASA Astrophysics Data System (ADS)

Waltz, R. E.; Dominguez, R. R.; Hammett, G. W.

1992-10-01

Gyro-Landau fluid model equations provide first-order time advancement for a limited number of moments of the gyrokinetic equation, while approximately preserving the effects of the gyroradius averaging and Landau damping. This paper extends the work of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for electrostatic motion parallel to the magnetic field and E×B motion to include the gyroaveraging linearly and the curvature drift motion. The equations are tested by comparing the ion-temperature-gradient mode linear growth rates for the model equations with those of the exact gyrokinetic theory over a full range of parameters.

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

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

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Analytic Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings

NASA Technical Reports Server (NTRS)

Bruckner, Robert J.; DellaCorte, Christopher; Prahl, Joseph M.

2005-01-01

A simulation and modeling effort is conducted on gas foil thrust bearings. A foil bearing is a self acting hydrodynamic device capable of separating stationary and rotating components of rotating machinery by a film of air or other gaseous lubricant. Although simple in appearance these bearings have proven to be complicated devices in analysis. They are sensitive to fluid structure interaction, use a compressible gas as a lubricant, may not be in the fully continuum range of fluid mechanics, and operate in the range where viscous heat generation is significant. These factors provide a challenge to the simulation and modeling task. The Reynolds equation with the addition of Knudsen number effects due to thin film thicknesses is used to simulate the hydrodynamics. The energy equation is manipulated to simulate the temperature field of the lubricant film and combined with the ideal gas relationship, provides density field input to the Reynolds equation. Heat transfer between the lubricant and the surroundings is also modeled. The structural deformations of the bearing are modeled with a single partial differential equation. The equation models the top foil as a thin, bending dominated membrane whose deflections are governed by the biharmonic equation. A linear superposition of hydrodynamic load and compliant foundation reaction is included. The stiffness of the compliant foundation is modeled as a distributed stiffness that supports the top foil. The system of governing equations is solved numerically by a computer program written in the Mathematica computing environment. Representative calculations and comparisons with experimental results are included for a generation I gas foil thrust bearing.

Control of Supercavitation Flow and Stability of Supercavitating Motion of Bodies

DTIC Science & Technology

2001-02-01

sign opposite to a sign of angle Vf - accidental deflection of the model Sgn M = -Sgn i. 4.3. EQUATIONS OF THE SCM DYNAMICS The most effective method of...the motion stability in interactive regime "researcher - computer" [ 16]. The complete mathematical model of the SCM motion includes a set of equations ...of solid body dynamics, equations to calculate the unsteady cavity shape and relations to calculate the acting forces. A set of dynamic equations of

Assessments of a Turbulence Model Based on Menter's Modification to Rotta's Two-Equation Model

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.

2013-01-01

The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter s modification to Rotta s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale L and kinetic energy. Rotta s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows. The model is implemented in the PAB3D solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and Large Eddy Simulation (LES) data. The results from this formulation are as good or better than the well-known SST turbulence model and much better than k-epsilon results. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.

Collaborative Understanding of Cyanobacteria in Lake Ecosystems

ERIC Educational Resources Information Center

Greer, Meredith L.; Ewing, Holly A.; Cottingham, Kathryn L.; Weathers, Kathleen C.

2013-01-01

We describe a collaboration between mathematicians and ecologists studying the cyanobacterium "Gloeotrichia echinulata" and its possible role in eutrophication of New England lakes. The mathematics includes compartmental modeling, differential equations, difference equations, and testing models against high-frequency data. The ecology…

Three Approaches to Using Lengthy Ordinal Scales in Structural Equation Models: Parceling, Latent Scoring, and Shortening Scales

ERIC Educational Resources Information Center

Yang, Chongming; Nay, Sandra; Hoyle, Rick H.

2010-01-01

Lengthy scales or testlets pose certain challenges for structural equation modeling (SEM) if all the items are included as indicators of a latent construct. Three general approaches to modeling lengthy scales in SEM (parceling, latent scoring, and shortening) have been reviewed and evaluated. A hypothetical population model is simulated containing…

Overview of the ArbiTER edge plasma eigenvalue code

NASA Astrophysics Data System (ADS)

Baver, Derek; Myra, James; Umansky, Maxim

2011-10-01

The Arbitrary Topology Equation Reader, or ArbiTER, is a flexible eigenvalue solver that is currently under development for plasma physics applications. The ArbiTER code builds on the equation parser framework of the existing 2DX code, extending it to include a topology parser. This will give the code the capability to model problems with complicated geometries (such as multiple X-points and scrape-off layers) or model equations with arbitrary numbers of dimensions (e.g. for kinetic analysis). In the equation parser framework, model equations are not included in the program's source code. Instead, an input file contains instructions for building a matrix from profile functions and elementary differential operators. The program then executes these instructions in a sequential manner. These instructions may also be translated into analytic form, thus giving the code transparency as well as flexibility. We will present an overview of how the ArbiTER code is to work, as well as preliminary results from early versions of this code. Work supported by the U.S. DOE.

Internally electrodynamic particle model: Its experimental basis and its predictions

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

Zheng-Johansson, J. X., E-mail: jxzj@iofpr.or

2010-03-15

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts: (a) electric charges present with all material particles, (b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation, and (c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schroedinger equation, mass, Einstein mass-energy relation, Newton's law of gravity,more » single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A conditioned solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.« less

Internally electrodynamic particle model: Its experimental basis and its predictions

NASA Astrophysics Data System (ADS)

Zheng-Johansson, J. X.

2010-03-01

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts: (a) electric charges present with all material particles, (b) an accelerated charge generates electromagnetic waves according to Maxwell’s equations and Planck energy equation, and (c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schrödinger equation, mass, Einstein mass-energy relation, Newton’s law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A conditioned solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.

A new theoretical basis for numerical simulations of nonlinear acoustic fields

NASA Astrophysics Data System (ADS)

Wójcik, Janusz

2000-07-01

Nonlinear acoustic equations can be considerably simplified. The presented model retains the accuracy of a more complex description of nonlinearity and a uniform description of near and far fields (in contrast to the KZK equation). A method has been presented for obtaining solutions of Kuznetsov's equation from the solutions of the model under consideration. Results of numerical calculations, including comparative ones, are presented.

Integral equations in the study of polar and ionic interaction site fluids

PubMed Central

Howard, Jesse J.

2011-01-01

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids. PMID:22383857

Modeling void growth and movement with phase change in thermal energy storage canisters

NASA Technical Reports Server (NTRS)

Darling, Douglas; Namkoong, David; Skarda, J. R. L.

1993-01-01

A scheme was developed to model the thermal hydrodynamic behavior of thermal energy storage salts. The model included buoyancy, surface tension, viscosity, phases change with density difference, and void growth and movement. The energy, momentum, and continuity equations were solved using a finite volume formulation. The momentum equation was divided into two pieces. The void growth and void movement are modeled between the two pieces of the momentum equations. Results showed this scheme was able to predict the behavior of thermal energy storage salts.

REVIEW OF THE GOVERNING EQUATIONS, COMPUTATIONAL ALGORITHMS, AND OTHER COMPONENTS OF THE MODELS-3 COMMUNITY MULTISCALE AIR QUALITY (CMAQ) MODELING SYSTEM

EPA Science Inventory

This article describes the governing equations, computational algorithms, and other components entering into the Community Multiscale Air Quality (CMAQ) modeling system. This system has been designed to approach air quality as a whole by including state-of-the-science capabiliti...

Comments on "Drill-string horizontal dynamics with uncertainty on the frictional force" by T.G. Ritto, M.R. Escalante, Rubens Sampaio, M.B. Rosales [J. Sound Vib. 332 (2013) 145-153

NASA Astrophysics Data System (ADS)

Li, Zifeng

2016-12-01

This paper analyzes the mechanical and mathematical models in "Ritto et al. (2013) [1]". The results are that: (1) the mechanical model is obviously incorrect; (2) the mathematical model is not complete; (3) the differential equation is obviously incorrect; (4) the finite element equation is obviously not discretized from the corresponding mathematical model above, and is obviously incorrect. A mathematical model of dynamics should include the differential equations, the boundary conditions and the initial conditions.

A Flight Dynamics Model for a Small Glider in Ambient Winds

NASA Technical Reports Server (NTRS)

Beeler, Scott C.; Moerder, Daniel D.; Cox, David E.

2003-01-01

In this paper we describe the equations of motion developed for a point-mass zero-thrust (gliding) aircraft model operating in an environment of spatially varying atmospheric winds. The wind effects are included as an integral part of the flight dynamics equations, and the model is controlled through the three aerodynamic control angles. Formulas for the aerodynamic coefficients for this model are constructed to include the effects of several different aspects contributing to the aerodynamic performance of the vehicle. Characteristic parameter values of the model are compared with those found in a different set of small glider simulations. We execute a set of example problems which solve the glider dynamics equations to find the aircraft trajectory given specified control inputs. The ambient wind conditions and glider characteristics are varied to compare the simulation results under these different circumstances.

A Flight Dynamics Model for a Small Glider in Ambient Winds

NASA Technical Reports Server (NTRS)

Beeler, Scott C.; Moerder, Daniel D.; Cox, David E.

2003-01-01

In this paper we describe the equations of motion developed for a point-mass zero-thrust (gliding) aircraft model operating in an environment of spatially varying atmospheric winds. The wind effects are included as an integral part of the flight dynamics equations, and the model is controlled through the three aerodynamic control angles. Formulas for the aerodynamic coefficients for this model are constructed to include the effects of several different aspects contributing to the aerodynamic performance of the vehicle. Characteristic parameter values of the model are compared with those found in a different set of small glider simulations. We execute a set of example problems which solve the glider dynamics equations to find aircraft trajectory given specified control inputs. The ambient wind conditions and glider characteristics are varied to compare the simulation results under these different circumstances.

Nonlinear static and dynamic analysis of beam structures using fully intrinsic equations

NASA Astrophysics Data System (ADS)

Sotoudeh, Zahra

2011-07-01

Beams are structural members with one dimension much larger than the other two. Examples of beams include propeller blades, helicopter rotor blades, and high aspect-ratio aircraft wings in aerospace engineering; shafts and wind turbine blades in mechanical engineering; towers, highways and bridges in civil engineering; and DNA modeling in biomedical engineering. Beam analysis includes two sets of equations: a generally linear two-dimensional problem over the cross-sectional plane and a nonlinear, global one-dimensional analysis. This research work deals with a relatively new set of equations for one-dimensional beam analysis, namely the so-called fully intrinsic equations. Fully intrinsic equations comprise a set of geometrically exact, nonlinear, first-order partial differential equations that is suitable for analyzing initially curved and twisted anisotropic beams. A fully intrinsic formulation is devoid of displacement and rotation variables, making it especially attractive because of the absence of singularities, infinite-degree nonlinearities, and other undesirable features associated with finite rotation variables. In spite of the advantages of these equations, using them with certain boundary conditions presents significant challenges. This research work will take a broad look at these challenges of modeling various boundary conditions when using the fully intrinsic equations. Hopefully it will clear the path for wider and easier use of the fully intrinsic equations in future research. This work also includes application of fully intrinsic equations in structural analysis of joined-wing aircraft, different rotor blade configuration and LCO analysis of HALE aircraft.

A novel coupled system of non-local integro-differential equations modelling Young's modulus evolution, nutrients' supply and consumption during bone fracture healing

NASA Astrophysics Data System (ADS)

Lu, Yanfei; Lekszycki, Tomasz

2016-10-01

During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.

Update to core reporting practices in structural equation modeling.

PubMed

Schreiber, James B

This paper is a technical update to "Core Reporting Practices in Structural Equation Modeling." 1 As such, the content covered in this paper includes, sample size, missing data, specification and identification of models, estimation method choices, fit and residual concerns, nested, alternative, and equivalent models, and unique issues within the SEM family of techniques. Copyright © 2016 Elsevier Inc. All rights reserved.

A Dynamic Model for Modern Military Conflict.

DTIC Science & Technology

1982-10-01

within the generalized form of the Lotka - Volterra equations, that can account for the important interactions of modern military conflicts described in...Mx + These equations are seen to be of the generalized Lotka - Volterra form; however, only 20 of the 32 parameters that might possibly be included...determine one equilibrium as the solution of a system of linear equations. The method is derived for the general nth order Lotka - Volterra model in

Cable logging production rate equations for thinning young-growth Douglas-fir

Treesearch

Chris B. LeDoux; Lawson W. Starnes

1986-01-01

A cable logging thinning simulation model and field study data from cable thinning production studies have been assembled and converted into a set of simple equations. These equations can be used to estimate the hourly production rates of various cable thinning machines operating in the mountainous terrain of western Oregon and western Washington. The equations include...

Toroidal gyrofluid equations for simulations of tokamak turbulence

NASA Astrophysics Data System (ADS)

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

1996-11-01

A set of nonlinear gyrofluid equations for simulations of tokamak turbulence are derived by taking moments of the nonlinear toroidal gyrokinetic equation. The moment hierarchy is closed with approximations that model the kinetic effects of parallel Landau damping, toroidal drift resonances, and finite Larmor radius effects. These equations generalize the work of Dorland and Hammett [Phys. Fluids B 5, 812 (1993)] to toroidal geometry by including essential toroidal effects. The closures for phase mixing from toroidal ∇B and curvature drifts take the basic form presented in Waltz et al. [Phys. Fluids B 4, 3138 (1992)], but here a more rigorous procedure is used, including an extension to higher moments, which provides significantly improved accuracy. In addition, trapped ion effects and collisions are incorporated. This reduced set of nonlinear equations accurately models most of the physics considered important for ion dynamics in core tokamak turbulence, and is simple enough to be used in high resolution direct numerical simulations.

An analytical model of a curved beam with a T shaped cross section

NASA Astrophysics Data System (ADS)

Hull, Andrew J.; Perez, Daniel; Cox, Donald L.

2018-03-01

This paper derives a comprehensive analytical dynamic model of a closed circular beam that has a T shaped cross section. The new model includes in-plane and out-of-plane vibrations derived using continuous media expressions which produces results that have a valid frequency range above those available from traditional lumped parameter models. The web is modeled using two-dimensional elasticity equations for in-plane motion and the classical flexural plate equation for out-of-plane motion. The flange is modeled using two sets of Donnell shell equations: one for the left side of the flange and one for the right side of the flange. The governing differential equations are solved with unknown wave propagation coefficients multiplied by spatial domain and time domain functions which are inserted into equilibrium and continuity equations at the intersection of the web and flange and into boundary conditions at the edges of the system resulting in 24 algebraic equations. These equations are solved to yield the wave propagation coefficients and this produces a solution to the displacement field in all three dimensions. An example problem is formulated and compared to results from finite element analysis.

Structural Equation Modeling: A Framework for Ocular and Other Medical Sciences Research

PubMed Central

Christ, Sharon L.; Lee, David J.; Lam, Byron L.; Diane, Zheng D.

2017-01-01

Structural equation modeling (SEM) is a modeling framework that encompasses many types of statistical models and can accommodate a variety of estimation and testing methods. SEM has been used primarily in social sciences but is increasingly used in epidemiology, public health, and the medical sciences. SEM provides many advantages for the analysis of survey and clinical data, including the ability to model latent constructs that may not be directly observable. Another major feature is simultaneous estimation of parameters in systems of equations that may include mediated relationships, correlated dependent variables, and in some instances feedback relationships. SEM allows for the specification of theoretically holistic models because multiple and varied relationships may be estimated together in the same model. SEM has recently expanded by adding generalized linear modeling capabilities that include the simultaneous estimation of parameters of different functional form for outcomes with different distributions in the same model. Therefore, mortality modeling and other relevant health outcomes may be evaluated. Random effects estimation using latent variables has been advanced in the SEM literature and software. In addition, SEM software has increased estimation options. Therefore, modern SEM is quite general and includes model types frequently used by health researchers, including generalized linear modeling, mixed effects linear modeling, and population average modeling. This article does not present any new information. It is meant as an introduction to SEM and its uses in ocular and other health research. PMID:24467557

Helioseismic Constraints on New Solar Models from the MoSEC Code

NASA Technical Reports Server (NTRS)

Elliott, J. R.

1998-01-01

Evolutionary solar models are computed using a new stellar evolution code, MOSEC (Modular Stellar Evolution Code). This code has been designed with carefully controlled truncation errors in order to achieve a precision which reflects the increasingly accurate determination of solar interior structure by helioseismology. A series of models is constructed to investigate the effects of the choice of equation of state (OPAL or MHD-E, the latter being a version of the MHD equation of state recalculated by the author), the inclusion of helium and heavy-element settling and diffusion, and the inclusion of a simple model of mixing associated with the solar tachocline. The neutrino flux predictions are discussed, while the sound speed of the computed models is compared to that of the sun via the latest inversion of SOI-NMI p-mode frequency data. The comparison between models calculated with the OPAL and MHD-E equations of state is particularly interesting because the MHD-E equation of state includes relativistic effects for the electrons, whereas neither MHD nor OPAL do. This has a significant effect on the sound speed of the computed model, worsening the agreement with the solar sound speed. Using the OPAL equation of state and including the settling and diffusion of helium and heavy elements produces agreement in sound speed with the helioseismic results to within about +.-0.2%; the inclusion of mixing slightly improves the agreement.

An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers

NASA Technical Reports Server (NTRS)

Hicks, Raymond M.; Cliff, Susan E.

1991-01-01

Full-potential, Euler, and Navier-Stokes computational fluid dynamics (CFD) codes were evaluated for use in analyzing the flow field about airfoils sections operating at Mach numbers from 0.20 to 0.60 and Reynolds numbers from 500,000 to 2,000,000. The potential code (LBAUER) includes weakly coupled integral boundary layer equations for laminar and turbulent flow with simple transition and separation models. The Navier-Stokes code (ARC2D) uses the thin-layer formulation of the Reynolds-averaged equations with an algebraic turbulence model. The Euler code (ISES) includes strongly coupled integral boundary layer equations and advanced transition and separation calculations with the capability to model laminar separation bubbles and limited zones of turbulent separation. The best experiment/CFD correlation was obtained with the Euler code because its boundary layer equations model the physics of the flow better than the other two codes. An unusual reversal of boundary layer separation with increasing angle of attack, following initial shock formation on the upper surface of the airfoil, was found in the experiment data. This phenomenon was not predicted by the CFD codes evaluated.

Stable Algorithm For Estimating Airdata From Flush Surface Pressure Measurements

NASA Technical Reports Server (NTRS)

Whitmore, Stephen, A. (Inventor); Cobleigh, Brent R. (Inventor); Haering, Edward A., Jr. (Inventor)

2001-01-01

An airdata estimation and evaluation system and method, including a stable algorithm for estimating airdata from nonintrusive surface pressure measurements. The airdata estimation and evaluation system is preferably implemented in a flush airdata sensing (FADS) system. The system and method of the present invention take a flow model equation and transform it into a triples formulation equation. The triples formulation equation eliminates the pressure related states from the flow model equation by strategically taking the differences of three surface pressures, known as triples. This triples formulation equation is then used to accurately estimate and compute vital airdata from nonintrusive surface pressure measurements.

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

PubMed

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

A review of physically based models for soil erosion by water

NASA Astrophysics Data System (ADS)

Le, Minh-Hoang; Cerdan, Olivier; Sochala, Pierre; Cheviron, Bruno; Brivois, Olivier; Cordier, Stéphane

2010-05-01

Physically-based models rely on fundamental physical equations describing stream flow and sediment and associated nutrient generation in a catchment. This paper reviews several existing erosion and sediment transport approaches. The process of erosion include soil detachment, transport and deposition, we present various forms of equations and empirical formulas used when modelling and quantifying each of these processes. In particular, we detail models describing rainfall and infiltration effects and the system of equations to describe the overland flow and the evolution of the topography. We also present the formulas for the flow transport capacity and the erodibility functions. Finally, we present some recent numerical schemes to approach the shallow water equations and it's coupling with infiltration and erosion source terms.

Photochemistry and dynamics of the ozone layer

NASA Technical Reports Server (NTRS)

Prinn, R. G.; Alyea, F. N.; Cunnold, D. M.

1978-01-01

The paper presents a broad review of the photochemical and dynamic theories of the ozone layer. The two theories are combined into the MIT three-dimensional dynamic-chemical quasi-geostrophic model with 26 levels in the vertical spaced in logarithmic pressure coordinates between the ground and 72-km altitude. The chemical scheme incorporates the important odd nitrogen, odd hydrogen, and odd oxygen chemistry, but is simplified in the sense that it requires specification of the distributions of NO2, OH and HO2. The prognostic equations are the vorticity equation, the perturbation thermodynamic equation, and the global mean and perturbation continuity equations for ozone; diagnostic equations include the hydrostatic equation, the balance condition, and the mass continuity equation. The model is applied to the investigation of the impact of supersonic aircraft on the ozone layer.

Computer modeling of heat pipe performance

NASA Technical Reports Server (NTRS)

Peterson, G. P.

1983-01-01

A parametric study of the defining equations which govern the steady state operational characteristics of the Grumman monogroove dual passage heat pipe is presented. These defining equations are combined to develop a mathematical model which describes and predicts the operational and performance capabilities of a specific heat pipe given the necessary physical characteristics and working fluid. Included is a brief review of the current literature, a discussion of the governing equations, and a description of both the mathematical and computer model. Final results of preliminary test runs of the model are presented and compared with experimental tests on actual prototypes.

Modelling of the internal dynamics and density in a tens of joules plasma focus device

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

Marquez, Ariel; Gonzalez, Jose; Tarifeno-Saldivia, Ariel

2012-01-15

Using MHD theory, coupled differential equations were generated using a lumped parameter model to describe the internal behaviour of the pinch compression phase in plasma focus discharges. In order to provide these equations with appropriate initial conditions, the modelling of previous phases was included by describing the plasma sheath as planar shockwaves. The equations were solved numerically, and the results were contrasted against experimental measurements performed on the device PF-50J. The model is able to predict satisfactorily the timing and the radial electron density profile at the maximum compression.

Experimentally validated multiphysics computational model of focusing and shock wave formation in an electromagnetic lithotripter.

PubMed

Fovargue, Daniel E; Mitran, Sorin; Smith, Nathan B; Sankin, Georgy N; Simmons, Walter N; Zhong, Pei

2013-08-01

A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model.

Experimentally validated multiphysics computational model of focusing and shock wave formation in an electromagnetic lithotripter

PubMed Central

Fovargue, Daniel E.; Mitran, Sorin; Smith, Nathan B.; Sankin, Georgy N.; Simmons, Walter N.; Zhong, Pei

2013-01-01

A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model. PMID:23927200

Toward Better Modeling of Supercritical Turbulent Mixing

NASA Technical Reports Server (NTRS)

Selle, Laurent; Okongo'o, Nora; Bellan, Josette; Harstad, Kenneth

2008-01-01

study was done as part of an effort to develop computational models representing turbulent mixing under thermodynamic supercritical (here, high pressure) conditions. The question was whether the large-eddy simulation (LES) approach, developed previously for atmospheric-pressure compressible-perfect-gas and incompressible flows, can be extended to real-gas non-ideal (including supercritical) fluid mixtures. [In LES, the governing equations are approximated such that the flow field is spatially filtered and subgrid-scale (SGS) phenomena are represented by models.] The study included analyses of results from direct numerical simulation (DNS) of several such mixing layers based on the Navier-Stokes, total-energy, and conservation- of-chemical-species governing equations. Comparison of LES and DNS results revealed the need to augment the atmospheric- pressure LES equations with additional SGS momentum and energy terms. These new terms are the direct result of high-density-gradient-magnitude regions found in the DNS and observed experimentally under fully turbulent flow conditions. A model has been derived for the new term in the momentum equation and was found to perform well at small filter size but to deteriorate with increasing filter size. Several alternative models were derived for the new SGS term in the energy equation that would need further investigations to determine if they are too computationally intensive in LES.

A nonequilibrium model for a moderate pressure hydrogen microwave discharge plasma

NASA Technical Reports Server (NTRS)

Scott, Carl D.

1993-01-01

This document describes a simple nonequilibrium energy exchange and chemical reaction model to be used in a computational fluid dynamics calculation for a hydrogen plasma excited by microwaves. The model takes into account the exchange between the electrons and excited states of molecular and atomic hydrogen. Specifically, electron-translation, electron-vibration, translation-vibration, ionization, and dissociation are included. The model assumes three temperatures, translational/rotational, vibrational, and electron, each describing a Boltzmann distribution for its respective energy mode. The energy from the microwave source is coupled to the energy equation via a source term that depends on an effective electric field which must be calculated outside the present model. This electric field must be found by coupling the results of the fluid dynamics and kinetics solution with a solution to Maxwell's equations that includes the effects of the plasma permittivity. The solution to Maxwell's equations is not within the scope of this present paper.

Transport of contaminants in the planetary boundary layer

NASA Technical Reports Server (NTRS)

Lee, I. Y.; Swan, P. R.

1978-01-01

A planetary boundary layer model is described and used to simulate PBL phenomena including cloud formation and pollution transport in the San Francisco Bay Area. The effect of events in the PBL on air pollution is considered, and governing equations for the average momentum, potential temperature, water vapor mixing ratio, and air contaminants are presented. These equations are derived by integrating the basic equations vertically through the mixed layer. Characteristics of the day selected for simulation are reported, and the results suggest that the diurnally cyclic features of the mesoscale motion, including clouds and air pollution, can be simulated in a readily interpretable way with the model.

A Robust Bayesian Approach for Structural Equation Models with Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Xia, Ye-Mao

2008-01-01

In this paper, normal/independent distributions, including but not limited to the multivariate t distribution, the multivariate contaminated distribution, and the multivariate slash distribution, are used to develop a robust Bayesian approach for analyzing structural equation models with complete or missing data. In the context of a nonlinear…

Structural Equation Modeling Reporting Practices for Language Assessment

ERIC Educational Resources Information Center

Ockey, Gary J.; Choi, Ikkyu

2015-01-01

Studies that use structural equation modeling (SEM) techniques are increasingly encountered in the language assessment literature. This popularity has created the need for a set of guidelines that can indicate what should be included in a research report and make it possible for research consumers to judge the appropriateness of the…

Potential Singularity for a Family of Models of the Axisymmetric Incompressible Flow

NASA Astrophysics Data System (ADS)

Hou, Thomas Y.; Jin, Tianling; Liu, Pengfei

2017-03-01

We study a family of 3D models for the incompressible axisymmetric Euler and Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the equations written using a set of transformed variables. The models share several regularity results with the Euler and Navier-Stokes equations, including an energy identity, the conservation of a modified circulation quantity, the BKM criterion and the Prodi-Serrin criterion. The inviscid models with weak convection are numerically observed to develop stable self-similar singularity with the singular region traveling along the symmetric axis, and such singularity scenario does not seem to persist for strong convection.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSGLRR full second-moment Reynolds stress models are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST) two-equation models.

A model for tides and currents in the English Channel and southern North Sea

USGS Publications Warehouse

Walters, Roy A.

1987-01-01

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations - the shallow water equations - are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O1, K1, M2, S2, N2, K2, M4, MS4, MN4, M6, and 2MS6.

Generalized heat-transport equations: parabolic and hyperbolic models

NASA Astrophysics Data System (ADS)

Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

2018-03-01

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Experimental investigation and numerical modelling of positive corona discharge: ozone generation

NASA Astrophysics Data System (ADS)

Yanallah, K; Pontiga, F; Fernández-Rueda, A; Castellanos, A

2009-03-01

The spatial distribution of the species generated in a wire-cylinder positive corona discharge in pure oxygen has been computed using a plasma chemistry model that includes the most significant reactions between electrons, ions, atoms and molecules. The plasma chemistry model is included in the continuity equations of each species, which are coupled with Poisson's equation for the electric field and the energy conservation equation for the gas temperature. The current-voltage characteristic measured in the experiments has been used as an input data to the numerical simulation. The numerical model is able to reproduce the basic structure of the positive corona discharge and highlights the importance of Joule heating on ozone generation. The average ozone density has been computed as a function of current intensity and compared with the experimental measurements of ozone concentration determined by UV absorption spectroscopy.

Three-dimensional time-dependent computer modeling of the electrothermal atomizers for analytical spectrometry

NASA Astrophysics Data System (ADS)

Tsivilskiy, I. V.; Nagulin, K. Yu.; Gilmutdinov, A. Kh.

2016-02-01

A full three-dimensional nonstationary numerical model of graphite electrothermal atomizers of various types is developed. The model is based on solution of a heat equation within solid walls of the atomizer with a radiative heat transfer and numerical solution of a full set of Navier-Stokes equations with an energy equation for a gas. Governing equations for the behavior of a discrete phase, i.e., atomic particles suspended in a gas (including gas-phase processes of evaporation and condensation), are derived from the formal equations molecular kinetics by numerical solution of the Hertz-Langmuir equation. The following atomizers test the model: a Varian standard heated electrothermal vaporizer (ETV), a Perkin Elmer standard THGA transversely heated graphite tube with integrated platform (THGA), and the original double-stage tube-helix atomizer (DSTHA). The experimental verification of computer calculations is carried out by a method of shadow spectral visualization of the spatial distributions of atomic and molecular vapors in an analytical space of an atomizer.

A root-mean-square pressure fluctuations model for internal flow applications

NASA Technical Reports Server (NTRS)

Chen, Y. S.

1985-01-01

A transport equation for the root-mean-square pressure fluctuations of turbulent flow is derived from the time-dependent momentum equation for incompressible flow. Approximate modeling of this transport equation is included to relate terms with higher order correlations to the mean quantities of turbulent flow. Three empirical constants are introduced in the model. Two of the empirical constants are estimated from homogeneous turbulence data and wall pressure fluctuations measurements. The third constant is determined by comparing the results of large eddy simulations for a plane channel flow and an annulus flow.

Periodicity computation of generalized mathematical biology problems involving delay differential equations.

PubMed

Jasim Mohammed, M; Ibrahim, Rabha W; Ahmad, M Z

2017-03-01

In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann-Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.

Modeling nuclear processes by Simulink

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

Rashid, Nahrul Khair Alang Md, E-mail: nahrul@iium.edu.my

2015-04-29

Modelling and simulation are essential parts in the study of dynamic systems behaviours. In nuclear engineering, modelling and simulation are important to assess the expected results of an experiment before the actual experiment is conducted or in the design of nuclear facilities. In education, modelling can give insight into the dynamic of systems and processes. Most nuclear processes can be described by ordinary or partial differential equations. Efforts expended to solve the equations using analytical or numerical solutions consume time and distract attention from the objectives of modelling itself. This paper presents the use of Simulink, a MATLAB toolbox softwaremore » that is widely used in control engineering, as a modelling platform for the study of nuclear processes including nuclear reactor behaviours. Starting from the describing equations, Simulink models for heat transfer, radionuclide decay process, delayed neutrons effect, reactor point kinetic equations with delayed neutron groups, and the effect of temperature feedback are used as examples.« less

Dynamic stiffness of chemically and physically ageing rubber vibration isolators in the audible frequency range. Part 1: constitutive equations

NASA Astrophysics Data System (ADS)

Kari, Leif

2017-09-01

The constitutive equations of chemically and physically ageing rubber in the audible frequency range are modelled as a function of ageing temperature, ageing time, actual temperature, time and frequency. The constitutive equations are derived by assuming nearly incompressible material with elastic spherical response and viscoelastic deviatoric response, using Mittag-Leffler relaxation function of fractional derivative type, the main advantage being the minimum material parameters needed to successfully fit experimental data over a broad frequency range. The material is furthermore assumed essentially entropic and thermo-mechanically simple while using a modified William-Landel-Ferry shift function to take into account temperature dependence and physical ageing, with fractional free volume evolution modelled by a nonlinear, fractional differential equation with relaxation time identical to that of the stress response and related to the fractional free volume by Doolittle equation. Physical ageing is a reversible ageing process, including trapping and freeing of polymer chain ends, polymer chain reorganizations and free volume changes. In contrast, chemical ageing is an irreversible process, mainly attributed to oxygen reaction with polymer network either damaging the network by scission or reformation of new polymer links. The chemical ageing is modelled by inner variables that are determined by inner fractional evolution equations. Finally, the model parameters are fitted to measurements results of natural rubber over a broad audible frequency range, and various parameter studies are performed including comparison with results obtained by ordinary, non-fractional ageing evolution differential equations.

BADGER v1.0: A Fortran equation of state library

NASA Astrophysics Data System (ADS)

Heltemes, T. A.; Moses, G. A.

2012-12-01

The BADGER equation of state library was developed to enable inertial confinement fusion plasma codes to more accurately model plasmas in the high-density, low-temperature regime. The code had the capability to calculate 1- and 2-T plasmas using the Thomas-Fermi model and an individual electron accounting model. Ion equation of state data can be calculated using an ideal gas model or via a quotidian equation of state with scaled binding energies. Electron equation of state data can be calculated via the ideal gas model or with an adaptation of the screened hydrogenic model with ℓ-splitting. The ionization and equation of state calculations can be done in local thermodynamic equilibrium or in a non-LTE mode using a variant of the Busquet equivalent temperature method. The code was written as a stand-alone Fortran library for ease of implementation by external codes. EOS results for aluminum are presented that show good agreement with the SESAME library and ionization calculations show good agreement with the FLYCHK code. Program summaryProgram title: BADGERLIB v1.0 Catalogue identifier: AEND_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEND_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 41 480 No. of bytes in distributed program, including test data, etc.: 2 904 451 Distribution format: tar.gz Programming language: Fortran 90. Computer: 32- or 64-bit PC, or Mac. Operating system: Windows, Linux, MacOS X. RAM: 249.496 kB plus 195.630 kB per isotope record in memory Classification: 19.1, 19.7. Nature of problem: Equation of State (EOS) calculations are necessary for the accurate simulation of high energy density plasmas. Historically, most EOS codes used in these simulations have relied on an ideal gas model. This model is inadequate for low-temperature, high-density plasma conditions; the gaseous and liquid phases; and the solid phase. The BADGER code was developed to give more realistic EOS data in these regimes. Solution method: BADGER has multiple, user-selectable models to treat the ions, average-atom ionization state and electrons. Ion models are ideal gas and quotidian equation of state (QEOS), ionization models are Thomas-Fermi and individual accounting method (IEM) formulation of the screened hydrogenic model (SHM) with l-splitting, electron ionization models are ideal gas and a Helmholtz free energy minimization method derived from the SHM. The default equation of state and ionization models are appropriate for plasmas in local thermodynamic equilibrium (LTE). The code can calculate non-LTE equation of state (EOS) and ionization data using a simplified form of the Busquet equivalent-temperature method. Restrictions: Physical data are only provided for elements Z=1 to Z=86. Multiple solid phases are not currently supported. Liquid, gas and plasma phases are combined into a generalized "fluid" phase. Unusual features: BADGER divorces the calculation of average-atom ionization from the electron equation of state model, allowing the user to select ionization and electron EOS models that are most appropriate to the simulation. The included ion ideal gas model uses ground-state nuclear spin data to differentiate between isotopes of a given element. Running time: Example provided only takes a few seconds to run.

Digital controller design: Continuous and discrete describing function analysis of the IPS system

NASA Technical Reports Server (NTRS)

1977-01-01

The dynamic equations and the mathematical model of the continuous-data IPS control system are developed. The IPS model considered included one flexible body mode and was hardmounted to the Orbiter/Pallet. The model contains equations describing a torque feed-forward loop (using accelerometers as inputs) which will aid in reducing the pointing errors caused by Orbiter disturbances.

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.

1986-01-01

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

An Equation for Moist Entropy in a Precipitating and Icy Atmosphere

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Simpson, Joanne; Zeng, Xiping

2003-01-01

Moist entropy is nearly conserved in adiabatic motion. It is redistributed rather than created by moist convection. Thus moist entropy and its equation, as a healthy direction, can be used to construct analytical and numerical models for the interaction between tropical convective clouds and large-scale circulations. Hence, an accurate equation of moist entropy is needed for the analysis and modeling of atmospheric convective clouds. On the basis of the consistency between the energy and the entropy equations, a complete equation of moist entropy is derived from the energy equation. The equation expresses explicitly the internal and external sources of moist entropy, including those in relation to the microphysics of clouds and precipitation. In addition, an accurate formula for the surface flux of moist entropy from the underlying surface into the air above is derived. Because moist entropy deals "easily" with the transition among three water phases, it will be used as a prognostic variable in the next generation of cloud-resolving models (e. g. a global cloud-resolving model) for low computational noise. Its equation that is derived in this paper is accurate and complete, providing a theoretical basis for using moist entropy as a prognostic variable in the long-term modeling of clouds and large-scale circulations.

A mathematical simulation model of the CH-47B helicopter, volume 1

NASA Technical Reports Server (NTRS)

Weber, J. M.; Liu, T. Y.; Chung, W.

1984-01-01

A nonlinear simulation model of the CH-47B helicopter was adapted for use in the NASA Ames Research Center (ARC) simulation facility. The model represents the specific configuration of the ARC variable stability CH-47B helicopter and will be used in ground simulation research and to expedite and verify flight experiment design. Modeling of the helicopter uses a total force approach in six rigid body degrees of freedom. Rotor dynamics are simulated using the Wheatlely-Bailey equations including steady-state flapping dynamics. Also included in the model is the option for simulation of external suspension, slung-load equations of motion.

Retrospective estimation of breeding phenology of American Goldfinch (Carduelis tristis) using pattern oriented modeling

EPA Science Inventory

Avian seasonal productivity is often modeled as a time-limited stochastic process. Many mathematical formulations have been proposed, including individual based models, continuous-time differential equations, and discrete Markov models. All such models typically include paramete...

Solving Differential Equations Analytically. Elementary Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 335.

ERIC Educational Resources Information Center

Goldston, J. W.

This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…

Modifying Bagnold's Sediment Transport Equation for Use in Watershed-Scale Channel Incision Models

NASA Astrophysics Data System (ADS)

Lammers, R. W.; Bledsoe, B. P.

2016-12-01

Destabilized stream channels may evolve through a sequence of stages, initiated by bed incision and followed by bank erosion and widening. Channel incision can be modeled using Exner-type mass balance equations, but model accuracy is limited by the accuracy and applicability of the selected sediment transport equation. Additionally, many sediment transport relationships require significant data inputs, limiting their usefulness in data-poor environments. Bagnold's empirical relationship for bedload transport is attractive because it is based on stream power, a relatively straightforward parameter to estimate using remote sensing data. However, the equation is also dependent on flow depth, which is more difficult to measure or estimate for entire drainage networks. We recast Bagnold's original sediment transport equation using specific discharge in place of flow depth. Using a large dataset of sediment transport rates from the literature, we show that this approach yields similar predictive accuracy as other stream power based relationships. We also explore the applicability of various critical stream power equations, including Bagnold's original, and support previous conclusions that these critical values can be predicted well based solely on sediment grain size. In addition, we propagate error in these sediment transport equations through channel incision modeling to compare the errors associated with our equation to alternative formulations. This new version of Bagnold's bedload transport equation has utility for channel incision modeling at larger spatial scales using widely available and remote sensing data.

Development of a Standalone Thermal Wellbore Simulator

NASA Astrophysics Data System (ADS)

Xiong, Wanqiang

With continuous developments of various different sophisticated wells in the petroleum industry, wellbore modeling and simulation have increasingly received more attention. Especially in unconventional oil and gas recovery processes, there is a growing demand for more accurate wellbore modeling. Despite notable advancements made in wellbore modeling, none of the existing wellbore simulators has been as successful as reservoir simulators such as Eclipse and CMG's and further research works on handling issues such as accurate heat loss modeling and multi-tubing wellbore modeling are really necessary. A series of mathematical equations including main governing equations, auxiliary equations, PVT equations, thermodynamic equations, drift-flux model equations, and wellbore heat loss calculation equations are collected and screened from publications. Based on these modeling equations, workflows for wellbore simulation and software development are proposed. Research works are conducted in key steps for developing a wellbore simulator: discretization, a grid system, a solution method, a linear equation solver, and computer language. A standalone thermal wellbore simulator is developed by using standard C++ language. This wellbore simulator can simulate single-phase injection and production, two-phase steam injection and two-phase oil and water production. By implementing a multi-part scheme which divides a wellbore with sophisticated configuration into several relative simple simulation running units, this simulator can handle different complex wellbores: wellbore with multistage casings, horizontal wells, multilateral wells and double tubing. In pursuance of improved accuracy of heat loss calculations to surrounding formations, a semi-numerical method is proposed and a series of FLUENT simulations have been conducted in this study. This semi-numerical method involves extending the 2D formation heat transfer simulation to include a casing wall and cement and adopting new correlations regressed by this study. Meanwhile, a correlation for handling heat transfer in double-tubing annulus is regressed. This work initiates the research on heat transfer in a double-tubing wellbore system. A series of validation and test works are performed in hot water injection, steam injection, real filed data, a horizontal well, a double-tubing well and comparison with the Ramey method. The program in this study also performs well in matching with real measured field data, simulation in horizontal wells and double-tubing wells.

Entrainment in the master equation.

PubMed

Margaliot, Michael; Grüne, Lars; Kriecherbauer, Thomas

2018-04-01

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology.

Entrainment in the master equation

PubMed Central

Grüne, Lars; Kriecherbauer, Thomas

2018-01-01

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology. PMID:29765669

Differential geometry-based solvation and electrolyte transport models for biomolecular modeling: a review

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

Wei, Guowei; Baker, Nathan A.

2016-11-11

This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces theory, as applied to the solvent-solute boundary. In these approaches, the solvent-solute boundary is determined by a variational principle that determines the major physical observables of interest, for example, biomolecular surface area, enclosed volume, electrostatic potential, ion density, electron density, etc. Recently, differential geometry theory has been used to define the surfaces that separate the microscopic (solute) domains for biomolecules from the macroscopic (solvent) domains. In thesemore » approaches, the microscopic domains are modeled with atomistic or quantum mechanical descriptions, while continuum mechanics models (including fluid mechanics, elastic mechanics, and continuum electrostatics) are applied to the macroscopic domains. This multiphysics description is integrated through an energy functional formalism and the resulting Euler-Lagrange equation is employed to derive a variety of governing partial differential equations for different solvation and transport processes; e.g., the Laplace-Beltrami equation for the solvent-solute interface, Poisson or Poisson-Boltzmann equations for electrostatic potentials, the Nernst-Planck equation for ion densities, and the Kohn-Sham equation for solute electron density. Extensive validation of these models has been carried out over hundreds of molecules, including proteins and ion channels, and the experimental data have been compared in terms of solvation energies, voltage-current curves, and density distributions. We also propose a new quantum model for electrolyte transport.« less

A mixture-energy-consistent six-equation two-phase numerical model for fluids with interfaces, cavitation and evaporation waves

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

Pelanti, Marica, E-mail: marica.pelanti@ensta-paristech.fr; Shyue, Keh-Ming, E-mail: shyue@ntu.edu.tw

2014-02-15

We model liquid–gas flows with cavitation by a variant of the six-equation single-velocity two-phase model with stiff mechanical relaxation of Saurel–Petitpas–Berry (Saurel et al., 2009) [9]. In our approach we employ phasic total energy equations instead of the phasic internal energy equations of the classical six-equation system. This alternative formulation allows us to easily design a simple numerical method that ensures consistency with mixture total energy conservation at the discrete level and agreement of the relaxed pressure at equilibrium with the correct mixture equation of state. Temperature and Gibbs free energy exchange terms are included in the equations as relaxationmore » terms to model heat and mass transfer and hence liquid–vapor transition. The algorithm uses a high-resolution wave propagation method for the numerical approximation of the homogeneous hyperbolic portion of the model. In two dimensions a fully-discretized scheme based on a hybrid HLLC/Roe Riemann solver is employed. Thermo-chemical terms are handled numerically via a stiff relaxation solver that forces thermodynamic equilibrium at liquid–vapor interfaces under metastable conditions. We present numerical results of sample tests in one and two space dimensions that show the ability of the proposed model to describe cavitation mechanisms and evaporation wave dynamics.« less

A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials.

PubMed

Richardson, G

2009-09-01

By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson-Nernst-Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE model has more general application than the Hodgkin-Huxley cable equation and can, e.g. be used to describe action potential propagation in myelinated axons and neuronal cell bodies.

Central Upwind Scheme for a Compressible Two-Phase Flow Model

PubMed Central

Ahmed, Munshoor; Saleem, M. Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme. PMID:26039242

Central upwind scheme for a compressible two-phase flow model.

PubMed

Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

2015-01-01

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

Three-phase Power Flow Calculation of Low Voltage Distribution Network Considering Characteristics of Residents Load

NASA Astrophysics Data System (ADS)

Wang, Yaping; Lin, Shunjiang; Yang, Zhibin

2017-05-01

In the traditional three-phase power flow calculation of the low voltage distribution network, the load model is described as constant power. Since this model cannot reflect the characteristics of actual loads, the result of the traditional calculation is always different from the actual situation. In this paper, the load model in which dynamic load represented by air conditioners parallel with static load represented by lighting loads is used to describe characteristics of residents load, and the three-phase power flow calculation model is proposed. The power flow calculation model includes the power balance equations of three-phase (A,B,C), the current balance equations of phase 0, and the torque balancing equations of induction motors in air conditioners. And then an alternating iterative algorithm of induction motor torque balance equations with each node balance equations is proposed to solve the three-phase power flow model. This method is applied to an actual low voltage distribution network of residents load, and by the calculation of three different operating states of air conditioners, the result demonstrates the effectiveness of the proposed model and the algorithm.

The Measurement and Cost of Removing Unexplained Gender Differences in Faculty Salaries.

ERIC Educational Resources Information Center

Becker, William E.; Toutkoushian, Robert K.

1995-01-01

In assessing sex-discrimination suit damages, debate rages over the type and number of variables included in a single-equation model of the salary-determination process. This article considers single- and multiple-equation models, providing 36 different damage calculations. For University of Minnesota data, equalization cost hinges on the…

Teacher's Corner: Structural Equation Modeling with the Sem Package in R

ERIC Educational Resources Information Center

Fox, John

2006-01-01

R is free, open-source, cooperatively developed software that implements the S statistical programming language and computing environment. The current capabilities of R are extensive, and it is in wide use, especially among statisticians. The sem package provides basic structural equation modeling facilities in R, including the ability to fit…

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

NASA Technical Reports Server (NTRS)

Zhao, C. Y.; So, R. M. C.; Gatski, T. B.

2001-01-01

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Chapman-Enskog expansion for the Vicsek model of self-propelled particles

NASA Astrophysics Data System (ADS)

Ihle, Thomas

2016-08-01

Using the standard Vicsek model, I show how the macroscopic transport equations can be systematically derived from microscopic collision rules. The approach starts with the exact evolution equation for the N-particle probability distribution and, after making the mean-field assumption of molecular chaos, leads to a multi-particle Enskog-type equation. This equation is treated by a non-standard Chapman-Enskog expansion to extract the macroscopic behavior. The expansion includes terms up to third order in a formal expansion parameter ɛ, and involves a fast time scale. A self-consistent closure of the moment equations is presented that leads to a continuity equation for the particle density and a Navier-Stokes-like equation for the momentum density. Expressions for all transport coefficients in these macroscopic equations are given explicitly in terms of microscopic parameters of the model. The transport coefficients depend on specific angular integrals which are evaluated asymptotically in the limit of infinitely many collision partners, using an analogy to a random walk. The consistency of the Chapman-Enskog approach is checked by an independent calculation of the shear viscosity using a Green-Kubo relation.

Flap-lag-torsional dynamic modelling of rotor blades in hover and in forward flight, including the effect of cubic nonlinearities

NASA Technical Reports Server (NTRS)

Crespodasilva, M. R. M.

1981-01-01

The differential equations of motion, and boundary conditions, describing the flap-lead/lag-torsional motion of a flexible rotor blade with a precone angle and a variable pitch angle, which incorporates a pretwist, are derived via Hamilton's principle. The meaning of inextensionality is discussed. The equations are reduced to a set of three integro partial differential equations by elimination of the extension variable. The generalized aerodynamic forces are modelled using Greenberg's extension of Theodorsen's strip theory. The equations of motion are systematically expanded into polynomial nonlinearities with the objective of retaining all terms up to third degree. The blade is modeled as a long, slender, of isotropic Hookean materials. Offsets from the blade's elastic axis through its shear center and the axes for the mass, area and aerodynamic centers, radial nonuniformaties of the blade's stiffnesses and cross section properties are considered and the effect of warp of the cross section is included in the formulation.

A model for tides and currents in the English Channel and southern North Sea

NASA Astrophysics Data System (ADS)

Walters, Roy. A.

The amplitude and phase of 11 tidal constituents for the English Channel and southern North Sea are calculated using a frequency domain, finite element model. The governing equations — the shallow water equations — are modifed such that sea level is calculated using an elliptic equation of the Helmholz type followed by a back-calculation of velocity using the primitive momentum equations. Triangular elements with linear basis functions are used. The modified form of the governing equations provides stable solutions with little numerical noise. In this field-scale test problem, the model was able to produce the details of the structure of 11 tidal constituents including O 1, K 1, M 2, S 2, N 2, K 2, M 4, MS 4, MN 4, M 6, and 2MS 6.

Investigating the Relationships among Metacognitive Strategy Training, Willingness to Read English Medical Texts, and Reading Comprehension Ability Using Structural Equation Modeling

ERIC Educational Resources Information Center

Hassanpour, Masoumeh; Ghonsooly, Behzad; Nooghabi, Mehdi Jabbari; Shafiee, Mohammad Naser

2017-01-01

This quasi-experimental study examined the relationship between students' metacognitive awareness and willingness to read English medical texts. So, a model was proposed and tested using structural equation modeling (SEM) with R software. Participants included 98 medical students of two classes. One class was assigned as the control group and the…

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

A Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Parsakhoo, Zahra; Shao, Yaping

2017-04-01

Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in Eulerian models directly. We have developed a Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different Lagrangian time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).

The present state and future direction of second order closure models for compressible flows

NASA Technical Reports Server (NTRS)

Gatski, Thomas B.; Sarkar, Sutanu; Speziale, Charles G.

1992-01-01

The topics are presented in viewgraph form and include: (1) Reynolds stress closure models; (2) Favre averages and governing equations; (3) the model for the deviatoric part of the pressure-strain rate correlation; (4) the SSG pressure-strain correlation model; (5) a compressible turbulent dissipation rate model; (6) variable viscosity effects; (7) near-wall stiffness problems; (8) models of the Reynolds mass and heat flux; and (9) a numerical solution of the compressible turbulent transport equation.

Numerical simulation of life cycles of advection warm fog

NASA Technical Reports Server (NTRS)

Hung, R. J.; Vaughan, O. H.

1977-01-01

The formation, development and dissipation of advection warm fog is investigated. The equations employed in the model include the equation of continuity, momentum and energy for the descriptions of density, wind component and potential temperature, respectively, together with two diffusion equations for the modification of water-vapor mixing ratio and liquid-water mixing ratios. A description of the vertical turbulent transfer of heat, moisture and momentum has been taken into consideration. The turbulent exchange coefficients adopted in the model are based on empirical flux-gradient relations.

Differential renormalization-group generators for static and dynamic critical phenomena

NASA Astrophysics Data System (ADS)

Chang, T. S.; Vvedensky, D. D.; Nicoll, J. F.

1992-09-01

The derivation of differential renormalization-group (DRG) equations for applications to static and dynamic critical phenomena is reviewed. The DRG approach provides a self-contained closed-form representation of the Wilson renormalization group (RG) and should be viewed as complementary to the Callan-Symanzik equations used in field-theoretic approaches to the RG. The various forms of DRG equations are derived to illustrate the general mathematical structure of each approach and to point out the advantages and disadvantages for performing practical calculations. Otherwise, the review focuses upon the one-particle-irreducible DRG equations derived by Nicoll and Chang and by Chang, Nicoll, and Young; no attempt is made to provide a general treatise of critical phenomena. A few specific examples are included to illustrate the utility of the DRG approach: the large- n limit of the classical n-vector model (the spherical model), multi- or higher-order critical phenomena, and crit ical dynamics far from equilibrium. The large- n limit of the n-vector model is used to introduce the application of DRG equations to a well-known example, with exact solution obtained for the nonlinear trajectories, generating functions for nonlinear scaling fields, and the equation of state. Trajectory integrals and nonlinear scaling fields within the framework of ɛ-expansions are then discussed for tricritical crossover, and briefly for certain aspects of multi- or higher-order critical points, including the derivation of the Helmholtz free energy and the equation of state. The discussion then turns to critical dynamics with a development of the path integral formulation for general dynamic processes. This is followed by an application to a model far-from-equilibrium system that undergoes a phase transformation analogous to a second-order critical point, the Schlögl model for a chemical instability.

Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows.

PubMed

Liang, H; Shi, B C; Guo, Z L; Chai, Z H

2014-05-01

In this paper, a phase-field-based multiple-relaxation-time lattice Boltzmann (LB) model is proposed for incompressible multiphase flow systems. In this model, one distribution function is used to solve the Chan-Hilliard equation and the other is adopted to solve the Navier-Stokes equations. Unlike previous phase-field-based LB models, a proper source term is incorporated in the interfacial evolution equation such that the Chan-Hilliard equation can be derived exactly and also a pressure distribution is designed to recover the correct hydrodynamic equations. Furthermore, the pressure and velocity fields can be calculated explicitly. A series of numerical tests, including Zalesak's disk rotation, a single vortex, a deformation field, and a static droplet, have been performed to test the accuracy and stability of the present model. The results show that, compared with the previous models, the present model is more stable and achieves an overall improvement in the accuracy of the capturing interface. In addition, compared to the single-relaxation-time LB model, the present model can effectively reduce the spurious velocity and fluctuation of the kinetic energy. Finally, as an application, the Rayleigh-Taylor instability at high Reynolds numbers is investigated.

Density-dependence as a size-independent regulatory mechanism.

PubMed

de Vladar, Harold P

2006-01-21

The growth function of populations is central in biomathematics. The main dogma is the existence of density-dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important class of regulatory functions is the theta-logistic, which generalizes the logistic equation. Using this model as a motivation, this paper introduces a simple dynamical reformulation that generalizes many growth functions. The reformulation consists of two equations, one for population size, and one for the growth rate. Furthermore, the model shows that although population is density-dependent, the dynamics of the growth rate does not depend either on population size, nor on the carrying capacity. Actually, the growth equation is uncoupled from the population size equation, and the model has only two parameters, a Malthusian parameter rho and a competition coefficient theta. Distinct sign combinations of these parameters reproduce not only the family of theta-logistics, but also the van Bertalanffy, Gompertz and Potential Growth equations, among other possibilities. It is also shown that, except for two critical points, there is a general size-scaling relation that includes those appearing in the most important allometric theories, including the recently proposed Metabolic Theory of Ecology. With this model, several issues of general interest are discussed such as the growth of animal population, extinctions, cell growth and allometry, and the effect of environment over a population.

Application of satellite data in variational analysis for global cyclonic systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.

1988-01-01

The goal of the research is a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity were defined. The research performed during the second year fall into four areas: sensitivity studies involving Model 1; evaluation of Model 2; reformation of Model 1 for greater compatibility with Model 2; development of Model 3 (radiative transfer equation); and making the model more responsive to the observations.

Turbulent reacting flow computations including turbulence-chemistry interactions

NASA Technical Reports Server (NTRS)

Narayan, J. R.; Girimaji, S. S.

1992-01-01

A two-equation (k-epsilon) turbulence model has been extended to be applicable for compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. A turbulence-chemistry interaction model is outlined. In this model, the effects of temperature and species mass concentrations fluctuations on the species mass production rates are decoupled. The effect of temperature fluctuations is modeled via a moment model, and the effect of concentration fluctuations is included using an assumed beta-pdf model. Preliminary results obtained using this model are presented. A two-dimensional reacting mixing layer has been used as a test case. Computations are carried out using the Navier-Stokes solver SPARK using a finite rate chemistry model for hydrogen-air combustion.

Multiscale Multiphysics and Multidomain Models I: Basic Theory

PubMed Central

Wei, Guo-Wei

2013-01-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field. PMID:25382892

Multiscale Multiphysics and Multidomain Models I: Basic Theory.

PubMed

Wei, Guo-Wei

2013-12-01

This work extends our earlier two-domain formulation of a differential geometry based multiscale paradigm into a multidomain theory, which endows us the ability to simultaneously accommodate multiphysical descriptions of aqueous chemical, physical and biological systems, such as fuel cells, solar cells, nanofluidics, ion channels, viruses, RNA polymerases, molecular motors and large macromolecular complexes. The essential idea is to make use of the differential geometry theory of surfaces as a natural means to geometrically separate the macroscopic domain of solvent from the microscopic domain of solute, and dynamically couple continuum and discrete descriptions. Our main strategy is to construct energy functionals to put on an equal footing of multiphysics, including polar (i.e., electrostatic) solvation, nonpolar solvation, chemical potential, quantum mechanics, fluid mechanics, molecular mechanics, coarse grained dynamics and elastic dynamics. The variational principle is applied to the energy functionals to derive desirable governing equations, such as multidomain Laplace-Beltrami (LB) equations for macromolecular morphologies, multidomain Poisson-Boltzmann (PB) equation or Poisson equation for electrostatic potential, generalized Nernst-Planck (NP) equations for the dynamics of charged solvent species, generalized Navier-Stokes (NS) equation for fluid dynamics, generalized Newton's equations for molecular dynamics (MD) or coarse-grained dynamics and equation of motion for elastic dynamics. Unlike the classical PB equation, our PB equation is an integral-differential equation due to solvent-solute interactions. To illustrate the proposed formalism, we have explicitly constructed three models, a multidomain solvation model, a multidomain charge transport model and a multidomain chemo-electro-fluid-MD-elastic model. Each solute domain is equipped with distinct surface tension, pressure, dielectric function, and charge density distribution. In addition to long-range Coulombic interactions, various non-electrostatic solvent-solute interactions are considered in the present modeling. We demonstrate the consistency between the non-equilibrium charge transport model and the equilibrium solvation model by showing the systematical reduction of the former to the latter at equilibrium. This paper also offers a brief review of the field.

Understanding the Impact of Trauma Exposure on Posttraumatic Stress Symptomatology: A Structural Equation Modeling Approach

ERIC Educational Resources Information Center

Chen, Wei; Wang, Long; Zhang, Xing-Li; Shi, Jian-Nong

2012-01-01

The objective of this study was to investigate the impact of trauma exposure on the posttraumatic stress symptomatology (PTSS) of children who resided near the epicenter of the 2008 Wenchuan earthquake. The mechanisms of this impact were explored via structural equation models with self-esteem and coping strategies included as mediators. The…

Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

PubMed

Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

2014-07-01

In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

Computerized power supply analysis: State equation generation and terminal models

NASA Technical Reports Server (NTRS)

Garrett, S. J.

1978-01-01

To aid engineers that design power supply systems two analysis tools that can be used with the state equation analysis package were developed. These tools include integration routines that start with the description of a power supply in state equation form and yield analytical results. The first tool uses a computer program that works with the SUPER SCEPTRE circuit analysis program and prints the state equation for an electrical network. The state equations developed automatically by the computer program are used to develop an algorithm for reducing the number of state variables required to describe an electrical network. In this way a second tool is obtained in which the order of the network is reduced and a simpler terminal model is obtained.

Development of a Pressure-Dependent Constitutive Model with Combined Multilinear Kinematic and Isotropic Hardening

NASA Technical Reports Server (NTRS)

Allen Phillip A.; Wilson, Christopher D.

2003-01-01

The development of a pressure-dependent constitutive model with combined multilinear kinematic and isotropic hardening is presented. The constitutive model is developed using the ABAQUS user material subroutine (UMAT). First the pressure-dependent plasticity model is derived. Following this, the combined bilinear and combined multilinear hardening equations are developed for von Mises plasticity theory. The hardening rule equations are then modified to include pressure dependency. The method for implementing the new constitutive model into ABAQUS is given.

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Bui, Trong T.

1993-01-01

A computer code called Proteus 3D has been developed to solve the three dimensional, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort has been to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation have been emphasized. The governing equations are solved in generalized non-orthogonal body-fitted coordinates by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. It describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Application of the order-of-magnitude analysis to a fourth-order RANS closure for simulating a 2D boundary layer

NASA Astrophysics Data System (ADS)

Poroseva, Svetlana V.

2013-11-01

Simulations of turbulent boundary-layer flows are usually conducted using a set of the simplified Reynolds-Averaged Navier-Stokes (RANS) equations obtained by order-of-magnitude analysis (OMA) of the original RANS equations. The resultant equations for the mean-velocity components are closed using the Boussinesq approximation for the Reynolds stresses. In this study OMA is applied to the fourth-order RANS (FORANS) set of equations. The FORANS equations are chosen as they can be closed on the level of the 5th-order correlations without using unknown model coefficients, i.e. no turbulent diffusion modeling is required. New models for the 2nd-, 3rd- and 4th-order velocity-pressure gradient correlations are derived for the current FORANS equations. This set of FORANS equations and models are analyzed for the case of two-dimensional mean flow. The equations include familiar transport terms for the mean-velocity components along with algebraic expressions for velocity correlations of different orders specific to the FORANS approach. Flat plate DNS data (Spalart, 1988) are used to verify these expressions and the areas of the OMA applicability within the boundary layer. The material is based upon work supported by NASA under award NNX12AJ61A.

Model predictive control of attitude maneuver of a geostationary flexible satellite based on genetic algorithm

NASA Astrophysics Data System (ADS)

TayyebTaher, M.; Esmaeilzadeh, S. Majid

2017-07-01

This article presents an application of Model Predictive Controller (MPC) to the attitude control of a geostationary flexible satellite. SIMO model has been used for the geostationary satellite, using the Lagrange equations. Flexibility is also included in the modelling equations. The state space equations are expressed in order to simplify the controller. Naturally there is no specific tuning rule to find the best parameters of an MPC controller which fits the desired controller. Being an intelligence method for optimizing problem, Genetic Algorithm has been used for optimizing the performance of MPC controller by tuning the controller parameter due to minimum rise time, settling time, overshoot of the target point of the flexible structure and its mode shape amplitudes to make large attitude maneuvers possible. The model included geosynchronous orbit environment and geostationary satellite parameters. The simulation results of the flexible satellite with attitude maneuver shows the efficiency of proposed optimization method in comparison with LQR optimal controller.

Derivation of equations of motion for multi-blade rotors employing coupled modes and including high twist capability

NASA Technical Reports Server (NTRS)

Sopher, R.

1975-01-01

The equations of motion are derived for a multiblade rotor. A high twist capability and coupled flatwise-edgewise assumed normal modes are employed instead of uncoupled flatwise - edgewise assumed normal models. The torsion mode is uncoupled. Support system models, consisting of complete helicopters in free flight, or grounded flexible supports, arbitrary rotor-induced inflow, and arbitrary vertical gust models are also used.

Spatial averaging of a dissipative particle dynamics model for active suspensions

NASA Astrophysics Data System (ADS)

Panchenko, Alexander; Hinz, Denis F.; Fried, Eliot

2018-03-01

Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving-Kirkwood-Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.

Growing surfaces with anomalous diffusion: Results for the fractal Kardar-Parisi-Zhang equation

NASA Astrophysics Data System (ADS)

Katzav, Eytan

2003-09-01

In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. It is shown that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, the self-consistent expansion (SCE) is used to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the fractal KPZ equation is suggested and the upper critical dimension of this model is discussed.

Aerodynamic Analyses Requiring Advanced Computers, Part 1

NASA Technical Reports Server (NTRS)

1975-01-01

Papers are presented which deal with results of theoretical research on aerodynamic flow problems requiring the use of advanced computers. Topics discussed include: viscous flows, boundary layer equations, turbulence modeling and Navier-Stokes equations, and internal flows.

Snow Micro-Structure Model

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

Micah Johnson, Andrew Slaughter

PIKA is a MOOSE-based application for modeling micro-structure evolution of seasonal snow. The model will be useful for environmental, atmospheric, and climate scientists. Possible applications include application to energy balance models, ice sheet modeling, and avalanche forecasting. The model implements physics from published, peer-reviewed articles. The main purpose is to foster university and laboratory collaboration to build a larger multi-scale snow model using MOOSE. The main feature of the code is that it is implemented using the MOOSE framework, thus making features such as multiphysics coupling, adaptive mesh refinement, and parallel scalability native to the application. PIKA implements three equations:more » the phase-field equation for tracking the evolution of the ice-air interface within seasonal snow at the grain-scale; the heat equation for computing the temperature of both the ice and air within the snow; and the mass transport equation for monitoring the diffusion of water vapor in the pore space of the snow.« less

Radiative transfer equation accounting for rotational Raman scattering and its solution by the discrete-ordinates method

NASA Astrophysics Data System (ADS)

Rozanov, Vladimir V.; Vountas, Marco

2014-01-01

Rotational Raman scattering of solar light in Earth's atmosphere leads to the filling-in of Fraunhofer and telluric lines observed in the reflected spectrum. The phenomenological derivation of the inelastic radiative transfer equation including rotational Raman scattering is presented. The different forms of the approximate radiative transfer equation with first-order rotational Raman scattering terms are obtained employing the Cabannes, Rayleigh, and Cabannes-Rayleigh scattering models. The solution of these equations is considered in the framework of the discrete-ordinates method using rigorous and approximate approaches to derive particular integrals. An alternative forward-adjoint technique is suggested as well. A detailed description of the model including the exact spectral matching and a binning scheme that significantly speeds up the calculations is given. The considered solution techniques are implemented in the radiative transfer software package SCIATRAN and a specified benchmark setup is presented to enable readers to compare with own results transparently.

An introduction to three-dimensional climate modeling

NASA Technical Reports Server (NTRS)

Washington, W. M.; Parkinson, C. L.

1986-01-01

The development and use of three-dimensional computer models of the earth's climate are discussed. The processes and interactions of the atmosphere, oceans, and sea ice are examined. The basic theory of climate simulation which includes the fundamental equations, models, and numerical techniques for simulating the atmosphere, oceans, and sea ice is described. Simulated wind, temperature, precipitation, ocean current, and sea ice distribution data are presented and compared to observational data. The responses of the climate to various environmental changes, such as variations in solar output or increases in atmospheric carbon dioxide, are modeled. Future developments in climate modeling are considered. Information is also provided on the derivation of the energy equation, the finite difference barotropic forecast model, the spectral transform technique, and the finite difference shallow water waved equation model.

A Simple and Accurate Rate-Driven Infiltration Model

NASA Astrophysics Data System (ADS)

Cui, G.; Zhu, J.

2017-12-01

In this study, we develop a novel Rate-Driven Infiltration Model (RDIMOD) for simulating infiltration into soils. Unlike traditional methods, RDIMOD avoids numerically solving the highly non-linear Richards equation or simply modeling with empirical parameters. RDIMOD employs infiltration rate as model input to simulate one-dimensional infiltration process by solving an ordinary differential equation. The model can simulate the evolutions of wetting front, infiltration rate, and cumulative infiltration on any surface slope including vertical and horizontal directions. Comparing to the results from the Richards equation for both vertical infiltration and horizontal infiltration, RDIMOD simply and accurately predicts infiltration processes for any type of soils and soil hydraulic models without numerical difficulty. Taking into account the accuracy, capability, and computational effectiveness and stability, RDIMOD can be used in large-scale hydrologic and land-atmosphere modeling.

Ill-posedness of Dynamic Equations of Compressible Granular Flow

NASA Astrophysics Data System (ADS)

Shearer, Michael; Gray, Nico

2017-11-01

We introduce models for 2-dimensional time-dependent compressible flow of granular materials and suspensions, based on the rheology of Pouliquen and Forterre. The models include density dependence through a constitutive equation in which the density or volume fraction of solid particles with material density ρ* is taken as a function of an inertial number I: ρ = ρ * Φ(I), in which Φ(I) is a decreasing function of I. This modelling has different implications from models relying on critical state soil mechanics, in which ρ is treated as a variable in the equations, contributing to a flow rule. The analysis of the system of equations builds on recent work of Barker et al in the incompressible case. The main result is the identification of a criterion for well-posedness of the equations. We additionally analyze a modification that applies to suspensions, for which the rheology takes a different form and the inertial number reflects the role of the fluid viscosity.

Computational Fluid Dynamics Modeling of Nickel Hydrogen Batteries

NASA Technical Reports Server (NTRS)

Cullion, R.; Gu, W. B.; Wang, C. Y.; Timmerman, P.

2000-01-01

An electrochemical Ni-H2 battery model has been expanded to include thermal effects. A thermal energy conservation equation was derived from first principles. An electrochemical and thermal coupled model was created by the addition of this equation to an existing multiphase, electrochemical model. Charging at various rates was investigated and the results validated against experimental data. Reaction currents, pressure changes, temperature profiles, and concentration variations within the cell are predicted numerically and compared with available data and theory.

Single and Double ITCZ in Aqua-Planet Models with Globally Uniform Sea Surface Temperature and Solar Insolation: An Interpretation

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode; Einaudi, Franco (Technical Monitor)

2001-01-01

It has been known for more than a decade that an aqua-planet model with globally uniform sea surface temperature and solar insolation angle can generate ITCZ (intertropical convergence zone). Previous studies have shown that the ITCZ under such model settings can be changed between a single ITCZ over the equator and a double ITCZ straddling the equator through one of several measures. These measures include switching to a different cumulus parameterization scheme, changes within the cumulus parameterization scheme, and changes in other aspects of the model design such as horizontal resolution. In this paper an interpretation for these findings is offered. The latitudinal location of the ITCZ is the latitude where the balance of two types of attraction on the ITCZ, both due to earth's rotation, exists. The first type is equator-ward and is directly related to the earth's rotation and thus not sensitive to model design changes. The second type is poleward and is related to the convective circulation and thus is sensitive to model design changes. Due to the shape of the attractors, the balance of the two types of attractions is reached either at the equator or more than 10 degrees away from the equator. The former case results in a single ITCZ over the equator and the latter case a double ITCZ straddling the equator.

Phase-space methods for the spin dynamics in condensed matter systems

PubMed Central

Hurst, Jérôme; Manfredi, Giovanni

2017-01-01

Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin- fermions (typically, electrons) including the Zeeman effect and the spin–orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’. PMID:28320903

Modeling of nonequilibrium space plasma flows

NASA Technical Reports Server (NTRS)

Gombosi, Tamas

1995-01-01

Godunov-type numerical solution of the 20 moment plasma transport equations. One of the centerpieces of our proposal was the development of a higher order Godunov-type numerical scheme to solve the gyration dominated 20 moment transport equations. In the first step we explored some fundamental analytic properties of the 20 moment transport equations for a low b plasma, including the eigenvectors and eigenvalues of propagating disturbances. The eigenvalues correspond to wave speeds, while the eigenvectors characterize the transported physical quantities. In this paper we also explored the physically meaningful parameter range of the normalized heat flow components. In the second step a new Godunov scheme type numerical method was developed to solve the coupled set of 20 moment transport equations for a quasineutral single-ion plasma. The numerical method and the first results were presented at several national and international meetings and a paper describing the method has been published in the Journal of Computational Physics. To our knowledge this is the first numerical method which is capable of producing stable time-dependent solutions to the full 20 (or 16) moment set of transport equations, including the full heat flow equation. Previous attempts resulted in unstable (oscillating) solutions of the heat flow equations. Our group invested over two man-years into the development and implementation of the new method. The present model solves the 20 moment transport equations for an ion species and thermal electrons in 8 domain extending from a collision dominated to a collisionless region (200 km to 12,000 km). This model has been applied to study O+ acceleration due to Joule heating in the lower ionosphere.

Converging shock flows for a Mie-Grüneisen equation of state

NASA Astrophysics Data System (ADS)

Ramsey, Scott D.; Schmidt, Emma M.; Boyd, Zachary M.; Lilieholm, Jennifer F.; Baty, Roy S.

2018-04-01

Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scale-invariant form. However, this scale-invariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of Mie-Grüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the Mie-Grüneisen EOS, which are otherwise absent from scale-invariant models that feature only dimensionless parameters (such as the adiabatic index in the ideal gas EOS). The current work extends previous efforts intended to rectify this inconsistency, by using a scale-invariant EOS model to approximate a Mie-Grüneisen EOS form. To this end, the adiabatic bulk modulus for the Mie-Grüneisen EOS is constructed, and its key features are used to motivate the selection of a scale-invariant approximation form. The remaining surrogate model parameters are selected through enforcement of the Rankine-Hugoniot jump conditions for an infinitely strong shock in a Mie-Grüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semi-analytical Guderley-like imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying Mie-Grüneisen EOS.

NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models

NASA Technical Reports Server (NTRS)

Rodio, J. J.; Xiao, X; Hassan, H. A.; Rumsey, C. L.

2014-01-01

The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.

Cardiovascular risk assessment: addition of CKD and race to the Framingham equation

PubMed Central

Drawz, Paul E.; Baraniuk, Sarah; Davis, Barry R.; Brown, Clinton D.; Colon, Pedro J.; Cujyet, Aloysius B.; Dart, Richard A.; Graumlich, James F.; Henriquez, Mario A.; Moloo, Jamaluddin; Sakalayen, Mohammed G.; Simmons, Debra L.; Stanford, Carol; Sweeney, Mary Ellen; Wong, Nathan D.; Rahman, Mahboob

2012-01-01

Background/Aims The value of the Framingham equation in predicting cardiovascular risk in African Americans and patients with chronic kidney disease (CKD) is unclear. The purpose of the study was to evaluate whether the addition of CKD and race to the Framingham equation improves risk stratification in hypertensive patients. Methods Participants in the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) were studied. Those randomized to doxazosin, age greater than 74 years, and those with a history of coronary heart disease (CHD) were excluded. Two risk stratification models were developed using Cox proportional hazards models in a two-thirds developmental sample. The first model included the traditional Framingham risk factors. The second model included the traditional risk factors plus CKD, defined by eGFR categories, and stratification by race (Black vs. Non-Black). The primary outcome was a composite of fatal CHD, nonfatal MI, coronary revascularization, and hospitalized angina. Results There were a total of 19,811 eligible subjects. In the validation cohort, there was no difference in C-statistics between the Framingham equation and the ALLHAT model including CKD and race. This was consistent across subgroups by race and gender and among those with CKD. One exception was among Non-Black women where the C-statistic was higher for the Framingham equation (0.68 vs 0.65, P=0.02). Additionally, net reclassification improvement was not significant for any subgroup based on race and gender, ranging from −5.5% to 4.4%. Conclusion The addition of CKD status and stratification by race does not improve risk prediction in high-risk hypertensive patients. PMID:23194494

Development of a set of equations for incorporating disk flexibility effects in rotordynamical analyses

NASA Technical Reports Server (NTRS)

Flowers, George T.; Ryan, Stephen G.

1991-01-01

Rotordynamical equations that account for disk flexibility are developed. These equations employ free-free rotor modes to model the rotor system. Only transverse vibrations of the disks are considered, with the shaft/disk system considered to be torsionally rigid. Second order elastic foreshortening effects that couple with the rotor speed to produce first order terms in the equations of motion are included. The approach developed in this study is readily adaptable for usage in many of the codes that are current used in rotordynamical simulations. The equations are similar to those used in standard rigid disk analyses but with additional terms that include the effects of disk flexibility. An example case is presented to demonstrate the use of the equations and to show the influence of disk flexibility on the rotordynamical behavior of a sample system.

Density-velocity equations with bulk modulus for computational hydro-acoustics

NASA Astrophysics Data System (ADS)

Lin, Po-Hsien; Chen, Yung-Yu; John Yu, S.-T.

2014-02-01

This paper reports a new set of model equations for Computational Hydro Acoustics (CHA). The governing equations include the continuity and the momentum equations. The definition of bulk modulus is used to relate density with pressure. For 3D flow fields, there are four equations with density and velocity components as the unknowns. The inviscid equations are proved to be hyperbolic because an arbitrary linear combination of the three Jacobian matrices is diagonalizable and has a real spectrum. The left and right eigenvector matrices are explicitly derived. Moreover, an analytical form of the Riemann invariants are derived. The model equations are indeed suitable for modeling wave propagation in low-speed, nearly incompressible air and water flows. To demonstrate the capability of the new formulation, we use the CESE method to solve the 2D equations for aeolian tones generated by air flows passing a circular cylinder at Re = 89,000, 46,000, and 22,000. Numerical results compare well with previously published data. By simply changing the value of the bulk modulus, the same code is then used to calculate three cases of water flows passing a cylinder at Re = 89,000, 67,000, and 44,000.

BHR equations re-derived with immiscible particle effects

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

Schwarzkopf, John Dennis; Horwitz, Jeremy A.

2015-05-01

Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied tomore » the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.« less

Data-driven discovery of partial differential equations.

PubMed

Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2017-04-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

Exact models for isotropic matter

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Maharaj, S. D.

2006-04-01

We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.

LINEAR - DERIVATION AND DEFINITION OF A LINEAR AIRCRAFT MODEL

NASA Technical Reports Server (NTRS)

Duke, E. L.

1994-01-01

The Derivation and Definition of a Linear Model program, LINEAR, provides the user with a powerful and flexible tool for the linearization of aircraft aerodynamic models. LINEAR was developed to provide a standard, documented, and verified tool to derive linear models for aircraft stability analysis and control law design. Linear system models define the aircraft system in the neighborhood of an analysis point and are determined by the linearization of the nonlinear equations defining vehicle dynamics and sensors. LINEAR numerically determines a linear system model using nonlinear equations of motion and a user supplied linear or nonlinear aerodynamic model. The nonlinear equations of motion used are six-degree-of-freedom equations with stationary atmosphere and flat, nonrotating earth assumptions. LINEAR is capable of extracting both linearized engine effects, such as net thrust, torque, and gyroscopic effects and including these effects in the linear system model. The point at which this linear model is defined is determined either by completely specifying the state and control variables, or by specifying an analysis point on a trajectory and directing the program to determine the control variables and the remaining state variables. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to provide easy selection of state, control, and observation variables to be used in a particular model. Thus, the order of the system model is completely under user control. Further, the program provides the flexibility of allowing alternate formulations of both the state and observation equations. Data describing the aircraft and the test case is input to the program through a terminal or formatted data files. All data can be modified interactively from case to case. The aerodynamic model can be defined in two ways: a set of nondimensional stability and control derivatives for the flight point of interest, or a full non-linear aerodynamic model as used in simulations. LINEAR is written in FORTRAN and has been implemented on a DEC VAX computer operating under VMS with a virtual memory requirement of approximately 296K of 8 bit bytes. Both an interactive and batch version are included. LINEAR was developed in 1988.

Taper and volume equations for selected Appalachian hardwood species

Treesearch

A. Jeff Martin

1981-01-01

Coefficients for five taper/volume models are developed for 18 Appalachian hardwood species. Each model can be used to estimate diameter at any point on the bole, height to any preselected diameter, and cubic-foot volume between any two points on the bole. The resulting equations were tested on six sets of independent data and an evaluation of these tests is included,...

The Martian climate: Energy balance models with CO2/H2O atmospheres

NASA Technical Reports Server (NTRS)

Hoffert, M. I.

1985-01-01

Coupled equations are developed for mass and heat transport in a seasonal Mars model with condensation and sublimation of CO2 at the polar caps. Topics covered include physical considerations of planetary as mass and energy balance; effects of phase changes at the surface on mass and heat flux; atmospheric transport and governing equations; and numerical analysis.

Localized states in a triangular set of linearly coupled complex Ginzburg-Landau equations.

PubMed

Sigler, Ariel; Malomed, Boris A; Skryabin, Dmitry V

2006-12-01

We introduce a pattern-formation model based on a symmetric system of three linearly coupled cubic-quintic complex Ginzburg-Landau equations, which form a triangular configuration. This is the simplest model of a multicore fiber laser. We identify stability regions for various types of localized patterns possible in this setting, which include stationary and breathing triangular vortices.

Self-consistent electro-opto-thermal model of quantum cascade lasers with coupled electron and phonon interactions far from equilibrium

NASA Astrophysics Data System (ADS)

Yousefvand, Hossein Reza

2017-12-01

A self-consistent model of quantum cascade lasers (QCLs) is presented here for the study of the QCL's behavior in the far from equilibrium conditions. The approach is developed by employing a number of physics-based models such as the carrier and photon rate equations, the energy balance equation, the heat transfer equation and a simplified rate equation for the creation and annihilation of nonequilibrium optical phonons. The temperature dependency of the relevant physical effects such as stimulated gain cross section, longitudinal optical (LO) phonons and hot-phonon generation rates are included in the model. Using the presented model, the static and transient device characteristics are calculated and analyzed for a wide range of heat sink temperatures. Besides the output characteristics, this model also provides a way to study the hot-phonon dynamics in the device, and to explore the electron temperature and thermal roll-over in the QCLs.

Iterative Methods to Solve Linear RF Fields in Hot Plasma

NASA Astrophysics Data System (ADS)

Spencer, Joseph; Svidzinski, Vladimir; Evstatiev, Evstati; Galkin, Sergei; Kim, Jin-Soo

2014-10-01

Most magnetic plasma confinement devices use radio frequency (RF) waves for current drive and/or heating. Numerical modeling of RF fields is an important part of performance analysis of such devices and a predictive tool aiding design and development of future devices. Prior attempts at this modeling have mostly used direct solvers to solve the formulated linear equations. Full wave modeling of RF fields in hot plasma with 3D nonuniformities is mostly prohibited, with memory demands of a direct solver placing a significant limitation on spatial resolution. Iterative methods can significantly increase spatial resolution. We explore the feasibility of using iterative methods in 3D full wave modeling. The linear wave equation is formulated using two approaches: for cold plasmas the local cold plasma dielectric tensor is used (resolving resonances by particle collisions), while for hot plasmas the conductivity kernel (which includes a nonlocal dielectric response) is calculated by integrating along test particle orbits. The wave equation is discretized using a finite difference approach. The initial guess is important in iterative methods, and we examine different initial guesses including the solution to the cold plasma wave equation. Work is supported by the U.S. DOE SBIR program.

Effects of Nonequilibrium Chemistry and Darcy-Forchheimer Pyrolysis Flow for Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2013-01-01

The fully implicit ablation and thermal response code simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid.This work describes new modeling capabilities that are added to a special version of code. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Two groups of parametric studies of the phenolic impregnated carbon ablator are performed. In the first group, an Orion flight environment for a proposed lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results indicate that the presence of chemical nonequilibrium pyrolysis gas flow does not significantly alter the in-depth thermal response performance predicted using the chemical equilibrium gas model.

GFSSP Training Course Lectures

NASA Technical Reports Server (NTRS)

Majumdar, Alok K.

2008-01-01

GFSSP has been extended to model conjugate heat transfer Fluid Solid Network Elements include: a) Fluid nodes and Flow Branches; b) Solid Nodes and Ambient Nodes; c) Conductors connecting Fluid-Solid, Solid-Solid and Solid-Ambient Nodes. Heat Conduction Equations are solved simultaneously with Fluid Conservation Equations for Mass, Momentum, Energy and Equation of State. The extended code was verified by comparing with analytical solution for simple conduction-convection problem The code was applied to model: a) Pressurization of Cryogenic Tank; b) Freezing and Thawing of Metal; c) Chilldown of Cryogenic Transfer Line; d) Boil-off from Cryogenic Tank.

Fluid equations in the presence of electron cyclotron current drive

NASA Astrophysics Data System (ADS)

Jenkins, Thomas G.; Kruger, Scott E.

2012-12-01

Two-fluid equations, which include the physics imparted by an externally applied radiofrequency source near electron cyclotron resonance, are derived in their extended magnetohydrodynamic forms using the formalism of Hegna and Callen [Phys. Plasmas 16, 112501 (2009)]. The equations are compatible with the closed fluid/drift-kinetic model developed by Ramos [Phys. Plasmas 17, 082502 (2010); 18, 102506 (2011)] for fusion-relevant regimes with low collisionality and slow dynamics, and they facilitate the development of advanced computational models for electron cyclotron current drive-induced suppression of neoclassical tearing modes.

Fluid equations in the presence of electron cyclotron current drive

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

Jenkins, Thomas G.; Kruger, Scott E.

Two-fluid equations, which include the physics imparted by an externally applied radiofrequency source near electron cyclotron resonance, are derived in their extended magnetohydrodynamic forms using the formalism of Hegna and Callen [Phys. Plasmas 16, 112501 (2009)]. The equations are compatible with the closed fluid/drift-kinetic model developed by Ramos [Phys. Plasmas 17, 082502 (2010); 18, 102506 (2011)] for fusion-relevant regimes with low collisionality and slow dynamics, and they facilitate the development of advanced computational models for electron cyclotron current drive-induced suppression of neoclassical tearing modes.

Pressure model of a four-way spool valve for simulating electrohydraulic control systems

NASA Technical Reports Server (NTRS)

Gebben, V. D.

1976-01-01

An equation that relates the pressure flow characteristics of hydraulic spool valves was developed. The dependent variable is valve output pressure, and the independent variables are spool position and flow. This causal form of equation is preferred in applications that simulate the effects of hydraulic line dynamics. Results from this equation are compared with those from the conventional valve equation, whose dependent variable is flow. A computer program of the valve equations includes spool stops, leakage spool clearances, and dead-zone characteristics of overlap spools.

Transient three-dimensional thermal-hydraulic analysis of nuclear reactor fuel rod arrays: general equations and numerical scheme

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

Wnek, W.J.; Ramshaw, J.D.; Trapp, J.A.

1975-11-01

A mathematical model and a numerical solution scheme for thermal- hydraulic analysis of fuel rod arrays are given. The model alleviates the two major deficiencies associated with existing rod array analysis models, that of a correct transverse momentum equation and the capability of handling reversing and circulatory flows. Possible applications of the model include steady state and transient subchannel calculations as well as analysis of flows in heat exchangers, other engineering equipment, and porous media. (auth)

Model for dynamic self-assembled magnetic surface structures

NASA Astrophysics Data System (ADS)

Belkin, M.; Glatz, A.; Snezhko, A.; Aranson, I. S.

2010-07-01

We propose a first-principles model for the dynamic self-assembly of magnetic structures at a water-air interface reported in earlier experiments. The model is based on the Navier-Stokes equation for liquids in shallow water approximation coupled to Newton equations for interacting magnetic particles suspended at a water-air interface. The model reproduces most of the observed phenomenology, including spontaneous formation of magnetic snakelike structures, generation of large-scale vortex flows, complex ferromagnetic-antiferromagnetic ordering of the snake, and self-propulsion of bead-snake hybrids.

Linear models for calculating digestibile energy for sheep diets.

PubMed

Fonnesbeck, P V; Christiansen, M L; Harris, L E

1981-05-01

Equations for estimating the digestible energy (DE) content of sheep diets were generated from the chemical contents and a factorial description of diets fed to lambs in digestion trials. The diet factors were two forages (alfalfa and grass hay), harvested at three stages of maturity (late vegetative, early bloom and full bloom), fed in two ingredient combinations (all hay or a 50:50 hay and corn grain mixture) and prepared by two forage texture processes (coarsely chopped or finely chopped and pelleted). The 2 x 3 x 2 x 2 factorial arrangement produced 24 diet treatments. These were replicated twice, for a total of 48 lamb digestion trials. In model 1 regression equations, DE was calculated directly from chemical composition of the diet. In model 2, regression equations predicted the percentage of digested nutrient from the chemical contents of the diet and then DE of the diet was calculated as the sum of the gross energy of the digested organic components. Expanded forms of model 1 and model 2 were also developed that included diet factors as qualitative indicator variables to adjust the regression constant and regression coefficients for the diet description. The expanded forms of the equations accounted for significantly more variation in DE than did the simple models and more accurately estimated DE of the diet. Information provided by the diet description proved as useful as chemical analyses for the prediction of digestibility of nutrients. The statistics indicate that, with model 1, neutral detergent fiber and plant cell wall analyses provided as much information for the estimation of DE as did model 2 with the combined information from crude protein, available carbohydrate, total lipid, cellulose and hemicellulose. Regression equations are presented for estimating DE with the most currently analyzed organic components, including linear and curvilinear variables and diet factors that significantly reduce the standard error of the estimate. To estimate De of a diet, the user utilizes the equation that uses the chemical analysis information and diet description most effectively.

Adding In-Plane Flexibility to the Equations of Motion of a Single Rotor Helicopter

NASA Technical Reports Server (NTRS)

Curtiss, H. C., Jr.

2000-01-01

This report describes a way to add the effects of main rotor blade flexibility in the in- plane or lead-lag direction to a large set of non-linear equations of motion for a single rotor helicopter with rigid blades(l). Differences between the frequency of the regressing lag mode predicted by the equations of (1) and that measured in flight (2) for a UH-60 helicopter indicate that some element is missing from the analytical model of (1) which assumes rigid blades. A previous study (3) noted a similar discrepancy for the CH-53 helicopter. Using a relatively simple analytical model in (3), compared to (1), it was shown that a mechanical lag damper increases significantly the coupling between the rigid lag mode and the first flexible mode. This increased coupling due to a powerful lag damper produces an increase in the lowest lag frequency when viewed in a frame rotating with the blade. Flight test measurements normally indicate the frequency of this mode in a non-rotating or fixed frame. This report presents the additions necessary to the full equations of motion, to include main rotor blade lag flexibility. Since these additions are made to a very complex nonlinear dynamic model, in order to provide physical insight, a discussion of the results obtained from a simplified set of equations of motion is included. The reduced model illustrates the physics involved in the coupling and should indicate trends in the full model.

PKPD model of interleukin-21 effects on thermoregulation in monkeys--application and evaluation of stochastic differential equations.

PubMed

Overgaard, Rune Viig; Holford, Nick; Rytved, Klaus A; Madsen, Henrik

2007-02-01

To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core body temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differential equations (SDEs) in pharmacokinetic pharmacodynamic (PKPD) modelling. A temperature model was formulated including circadian rhythm, metabolism, heat loss, and a thermoregulatory set-point. This model was formulated as a mixed-effects model based on SDEs using NONMEM. The effects of IL-21 were on the set-point and the circadian rhythm of metabolism. The model was able to describe a complex set of IL-21 induced phenomena, including 1) disappearance of the circadian rhythm, 2) no effect after first dose, and 3) high variability after second dose. SDEs provided a more realistic description with improved simulation properties, and further changed the model into one that could not be falsified by the autocorrelation function. The IL-21 induced effects on thermoregulation in cynomolgus monkeys are explained by a biologically plausible model. The quality of the model was improved by the use of SDEs.

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Unsteady Analysis of Separated Aerodynamic Flows Using an Unstructured Multigrid Algorithm

NASA Technical Reports Server (NTRS)

Pelaez, Juan; Mavriplis, Dimitri J.; Kandil, Osama

2001-01-01

An implicit method for the computation of unsteady flows on unstructured grids is presented. The resulting nonlinear system of equations is solved at each time step using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Validation of the code using a one-equation turbulence model is performed for the well-known case of flow over a cylinder. A Detached Eddy Simulation model is also implemented and its performance compared to the one equation Spalart-Allmaras Reynolds Averaged Navier-Stokes (RANS) turbulence model. Validation cases using DES and RANS include flow over a sphere and flow over a NACA 0012 wing including massive stall regimes. The project was driven by the ultimate goal of computing separated flows of aerodynamic interest, such as massive stall or flows over complex non-streamlined geometries.

Mathematical modelling of a human external respiratory system

NASA Technical Reports Server (NTRS)

1977-01-01

A closed system of algebraic and common differential equations solved by computer is investigated. It includes equations which describe the activity pattern of the respiratory center, the phrenic nerve, the thrust produced by the diaphragm as a function of the lung volume and discharge frequency of the phrenic nerve, as well as certain relations of the lung stretch receptors and chemoreceptors on various lung and blood characteristics, equations for lung biomechanics, pulmonary blood flow, alveolar gas exchange and capillary blood composition equations to determine various air and blood flow and gas exchange parameters, and various gas mixing and arterial and venous blood composition equations, to determine other blood, air and gas mixing characteristics. Data are presented by means of graphs and tables, and some advantages of this model over others are demonstrated by test results.

Numerical modelling of multiphase liquid-vapor-gas flows with interfaces and cavitation

NASA Astrophysics Data System (ADS)

Pelanti, Marica

2017-11-01

We are interested in the simulation of multiphase flows where the dynamical appearance of vapor cavities and evaporation fronts in a liquid is coupled to the dynamics of a third non-condensable gaseous phase. We describe these flows by a single-velocity three-phase compressible flow model composed of the phasic mass and total energy equations, the volume fraction equations, and the mixture momentum equation. The model includes stiff mechanical and thermal relaxation source terms for all the phases, and chemical relaxation terms to describe mass transfer between the liquid and vapor phases of the species that may undergo transition. The flow equations are solved by a mixture-energy-consistent finite volume wave propagation scheme, combined with simple and robust procedures for the treatment of the stiff relaxation terms. An analytical study of the characteristic wave speeds of the hierarchy of relaxed models associated to the parent model system is also presented. We show several numerical experiments, including two-dimensional simulations of underwater explosive phenomena where highly pressurized gases trigger cavitation processes close to a rigid surface or to a free surface. This work was supported by the French Government Grant DGA N. 2012.60.0011.00.470.75.01, and partially by the Norwegian Grant RCN N. 234126/E30.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools.

PubMed

Siettos, Constantinos; Starke, Jens

2016-09-01

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

A model for rotorcraft flying qualities studies

NASA Technical Reports Server (NTRS)

Mittal, Manoj; Costello, Mark F.

1993-01-01

This paper outlines the development of a mathematical model that is expected to be useful for rotorcraft flying qualities research. A computer model is presented that can be applied to a range of different rotorcraft configurations. The algorithm computes vehicle trim and a linear state-space model of the aircraft. The trim algorithm uses non linear optimization theory to solve the nonlinear algebraic trim equations. The linear aircraft equations consist of an airframe model and a flight control system dynamic model. The airframe model includes coupled rotor and fuselage rigid body dynamics and aerodynamics. The aerodynamic model for the rotors utilizes blade element theory and a three state dynamic inflow model. Aerodynamics of the fuselage and fuselage empennages are included. The linear state-space description for the flight control system is developed using standard block diagram data.

Finite difference model for aquifer simulation in two dimensions with results of numerical experiments

USGS Publications Warehouse

Trescott, Peter C.; Pinder, George Francis; Larson, S.P.

1976-01-01

The model will simulate ground-water flow in an artesian aquifer, a water-table aquifer, or a combined artesian and water-table aquifer. The aquifer may be heterogeneous and anisotropic and have irregular boundaries. The source term in the flow equation may include well discharge, constant recharge, leakage from confining beds in which the effects of storage are considered, and evapotranspiration as a linear function of depth to water. The theoretical development includes presentation of the appropriate flow equations and derivation of the finite-difference approximations (written for a variable grid). The documentation emphasizes the numerical techniques that can be used for solving the simultaneous equations and describes the results of numerical experiments using these techniques. Of the three numerical techniques available in the model, the strongly implicit procedure, in general, requires less computer time and has fewer numerical difficulties than do the iterative alternating direction implicit procedure and line successive overrelaxation (which includes a two-dimensional correction procedure to accelerate convergence). The documentation includes a flow chart, program listing, an example simulation, and sections on designing an aquifer model and requirements for data input. It illustrates how model results can be presented on the line printer and pen plotters with a program that utilizes the graphical display software available from the Geological Survey Computer Center Division. In addition the model includes options for reading input data from a disk and writing intermediate results on a disk.

Static Chemistry in Disks or Clouds

NASA Astrophysics Data System (ADS)

Semenov, D.; Wiebe, D.

2006-11-01

This FORTRAN77 code can be used to model static, time-dependent chemistry in ISM and circumstellar disks. Current version is based on the OSU'06 gas-grain astrochemical network with all updates to the reaction rates, and includes surface chemistry from Hasegawa & Herbst (1993) and Hasegawa, Herbst, and Leung (1992). Surface chemistry can be modeled either with the standard rate equation approach or modified rate equation approach (useful in disks). Gas-grain interactions include sticking of neutral molecules to grains, dissociative recombination of ions on grains as well as thermal, UV, X-ray, and CRP-induced desorption of frozen species. An advanced X-ray chemistry and 3 grain sizes with power-law size distribution are also included. An deuterium extension to this chemical model is available.

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

USGS Publications Warehouse

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The accuracy and convergence of the numerical routines in the model are demonstrated for the case of laboratory measurements of unsteady flow in a sewer pipe. Verification of the routines in the model for field data on the Fox River in northeastern Illinois also is briefly discussed. The basic principles of unsteady-flow modeling and the relation between steady flow and unsteady flow are presented. Assumptions and the limitations of the model also are presented. The schematization of the stream system and the conversion of the physical characteristics of the stream reaches and a wide range of special features into function tables for model applications are described. The modified dynamic-wave equation used in FEQ for unsteady flow in curvilinear channels with drag on minor hydraulic structures and channel constrictions determined from an equivalent energy slope is developed. The matrix equation relating flows and depths at computational nodes throughout the stream system by the continuity (conservation of mass) and modified dynamic-wave equations is illustrated for four sequential examples. The solution of the matrix equation by Newton's method is discussed. Finally, the input for FEQ and the error messages and warnings issued are presented.

Steady state model for the thermal regimes of shells of airships and hot air balloons

NASA Astrophysics Data System (ADS)

Luchev, Oleg A.

1992-10-01

A steady state model of the temperature regime of airships and hot air balloons shells is developed. The model includes three governing equations: the equation of the temperature field of airships or balloons shell, the integral equation for the radiative fluxes on the internal surface of the shell, and the integral equation for the natural convective heat exchange between the shell and the internal gas. In the model the following radiative fluxes on the shell external surface are considered: the direct and the earth reflected solar radiation, the diffuse solar radiation, the infrared radiation of the earth surface and that of the atmosphere. For the calculations of the infrared external radiation the model of the plane layer of the atmosphere is used. The convective heat transfer on the external surface of the shell is considered for the cases of the forced and the natural convection. To solve the mentioned set of the equations the numerical iterative procedure is developed. The model and the numerical procedure are used for the simulation study of the temperature fields of an airship shell under the forced and the natural convective heat transfer.

Kinetic equations for cylindrically symmetric plasmas including atomic coherence and Coulomb potential effects

NASA Astrophysics Data System (ADS)

Csanak, G.; Fontes, C. J.; Kilcrease, D. P.; Hakel, P.; Inal, M. K.

2017-05-01

The rate equations used to model plasma kinetics and spectroscopy are typically obtained from intuitive considerations. A few years ago, the authors (Csanak et al 2011 J. Phys. B: At. Mol. Opt. Phys. 44 215701) have shown that the population-alignment collisional-radiative (CR) model and the magnetic sublevel to magnetic sublevel rate-equation scheme can be obtained from the Fano-Ben-Reuven quantum impact approximation (QIA). Here we provide a formal derivation of the rate-equation schemes for modeling hydrogenic plasmas and highly charged ionic plasmas with cylindrical symmetry using the QIA under certain approximations. In the case of hydrogenic plasmas the ‘accidental degeneracy’ (if present) leads to some coherences among the excited states of the atom (or ion) that have to be taken into account when constructing the rate equations. In the case of highly charged plasmas the Coulomb potential can be taken into account (as suggested originally by Baranger) in defining the ‘bath particles’, which leads to a derivation of the kinetic equations where no singularity occurs. For the case of spherically symmetric plasmas, this method also provides a derivation of the standard CR equations that have been implemented in many codes to successfully model the kinetics and spectra of highly charged ions.

Six-degree-of-freedom aircraft simulation with mixed-data structure using the applied dynamics simulation language, ADSIM

NASA Technical Reports Server (NTRS)

Savaglio, Clare

1989-01-01

A realistic simulation of an aircraft in the flight using the AD 100 digital computer is presented. The implementation of three model features is specifically discussed: (1) a large aerodynamic data base (130,00 function values) which is evaluated using function interpolation to obtain the aerodynamic coefficients; (2) an option to trim the aircraft in longitudinal flight; and (3) a flight control system which includes a digital controller. Since the model includes a digital controller the simulation implements not only continuous time equations but also discrete time equations, thus the model has a mixed-data structure.

Turbulence: The chief outstanding difficulty of our subject

NASA Technical Reports Server (NTRS)

Bradshaw, Peter

1992-01-01

A review of interesting current topics in turbulence research is decorated with examples of popular fallacies about the behavior of turbulence. Topics include the status of the Law of the Wall, especially in compressible flow; analogies between the effects of Reynolds numbers, pressure gradient, unsteadiness and roughness change; the status of Kolmogorov's universal equilibrium theory and local isotropy of the small eddies; turbulence modelling, with reference to universality, pressure-strain modelling and the dissipation equation; and chaos. Fallacies include the mixing-length concept; the effect of pressure gradient on Reynolds shear stress; the separability of time and space derivatives; models of the dissipation equation; and chaos.

Three-pattern decomposition of global atmospheric circulation: part II—dynamical equations of horizontal, meridional and zonal circulations

NASA Astrophysics Data System (ADS)

Hu, Shujuan; Cheng, Jianbo; Xu, Ming; Chou, Jifan

2018-04-01

The three-pattern decomposition of global atmospheric circulation (TPDGAC) partitions three-dimensional (3D) atmospheric circulation into horizontal, meridional and zonal components to study the 3D structures of global atmospheric circulation. This paper incorporates the three-pattern decomposition model (TPDM) into primitive equations of atmospheric dynamics and establishes a new set of dynamical equations of the horizontal, meridional and zonal circulations in which the operator properties are studied and energy conservation laws are preserved, as in the primitive equations. The physical significance of the newly established equations is demonstrated. Our findings reveal that the new equations are essentially the 3D vorticity equations of atmosphere and that the time evolution rules of the horizontal, meridional and zonal circulations can be described from the perspective of 3D vorticity evolution. The new set of dynamical equations includes decomposed expressions that can be used to explore the source terms of large-scale atmospheric circulation variations. A simplified model is presented to demonstrate the potential applications of the new equations for studying the dynamics of the Rossby, Hadley and Walker circulations. The model shows that the horizontal air temperature anomaly gradient (ATAG) induces changes in meridional and zonal circulations and promotes the baroclinic evolution of the horizontal circulation. The simplified model also indicates that the absolute vorticity of the horizontal circulation is not conserved, and its changes can be described by changes in the vertical vorticities of the meridional and zonal circulations. Moreover, the thermodynamic equation shows that the induced meridional and zonal circulations and advection transport by the horizontal circulation in turn cause a redistribution of the air temperature. The simplified model reveals the fundamental rules between the evolution of the air temperature and the horizontal, meridional and zonal components of global atmospheric circulation.

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

Modeling of a complex, polar system with a modified Soave-Redlich-Kwong equation

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

Sturnfield, E.A.; Matherne, J.L.

1988-01-01

It is computationally feasible to use a simple equation of state (like a Redlich-Kwong) to calculate liquid fugacity but the simpler equations work well only for moderately non-ideal systems. More complex equations (like Ghemling-Lui-Prausnitz) predict system behavior more accurately but are much more complicated to use and can require fitting many parameters to data. This paper illustrates success in using a modified Redlich-Kwong to model a complex system including water, hydrogen, sub and supercritical ammonia, and amines. The binary interaction parameter ({Kappa}/sub ij/) of the Soave-Redlich-Kwong equation has been modified to be both asymmetric and temperature dependent. Further, the aimore » constant was determined by fitting vapor pressure data. Predicted model results are compared to literature (example 1) or plant data (examples 2-4) for four systems: 1. The ammonia-water binary over a wide range of pressure and temperature including ammonia above its critical. 2. A multicomponent Vapor-Liquid equilibrium flash tank and condenser containg hydrogen, amonia, water, and other heavier compounds. 3. A multicomponent vapor-liquid equilibrium flash tank containing water, heavier mines, and the amine salts. 4. A Liquid-Liquid-Vapor equilibrium decanter system containing water, ammonia, and an organic chloride.« less

The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions

NASA Technical Reports Server (NTRS)

Grossman, B.; Cinella, P.

1988-01-01

A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.

Dynamic characteristics of a hydrostatic gas bearing driven by oscillating exhaust pressure

NASA Technical Reports Server (NTRS)

Watkins, C. B.; Eronini, I. E.; Branch, H. D.

1984-01-01

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference aproximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

Middle atmosphere project. A semi-spectral numerical model for the large-scale stratospheric circulation

NASA Technical Reports Server (NTRS)

Holton, J. R.; Wehrbein, W.

1979-01-01

The complete model is a semispectral model in which the longitudinal dependence is represented by expansion in zonal harmonics while the latitude and height dependencies are represented by a finite difference grid. The model is based on the primitive equations in the log pressure coordinate system. The lower boundary of the model domain is set at the 100 mb level (i.e., near the tropopause) and the effects of tropospheric forcing are included in the lower boundary condition. The upper boundary is at approximately 96 km, and the latitudinal extent is either global or hemispheric. The basic differential equations and boundary conditions are outlined. The finite difference equations are described. The initial conditions are discussed and a sample calculation is presented. The FORTRAN code is given in the appendix.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are promising tools for today’s aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

A New Constitutive Model for the Plastic Flow of Metals at Elevated Temperatures

NASA Astrophysics Data System (ADS)

Spigarelli, S.; El Mehtedi, M.

2014-02-01

A new constitutive model based on the combination of the Garofalo and Hensel-Spittel equations has been used to describe the plastic flow behavior of an AA6005 aluminum alloy tested in torsion. The analysis of the experimental data by the constitutive model resulted in an excellent description of the flow curves. The model equation was then rewritten to explicitly include the Arrhenius term describing the temperature dependence of plastic deformation. The calculation indicated that the activation energy for hot working slowly decreased with increasing strain, leading to thermally activated flow softening. The combined use of the new equation and torsion testing led to the development of a constitutive model which can be safely adopted in a computer code to simulate forging or extrusion.

OAKSIM: An individual-tree growth and yield simulator for managed, even-aged, upland oak stands

Treesearch

Donald E. Hilt; Donald E. Hilt

1985-01-01

OAKSIM is an individual-tree growth and yield simulator for managed, even-aged, upland oak stands. Growth and yield projections for various thinning alternatives can be made with OAKSIM for a period of up to 50 years. Simulator components include an individual-tree diameter growth model, a mortality model, height prediction equations, bark ratio equations, a taper-...

Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Rajiyah, H.

1991-01-01

Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

A model of a fishery with fish stock involving delay equations.

PubMed

Auger, P; Ducrot, Arnaud

2009-12-13

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

Small-Caliber Projectile Target Impact Angle Determined From Close Proximity Radiographs

DTIC Science & Technology

2006-10-01

discrete motion data that can be numerically modeled using linear aerodynamic theory or 6-degrees-of- freedom equations of motion. The values of Fφ...Prediction Excel® Spreadsheet shown in figure 9. The Gamma at Impact Spreadsheet uses the linear aerodynamics model , equations 5 and 6, to calculate αT...trajectory angle error via consideration of the RMS fit errors of the actual firings. However, the linear aerodynamics model does not include this effect

Two-stream modeling of plasmaspheric refilling

NASA Technical Reports Server (NTRS)

Guiter, S. M.; Gombosi, T. I.; Rasmussen, C. E.

1995-01-01

Plasmaspheric refilling on an L = 4 flux tube was studied by using a time-dependent, hydrodynamic plasmaspheric flow model in which the ion streams from the two hemispheres are treated as distinct fluids. In the model the continuity, momentum, and energy equations of a two-ion (O(+) and H(+)), quasi-neutral, currentless plasma are solved along a closed geomagnetic field line; diffusive equilibrium is not assumed. collisions between all stream pairs and with neutral species are included. The model includes a corotating, tilted dipole magnetic field and neutral winds. Ionospheric sources and sinks are accounted for in a self-consistent manner. Electrons are assumed to be heated by photoelectrons. The model flux tube extends from a 200-km altitude in one hemisphere to a 200-km altitude in the other hemisphere. Initially, the upwelling streams pass through each other practically unimpeded. When the streams approach the boundary in the conjugate ionosphere, a shock develops there, which moves upward and dissipates slowly; at about the same time a reverse shock develops in the hemisphere of origin, which moves upward. After about 1 hour, large shocks develop in each stream near the equator; these shocks move toward the equator and downward after crossing the equator. However, these shocks are probably artificial, because counterstreaming flows occur in each H(+) fluid, which the model can only handle by creating shocks.

A LES-Langevin model for turbulence

NASA Astrophysics Data System (ADS)

Dolganov, Rostislav; Dubrulle, Bérengère; Laval, Jean-Philippe

2006-11-01

The rationale for Large Eddy Simulation is rooted in our inability to handle all degrees of freedom (N˜10^16 for Re˜10^7). ``Deterministic'' models based on eddy-viscosity seek to reproduce the intensification of the energy transport. However, they fail to reproduce backward energy transfer (backscatter) from small to large scale, which is an essentiel feature of the turbulence near wall or in boundary layer. To capture this backscatter, ``stochastic'' strategies have been developed. In the present talk, we shall discuss such a strategy, based on a Rapid Distorsion Theory (RDT). Specifically, we first divide the small scale contribution to the Reynolds Stress Tensor in two parts: a turbulent viscosity and the pseudo-Lamb vector, representing the nonlinear cross terms of resolved and sub-grid scales. We then estimate the dynamics of small-scale motion by the RDT applied to Navier-Stockes equation. We use this to model the cross term evolution by a Langevin equation, in which the random force is provided by sub-grid pressure terms. Our LES model is thus made of a truncated Navier-Stockes equation including the turbulent force and a generalized Langevin equation for the latter, integrated on a twice-finer grid. The backscatter is automatically included in our stochastic model of the pseudo-Lamb vector. We apply this model to the case of homogeneous isotropic turbulence and turbulent channel flow.

2-3D nonlocal transport model in magnetized laser plasmas.

NASA Astrophysics Data System (ADS)

Nicolaï, Philippe; Feugeas, Jean-Luc; Schurtz, Guy

2004-11-01

We present a model of nonlocal transport for multidimensional radiation magneto-hydrodynamics codes. This model, based on simplified Fokker-Planck equations, aims at extending the formulae of G Schurtz,Ph.Nicolaï and M. Busquet [Phys. Plasmas,7,4238 (2000)] to magnetized plasmas.The improvements concern various points as the electric field effects on nonlocal transport or conversely the kinetic effects on E field. However the main purpose of this work is to generalize the previous model by including magnetic field effects. A complete system of nonlocal equations is derived from kinetic equations with self-consistent E and B fields. These equations are analyzed and simplified in order to be implemented into large laser fusion codes and coupled to other relevent physics. Finally, our model allows to obtain the deformation of the electron distribution function due to nonlocal effects. This deformation leads to a non-maxwellian function which could be used to compute the influence on other physical processes.

Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

2017-07-01

The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.

Transition and separation process in brine channels formation

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

Berti, Alessia, E-mail: alessia.berti@unibs.it; Bochicchio, Ivana, E-mail: ibochicchio@unisa.it; Fabrizio, Mauro, E-mail: mauro.fabrizio@unibo.it

2016-02-15

In this paper, we discuss the formation of brine channels in sea ice. The model includes a time-dependent Ginzburg-Landau equation for the solid-liquid phase change, a diffusion equation of the Cahn-Hilliard kind for the solute dynamics, and the heat equation for the temperature change. The macroscopic motion of the fluid is also considered, so the resulting differential system couples with the Navier-Stokes equation. The compatibility of this system with the thermodynamic laws and a maximum theorem is proved.

Finite-volume spectra of the Lee-Yang model

NASA Astrophysics Data System (ADS)

Bajnok, Zoltan; el Deeb, Omar; Pearce, Paul A.

2015-04-01

We consider the non-unitary Lee-Yang minimal model in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels ( r, s) = (1 , 1) , (1 , 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ 1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A 4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of ( m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

Dynamic Modeling and Simulation of a Rotational Inverted Pendulum

NASA Astrophysics Data System (ADS)

Duart, J. L.; Montero, B.; Ospina, P. A.; González, E.

2017-01-01

This paper presents an alternative way to the dynamic modeling of a rotational inverted pendulum using the classic mechanics known as Euler-Lagrange allows to find motion equations that describe our model. It also has a design of the basic model of the system in SolidWorks software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the theoretical results, It was made a contrast between the solutions obtained by simulation SimMechanics-Matlab and the system of equations Euler-Lagrange, solved through ODE23tb method included in Matlab bookstores for solving equations systems of the type and order obtained. This article comprises a pendulum trajectory analysis by a phase space diagram that allows the identification of stable and unstable regions of the system.

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

On the breakup of viscous liquid threads

NASA Technical Reports Server (NTRS)

Papageorgiou, Demetrios T.

1995-01-01

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Flame-conditioned turbulence modeling for reacting flows

NASA Astrophysics Data System (ADS)

Macart, Jonathan F.; Mueller, Michael E.

2017-11-01

Conventional approaches to turbulence modeling in reacting flows rely on unconditional averaging or filtering, that is, consideration of the momentum equations only in physical space, implicitly assuming that the flame only weakly affects the turbulence, aside from a variation in density. Conversely, for scalars, which are strongly coupled to the flame structure, their evolution equations are often projected onto a reduced-order manifold, that is, conditionally averaged or filtered, on a flame variable such as a mixture fraction or progress variable. Such approaches include Conditional Moment Closure (CMC) and related variants. However, recent observations from Direct Numerical Simulation (DNS) have indicated that the flame can strongly affect turbulence in premixed combustion at low Karlovitz number. In this work, a new approach to turbulence modeling for reacting flows is investigated in which conditionally averaged or filtered equations are evolved for the momentum. The conditionally-averaged equations for the velocity and its covariances are derived, and budgets are evaluated from DNS databases of turbulent premixed planar jet flames. The most important terms in these equations are identified, and preliminary closure models are proposed.

Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)

1996-01-01

There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

NASA Astrophysics Data System (ADS)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Prediction equations of forced oscillation technique: the insidious role of collinearity.

PubMed

Narchi, Hassib; AlBlooshi, Afaf

2018-03-27

Many studies have reported reference data for forced oscillation technique (FOT) in healthy children. The prediction equation of FOT parameters were derived from a multivariable regression model examining the effect of age, gender, weight and height on each parameter. As many of these variables are likely to be correlated, collinearity might have affected the accuracy of the model, potentially resulting in misleading, erroneous or difficult to interpret conclusions.The aim of this work was: To review all FOT publications in children since 2005 to analyze whether collinearity was considered in the construction of the published prediction equations. Then to compare these prediction equations with our own study. And to analyse, in our study, how collinearity between the explanatory variables might affect the predicted equations if it was not considered in the model. The results showed that none of the ten reviewed studies had stated whether collinearity was checked for. Half of the reports had also included in their equations variables which are physiologically correlated, such as age, weight and height. The predicted resistance varied by up to 28% amongst these studies. And in our study, multicollinearity was identified between the explanatory variables initially considered for the regression model (age, weight and height). Ignoring it would have resulted in inaccuracies in the coefficients of the equation, their signs (positive or negative), their 95% confidence intervals, their significance level and the model goodness of fit. In Conclusion with inaccurately constructed and improperly reported models, understanding the results and reproducing the models for future research might be compromised.

Data-driven discovery of partial differential equations

PubMed Central

Rudy, Samuel H.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2017-01-01

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable. PMID:28508044

Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation

NASA Astrophysics Data System (ADS)

Debusschere, Bert J.; Najm, Habib N.; Matta, Alain; Knio, Omar M.; Ghanem, Roger G.; Le Maître, Olivier P.

2003-08-01

This paper presents a model for two-dimensional electrochemical microchannel flow including the propagation of uncertainty from model parameters to the simulation results. For a detailed representation of electroosmotic and pressure-driven microchannel flow, the model considers the coupled momentum, species transport, and electrostatic field equations, including variable zeta potential. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. Uncertainty from the model parameters and boundary conditions is propagated to the model predictions using a pseudo-spectral stochastic formulation with polynomial chaos (PC) representations for parameters and field quantities. Using a Galerkin approach, the governing equations are reformulated into equations for the coefficients in the PC expansion. The implementation of the physical model with the stochastic uncertainty propagation is applied to protein-labeling in a homogeneous buffer, as well as in two-dimensional electrochemical microchannel flow. The results for the two-dimensional channel show strong distortion of sample profiles due to ion movement and consequent buffer disturbances. The uncertainty in these results is dominated by the uncertainty in the applied voltage across the channel.

VNAP2: A Computer Program for Computation of Two-dimensional, Time-dependent, Compressible, Turbulent Flow

NASA Technical Reports Server (NTRS)

Cline, M. C.

1981-01-01

A computer program, VNAP2, for calculating turbulent (as well as laminar and inviscid), steady, and unsteady flow is presented. It solves the two dimensional, time dependent, compressible Navier-Stokes equations. The turbulence is modeled with either an algebraic mixing length model, a one equation model, or the Jones-Launder two equation model. The geometry may be a single or a dual flowing stream. The interior grid points are computed using the unsplit MacCormack scheme. Two options to speed up the calculations for high Reynolds number flows are included. The boundary grid points are computed using a reference plane characteristic scheme with the viscous terms treated as source functions. An explicit artificial viscosity is included for shock computations. The fluid is assumed to be a perfect gas. The flow boundaries may be arbitrary curved solid walls, inflow/outflow boundaries, or free jet envelopes. Typical problems that can be solved concern nozzles, inlets, jet powered afterbodies, airfoils, and free jet expansions. The accuracy and efficiency of the program are shown by calculations of several inviscid and turbulent flows. The program and its use are described completely, and six sample cases and a code listing are included.

Computationally efficient modeling and simulation of large scale systems

NASA Technical Reports Server (NTRS)

Jain, Jitesh (Inventor); Cauley, Stephen F. (Inventor); Li, Hong (Inventor); Koh, Cheng-Kok (Inventor); Balakrishnan, Venkataramanan (Inventor)

2010-01-01

A method of simulating operation of a VLSI interconnect structure having capacitive and inductive coupling between nodes thereof. A matrix X and a matrix Y containing different combinations of passive circuit element values for the interconnect structure are obtained where the element values for each matrix include inductance L and inverse capacitance P. An adjacency matrix A associated with the interconnect structure is obtained. Numerical integration is used to solve first and second equations, each including as a factor the product of the inverse matrix X.sup.1 and at least one other matrix, with first equation including X.sup.1Y, X.sup.1A, and X.sup.1P, and the second equation including X.sup.1A and X.sup.1P.

Simulations of Turbulent Momentum and Scalar Transport in Confined Swirling Coaxial Jets

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey

2014-01-01

This paper presents the numerical simulations of confined three dimensional coaxial water jets. The objectives are to validate the newly proposed nonlinear turbulence models of momentum and scalar transport, and to evaluate the newly introduced scalar APDF and DWFDF equation along with its Eulerian implementation in the National Combustion Code (NCC). Simulations conducted include the steady RANS, the unsteady RANS (URANS), and the time-filtered Navier-Stokes (TFNS) with and without invoking the APDF or DWFDF equation. When the APDF or DWFDF equation is invoked, the simulations are of a hybrid nature, i.e., the transport equations of energy and species are replaced by the APDF or DWFDF equation. Results of simulations are compared with the available experimental data. Some positive impacts of the nonlinear turbulence models and the Eulerian scalar APDF and DWFDF approach are observed.

Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations

PubMed Central

Liao, David; Tlsty, Thea D.

2014-01-01

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

Quasi-Static Viscoelastic Finite Element Model of an Aircraft Tire

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1999-01-01

An elastic large displacement thick-shell mixed finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at the element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses is included in the mixed variational functional. The nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the nonlinear elastic equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to computationally simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

Analysis of nonlocal neural fields for both general and gamma-distributed connectivities

NASA Astrophysics Data System (ADS)

Hutt, Axel; Atay, Fatihcan M.

2005-04-01

This work studies the stability of equilibria in spatially extended neuronal ensembles. We first derive the model equation from statistical properties of the neuron population. The obtained integro-differential equation includes synaptic and space-dependent transmission delay for both general and gamma-distributed synaptic connectivities. The latter connectivity type reveals infinite, finite, and vanishing self-connectivities. The work derives conditions for stationary and nonstationary instabilities for both kernel types. In addition, a nonlinear analysis for general kernels yields the order parameter equation of the Turing instability. To compare the results to findings for partial differential equations (PDEs), two typical PDE-types are derived from the examined model equation, namely the general reaction-diffusion equation and the Swift-Hohenberg equation. Hence, the discussed integro-differential equation generalizes these PDEs. In the case of the gamma-distributed kernels, the stability conditions are formulated in terms of the mean excitatory and inhibitory interaction ranges. As a novel finding, we obtain Turing instabilities in fields with local inhibition-lateral excitation, while wave instabilities occur in fields with local excitation and lateral inhibition. Numerical simulations support the analytical results.

Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong

2017-10-01

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.

Optimal control of CPR procedure using hemodynamic circulation model

DOEpatents

Lenhart, Suzanne M.; Protopopescu, Vladimir A.; Jung, Eunok

2007-12-25

A method for determining a chest pressure profile for cardiopulmonary resuscitation (CPR) includes the steps of representing a hemodynamic circulation model based on a plurality of difference equations for a patient, applying an optimal control (OC) algorithm to the circulation model, and determining a chest pressure profile. The chest pressure profile defines a timing pattern of externally applied pressure to a chest of the patient to maximize blood flow through the patient. A CPR device includes a chest compressor, a controller communicably connected to the chest compressor, and a computer communicably connected to the controller. The computer determines the chest pressure profile by applying an OC algorithm to a hemodynamic circulation model based on the plurality of difference equations.

SARAH 4: A tool for (not only SUSY) model builders

NASA Astrophysics Data System (ADS)

Staub, Florian

2014-06-01

We present the new version of the Mathematica package SARAH which provides the same features for a non-supersymmetric model as previous versions for supersymmetric models. This includes an easy and straightforward definition of the model, the calculation of all vertices, mass matrices, tadpole equations, and self-energies. Also the two-loop renormalization group equations for a general gauge theory are now included and have been validated with the independent Python code PyR@TE. Model files for FeynArts, CalcHep/CompHep, WHIZARD and in the UFO format can be written, and source code for SPheno for the calculation of the mass spectrum, a set of precision observables, and the decay widths and branching ratios of all states can be generated. Furthermore, the new version includes routines to output model files for Vevacious for both, supersymmetric and non-supersymmetric, models. Global symmetries are also supported with this version and by linking Susyno the handling of Lie groups has been improved and extended.

Modeling Hemispheric Detonation Experiments in 2-Dimensions

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

Howard, W M; Fried, L E; Vitello, P A

2006-06-22

Experiments have been performed with LX-17 (92.5% TATB and 7.5% Kel-F 800 binder) to study scaling of detonation waves using a dimensional scaling in a hemispherical divergent geometry. We model these experiments using an arbitrary Lagrange-Eulerian (ALE3D) hydrodynamics code, with reactive flow models based on the thermo-chemical code, Cheetah. The thermo-chemical code Cheetah provides a pressure-dependent kinetic rate law, along with an equation of state based on exponential-6 fluid potentials for individual detonation product species, calibrated to high pressures ({approx} few Mbars) and high temperatures (20000K). The parameters for these potentials are fit to a wide variety of experimental data,more » including shock, compression and sound speed data. For the un-reacted high explosive equation of state we use a modified Murnaghan form. We model the detonator (including the flyer plate) and initiation system in detail. The detonator is composed of LX-16, for which we use a program burn model. Steinberg-Guinan models5 are used for the metal components of the detonator. The booster and high explosive are LX-10 and LX-17, respectively. For both the LX-10 and LX-17, we use a pressure dependent rate law, coupled with a chemical equilibrium equation of state based on Cheetah. For LX-17, the kinetic model includes carbon clustering on the nanometer size scale.« less

Does Geophysics Need "A new kind of Science"?

NASA Astrophysics Data System (ADS)

Turcotte, D. L.; Rundle, J. B.

2002-12-01

Stephen Wolfram's book "A New Kind of Science" has received a great deal of attention in the last six months, both positive and negative. The theme of the book is that "cellular automata", which arise from spatial and temporal coarse-graining of equations of motion, provide the foundations for a new nonlinear science of "complexity". The old science is the science of partial differential equations. Some of the major contributions of this old science have been in geophysics, i.e. gravity, magnetics, seismic waves, heat flow. The basis of the new science is the use of massive computing and numerical simulations. The new science is motivated by the observations that many physical systems display a vast multiplicity of space and time scales, and have hidden dynamics that in many cases are impossible to directly observe. An example would be molecular dynamics. Statistical physics derives continuum equations from the discrete interactions between atoms and molecules, in the modern world the continuum equations are then discretized using finite differences, finite elements, etc. in order to obtain numerical solutions. Examples of widely used cellular automata models include diffusion limited aggregation and site percolation. Also the class of models that are said to exhibit self-organized criticality, the sand-pile model, the slider-block model, the forest-fire model. Applications of these models include drainage networks, seismicity, distributions of minerals,and the evolution of landforms and coastlines. Simple cellular automata models generate deterministic chaos, i.e. the logistic map.

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations. [waste heat discharge from power plants and effects on ecosystems

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.

1978-01-01

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

Assessment and application of Reynolds stress closure models to high-speed compressible flows

NASA Technical Reports Server (NTRS)

Gatski, T. B.; Sarkar, S.; Speziale, C. G.; Balakrishnan, L.; Abid, R.; Anderson, E. C.

1990-01-01

The paper presents results from the development of higher order closure models for the phenomological modeling of high-speed compressible flows. The work presented includes the introduction of an improved pressure-strain correlationi model applicable in both the low- and high-speed regime as well as modifications to the isotropic dissipation rate to account for dilatational effects. Finally, the question of stiffness commonly associated with the solution of two-equation and Reynolds stress transport equations in wall-bounded flows is examined and ways of relaxing these restrictions are discussed.

Enthalpy measurement of coal-derived liquids. Final report, April 1981-September 1983. [517 to 10342 kPa; 340 to 664 K

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

Kidnay, A.J.; Yesavage, V.F.

This report summarizes the results of experimental measurements of enthalpies for quinoline using a freon boil-off flow calorimeter, and an investigation of the applicability of cubic equations of state to correlating the enthalpy of coal-liquids. In Part A the compound quinoline is discussed. Process flow in the flow calorimeter, operational problems, and equipment modifications are described. Procedural modifications, including a new sample purification procedure, are described. Part B discusses the correlational effort. This includes a discussion of past correlational work and the difficulties associated with a general correlation for coal liquid enthalpy. In addition experimental data and computer generated predictionsmore » are presented. Three equations of state were used to predict vapor pressures and enthalpies for ten pure component systems previously studied in the lab. In general, the results were encouraging. All three equations were found to be effective in predicting both enthalpies and vapor pressures. In addition, the equations worked well when fit to mixture enthalpies. The Modified SRK equation was found to be superior to the other equations and modeled all properties for both associating and nonassociating systems well. The Modified SRK equation did have a drawback in that it was not readily generalized since it required two parameters which must be fit to data for best results. In sum, it was shown that a four parameter equation of state could be used successfully to correlate the enthalpy of coal-liquid model compounds.« less

A compressible solution of the Navier-Stokes equations for turbulent flow about an airfoil

NASA Technical Reports Server (NTRS)

Shamroth, S. J.; Gibeling, H. J.

1979-01-01

A compressible time dependent solution of the Navier-Stokes equations including a transition turbulence model is obtained for the isolated airfoil flow field problem. The equations are solved by a consistently split linearized block implicit scheme. A nonorthogonal body-fitted coordinate system is used which has maximum resolution near the airfoil surface and in the region of the airfoil leading edge. The transition turbulence model is based upon the turbulence kinetic energy equation and predicts regions of laminar, transitional, and turbulent flow. Mean flow field and turbulence field results are presented for an NACA 0012 airfoil at zero and nonzero incidence angles of Reynolds number up to one million and low subsonic Mach numbers.

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

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

Feng, Wenqiang, E-mail: wfeng1@vols.utk.edu; Salgado, Abner J., E-mail: asalgad1@utk.edu; Wang, Cheng, E-mail: cwang1@umassd.edu

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a generalmore » framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems – including thin film epitaxy with slope selection and the square phase field crystal model – are carried out to verify the efficiency of the scheme.« less

Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Salgado, Abner J.; Wang, Cheng; Wise, Steven M.

2017-04-01

We describe and analyze preconditioned steepest descent (PSD) solvers for fourth and sixth-order nonlinear elliptic equations that include p-Laplacian terms on periodic domains in 2 and 3 dimensions. The highest and lowest order terms of the equations are constant-coefficient, positive linear operators, which suggests a natural preconditioning strategy. Such nonlinear elliptic equations often arise from time discretization of parabolic equations that model various biological and physical phenomena, in particular, liquid crystals, thin film epitaxial growth and phase transformations. The analyses of the schemes involve the characterization of the strictly convex energies associated with the equations. We first give a general framework for PSD in Hilbert spaces. Based on certain reasonable assumptions of the linear pre-conditioner, a geometric convergence rate is shown for the nonlinear PSD iteration. We then apply the general theory to the fourth and sixth-order problems of interest, making use of Sobolev embedding and regularity results to confirm the appropriateness of our pre-conditioners for the regularized p-Lapacian problems. Our results include a sharper theoretical convergence result for p-Laplacian systems compared to what may be found in existing works. We demonstrate rigorously how to apply the theory in the finite dimensional setting using finite difference discretization methods. Numerical simulations for some important physical application problems - including thin film epitaxy with slope selection and the square phase field crystal model - are carried out to verify the efficiency of the scheme.

Finite Element Modeling of Coupled Flexible Multibody Dynamics and Liquid Sloshing

DTIC Science & Technology

2006-09-01

tanks is presented. The semi-discrete combined solid and fluid equations of motions are integrated using a time- accurate parallel explicit solver...Incompressible fluid flow in a moving/deforming container including accurate modeling of the free-surface, turbulence, and viscous effects ...paper, a single computational code which uses a time- accurate explicit solution procedure is used to solve both the solid and fluid equations of

Forest volume-to-biomass models and estimates of mass for live and standing dead trees of U.S. forests.

Treesearch

James E. Smith; Linda S. Heath; Jennifer C. Jenkins

2003-01-01

Includes methods and equations for nationally consistent estimates of tree-mass density at the stand level (Mg/ha) as predicted by growing-stock volumes reported by the USDA Forest Service for forests of the conterminous United States. Developed for use in FORCARB, a carbon budget model for U.S. forests, the equations also are useful for converting plot-, stand- and...

Effects of Non-Equilibrium Chemistry and Darcy-Forchheimer Flow of Pyrolysis Gas for a Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2011-01-01

The Fully Implicit Ablation and Thermal Response code, FIAT, simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid. This work describes new modeling capabilities that are added to a special version of FIAT. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite-rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Parametric studies are performed using this enhanced version of FIAT. Two groups of analyses of Phenolic Impregnated Carbon Ablator (PICA) are presented. In the first group, an Orion flight environment for a proposed Lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on PICA material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results are presented, discussed, and compared with those predicted by the baseline PICA/FIAT ablation and thermal response model developed by the Orion Thermal Protection System Advanced Development Project.

Kinetic theory of age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Greenman, Chris D.; Chou, Tom

2016-01-01

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.

Computation of rotor-stator interaction using the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Chen, Jen-Ping

1995-01-01

The numerical scheme presented belongs to a family of codes known as UNCLE (UNsteady Computation of fieLd Equations) as reported by Whitfield (1995), that is being used to solve problems in a variety of areas including compressible and incompressible flows. This derivation is specifically developed for general unsteady multi-blade-row turbomachinery problems. The scheme solves the Reynolds-averaged N-S equations with the Baldwin-Lomax turbulence model.

Simple Model of Macroscopic Instability in XeCl Discharge Pumped Lasers

NASA Astrophysics Data System (ADS)

Ahmed, Belasri; Zoheir, Harrache

2003-10-01

The aim of this work is to study the development of the macroscopic non uniformity of the electron density of high pressure discharge for excimer lasers and eventually its propagation because of the medium kinetics phenomena. This study is executed using a transverse mono-dimensional model, in which the plasma is represented by a set of resistance's in parallel. This model was employed using a numerical code including three strongly coupled parts: electric circuit equations, electron Boltzmann equation, and kinetics equations (chemical kinetics model). The time variations of the electron density in each plasma element are obtained by solving a set of ordinary differential equations describing the plasma kinetics and external circuit. The use of the present model allows a good comprehension of the halogen depletion phenomena, which is the principal cause of laser ending and allows a simple study of a large-scale non uniformity in preionization density and its effects on electrical and chemical plasma properties. The obtained results indicate clearly that about 50consumed at the end of the pulse. KEY WORDS Excimer laser, XeCl, Modeling, Cold plasma, Kinetic, Halogen depletion, Macroscopic instability.

The usefulness of "corrected" body mass index vs. self-reported body mass index: comparing the population distributions, sensitivity, specificity, and predictive utility of three correction equations using Canadian population-based data.

PubMed

Dutton, Daniel J; McLaren, Lindsay

2014-05-06

National data on body mass index (BMI), computed from self-reported height and weight, is readily available for many populations including the Canadian population. Because self-reported weight is found to be systematically under-reported, it has been proposed that the bias in self-reported BMI can be corrected using equations derived from data sets which include both self-reported and measured height and weight. Such correction equations have been developed and adopted. We aim to evaluate the usefulness (i.e., distributional similarity; sensitivity and specificity; and predictive utility vis-à-vis disease outcomes) of existing and new correction equations in population-based research. The Canadian Community Health Surveys from 2005 and 2008 include both measured and self-reported values of height and weight, which allows for construction and evaluation of correction equations. We focused on adults age 18-65, and compared three correction equations (two correcting weight only, and one correcting BMI) against self-reported and measured BMI. We first compared population distributions of BMI. Second, we compared the sensitivity and specificity of self-reported BMI and corrected BMI against measured BMI. Third, we compared the self-reported and corrected BMI in terms of association with health outcomes using logistic regression. All corrections outperformed self-report when estimating the full BMI distribution; the weight-only correction outperformed the BMI-only correction for females in the 23-28 kg/m2 BMI range. In terms of sensitivity/specificity, when estimating obesity prevalence, corrected values of BMI (from any equation) were superior to self-report. In terms of modelling BMI-disease outcome associations, findings were mixed, with no correction proving consistently superior to self-report. If researchers are interested in modelling the full population distribution of BMI, or estimating the prevalence of obesity in a population, then a correction of any kind included in this study is recommended. If the researcher is interested in using BMI as a predictor variable for modelling disease, then both self-reported and corrected BMI result in biased estimates of association.

Exact solution for the time evolution of network rewiring models

NASA Astrophysics Data System (ADS)

Evans, T. S.; Plato, A. D. K.

2007-05-01

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean-field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature, including examples of urn, backgammon, and balls-in-boxes models, the Watts and Strogatz rewiring problem, and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a minority game also show features described by our model.

Mean-field hierarchical equations for some A+BC catalytic reaction models

NASA Astrophysics Data System (ADS)

Cortés, Joaquín; Puschmann, Heinrich; Valencia, Eliana

1998-10-01

A mean-field study of the (A+BC→AC+1/2B2) system is developed from hierarchical equations, considering mechanisms that include dissociation, reaction with finite rates, desorption, and diffusion of the adsorbed species. The phase diagrams are compared to Monte Carlo simulations.

The ACC/AHA 2013 pooled cohort equations compared to a Korean Risk Prediction Model for atherosclerotic cardiovascular disease.

PubMed

Jung, Keum Ji; Jang, Yangsoo; Oh, Dong Joo; Oh, Byung-Hee; Lee, Sang Hoon; Park, Seong-Wook; Seung, Ki-Bae; Kim, Hong-Kyu; Yun, Young Duk; Choi, Sung Hee; Sung, Jidong; Lee, Tae-Yong; Kim, Sung Hi; Koh, Sang Baek; Kim, Moon Chan; Chang Kim, Hyeon; Kimm, Heejin; Nam, Chungmo; Park, Sungha; Jee, Sun Ha

2015-09-01

To evaluate the performance of the American College of Cardiology/American Heart Association (ACC/AHA) 2013 Pooled Cohort Equations in the Korean Heart Study (KHS) population and to develop a Korean Risk Prediction Model (KRPM) for atherosclerotic cardiovascular disease (ASCVD) events. The KHS cohort included 200,010 Korean adults aged 40-79 years who were free from ASCVD at baseline. Discrimination, calibration, and recalibration of the ACC/AHA Equations in predicting 10-year ASCVD risk in the KHS cohort were evaluated. The KRPM was derived using Cox model coefficients, mean risk factor values, and mean incidences from the KHS cohort. In the discriminatory analysis, the ACC/AHA Equations' White and African-American (AA) models moderately distinguished cases from non-cases, and were similar to the KRPM: For men, the area under the receiver operating characteristic curve (AUROCs) were 0.727 (White model), 0.725 (AA model), and 0.741 (KRPM); for women, the corresponding AUROCs were 0.738, 0.739, and 0.745. Absolute 10-year ASCVD risk for men in the KHS cohort was overestimated by 56.5% (White model) and 74.1% (AA model), while the risk for women was underestimated by 27.9% (White model) and overestimated by 29.1% (AA model). Recalibration of the ACC/AHA Equations did not affect discriminatory ability but improved calibration substantially, especially in men in the White model. Of the three ASCVD risk prediction models, the KRPM showed best calibration. The ACC/AHA Equations should not be directly applied for ASCVD risk prediction in a Korean population. The KRPM showed best predictive ability for ASCVD risk. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Stable static structures in models with higher-order derivatives

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

Bazeia, D., E-mail: bazeia@fisica.ufpb.br; Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB; Lobão, A.S.

2015-09-15

We investigate the presence of static solutions in generalized models described by a real scalar field in four-dimensional space–time. We study models in which the scalar field engenders higher-order derivatives and spontaneous symmetry breaking, inducing the presence of domain walls. Despite the presence of higher-order derivatives, the models keep to equations of motion second-order differential equations, so we focus on the presence of first-order equations that help us to obtain analytical solutions and investigate linear stability on general grounds. We then illustrate the general results with some specific examples, showing that the domain wall may become compact and that themore » zero mode may split. Moreover, if the model is further generalized to include k-field behavior, it may contribute to split the static structure itself.« less

The dynamics and control of large-flexible space structures, part 10

NASA Technical Reports Server (NTRS)

Bainum, Peter M.; Reddy, A. S. S. R.

1988-01-01

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment (SCOLE) during the station keeping phase. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttle's three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. The modal shape functions are derived using the fourth order beam equation. The generic mode equations are derived to account for the effects of the control forces on the modal shape and frequencies. The equations are linearized about a nominal equilibrium position. The linear regulator theory is used to derive control laws for both the linear model of the rigidized SCOLE as well as that of the actual SCOLE including the first four flexible modes. The control strategy previously derived for the linear model of the rigidized SCOLE is applied to the nonlinear model of the same configuration of the system and preliminary single axis slewing maneuvers conducted. The results obtained confirm the applicability of the intuitive and appealing two-stage control strategy which would slew the SCOLE system, as if rigid to its desired position and then concentrate on damping out the residual flexible motions.

The Fundamental Solution of the Linearized Navier Stokes Equations for Spinning Bodies in Three Spatial Dimensions Time Dependent Case

NASA Astrophysics Data System (ADS)

Thomann, Enrique A.; Guenther, Ronald B.

2006-02-01

Explicit formulae for the fundamental solution of the linearized time dependent Navier Stokes equations in three spatial dimensions are obtained. The linear equations considered in this paper include those used to model rigid bodies that are translating and rotating at a constant velocity. Estimates extending those obtained by Solonnikov in [23] for the fundamental solution of the time dependent Stokes equations, corresponding to zero translational and angular velocity, are established. Existence and uniqueness of solutions of these linearized problems is obtained for a class of functions that includes the classical Lebesgue spaces L p (R 3), 1 < p < ∞. Finally, the asymptotic behavior and semigroup properties of the fundamental solution are established.

Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory

NASA Astrophysics Data System (ADS)

Wang, Liming; Zheng, Shijie

2018-02-01

In this study, based on the new modified couple stress theory, the size- dependent model for nonlinear bending analysis of a pure 0-3 polarized PLZT plate is developed for the first time. The equilibrium equations are derived from a variational formulation based on the potential energy principle and the new modified couple stress theory. The Galerkin method is adopted to derive the nonlinear algebraic equations from governing differential equations. And then the nonlinear algebraic equations are solved by using Newton-Raphson method. After simplification, the new model includes only a material length scale parameter. In addition, numerical examples are carried out to study the effect of material length scale parameter on the nonlinear bending of a simply supported pure 0-3 polarized PLZT plate subjected to light illumination and uniform distributed load. The results indicate the new model is able to capture the size effect and geometric nonlinearity.

Photonic band gap structure simulator

DOEpatents

Chen, Chiping; Shapiro, Michael A.; Smirnova, Evgenya I.; Temkin, Richard J.; Sirigiri, Jagadishwar R.

2006-10-03

A system and method for designing photonic band gap structures. The system and method provide a user with the capability to produce a model of a two-dimensional array of conductors corresponding to a unit cell. The model involves a linear equation. Boundary conditions representative of conditions at the boundary of the unit cell are applied to a solution of the Helmholtz equation defined for the unit cell. The linear equation can be approximated by a Hermitian matrix. An eigenvalue of the Helmholtz equation is calculated. One computation approach involves calculating finite differences. The model can include a symmetry element, such as a center of inversion, a rotation axis, and a mirror plane. A graphical user interface is provided for the user's convenience. A display is provided to display to a user the calculated eigenvalue, corresponding to a photonic energy level in the Brilloin zone of the unit cell.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

Health Promotion Behavior of Chinese International Students in Korea Including Acculturation Factors: A Structural Equation Model.

PubMed

Kim, Sun Jung; Yoo, Il Young

2016-03-01

The purpose of this study was to explain the health promotion behavior of Chinese international students in Korea using a structural equation model including acculturation factors. A survey using self-administered questionnaires was employed. Data were collected from 272 Chinese students who have resided in Korea for longer than 6 months. The data were analyzed using structural equation modeling. The p value of final model is .31. The fitness parameters of the final model such as goodness of fit index, adjusted goodness of fit index, normed fit index, non-normed fit index, and comparative fit index were more than .95. Root mean square of residual and root mean square error of approximation also met the criteria. Self-esteem, perceived health status, acculturative stress and acculturation level had direct effects on health promotion behavior of the participants and the model explained 30.0% of variance. The Chinese students in Korea with higher self-esteem, perceived health status, acculturation level, and lower acculturative stress reported higher health promotion behavior. The findings can be applied to develop health promotion strategies for this population. Copyright © 2016. Published by Elsevier B.V.

Development and validation of a general purpose linearization program for rigid aircraft models

NASA Technical Reports Server (NTRS)

Duke, E. L.; Antoniewicz, R. F.

1985-01-01

A FORTRAN program that provides the user with a powerful and flexible tool for the linearization of aircraft models is discussed. The program LINEAR numerically determines a linear systems model using nonlinear equations of motion and a user-supplied, nonlinear aerodynamic model. The system model determined by LINEAR consists of matrices for both the state and observation equations. The program has been designed to allow easy selection and definition of the state, control, and observation variables to be used in a particular model. Also, included in the report is a comparison of linear and nonlinear models for a high performance aircraft.

Nonlinear GARCH model and 1 / f noise

NASA Astrophysics Data System (ADS)

Kononovicius, A.; Ruseckas, J.

2015-06-01

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.

Dynamic Modeling and Simulation of an Underactuated System

NASA Astrophysics Data System (ADS)

Libardo Duarte Madrid, Juan; Ospina Henao, P. A.; González Querubín, E.

2017-06-01

In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in SOLIDWORKS 3D CAD software, which based on the material and dimensions of the model provides some physical variables necessary for modeling. In order to verify the results obtained, a comparison the CAD model simulated in the environment SimMechanics of MATLAB software with the mathematical model who was consisting of Euler-Lagrange’s equations implemented in Simulink MATLAB, solved with the ODE23tb method, included in the MATLAB libraries for the solution of systems of equations of the type and order obtained. This article also has a topological analysis of pendulum trajectories through a phase space diagram, which allows the identification of stable and unstable regions of the system.

Gyrofluid theory and simulation of electromagnetic turbulence and transport in tokamak plasmas

NASA Astrophysics Data System (ADS)

Snyder, Philip Benjamin

1999-11-01

Turbulence and transport in toroidal plasmas is studied via the development of an electromagnetic gyrofluid model, and its implementation in realistic nonlinear simulations. This work extends earlier electrostatic gyrofluid models to include magnetic fluctuations and non-adiabatic passing electron dynamics. A new set of electron fluid equations is derived from the drift kinetic equation, via an expansion in the electron-ion mass ratio. These electron equations include descriptions of linear and nonlinear drift motion, Landau damping, and electron-ion collisions. Ion moment equations are derived from the electromagnetic gyrokinetic equation, and the gyrokinetic Poisson's Equation and Ampere's Law close the system. The model is benchmarked with linear gyrokinetic calculations, and good agreement is found for both the finite-β ion temperature gradient (ITG) and kinetic Alfvén ballooning (KBM) instabilities. Nonlinear simulations of ITG and KBM-driven turbulence are performed in toroidal flux tube geometry at a range of values of plasma β, and electromagnetic effects are found to significantly impact turbulent heat and particle transport. At low values of β, transport is reduced, as expected due to the finite-β stabilization of the ITG mode. However, as β approaches the Ideal-MHD stability threshold, transport can increase. In the presence of dissipation provided by a model of electron Landau damping and electron-ion collisions, this transport increase can be quite dramatic. Finally, the results of the simulations are compared to tokamak experiments, and encouraging agreement is found with measured density and temperature fluctuation spectra. Direct comparisons of transport fluxes reveal that electromagnetic effects are important at characteristic edge parameters, bringing predicted fluxes more closely in line with observations.

Relationships of models of the inner magnetosphere to the Rice Convection Model

NASA Astrophysics Data System (ADS)

Heinemann, M.; Wolf, R. A.

2001-08-01

Ideal magnetohydrodynamics is known to be inaccurate for the Earth's inner magnetosphere, where transport by gradient-curvature drift is nonnegligible compared to E×B drift. Most theoretical treatments of the inner plasma sheet and ring current, including the Rice Convection Model (RCM), treat the inner magnetospheric plasma in terms of guiding center drifts. The RCM assumes that the distribution function is isotropic, but particles with different energy invariants are treated as separate guiding center fluids. However, Peymirat and Fontaine [1994] developed a two-fluid picture of the inner magnetosphere, which utilizes modified forms of the conventional fluid equations, not guiding center drift equations. Heinemann [1999] argued theoretically that for inner magnetospheric conditions the fluid energy equation should include a heat flux term, which, in the case of Maxwellian plasma, was derived by Braginskii [1965]. We have now reconciled the Heinemann [1999] fluid approach with the RCM. The fluid equations, including the Braginskii heat flux, can be derived by taking appropriate moments of the RCM equations for the case of the Maxwellian distribution. The physical difference between the RCM formalism and the Heinemann [1999] fluid approach is that the RCM pretends that particles suffer elastic collisions that maintain the isotropy of the distribution function but do not change particle energies. The Heinemann [1999] fluid treatment makes a different physical approximation, namely that the collisions maintain local thermal equilibrium among the ions and separately among the electrons. For some simple cases, numerical results are presented that illustrate the differences in the predictions of the two formalisms, along with those of MHD, guiding center theory, and Peymirat and Fontaine [1994].

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

PubMed Central

Kurihara, Eru; Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2011-01-01

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009

Detecting Moving Targets by Use of Soliton Resonances

NASA Technical Reports Server (NTRS)

Zak, Michael; Kulikov, Igor

2003-01-01

A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.

Numerical Modeling of Electroacoustic Logging Including Joule Heating

NASA Astrophysics Data System (ADS)

Plyushchenkov, Boris D.; Nikitin, Anatoly A.; Turchaninov, Victor I.

It is well known that electromagnetic field excites acoustic wave in a porous elastic medium saturated with fluid electrolyte due to electrokinetic conversion effect. Pride's equations describing this process are written in isothermal approximation. Update of these equations, which allows to take influence of Joule heating on acoustic waves propagation into account, is proposed here. This update includes terms describing the initiation of additional acoustic waves excited by thermoelastic stresses and the heat conduction equation with right side defined by Joule heating. Results of numerical modeling of several problems of propagation of acoustic waves excited by an electric field source with and without consideration of Joule heating effect in their statements are presented. From these results, it follows that influence of Joule heating should be taken into account at the numerical simulation of electroacoustic logging and at the interpretation of its log data.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

PubMed

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

Modeling RF Fields in Hot Plasmas with Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, Andrew; Svidzinski, Vladimir; Zhao, Liangji; Galkin, Sergei; Kim, Jin-Soo

2016-10-01

FAR-TECH, Inc. is developing a suite of full wave RF plasma codes. It is based on a meshless formulation in configuration space with adapted cloud of computational points (CCP) capability and using the hot plasma conductivity kernel to model the nonlocal plasma dielectric response. The conductivity kernel is calculated by numerically integrating the linearized Vlasov equation along unperturbed particle trajectories. Work has been done on the following calculations: 1) the conductivity kernel in hot plasmas, 2) a monitor function based on analytic solutions of the cold-plasma dispersion relation, 3) an adaptive CCP based on the monitor function, 4) stencils to approximate the wave equations on the CCP, 5) the solution to the full wave equations in the cold-plasma model in tokamak geometry for ECRH and ICRH range of frequencies, and 6) the solution to the wave equations using the calculated hot plasma conductivity kernel. We will present results on using a meshless formulation on adaptive CCP to solve the wave equations and on implementing the non-local hot plasma dielectric response to the wave equations. The presentation will include numerical results of wave propagation and absorption in the cold and hot tokamak plasma RF models, using DIII-D geometry and plasma parameters. Work is supported by the U.S. DOE SBIR program.

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Turbulent Flow Validation in the Helios Strand Solver

DTIC Science & Technology

2014-01-07

usual (̄) notation is omitted for simplicity). The pressure is obtained from the ideal gas equation of state given as: P = (γ−1) [ Et − 1 2 ρ ( u2 + v2...2. SA-RANS System The state vector and flux vectors including those of the SA model equation for three-dimensional flow are explicitly given as: u...number, PrT is the turbulent Prandtl number, and T is the temperature. The ideal gas equation of state , p = ρRT is used to close the equations . IV.A

a Numerical Model for Flue Gas Desulfurization System.

NASA Astrophysics Data System (ADS)

Kim, Sung Joon

The purpose of this work is to develop a reliable numerical model for spray dryer desulfurization systems. The shape of the spray dryer requires that a body fitted orthogonal coordinate system be used for the numerical model. The governing equations are developed in the general orthogonal coordinates and discretized to yield a system of algebraic equations. A turbulence model is also included in the numerical program. A new second order numerical scheme is developed and included in the numerical model. The trajectory approach is used to simulate the flow of the dispersed phase. Two-way coupling phenomena is modeled by this scheme. The absorption of sulfur dioxide into lime slurry droplets is simulated by a model based on gas -phase mass transfer. The program is applied to a typical spray dryer desulfurization system. The results show the capability of the program to predict the sensitivity of system performance to changes in operational parameters.

Titan I propulsion system modeling and possible performance improvements

NASA Astrophysics Data System (ADS)

Giusti, Oreste

This thesis features the Titan I propulsion systems and offers data-supported suggestions for improvements to increase performance. The original propulsion systems were modeled both graphically in CAD and via equations. Due to the limited availability of published information, it was necessary to create a more detailed, secondary set of models. Various engineering equations---pertinent to rocket engine design---were implemented in order to generate the desired extra detail. This study describes how these new models were then imported into the ESI CFD Suite. Various parameters are applied to these imported models as inputs that include, for example, bi-propellant combinations, pressure, temperatures, and mass flow rates. The results were then processed with ESI VIEW, which is visualization software. The output files were analyzed for forces in the nozzle, and various results were generated, including sea level thrust and ISP. Experimental data are provided to compare the original engine configuration models to the derivative suggested improvement models.

A Posteriori Study of a DNS Database Describing Super critical Binary-Species Mixing

NASA Technical Reports Server (NTRS)

Bellan, Josette; Taskinoglu, Ezgi

2012-01-01

Currently, the modeling of supercritical-pressure flows through Large Eddy Simulation (LES) uses models derived for atmospheric-pressure flows. Those atmospheric-pressure flows do not exhibit the particularities of high densitygradient magnitude features observed both in experiments and simulations of supercritical-pressure flows in the case of two species mixing. To assess whether the current LES modeling is appropriate and if found not appropriate to propose higher-fidelity models, a LES a posteriori study has been conducted for a mixing layer that initially contains different species in the lower and upper streams, and where the initial pressure is larger than the critical pressure of either species. An initially-imposed vorticity perturbation promotes roll-up and a double pairing of four initial span-wise vortices into an ultimate vortex that reaches a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equation set uses transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid scale (SGS) fluxes, a new SGS term that is a pressure correction in the momentum equation. This additional term results from filtering of Direct Numerical Simulation (DNS) equations, and represents the gradient of the difference between the filtered pressure and the pressure computed from the filtered flow field. A previous a priori analysis, using a DNS database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of high-densitygradient magnitude regions that populated the entire flow; in the study, models were proposed for the SGS fluxes as well as this new term. In the present study, the previously proposed constantcoefficient SGS-flux models of the a priori investigation are tested a posteriori in LES, devoid of or including, the SGS pressure correction term. The present pressure-correction model is different from, and more accurate as well as less computationally intensive than that of the a priori study. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC), in conjunction with the Yoshizawa (YO) model for the trace, the Gradient (GRC) and the Scale Similarity (SSC) models, all exercised with the a priori study constant coefficients calibrated at the transitional state. The LES comparison is performed with the filtered- and-coarsened (FC) DNS, which represents an ideal LES solution. Expectably, an LES model devoid of SGS terms is shown to be considerably inferior to models containing SGS effects. Among models containing SGS effects, those including the pressure-correction term are substantially superior to those devoid of it. The sensitivity of the predictions to the initial conditions and grid size are also investigated. Thus, it has been discovered that, additional to the atmospheric-pressure models currently used, a new model is necessary to simulate supercritical-pressure flows. This model depends on the thermodynamic characteristics of the chemical species involved.

The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules

NASA Technical Reports Server (NTRS)

Cheremisin, F. G.

1972-01-01

Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Simulations of Turbulent Momentum and Scalar Transport in Non-Reacting Confined Swirling Coaxial Jets

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Liu, Nan-Suey; Moder, Jeffrey P.

2015-01-01

This paper presents the numerical simulations of confined three-dimensional coaxial water jets. The objectives are to validate the newly proposed nonlinear turbulence models of momentum and scalar transport, and to evaluate the newly introduced scalar APDF and DWFDF equation along with its Eulerian implementation in the National Combustion Code (NCC). Simulations conducted include the steady RANS, the unsteady RANS (URANS), and the time-filtered Navier-Stokes (TFNS); both without and with invoking the APDF or DWFDF equation. When the APDF (ensemble averaged probability density function) or DWFDF (density weighted filtered density function) equation is invoked, the simulations are of a hybrid nature, i.e., the transport equations of energy and species are replaced by the APDF or DWFDF equation. Results of simulations are compared with the available experimental data. Some positive impacts of the nonlinear turbulence models and the Eulerian scalar APDF and DWFDF approach are observed.

A three-dimensional method-of-characteristics solute-transport model (MOC3D)

USGS Publications Warehouse

Konikow, Leonard F.; Goode, D.J.; Hornberger, G.Z.

1996-01-01

This report presents a model, MOC3D, that simulates three-dimensional solute transport in flowing ground water. The model computes changes in concentration of a single dissolved chemical constituent over time that are caused by advective transport, hydrodynamic dispersion (including both mechanical dispersion and diffusion), mixing (or dilution) from fluid sources, and mathematically simple chemical reactions (including linear sorption, which is represented by a retardation factor, and decay). The transport model is integrated with MODFLOW, a three-dimensional ground-water flow model that uses implicit finite-difference methods to solve the transient flow equation. MOC3D uses the method of characteristics to solve the transport equation on the basis of the hydraulic gradients computed with MODFLOW for a given time step. This implementation of the method of characteristics uses particle tracking to represent advective transport and explicit finite-difference methods to calculate the effects of other processes. However, the explicit procedure has several stability criteria that may limit the size of time increments for solving the transport equation; these are automatically determined by the program. For improved efficiency, the user can apply MOC3D to a subgrid of the primary MODFLOW grid that is used to solve the flow equation. However, the transport subgrid must have uniform grid spacing along rows and columns. The report includes a description of the theoretical basis of the model, a detailed description of input requirements and output options, and the results of model testing and evaluation. The model was evaluated for several problems for which exact analytical solutions are available and by benchmarking against other numerical codes for selected complex problems for which no exact solutions are available. These test results indicate that the model is very accurate for a wide range of conditions and yields minimal numerical dispersion for advection-dominated problems. Mass-balance errors are generally less than 10 percent, and tend to decrease and stabilize with time.

A kinetics database and scripts for PHREEQC

NASA Astrophysics Data System (ADS)

Hu, B.; Zhang, Y.; Teng, Y.; Zhu, C.

2017-12-01

Kinetics of geochemical reactions has been increasingly used in numerical models to simulate coupled flow, mass transport, and chemical reactions. However, the kinetic data are scattered in the literature. To assemble a kinetic dataset for a modeling project is an intimidating task for most. In order to facilitate the application of kinetics in geochemical modeling, we assembled kinetics parameters into a database for the geochemical simulation program, PHREEQC (version 3.0). Kinetics data were collected from the literature. Our database includes kinetic data for over 70 minerals. The rate equations are also programmed into scripts with the Basic language. Using the new kinetic database, we simulated reaction path during the albite dissolution process using various rate equations in the literature. The simulation results with three different rate equations gave difference reaction paths at different time scale. Another application involves a coupled reactive transport model simulating the advancement of an acid plume in an acid mine drainage site associated with Bear Creek Uranium tailings pond. Geochemical reactions including calcite, gypsum, and illite were simulated with PHREEQC using the new kinetic database. The simulation results successfully demonstrated the utility of new kinetic database.

Simple equations to simulate closed-loop recycling liquid-liquid chromatography: Ideal and non-ideal recycling models.

PubMed

Kostanyan, Artak E

2015-12-04

The ideal (the column outlet is directly connected to the column inlet) and non-ideal (includes the effects of extra-column dispersion) recycling equilibrium-cell models are used to simulate closed-loop recycling counter-current chromatography (CLR CCC). Simple chromatogram equations for the individual cycles and equations describing the transport and broadening of single peaks and complex chromatograms inside the recycling closed-loop column for ideal and non-ideal recycling models are presented. The extra-column dispersion is included in the theoretical analysis, by replacing the recycling system (connecting lines, pump and valving) by a cascade of Nec perfectly mixed cells. To evaluate extra-column contribution to band broadening, two limiting regimes of recycling are analyzed: plug-flow, Nec→∞, and maximum extra-column dispersion, Nec=1. Comparative analysis of ideal and non-ideal models has shown that when the volume of the recycling system is less than one percent of the column volume, the influence of the extra-column processes on the CLR CCC separation may be neglected. Copyright © 2015 Elsevier B.V. All rights reserved.

Computation of turbulent boundary layer flows with an algebraic stress turbulence model

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Chen, Yen-Sen

1986-01-01

An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

A mathematical model of the heat and fluid flows in direct-chill casting of aluminum sheet ingots and billets

NASA Astrophysics Data System (ADS)

Mortensen, Dag

1999-02-01

A finite-element method model for the time-dependent heat and fluid flows that develop during direct-chill (DC) semicontinuous casting of aluminium ingots is presented. Thermal convection and turbulence are included in the model formulation and, in the mushy zone, the momentum equations are modified with a Darcy-type source term dependent on the liquid fraction. The boundary conditions involve calculations of the air gap along the mold wall as well as the heat transfer to the falling water film with forced convection, nucleate boiling, and film boiling. The mold wall and the starting block are included in the computational domain. In the start-up period of the casting, the ingot domain expands over the starting-block level. The numerical method applies a fractional-step method for the dynamic Navier-Stokes equations and the “streamline upwind Petrov-Galerkin” (SUPG) method for mixed diffusion and convection in the momentum and energy equations. The modeling of the start-up period of the casting is demonstrated and compared to temperature measurements in an AA1050 200×600 mm sheet ingot.

Annotated bibliography of structural equation modelling: technical work.

PubMed

Austin, J T; Wolfle, L M

1991-05-01

Researchers must be familiar with a variety of source literature to facilitate the informed use of structural equation modelling. Knowledge can be acquired through the study of an expanding literature found in a diverse set of publishing forums. We propose that structural equation modelling publications can be roughly classified into two groups: (a) technical and (b) substantive applications. Technical materials focus on the procedures rather than substantive conclusions derived from applications. The focus of this article is the former category; included are foundational/major contributions, minor contributions, critical and evaluative reviews, integrations, simulations and computer applications, precursor and historical material, and pedagogical textbooks. After a brief introduction, we annotate 294 articles in the technical category dating back to Sewall Wright (1921).

About the coupling of turbulence closure models with averaged Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Vandromme, D.; Ha Minh, H.

1986-01-01

The MacCormack implicit predictor-corrector model (1981) for numerical solution of the coupled Navier-Stokes equations for turbulent flows is extended to nonconservative multiequation turbulence models, as well as the inclusion of second-order Reynolds stress turbulence closure. A scalar effective pressure turbulent contribution to the pressure field is defined to approximate the effects of the Reynolds stress in strongly sheared flows. The Jacobian matrices of the transport equations are diagonalized to reduce the required computer memory and run time. Techniques are defined for including turbulence in the diagonalization. Application of the method is demonstrated with solutions generated for transonic nozzle flow and for the interaction between a supersonic flat plate boundary layer and a 12 deg compression-expansion ramp.

Atmospheric flow over two-dimensional bluff surface obstructions

NASA Technical Reports Server (NTRS)

Bitte, J.; Frost, W.

1976-01-01

The phenomenon of atmospheric flow over a two-dimensional surface obstruction, such as a building (modeled as a rectangular block, a fence or a forward-facing step), is analyzed by three methods: (1) an inviscid free streamline approach, (2) a turbulent boundary layer approach using an eddy viscosity turbulence model and a horizontal pressure gradient determined by the inviscid model, and (3) an approach using the full Navier-Stokes equations with three turbulence models; i.e., an eddy viscosity model, a turbulence kinetic-energy model and a two-equation model with an additional transport equation for the turbulence length scale. A comparison of the performance of the different turbulence models is given, indicating that only the two-equation model adequately accounts for the convective character of turbulence. Turbulence flow property predictions obtained from the turbulence kinetic-energy model with prescribed length scale are only insignificantly better than those obtained from the eddy viscosity model. A parametric study includes the effects of the variation of the characteristics parameters of the assumed logarithmic approach velocity profile. For the case of the forward-facing step, it is shown that in the downstream flow region an increase of the surface roughness gives rise to higher turbulence levels in the shear layer originating from the step corner.

Foundations of modelling of nonequilibrium low-temperature plasmas

NASA Astrophysics Data System (ADS)

Alves, L. L.; Bogaerts, A.; Guerra, V.; Turner, M. M.

2018-02-01

This work explains the need for plasma models, introduces arguments for choosing the type of model that better fits the purpose of each study, and presents the basics of the most common nonequilibrium low-temperature plasma models and the information available from each one, along with an extensive list of references for complementary in-depth reading. The paper presents the following models, organised according to the level of multi-dimensional description of the plasma: kinetic models, based on either a statistical particle-in-cell/Monte-Carlo approach or the solution to the Boltzmann equation (in the latter case, special focus is given to the description of the electron kinetics); multi-fluid models, based on the solution to the hydrodynamic equations; global (spatially-average) models, based on the solution to the particle and energy rate-balance equations for the main plasma species, usually including a very complete reaction chemistry; mesoscopic models for plasma-surface interaction, adopting either a deterministic approach or a stochastic dynamical Monte-Carlo approach. For each plasma model, the paper puts forward the physics context, introduces the fundamental equations, presents advantages and limitations, also from a numerical perspective, and illustrates its application with some examples. Whenever pertinent, the interconnection between models is also discussed, in view of multi-scale hybrid approaches.

Theoretical Foundation for Weld Modeling

NASA Technical Reports Server (NTRS)

Traugott, S.

1986-01-01

Differential equations describe physics of tungsten/inert-gas and plasma-arc welding in aluminum. Report collects and describes necessary theoretical foundation upon which numerical welding model is constructed for tungsten/inert gas or plasma-arc welding in aluminum without keyhole. Governing partial differential equations for flow of heat, metal, and current given, together with boundary conditions relevant to welding process. Numerical estimates for relative importance of various phenomena and required properties of 2219 aluminum included

Diffusion Of Mass In Evaporating Multicomponent Drops

NASA Technical Reports Server (NTRS)

Bellan, Josette; Harstad, Kenneth G.

1992-01-01

Report summarizes study of diffusion of mass and related phenomena occurring in evaporation of dense and dilute clusters of drops of multicomponent liquids intended to represent fuels as oil, kerosene, and gasoline. Cluster represented by simplified mathematical model, including global conservation equations for entire cluster and conditions on boundary between cluster and ambient gas. Differential equations of model integrated numerically. One of series of reports by same authors discussing evaporation and combustion of sprayed liquid fuels.

Analytical approximate solutions for a general class of nonlinear delay differential equations.

PubMed

Căruntu, Bogdan; Bota, Constantin

2014-01-01

We use the polynomial least squares method (PLSM), which allows us to compute analytical approximate polynomial solutions for a very general class of strongly nonlinear delay differential equations. The method is tested by computing approximate solutions for several applications including the pantograph equations and a nonlinear time-delay model from biology. The accuracy of the method is illustrated by a comparison with approximate solutions previously computed using other methods.

Development of control systems for space shuttle vehicles. Volume 2: Appendixes

NASA Technical Reports Server (NTRS)

Stone, C. R.; Chase, T. W.; Kiziloz, B. M.; Ward, M. D.

1971-01-01

A launch phase random normal wind model is presented for delta wing, two-stage, space shuttle control system studies. Equations, data, and simulations for conventional launch studies are given as well as pitch and lateral equations and data for covariance analyses of the launch phase of MSFC vehicle B. Lateral equations and data for North American 130G and 134D are also included along with a high-altitude abort simulation.

A Tree Taper Model Based on Similar Triangles and Use of Crown Ratio as a Measure of Form in Taper Equations for Longleaf Pine

Treesearch

Dennis J. Shaw; Ralph S. Meldahl; John S. Kush; Greg L. Somers

2003-01-01

We used data from 322 natural longleaf pine (Pinus palustris Mill.) trees to include crown ratio as a continuous variable in taper equations. The data were divided into 10 crown-ratio classes and fitted taper equations into each class to detect trends in the coefficients. For application to longleaf pine, we replaced coefficients that exhibited a...

Micropolar curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

NASA Astrophysics Data System (ADS)

Kou, Jisheng; Sun, Shuyu

2016-08-01

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.

Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility

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

Kou, Jisheng; Sun, Shuyu, E-mail: shuyu.sun@kaust.edu.sa; School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049

2016-08-01

In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng–Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from themore » microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young–Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young–Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young–Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests are carried out to verify the effectiveness of the proposed multi-scale method.« less

External intermittency prediction using AMR solutions of RANS turbulence and transported PDF models

NASA Astrophysics Data System (ADS)

Olivieri, D. A.; Fairweather, M.; Falle, S. A. E. G.

2011-12-01

External intermittency in turbulent round jets is predicted using a Reynolds-averaged Navier-Stokes modelling approach coupled to solutions of the transported probability density function (pdf) equation for scalar variables. Solutions to the descriptive equations are obtained using a finite-volume method, combined with an adaptive mesh refinement algorithm, applied in both physical and compositional space. This method contrasts with conventional approaches to solving the transported pdf equation which generally employ Monte Carlo techniques. Intermittency-modified eddy viscosity and second-moment turbulence closures are used to accommodate the effects of intermittency on the flow field, with the influence of intermittency also included, through modifications to the mixing model, in the transported pdf equation. Predictions of the overall model are compared with experimental data on the velocity and scalar fields in a round jet, as well as against measurements of intermittency profiles and scalar pdfs in a number of flows, with good agreement obtained. For the cases considered, predictions based on the second-moment turbulence closure are clearly superior, although both turbulence models give realistic predictions of the bimodal scalar pdfs observed experimentally.

Generalized large-scale semigeostrophic approximations for the f-plane primitive equations

NASA Astrophysics Data System (ADS)

Oliver, Marcel; Vasylkevych, Sergiy

2016-05-01

We derive a family of balance models for rotating stratified flow in the primitive equation (PE) setting. By construction, the models possess conservation laws for energy and potential vorticity and are formally of the same order of accuracy as Hoskins’ semigeostrophic equations. Our construction is based on choosing a new coordinate frame for the PE variational principle in such a way that the consistently truncated Lagrangian degenerates. We show that the balance relations so obtained are elliptic when the fluid is stably stratified and certain smallness assumptions are satisfied. Moreover, the potential temperature can be recovered from the potential vorticity via inversion of a non-standard Monge-Ampère problem which is subject to the same ellipticity condition. While the present work is entirely formal, we conjecture, based on a careful rewriting of the equations of motion and a straightforward derivative count, that the Cauchy problem for the balance models is well posed subject to conditions on the initial data. Our family of models includes, in particular, the stratified analog of the L 1 balance model of Salmon.

Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.

PubMed

Alias, Norma; Saipol, Hafizah Farhah Saipan; Ghani, Asnida Che Abd

2014-12-01

A chronology of mathematical models for heat and mass transfer equation is proposed for the prediction of moisture and temperature behavior during drying using DIC (Détente Instantanée Contrôlée) or instant controlled pressure drop technique. DIC technique has the potential as most commonly used dehydration method for high impact food value including the nutrition maintenance and the best possible quality for food storage. The model is governed by the regression model, followed by 2D Fick's and Fourier's parabolic equation and 2D elliptic-parabolic equation in a rectangular slice. The models neglect the effect of shrinkage and radiation effects. The simulations of heat and mass transfer equations with parabolic and elliptic-parabolic types through some numerical methods based on finite difference method (FDM) have been illustrated. Intel®Core™2Duo processors with Linux operating system and C programming language have been considered as a computational platform for the simulation. Qualitative and quantitative differences between DIC technique and the conventional drying methods have been shown as a comparative.

Determination and evaluation of gas holdup time with the quadratic equation model and comparison with nonlinear equation models for isothermal gas chromatography

PubMed Central

Wu, Liejun; Chen, Maoxue; Chen, Yongli; Li, Qing X.

2013-01-01

Gas holdup time (tM) is a basic parameter in isothermal gas chromatography (GC). Determination and evaluation of tM and retention behaviors of n-alkanes under isothermal GC conditions have been extensively studied since the 1950s, but still remains unresolved. The difference equation (DE) model [J. Chromatogr. A 1260:215–223] reveals retention behaviors of n-alkanes excluding tM, while the quadratic equation (QE) model [J. Chromatogr. A 1260:224–231] including tM is suitable for applications. In the present study, tM values were calculated with the QE model, which is referred to as tMT, evaluated and compared with other three typical nonlinear models. The QE model gives an accurate estimation of tM in isothermal GC. The tMT values are highly accurate, stable, and easy to calculate and use. There is only one tMT value at each GC condition. The proper classification of tM values can clarify their disagreement and facilitate GC retention data standardization for which tMT values are promising reference tM values. PMID:23726077

Traveling-Wave Solutions of the Kolmogorov-Petrovskii-Piskunov Equation

NASA Astrophysics Data System (ADS)

Pikulin, S. V.

2018-02-01

We consider quasi-stationary solutions of a problem without initial conditions for the Kolmogorov-Petrovskii-Piskunov (KPP) equation, which is a quasilinear parabolic one arising in the modeling of certain reaction-diffusion processes in the theory of combustion, mathematical biology, and other areas of natural sciences. A new efficiently numerically implementable analytical representation is constructed for self-similar plane traveling-wave solutions of the KPP equation with a special right-hand side. Sufficient conditions for an auxiliary function involved in this representation to be analytical for all values of its argument, including the endpoints, are obtained. Numerical results are obtained for model examples.

The cosmological model with a wormhole and Hawking temperature near apparent horizon

NASA Astrophysics Data System (ADS)

Kim, Sung-Won

2018-05-01

In this paper, a cosmological model with an isotropic form of the Morris-Thorne type wormhole was derived in a similar way to the McVittie solution to the black hole in the expanding universe. By solving Einstein's field equation with plausible matter distribution, we found the exact solution of the wormhole embedded in Friedmann-Lemaître-Robertson-Walker universe. We also found the apparent cosmological horizons from the redefined metric and analyzed the geometric natures, including causal and dynamic structures. The Hawking temperature for thermal radiation was obtained by the WKB approximation using the Hamilton-Jacobi equation and Hamilton's equation, near the apparent cosmological horizon.

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

NASA Technical Reports Server (NTRS)

Neitzel, G. P.; Chang, K.-T.; Jankowski, D. F.; Mittelmann, H. D.

1992-01-01

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio.

PubMed

Hu, Kainan; Zhang, Hongwu; Geng, Shaojuan

2016-10-01

A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio is proposed. The local equilibrium distribution function including the rotational velocity of particle is decoupled into two parts, i.e., the local equilibrium distribution function of the translational velocity of particle and that of the rotational velocity of particle. From these two local equilibrium functions, two lattice Boltzmann models are derived via the Hermite expansion, namely one is in relation to the translational velocity and the other is connected with the rotational velocity. Accordingly, the distribution function is also decoupled. After this, the evolution equation is decoupled into the evolution equation of the translational velocity and that of the rotational velocity. The two evolution equations evolve separately. The lattice Boltzmann models used in the scheme proposed by this work are constructed via the Hermite expansion, so it is easy to construct new schemes of higher-order accuracy. To validate the proposed scheme, a one-dimensional shock tube simulation is performed. The numerical results agree with the analytical solutions very well.

Model dynamics for quantum computing

NASA Astrophysics Data System (ADS)

Tabakin, Frank

2017-08-01

A model master equation suitable for quantum computing dynamics is presented. In an ideal quantum computer (QC), a system of qubits evolves in time unitarily and, by virtue of their entanglement, interfere quantum mechanically to solve otherwise intractable problems. In the real situation, a QC is subject to decoherence and attenuation effects due to interaction with an environment and with possible short-term random disturbances and gate deficiencies. The stability of a QC under such attacks is a key issue for the development of realistic devices. We assume that the influence of the environment can be incorporated by a master equation that includes unitary evolution with gates, supplemented by a Lindblad term. Lindblad operators of various types are explored; namely, steady, pulsed, gate friction, and measurement operators. In the master equation, we use the Lindblad term to describe short time intrusions by random Lindblad pulses. The phenomenological master equation is then extended to include a nonlinear Beretta term that describes the evolution of a closed system with increasing entropy. An external Bath environment is stipulated by a fixed temperature in two different ways. Here we explore the case of a simple one-qubit system in preparation for generalization to multi-qubit, qutrit and hybrid qubit-qutrit systems. This model master equation can be used to test the stability of memory and the efficacy of quantum gates. The properties of such hybrid master equations are explored, with emphasis on the role of thermal equilibrium and entropy constraints. Several significant properties of time-dependent qubit evolution are revealed by this simple study.

Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

PubMed

Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

2013-06-01

A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

Study of Two-Dimensional Compressible Non-Acoustic Modeling of Stirling Machine Type Components

NASA Technical Reports Server (NTRS)

Tew, Roy C., Jr.; Ibrahim, Mounir B.

2001-01-01

A two-dimensional (2-D) computer code was developed for modeling enclosed volumes of gas with oscillating boundaries, such as Stirling machine components. An existing 2-D incompressible flow computer code, CAST, was used as the starting point for the project. CAST was modified to use the compressible non-acoustic Navier-Stokes equations to model an enclosed volume including an oscillating piston. The devices modeled have low Mach numbers and are sufficiently small that the time required for acoustics to propagate across them is negligible. Therefore, acoustics were excluded to enable more time efficient computation. Background information about the project is presented. The compressible non-acoustic flow assumptions are discussed. The governing equations used in the model are presented in transport equation format. A brief description is given of the numerical methods used. Comparisons of code predictions with experimental data are then discussed.

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet Churyumov-Gerasimenko Near Perihelion

NASA Astrophysics Data System (ADS)

Huang, Z.; Toth, G.; Gombosi, T.; Jia, X.; Rubin, M.; Fougere, N.; Tenishev, V.; Combi, M.; Bieler, A.; Hansen, K.; Shou, Y.; Altwegg, K.

2015-10-01

We develop a 3-D four fluid model to study the plasma environment of comet Churyumov- Gerasimenko (CG), which is the target of the Rosetta mission. Our model is based on BATS-R-US within the SWMF (Space Weather Modeling Framework) that solves the governing multifluid MHD equations and and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates mass loading processes, including photo and electron impact ionization, furthermore taken into account are charge exchange, dissociative ion-electron recombination, as well as collisional interactions between different fluids. We simulate the near nucleus plasma and neutral gas environment with a realistic shape model of CG near perihelion and compare our simulation results with Rosetta observations.

A mathematical model of intestinal oedema formation.

PubMed

Young, Jennifer; Rivière, Béatrice; Cox, Charles S; Uray, Karen

2014-03-01

Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall.

Validation of a Node-Centered Wall Function Model for the Unstructured Flow Code FUN3D

NASA Technical Reports Server (NTRS)

Carlson, Jan-Renee; Vasta, Veer N.; White, Jeffery

2015-01-01

In this paper, the implementation of two wall function models in the Reynolds averaged Navier-Stokes (RANS) computational uid dynamics (CFD) code FUN3D is described. FUN3D is a node centered method for solving the three-dimensional Navier-Stokes equations on unstructured computational grids. The first wall function model, based on the work of Knopp et al., is used in conjunction with the one-equation turbulence model of Spalart-Allmaras. The second wall function model, also based on the work of Knopp, is used in conjunction with the two-equation k-! turbulence model of Menter. The wall function models compute the wall momentum and energy flux, which are used to weakly enforce the wall velocity and pressure flux boundary conditions in the mean flow momentum and energy equations. These wall conditions are implemented in an implicit form where the contribution of the wall function model to the Jacobian are also included. The boundary conditions of the turbulence transport equations are enforced explicitly (strongly) on all solid boundaries. The use of the wall function models is demonstrated on four test cases: a at plate boundary layer, a subsonic di user, a 2D airfoil, and a 3D semi-span wing. Where possible, different near-wall viscous spacing tactics are examined. Iterative residual convergence was obtained in most cases. Solution results are compared with theoretical and experimental data for several variations of grid spacing. In general, very good comparisons with data were achieved.

Extension of the general thermal field equation for nanosized emitters

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

Kyritsakis, A., E-mail: akyritsos1@gmail.com; Xanthakis, J. P.

2016-01-28

During the previous decade, Jensen et al. developed a general analytical model that successfully describes electron emission from metals both in the field and thermionic regimes, as well as in the transition region. In that development, the standard image corrected triangular potential barrier was used. This barrier model is valid only for planar surfaces and therefore cannot be used in general for modern nanometric emitters. In a recent publication, the authors showed that the standard Fowler-Nordheim theory can be generalized for highly curved emitters if a quadratic term is included to the potential model. In this paper, we extend thismore » generalization for high temperatures and include both the thermal and intermediate regimes. This is achieved by applying the general method developed by Jensen to the quadratic barrier model of our previous publication. We obtain results that are in good agreement with fully numerical calculations for radii R > 4 nm, while our calculated current density differs by a factor up to 27 from the one predicted by the Jensen's standard General-Thermal-Field (GTF) equation. Our extended GTF equation has application to modern sharp electron sources, beam simulation models, and vacuum breakdown theory.« less

Minimal Cohomological Model of a Scalar Field on a Riemannian Manifold

NASA Astrophysics Data System (ADS)

Arkhipov, V. V.

2018-04-01

Lagrangians of the field-theory model of a scalar field are considered as 4-forms on a Riemannian manifold. The model is constructed on the basis of the Hodge inner product, this latter being an analog of the scalar product of two functions. Including the basis fields in the action of the terms with tetrads makes it possible to reproduce the Klein-Gordon equation and the Maxwell equations, and also the Einstein-Hilbert action. We conjecture that the principle of construction of the Lagrangians as 4-forms can give a criterion restricting possible forms of the field-theory models.

An Investigation of the Connection between Outdoor Orientation and Thriving

ERIC Educational Resources Information Center

Rude, Wally James; Bobilya, Andrew J.; Bell, Brent J.

2017-01-01

This study explored the contribution of outdoor orientation experiences to student thriving. Participants included 295 first-year college students from three institutions across North America. A thriving model was tested using structural equation modeling and included the following variables: outdoor orientation, thriving, involvement,…

Effects of slope smoothing in river channel modeling

NASA Astrophysics Data System (ADS)

Kim, Kyungmin; Liu, Frank; Hodges, Ben R.

2017-04-01

In extending dynamic river modeling with the 1D Saint-Venant equations from a single reach to a large watershed there are critical questions as to how much bathymetric knowledge is necessary and how it should be represented parsimoniously. The ideal model will include the detail necessary to provide realism, but not include extraneous detail that should not exert a control on a 1D (cross-section averaged) solution. In a Saint-Venant model, the overall complexity of the river channel morphometry is typically abstracted into metrics for the channel slope, cross-sectional area, hydraulic radius, and roughness. In stream segments where cross-section surveys are closely spaced, it is not uncommon to have sharp changes in slope or even negative values (where a positive slope is the downstream direction). However, solving river flow with the Saint-Venant equations requires a degree of smoothness in the equation parameters or the equation set with the directly measured channel slopes may not be Lipschitz continuous. The results of non-smoothness are typically extended computational time to converge solutions (or complete failure to converge) and/or numerical instabilities under transient conditions. We have investigated using cubic splines to smooth the bottom slope and ensure always positive reference slopes within a 1D model. This method has been implemented in the Simulation Program for River Networks (SPRNT) and is compared to the standard HEC-RAS river solver. It is shown that the reformulation of the reference slope is both in keeping with the underlying derivation of the Saint-Venant equations and provides practical numerical stability without altering the realism of the simulation. This research was supported in part by the National Science Foundation under grant number CCF-1331610.

A shallow water model for the propagation of tsunami via Lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zergani, Sara; Aziz, Z. A.; Viswanathan, K. K.

2015-01-01

An efficient implementation of the lattice Boltzmann method (LBM) for the numerical simulation of the propagation of long ocean waves (e.g. tsunami), based on the nonlinear shallow water (NSW) wave equation is presented. The LBM is an alternative numerical procedure for the description of incompressible hydrodynamics and has the potential to serve as an efficient solver for incompressible flows in complex geometries. This work proposes the NSW equations for the irrotational surface waves in the case of complex bottom elevation. In recent time, equation involving shallow water is the current norm in modelling tsunami operations which include the propagation zone estimation. Several test-cases are presented to verify our model. Some implications to tsunami wave modelling are also discussed. Numerical results are found to be in excellent agreement with theory.

Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Sprittles, James; Lockerby, Duncan

2017-11-01

Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Inclusion of unsteady aerodynamics in longitudinal parameter estimation from flight data. [use of vortices and mathematical models for parameterization from flight characteristics

NASA Technical Reports Server (NTRS)

Queijo, M. J.; Wells, W. R.; Keskar, D. A.

1979-01-01

A simple vortex system, used to model unsteady aerodynamic effects into the rigid body longitudinal equations of motion of an aircraft, is described. The equations are used in the development of a parameter extraction algorithm. Use of the two parameter-estimation modes, one including and the other omitting unsteady aerodynamic modeling, is discussed as a means of estimating some acceleration derivatives. Computer generated data and flight data, used to demonstrate the use of the parameter-extraction algorithm are studied.

Geometrothermodynamic model for the evolution of the Universe

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

Gruber, Christine; Quevedo, Hernando, E-mail: christine.gruber@correo.nucleares.unam.mx, E-mail: quevedo@nucleares.unam.mx

Using the formalism of geometrothermodynamics to derive a fundamental thermodynamic equation, we construct a cosmological model in the framework of relativistic cosmology. In a first step, we describe a system without thermodynamic interaction, and show it to be equivalent to the standard ΛCDM paradigm. The second step includes thermodynamic interaction and produces a model consistent with the main features of inflation. With the proposed fundamental equation we are thus able to describe all the known epochs in the evolution of our Universe, starting from the inflationary phase.

Application of satellite data in variational analysis for global cyclonic systems

NASA Technical Reports Server (NTRS)

Achtemeier, G. L.

1987-01-01

The research goal was a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. This presents a formidable mathematical problem. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity are defined. Each model is summarized.

Nitrate removal in stream ecosystems measured by 15N addition experiments: Total uptake

USGS Publications Warehouse

Hall, R.O.; Tank, J.L.; Sobota, D.J.; Mulholland, P.J.; O'Brien, J. M.; Dodds, W.K.; Webster, J.R.; Valett, H.M.; Poole, G.C.; Peterson, B.J.; Meyer, J.L.; McDowell, W.H.; Johnson, S.L.; Hamilton, S.K.; Grimm, N. B.; Gregory, S.V.; Dahm, Clifford N.; Cooper, L.W.; Ashkenas, L.R.; Thomas, S.M.; Sheibley, R.W.; Potter, J.D.; Niederlehner, B.R.; Johnson, L.T.; Helton, A.M.; Crenshaw, C.M.; Burgin, A.J.; Bernot, M.J.; Beaulieu, J.J.; Arangob, C.P.

2009-01-01

We measured uptake length of 15NO-3 in 72 streams in eight regions across the United States and Puerto Rico to develop quantitative predictive models on controls of NO-3 uptake length. As part of the Lotic Intersite Nitrogen eXperiment II project, we chose nine streams in each region corresponding to natural (reference), suburban-urban, and agricultural land uses. Study streams spanned a range of human land use to maximize variation in NO-3 concentration, geomorphology, and metabolism. We tested a causal model predicting controls on NO-3 uptake length using structural equation modeling. The model included concomitant measurements of ecosystem metabolism, hydraulic parameters, and nitrogen concentration. We compared this structural equation model to multiple regression models which included additional biotic, catchment, and riparian variables. The structural equation model explained 79% of the variation in log uptake length (S Wtot). Uptake length increased with specific discharge (Q/w) and increasing NO-3 concentrations, showing a loss in removal efficiency in streams with high NO-3 concentration. Uptake lengths shortened with increasing gross primary production, suggesting autotrophic assimilation dominated NO-3 removal. The fraction of catchment area as agriculture and suburban-urban land use weakly predicted NO-3 uptake in bivariate regression, and did improve prediction in a set of multiple regression models. Adding land use to the structural equation model showed that land use indirectly affected NO-3 uptake lengths via directly increasing both gross primary production and NO-3 concentration. Gross primary production shortened SWtot, while increasing NO-3 lengthened SWtot resulting in no net effect of land use on NO- 3 removal. ?? 2009.

A 3D, finite element model for baroclinic circulation on the Vancouver Island continental shelf

USGS Publications Warehouse

Walters, R.A.; Foreman, M.G.G.

1992-01-01

This paper describes the development and application of a 3-dimensional model of the barotropic and baroclinic circulation on the continental shelf west of Vancouver Island, Canada. A previous study with a 2D barotropic model and field data revealed that several tidal constituents have a significant baroclinic component (the K1 in particular). Thus we embarked on another study with a 3D model to study the baroclinic effects on the residual and several selected tidal constituents. The 3D model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for density so that density gradient forcing is included in the momentum equations. However, the study presented here describes diagnostic calculations for the baroclinic residual circulation only. The model is sufficiently efficient that it encourages sensitivity testing with a large number of model runs. In this sense, the model is akin to an extension of analytical solutions to the domain of irregular geometry and bottom topography where this parameter space can be explored in some detail. In particular, the consequences of the sigma coordinate system used by the model are explored. Test cases using an idealized representation of the continental shelf, shelf break and shelf slope, lead to an estimation of the velocity errors caused by interpolation errors inherent in the sigma coordinate system. On the basis of these estimates, the computational grid used in the 2D model is found to have inadequate resolution. Thus a new grid is generated with increased accuracy in the region of the shelf break. However, even with increased resolution, spurious baroclinic circulation seaward of the shelf break and in the vicinity of Juan de Fuca canyon remained a significant problem when the pressure gradient terms were evaluated using the ?? coordinate system and using a realistic density profile. With the new grid, diagnostic calculations of the barotropic and baroclinic residual circulation are performed using forcing from the observed ??t (density) field and from the gradient of this field. ?? 1992.

Neutron Star Models in Alternative Theories of Gravity

NASA Astrophysics Data System (ADS)

Manolidis, Dimitrios

We study the structure of neutron stars in a broad class of alternative theories of gravity. In particular, we focus on Scalar-Tensor theories and f(R) theories of gravity. We construct static and slowly rotating numerical star models for a set of equations of state, including a polytropic model and more realistic equations of state motivated by nuclear physics. Observable quantities such as masses, radii, etc are calculated for a set of parameters of the theories. Specifically for Scalar-Tensor theories, we also calculate the sensitivities of the mass and moment of inertia of the models to variations in the asymptotic value of the scalar field at infinity. These quantities enter post-Newtonian equations of motion and gravitational waveforms of two body systems that are used for gravitational-wave parameter estimation, in order to test these theories against observations. The construction of numerical models of neutron stars in f(R) theories of gravity has been difficult in the past. Using a new formalism by Jaime, Patino and Salgado we were able to construct models with high interior pressure, namely pc > rho c/3, both for constant density models and models with a polytropic equation of state. Thus, we have shown that earlier objections to f(R) theories on the basis of the inability to construct viable neutron star models are unfounded.

Dayside Magnetosphere-Ionosphere Coupling and Prompt Response of Low-Latitude/Equatorial Ionosphere

NASA Astrophysics Data System (ADS)

Tu, J.; Song, P.

2017-12-01

We use a newly developed numerical simulation model of the ionosphere/thermosphere to investigate magnetosphere-ionosphere coupling and response of the low-latitude/equatorial ionosphere. The simulation model adapts an inductive-dynamic approach (including self-consistent solutions of Faraday's law and retaining inertia terms in ion momentum equations), that is, based on magnetic field B and plasma velocity v (B-v paradigm), in contrast to the conventional modeling based on electric field E and current j (E-j paradigm). The most distinct feature of this model is that the magnetic field in the ionosphere is not constant but self-consistently varies, e.g., with currents, in time. The model solves self-consistently time-dependent continuity, momentum, and energy equations for multiple species of ions and neutrals including photochemistry, and Maxwell's equations. The governing equations solved in the model are a set of multifluid-collisional-Hall MHD equations which are one of unique features of our ionosphere/thermosphere model. With such an inductive-dynamic approach, all possible MHD wave modes, each of which may refract and reflect depending on the local conditions, are retained in the solutions so that the dynamic coupling between the magnetosphere and ionosphere and among different regions of the ionosphere can be self-consistently investigated. In this presentation, we show that the disturbances propagate in the Alfven speed from the magnetosphere along the magnetic field lines down to the ionosphere/thermosphere and that they experience a mode conversion to compressional mode MHD waves (particularly fast mode) in the ionosphere. Because the fast modes can propagate perpendicular to the field, they propagate from the dayside high-latitude to the nightside as compressional waves and to the dayside low-latitude/equatorial ionosphere as rarefaction waves. The apparent prompt response of the low-latitude/equatorial ionosphere, manifesting as the sudden increase of the upward flow around the equator and global antisunward convection, is the result of such coupling of the high-latitude and the low-latitude/equatorial ionosphere, and the requirement of the flow continuity, instead of mechanisms such as the penetration electric field.

The analysis of 3-phase squirrel-cage induction motors including space harmonics and mutual slotting in transient and steady state

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

Paap, G.C.

1991-03-01

From general equations which describe the transient electromechanical behavior of the asynchronous squirrel-cage motor, and which include the influence of space harmonics and mutual slotting, simplified models are derived and compared. The models derived are demonstrated in examples where special attention is paid to the influence of the place of the harmonics in the mutual inductance matrix and the influence of mutual slotting. Further, the steady-state equations are derived and the back-transformation for the stator and rotor currents is given. One example is compared with the result of measurements.

Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations

NASA Technical Reports Server (NTRS)

Shapiro, Bruce E.; Levchenko, Andre; Meyerowitz, Elliot M.; Wold, Barbara J.; Mjolsness, Eric D.

2003-01-01

Cellerator describes single and multi-cellular signal transduction networks (STN) with a compact, optionally palette-driven, arrow-based notation to represent biochemical reactions and transcriptional activation. Multi-compartment systems are represented as graphs with STNs embedded in each node. Interactions include mass-action, enzymatic, allosteric and connectionist models. Reactions are translated into differential equations and can be solved numerically to generate predictive time courses or output as systems of equations that can be read by other programs. Cellerator simulations are fully extensible and portable to any operating system that supports Mathematica, and can be indefinitely nested within larger data structures to produce highly scaleable models.

Viscous-shock-layer analysis of hypersonic flows over long slender vehicles. Ph.D. Thesis, 1988

NASA Technical Reports Server (NTRS)

Lee, Kam-Pui; Gupta, Roop N.

1992-01-01

An efficient and accurate method for solving the viscous shock layer equations for hypersonic flows over long slender bodies is presented. The two first order equations, continuity and normal momentum, are solved simultaneously as a coupled set. The flow conditions included are from high Reynolds numbers at low altitudes to low Reynolds numbers at high altitudes. For high Reynolds number flows, both chemical nonequilibrium and perfect gas cases are analyzed with surface catalytic effects and different turbulence models, respectively. At low Reynolds number flow conditions, corrected slip models are implemented with perfect gas case. Detailed comparisons are included with other predictions and experimental data.

Toward the Development of a Model to Estimate the Readability of Credentialing-Examination Materials

ERIC Educational Resources Information Center

Badgett, Barbara A.

2010-01-01

The purpose of this study was to develop a set of procedures to establish readability, including an equation, that accommodates the multiple-choice item format and occupational-specific language related to credentialing examinations. The procedures and equation should be appropriate for learning materials, examination materials, and occupational…

Hpm of Estrogen Model on the Dynamics of Breast Cancer

NASA Astrophysics Data System (ADS)

Govindarajan, A.; Balamuralitharan, S.; Sundaresan, T.

2018-04-01

We enhance a deterministic mathematical model involving universal dynamics on breast cancer with immune response. This is population model so includes Normal cells class, Tumor cells, Immune cells and Estrogen. The eects regarding Estrogen are below incorporated in the model. The effects show to that amount the arrival of greater Estrogen increases the danger over growing breast cancer. Furthermore, approximate solution regarding nonlinear differential equations is arrived by Homotopy Perturbation Method (HPM). Hes HPM is good and correct technique after solve nonlinear differential equation directly. Approximate solution learnt with the support of that method is suitable same as like the actual results in accordance with this models.

A computer model for one-dimensional mass and energy transport in and around chemically reacting particles, including complex gas-phase chemistry, multicomponent molecular diffusion, surface evaporation, and heterogeneous reaction

NASA Technical Reports Server (NTRS)

Cho, S. Y.; Yetter, R. A.; Dryer, F. L.

1992-01-01

Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.

Modeling Climate Dynamically

ERIC Educational Resources Information Center

Walsh, Jim; McGehee, Richard

2013-01-01

A dynamical systems approach to energy balance models of climate is presented, focusing on low order, or conceptual, models. Included are global average and latitude-dependent, surface temperature models. The development and analysis of the differential equations and corresponding bifurcation diagrams provides a host of appropriate material for…

A k-Omega Turbulence Model for Quasi-Three-Dimensional Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Chima, Rodrick V.

1995-01-01

A two-equation k-omega turbulence model has been developed and applied to a quasi-three-dimensional viscous analysis code for blade-to-blade flows in turbomachinery. the code includes the effects of rotation, radius change, and variable stream sheet thickness. The flow equations are given and the explicit runge-Kutta solution scheme is described. the k-omega model equations are also given and the upwind implicit approximate-factorization solution scheme is described. Three cases were calculated: transitional flow over a flat plate, a transonic compressor rotor, and transonic turbine vane with heat transfer. Results were compared to theory, experimental data, and to results using the Baldwin-Lomax turbulence model. The two models compared reasonably well with the data and surprisingly well with each other. Although the k-omega model behaves well numerically and simulates effects of transition, freestream turbulence, and wall roughness, it was not decisively better than the Baldwin-Lomax model for the cases considered here.

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model.

NASA Astrophysics Data System (ADS)

Wan, S.; He, W.

2016-12-01

The inverse problem of using the information of historical data to estimate model errors is one of the science frontier research topics. In this study, we investigate such a problem using the classic Lorenz (1963) equation as a prediction model and the Lorenz equation with a periodic evolutionary function as an accurate representation of reality to generate "observational data." On the basis of the intelligent features of evolutionary modeling (EM), including self-organization, self-adaptive and self-learning, the dynamic information contained in the historical data can be identified and extracted by computer automatically. Thereby, a new approach is proposed to estimate model errors based on EM in the present paper. Numerical tests demonstrate the ability of the new approach to correct model structural errors. In fact, it can actualize the combination of the statistics and dynamics to certain extent.

An upscaled two-equation model of transport in porous media through unsteady-state closure of volume averaged formulations

NASA Astrophysics Data System (ADS)

Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.

2012-04-01

We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell. Consistently with the two-region model working hypotheses, we subdivide the pore space into two volumes, which we select according to the features of the local micro-scale velocity field. Assuming separation of the scales, the mathematical development associated with the averaging method in the two volumes leads to a generalized two-equation model. The final (upscaled) formulation includes the standard first order mass exchange term together with additional terms, which we discuss. Our developments allow to identify the assumptions which are usually implicitly embedded in the usual adoption of a two region mobile-mobile model. All macro-scale properties introduced in this model can be determined explicitly from the pore-scale geometry and hydrodynamics through the solution of a set of closure equations. We pursue here an unsteady closure of the problem, leading to the occurrence of nonlocal (in time) terms in the upscaled system of equations. We provide the solution of the closure problems for a simple application documenting the time dependent and the asymptotic behavior of the system.

Multi-Body Analysis of a Tiltrotor Configuration

NASA Technical Reports Server (NTRS)

Ghiringhelli, G. L.; Masarati, P.; Mantegazza, P.; Nixon, M. W.

1997-01-01

The paper describes the aeroelastic analysis of a tiltrotor configuration. The 1/5 scale wind tunnel semispan model of the V-22 tiltrotor aircraft is considered. The analysis is performed by means of a multi-body code, based on an original formulation. The differential equilibrium problem is stated in terms of first order differential equations. The equilibrium equations of every rigid body are written, together with the definitions of the momenta. The bodies are connected by kinematic constraints, applied in form of Lagrangian multipliers. Deformable components are mainly modelled by means of beam elements, based on an original finite volume formulation. Multi-disciplinar problems can be solved by adding user-defined differential equations. In the presented analysis the equations related to the control of the swash-plate of the model are considered. Advantages of a multi-body aeroelastic code over existing comprehensive rotorcraft codes include the exact modelling of the kinematics of the hub, the detailed modelling of the flexibility of critical hub components, and the possibility to simulate steady flight conditions as well as wind-up and maneuvers. The simulations described in the paper include: 1) the analysis of the aeroelastic stability, with particular regard to the proprotor/pylon instability that is peculiar to tiltrotors, 2) the determination of the dynamic behavior of the system and of the loads due to typical maneuvers, with particular regard to the conversion from helicopter to airplane mode, and 3) the stress evaluation in critical components, such as the pitch links and the conversion downstop spring.

Numerical solution of a logistic growth model for a population with Allee effect considering fuzzy initial values and fuzzy parameters

NASA Astrophysics Data System (ADS)

Amarti, Z.; Nurkholipah, N. S.; Anggriani, N.; Supriatna, A. K.

2018-03-01

Predicting the future of population number is among the important factors that affect the consideration in preparing a good management for the population. This has been done by various known method, one among them is by developing a mathematical model describing the growth of the population. The model usually takes form in a differential equation or a system of differential equations, depending on the complexity of the underlying properties of the population. The most widely used growth models currently are those having a sigmoid solution of time series, including the Verhulst logistic equation and the Gompertz equation. In this paper we consider the Allee effect of the Verhulst’s logistic population model. The Allee effect is a phenomenon in biology showing a high correlation between population size or density and the mean individual fitness of the population. The method used to derive the solution is the Runge-Kutta numerical scheme, since it is in general regarded as one among the good numerical scheme which is relatively easy to implement. Further exploration is done via the fuzzy theoretical approach to accommodate the impreciseness of the initial values and parameters in the model.

WASP7 Stream Transport - Model Theory and User's Guide: Supplement to Water Quality Analysis Simulation Program (WASP) User Documentation

EPA Science Inventory

The standard WASP7 stream transport model calculates water flow through a branching stream network that may include both free-flowing and ponded segments. This supplemental user manual documents the hydraulic algorithms, including the transport and hydrogeometry equations, the m...

Modelling biochemical reaction systems by stochastic differential equations with reflection.

PubMed

Niu, Yuanling; Burrage, Kevin; Chen, Luonan

2016-05-07

In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

Measurement Model Specification Error in LISREL Structural Equation Models.

ERIC Educational Resources Information Center

Baldwin, Beatrice; Lomax, Richard

This LISREL study examines the robustness of the maximum likelihood estimates under varying degrees of measurement model misspecification. A true model containing five latent variables (two endogenous and three exogenous) and two indicator variables per latent variable was used. Measurement model misspecification considered included errors of…

The NURBS curves in modelling the shape of the boundary in the parametric integral equations systems for solving the Laplace equation

NASA Astrophysics Data System (ADS)

Zieniuk, Eugeniusz; Kapturczak, Marta; Sawicki, Dominik

2016-06-01

In solving of boundary value problems the shapes of the boundary can be modelled by the curves widely used in computer graphics. In parametric integral equations system (PIES) such curves are directly included into the mathematical formalism. Its simplify the way of definition and modification of the shape of the boundary. Until now in PIES the B-spline, Bézier and Hermite curves were used. Recent developments in the computer graphics paid our attention, therefore we implemented in PIES possibility of defining the shape of boundary using the NURBS curves. The curves will allow us to modeling different shapes more precisely. In this paper we will compare PIES solutions (with applied NURBS) with the solutions existing in the literature.

Modeling tree crown dynamics with 3D partial differential equations.

PubMed

Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

2014-01-01

We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

A Multi-Fidelity Surrogate Model for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S."bala"

2016-11-01

The explosive dispersal of particles is an example of a complex multiphase and multi-species fluid flow problem. This problem has many engineering applications including particle-laden explosives. In these flows, the detonation products of the explosive cannot be treated as a perfect gas so a real gas equation of state is used to close the governing equations (unlike air, which uses the ideal gas equation for closure). As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both of the state equations must be satisfied. One of the more accurate, yet computationally expensive, methods to deal with this is a scheme that iterates between the two equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work strives to create a multi-fidelity surrogate model of this process. We then study the performance of the model with respect to the iterative method by performing both gas-only and particle laden flow simulations using an Eulerian-Lagrangian approach with a finite volume code. Specifically, the model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel modeling approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

Modelling the evaporation of a tear film over a contact lens.

PubMed

Talbott, Kevin; Xu, Amber; Anderson, Daniel M; Seshaiyer, Padmanabhan

2015-06-01

A contact lens (CL) separates the tear film into a pre-lens tear film (PrLTF), the fluid layer between the CL and the outside environment, and a post-lens tear film (PoLTF), the fluid layer between the CL and the cornea. We examine a model for evaporation of a PrLTF on a modern permeable CL allowing fluid transfer between the PrLTF and the PoLTF. Evaporation depletes the PrLTF, and continued evaporation causes depletion of the PoLTF via fluid loss through the CL. Governing equations include Navier-Stokes, heat and Darcy's equations for the fluid flow and heat transfer in the PrLTF and porous layer. The PoLTF is modelled by a fixed pressure condition on the posterior surface of the CL. The original model is simplified using lubrication theory for the PrLTF and CL applied to a sagittal plane through the eye. We obtain a partial differential equation (PDE) for the PrLTF thickness that is first-order in time and fourth-order in space. This model incorporates evaporation, conjoining pressure effects in the PrLTF, capillarity and heat transfer. For a planar film, we find that this PDE can be reduced to an ordinary differential equation (ODE) that can be solved analytically or numerically. This reduced model allows for interpretation of the various system parameters and captures most of the basic physics contained in the model. Comparisons of ODE and PDE models, including estimates for the loss of fluid through the lens due to evaporation, are given. © The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Comparison of artificial intelligence methods and empirical equations to estimate daily solar radiation

NASA Astrophysics Data System (ADS)

Mehdizadeh, Saeid; Behmanesh, Javad; Khalili, Keivan

2016-08-01

In the present research, three artificial intelligence methods including Gene Expression Programming (GEP), Artificial Neural Networks (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) as well as, 48 empirical equations (10, 12 and 26 equations were temperature-based, sunshine-based and meteorological parameters-based, respectively) were used to estimate daily solar radiation in Kerman, Iran in the period of 1992-2009. To develop the GEP, ANN and ANFIS models, depending on the used empirical equations, various combinations of minimum air temperature, maximum air temperature, mean air temperature, extraterrestrial radiation, actual sunshine duration, maximum possible sunshine duration, sunshine duration ratio, relative humidity and precipitation were considered as inputs in the mentioned intelligent methods. To compare the accuracy of empirical equations and intelligent models, root mean square error (RMSE), mean absolute error (MAE), mean absolute relative error (MARE) and determination coefficient (R2) indices were used. The results showed that in general, sunshine-based and meteorological parameters-based scenarios in ANN and ANFIS models presented high accuracy than mentioned empirical equations. Moreover, the most accurate method in the studied region was ANN11 scenario with five inputs. The values of RMSE, MAE, MARE and R2 indices for the mentioned model were 1.850 MJ m-2 day-1, 1.184 MJ m-2 day-1, 9.58% and 0.935, respectively.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

Analysis of control system responses for aircraft stability and efficient numerical techniques for real-time simulations

NASA Astrophysics Data System (ADS)

Stroe, Gabriela; Andrei, Irina-Carmen; Frunzulica, Florin

2017-01-01

The objectives of this paper are the study and the implementation of both aerodynamic and propulsion models, as linear interpolations using look-up tables in a database. The aerodynamic and propulsion dependencies on state and control variable have been described by analytic polynomial models. Some simplifying hypotheses were made in the development of the nonlinear aircraft simulations. The choice of a certain technique to use depends on the desired accuracy of the solution and the computational effort to be expended. Each nonlinear simulation includes the full nonlinear dynamics of the bare airframe, with a scaled direct connection from pilot inputs to control surface deflections to provide adequate pilot control. The engine power dynamic response was modeled with an additional state equation as first order lag in the actual power level response to commanded power level was computed as a function of throttle position. The number of control inputs and engine power states varied depending on the number of control surfaces and aircraft engines. The set of coupled, nonlinear, first-order ordinary differential equations that comprise the simulation model can be represented by the vector differential equation. A linear time-invariant (LTI) system representing aircraft dynamics for small perturbations about a reference trim condition is given by the state and output equations present. The gradients are obtained numerically by perturbing each state and control input independently and recording the changes in the trimmed state and output equations. This is done using the numerical technique of central finite differences, including the perturbations of the state and control variables. For a reference trim condition of straight and level flight, linearization results in two decoupled sets of linear, constant-coefficient differential equations for longitudinal and lateral / directional motion. The linearization is valid for small perturbations about the reference trim condition. Experimental aerodynamic and thrust data are used to model the applied aerodynamic and propulsion forces and moments for arbitrary states and controls. There is no closed form solution to such problems, so the equations must be solved using numerical integration. Techniques for solving this initial value problem for ordinary differential equations are employed to obtain approximate solutions at discrete points along the aircraft state trajectory.

Non-Riemannian geometry, Born-Infeld models and trace free gravitational equations

NASA Astrophysics Data System (ADS)

Cirilo-Lombardo, Diego Julio

2017-12-01

Non-Riemannian generalization of the standard Born-Infeld (BI) Lagrangian is introduced and analyzed from a theory of gravitation with dynamical torsion field. The field equations derived from the proposed action lead to a trace free gravitational equation (non-Riemannian analog to the trace free equation (TFE) from Finkelstein et al., 2001; Ellis et al., 2011; Ellis, 2014) and the field equations for the torsion respectively. In this theoretical context, the fundamental constants arise all from the same geometry through geometrical invariant quantities (as from the curvature R). New results involving generation of primordial magnetic fields and the link with leptogenesis and baryogenesis are presented and possible explanations given. The physically admissible matter fields can be introduced in the model via the torsion vector hμ. Such fields include some dark matter candidates such as axion, right neutrinos and Majorana and moreover, physical observables as vorticity can be included in the same way. From a new wormhole solution in a cosmological spacetime with torsion we also show that the primordial cosmic magnetic fields can originate from hμ with the axion field (that is contained in hμ) the responsible to control the dynamics and stability of the cosmic magnetic field but not the magnetogenesis itself. As we pointed out before (Cirilo-Lombardo, 2017), the analysis of Grand Unified Theories (GUT) in the context of this model indicates that the group manifold candidates are based in SO (10), SU (5) or some exceptional groups as E (6), E (7) , etc.

Center manifolds for a class of degenerate evolution equations and existence of small-amplitude kinetic shocks

NASA Astrophysics Data System (ADS)

Pogan, Alin; Zumbrun, Kevin

2018-06-01

We construct center manifolds for a class of degenerate evolution equations including the steady Boltzmann equation and related kinetic models, establishing in the process existence and behavior of small-amplitude kinetic shock and boundary layers. Notably, for Boltzmann's equation, we show that elements of the center manifold decay in velocity at near-Maxwellian rate, in accord with the formal Chapman-Enskog picture of near-equilibrium flow as evolution along the manifold of Maxwellian states, or Grad moment approximation via Hermite polynomials in velocity. Our analysis is from a classical dynamical systems point of view, with a number of interesting modifications to accommodate ill-posedness of the underlying evolution equation.

Model of formation of droplets during electric arc surfacing of functional coatings

NASA Astrophysics Data System (ADS)

Sarychev, Vladimir D.; Granovskii, Alexei Yu; Nevskii, Sergey A.; Gromov, Victor E.

2016-01-01

The mathematical model was developed for the initial stage of formation of an electrode metal droplet in the process of arc welding. Its essence lies in the fact that the presence of a temperature gradient in the boundary layer of the molten metal causes thermo-capillary instability, which leads to the formation of electrode metal droplets. A system of equations including Navier-Stokes equations, heat conduction and Maxwell's equations was solved as well as the boundary conditions for the system electrodes-plasma. Dispersion equation for thermo-capillary waves in the linear approximation for the plane layer was received and analyzed. The values of critical wavelengths, at which thermo-capillary instability appears in the nanometer wavelength range, were found. The parameters at which the mode of a fine-droplet transfer of the material takes place were theoretically defined.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

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

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

The usefulness of “corrected” body mass index vs. self-reported body mass index: comparing the population distributions, sensitivity, specificity, and predictive utility of three correction equations using Canadian population-based data

PubMed Central

2014-01-01

Background National data on body mass index (BMI), computed from self-reported height and weight, is readily available for many populations including the Canadian population. Because self-reported weight is found to be systematically under-reported, it has been proposed that the bias in self-reported BMI can be corrected using equations derived from data sets which include both self-reported and measured height and weight. Such correction equations have been developed and adopted. We aim to evaluate the usefulness (i.e., distributional similarity; sensitivity and specificity; and predictive utility vis-à-vis disease outcomes) of existing and new correction equations in population-based research. Methods The Canadian Community Health Surveys from 2005 and 2008 include both measured and self-reported values of height and weight, which allows for construction and evaluation of correction equations. We focused on adults age 18–65, and compared three correction equations (two correcting weight only, and one correcting BMI) against self-reported and measured BMI. We first compared population distributions of BMI. Second, we compared the sensitivity and specificity of self-reported BMI and corrected BMI against measured BMI. Third, we compared the self-reported and corrected BMI in terms of association with health outcomes using logistic regression. Results All corrections outperformed self-report when estimating the full BMI distribution; the weight-only correction outperformed the BMI-only correction for females in the 23–28 kg/m2 BMI range. In terms of sensitivity/specificity, when estimating obesity prevalence, corrected values of BMI (from any equation) were superior to self-report. In terms of modelling BMI-disease outcome associations, findings were mixed, with no correction proving consistently superior to self-report. Conclusions If researchers are interested in modelling the full population distribution of BMI, or estimating the prevalence of obesity in a population, then a correction of any kind included in this study is recommended. If the researcher is interested in using BMI as a predictor variable for modelling disease, then both self-reported and corrected BMI result in biased estimates of association. PMID:24885210

Multipath analysis diffraction calculations

NASA Technical Reports Server (NTRS)

Statham, Richard B.

1996-01-01

This report describes extensions of the Kirchhoff diffraction equation to higher edge terms and discusses their suitability to model diffraction multipath effects of a small satellite structure. When receiving signals, at a satellite, from the Global Positioning System (GPS), reflected signals from the satellite structure result in multipath errors in the determination of the satellite position. Multipath error can be caused by diffraction of the reflected signals and a method of calculating this diffraction is required when using a facet model of the satellite. Several aspects of the Kirchhoff equation are discussed and numerical examples, in the near and far fields, are shown. The vector form of the extended Kirchhoff equation, by adding the Larmor-Tedone and Kottler edge terms, is given as a mathematical model in an appendix. The Kirchhoff equation was investigated as being easily implemented and of good accuracy in the basic form, especially in phase determination. The basic Kirchhoff can be extended for higher accuracy if desired. A brief discussion of the method of moments and the geometric theory of diffraction is included, but seems to offer no clear advantage in implementation over the Kirchhoff for facet models.

Kinetics of wealth and the Pareto law

NASA Astrophysics Data System (ADS)

Boghosian, Bruce M.

2014-04-01

An important class of economic models involve agents whose wealth changes due to transactions with other agents. Several authors have pointed out an analogy with kinetic theory, which describes molecules whose momentum and energy change due to interactions with other molecules. We pursue this analogy and derive a Boltzmann equation for the time evolution of the wealth distribution of a population of agents for the so-called Yard-Sale Model of wealth exchange. We examine the solutions to this equation by a combination of analytical and numerical methods and investigate its long-time limit. We study an important limit of this equation for small transaction sizes and derive a partial integrodifferential equation governing the evolution of the wealth distribution in a closed economy. We then describe how this model can be extended to include features such as inflation, production, and taxation. In particular, we show that the model with taxation exhibits the basic features of the Pareto law, namely, a lower cutoff to the wealth density at small values of wealth, and approximate power-law behavior at large values of wealth.

Modeling of the heat transfer in bypass transitional boundary-layer flows

NASA Technical Reports Server (NTRS)

Simon, Frederick F.; Stephens, Craig A.

1991-01-01

A low Reynolds number k-epsilon turbulence model and conditioned momentum, energy and turbulence equations were used to predict bypass transition heat transfer on a flat plate in a high-disturbance environment with zero pressure gradient. The use of conditioned equations was demonstrated to be an improvement over the use of the global-time-averaged equations for the calculation of velocity profiles and turbulence intensity profiles in the transition region of a boundary layer. The approach of conditioned equations is extended to include heat transfer and a modeling of transition events is used to predict transition onset and the extent of transition on a flat plate. The events, which describe the boundary layer at the leading edge, result in boundary-layer regions consisting of: (1) the laminar, (2) pseudolaminar, (3) transitional, and (4) turbulent boundary layers. The modeled transition events were incorporated into the TEXSTAN 2-D boundary-layer code which is used to numerically predict the heat transfer. The numerical predictions in general compared well with the experimental data and revealed areas where additional experimental information is needed.

Population Modelling with M&M's[R

ERIC Educational Resources Information Center

Winkel, Brian

2009-01-01

Several activities in which population dynamics can be modelled by tossing M&M's[R] candy are presented. Physical activities involving M&M's[R] can be modelled by difference equations and several population phenomena, including death and immigration, are studied. (Contains 1 note.)

An ill-posed problem for the Black-Scholes equation for a profitable forecast of prices of stock options on real market data

NASA Astrophysics Data System (ADS)

Klibanov, Michael V.; Kuzhuget, Andrey V.; Golubnichiy, Kirill V.

2016-01-01

A new empirical mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock, new initial and new boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. To verify the validity of our model, real market data for 368 randomly selected liquid options are used. A new trading strategy is proposed. Our results indicates that our method is profitable on those options. Furthermore, it is shown that the performance of two simple extrapolation-based techniques is much worse. We conjecture that our method might lead to significant profits of those financial insitutions which trade large amounts of options. We caution, however, that further studies are necessary to verify this conjecture.

Diffuse-Interface Modelling of Flow in Porous Media

NASA Astrophysics Data System (ADS)

Addy, Doug; Pradas, Marc; Schmuck, Marcus; Kalliadasis, Serafim

2016-11-01

Multiphase flows are ubiquitous in a wide spectrum of scientific and engineering applications, and their computational modelling often poses many challenges associated with the presence of free boundaries and interfaces. Interfacial flows in porous media encounter additional challenges and complexities due to their inherently multiscale behaviour. Here we investigate the dynamics of interfaces in porous media using an effective convective Cahn-Hilliard (CH) equation recently developed in from a Stokes-CH equation for microscopic heterogeneous domains by means of a homogenization methodology, where the microscopic details are taken into account as effective tensor coefficients which are given by a Poisson equation. The equations are decoupled under appropriate assumptions and solved in series using a classic finite-element formulation with the open-source software FEniCS. We investigate the effects of different microscopic geometries, including periodic and non-periodic, at the bulk fluid flow, and find that our model is able to describe the effective macroscopic behaviour without the need to resolve the microscopic details.

Global boundary flattening transforms for acoustic propagation under rough sea surfaces.

PubMed

Oba, Roger M

2010-07-01

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.

General Rotorcraft Aeromechanical Stability Program (GRASP): Theory manual

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Hopkins, A. Stewart; Kunz, Donald L.; Hinnant, Howard E.

1990-01-01

The general rotorcraft aeromechanical stability program (GRASP) was developed to calculate aeroelastic stability for rotorcraft in hovering flight, vertical flight, and ground contact conditions. GRASP is described in terms of its capabilities and its philosophy of modeling. The equations of motion that govern the physical system are described, as well as the analytical approximations used to derive them. The equations include the kinematical equation, the element equations, and the constraint equations. In addition, the solution procedures used by GRASP are described. GRASP is capable of treating the nonlinear static and linearized dynamic behavior of structures represented by arbitrary collections of rigid-body and beam elements. These elements may be connected in an arbitrary fashion, and are permitted to have large relative motions. The main limitation of this analysis is that periodic coefficient effects are not treated, restricting rotorcraft flight conditions to hover, axial flight, and ground contact. Instead of following the methods employed in other rotorcraft programs. GRASP is designed to be a hybrid of the finite-element method and the multibody methods used in spacecraft analysis. GRASP differs from traditional finite-element programs by allowing multiple levels of substructure in which the substructures can move and/or rotate relative to others with no small-angle approximations. This capability facilitates the modeling of rotorcraft structures, including the rotating/nonrotating interface and the details of the blade/root kinematics for various types. GRASP differs from traditional multibody programs by considering aeroelastic effects, including inflow dynamics (simple unsteady aerodynamics) and nonlinear aerodynamic coefficients.

Waves in magnetized quark matter

NASA Astrophysics Data System (ADS)

Fogaça, D. A.; Sanches, S. M.; Navarra, F. S.

2018-05-01

We study wave propagation in a non-relativistic cold quark-gluon plasma immersed in a constant magnetic field. Starting from the Euler equation we derive linear wave equations and investigate their stability and causality. We use a generic form for the equation of state, the EOS derived from the MIT bag model and also a variant of the this model which includes gluon degrees of freedom. The results of this analysis may be relevant for perturbations propagating through the quark matter phase in the core of compact stars and also for perturbations propagating in the low temperature quark-gluon plasma formed in low energy heavy ion collisions, to be carried out at FAIR and NICA.

Maximal regularity in lp spaces for discrete time fractional shifted equations

NASA Astrophysics Data System (ADS)

Lizama, Carlos; Murillo-Arcila, Marina

2017-09-01

In this paper, we are presenting a new method based on operator-valued Fourier multipliers to characterize the existence and uniqueness of ℓp-solutions for discrete time fractional models in the form where A is a closed linear operator defined on a Banach space X and Δα denotes the Grünwald-Letnikov fractional derivative of order α > 0. If X is a UMD space, we provide this characterization only in terms of the R-boundedness of the operator-valued symbol associated to the abstract model. To illustrate our results, we derive new qualitative properties of nonlinear difference equations with shiftings, including fractional versions of the logistic and Nagumo equations.

SU(N) affine Toda solitons and breathers from transparent Dirac potentials

NASA Astrophysics Data System (ADS)

Thies, Michael

2017-05-01

Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1  +  1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-de Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multi-soliton and multi-breather solutions of su(N) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.

Couple stress theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

Equivalent circuit-level model of quantum cascade lasers with integrated hot-electron and hot-phonon effects

NASA Astrophysics Data System (ADS)

Yousefvand, H. R.

2017-12-01

We report a study of the effects of hot-electron and hot-phonon dynamics on the output characteristics of quantum cascade lasers (QCLs) using an equivalent circuit-level model. The model is developed from the energy balance equation to adopt the electron temperature in the active region levels, the heat transfer equation to include the lattice temperature, the nonequilibrium phonon rate to account for the hot phonon dynamics and simplified two-level rate equations to incorporate the carrier and photon dynamics in the active region. This technique simplifies the description of the electron-phonon interaction in QCLs far from the equilibrium condition. Using the presented model, the steady and transient responses of the QCLs for a wide range of sink temperatures (80 to 320 K) are investigated and analysed. The model enables us to explain the operating characteristics found in QCLs. This predictive model is expected to be applicable to all QCL material systems operating in pulsed and cw regimes.

'Constraint consistency' at all orders in cosmological perturbation theory

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

Nandi, Debottam; Shankaranarayanan, S., E-mail: debottam@iisertvm.ac.in, E-mail: shanki@iisertvm.ac.in

2015-08-01

We study the equivalence of two—order-by-order Einstein's equation and Reduced action—approaches to cosmological perturbation theory at all orders for different models of inflation. We point out a crucial consistency check which we refer to as 'Constraint consistency' condition that needs to be satisfied in order for the two approaches to lead to identical single variable equation of motion. The method we propose here is quick and efficient to check the consistency for any model including modified gravity models. Our analysis points out an important feature which is crucial for inflationary model building i.e., all 'constraint' inconsistent models have higher ordermore » Ostrogradsky's instabilities but the reverse is not true. In other words, one can have models with constraint Lapse function and Shift vector, though it may have Ostrogradsky's instabilities. We also obtain single variable equation for non-canonical scalar field in the limit of power-law inflation for the second-order perturbed variables.« less

Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1, 1)

NASA Astrophysics Data System (ADS)

Chen, Chun-I.; Chen, Hong Long; Chen, Shuo-Pei

2008-08-01

The traditional Grey Model is easy to understand and simple to calculate, with satisfactory accuracy, but it is also lack of flexibility to adjust the model to acquire higher forecasting precision. This research studies feasibility and effectiveness of a novel Grey model together with the concept of the Bernoulli differential equation in ordinary differential equation. In this research, the author names this newly proposed model as Nonlinear Grey Bernoulli Model (NGBM). The NGBM is nonlinear differential equation with power index n. By controlling n, the curvature of the solution curve could be adjusted to fit the result of one time accumulated generating operation (1-AGO) of raw data. One extreme case from Grey system textbook is studied by NGBM, and two published articles are chosen for practical tests of NGBM. The results prove the novel NGBM is feasible and efficient. Finally, NGBM is used to forecast 2005 foreign exchange rates of twelve Taiwan major trading partners, including Taiwan.

A FORTRAN program for interpretation of relative permeability from unsteady-state displacements with capillary pressure included

USGS Publications Warehouse

Udegbunam, E.O.

1991-01-01

This paper presents a FORTRAN program for the determination of two-phase relative permeabilities from unsteady-state displacement data with capillary pressure terms included. The interpretative model employed in this program combines the simultaneous solution of a variant of the fractional flow equation which includes a capillary pressure term and an integro-differential equation derived from Darcy's law without assuming the simplified Buckley-Leverett flow. The incorporation of capillary pressure in the governing equations dispenses with the high flowrate experimental requirements normally employed to overcome capillarity effects. An illustrative example is presented herein which implements this program for the determination of oil/water relative permeabilities from a sandstone core sample. Results obtained compares favorably with results previously given in the literature. ?? 1991.

Wind Factor Simulation Model: User’s Manual.

DTIC Science & Technology

1980-04-01

computer program documentation; com- puterized simulation; equivalent headwind technique; great circle; great circle distance; great circle equation ; great... equation of a great circle. Program listing and flow chart are included. iv UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(WIh.n Date EnItrd) USER’S...THE EQUATOR . 336 C 337 NTRIFG = 0 338 C 339 C END OF FUNCTION ICONV I 1. RETURN TO MAIN PROGRAM . 340 C 42 341 RETURN 34? C 343 C 344 C 345 C * PART II

BOOK REVIEW: Statistical Mechanics of Turbulent Flows

NASA Astrophysics Data System (ADS)

Cambon, C.

2004-10-01

This is a handbook for a computational approach to reacting flows, including background material on statistical mechanics. In this sense, the title is somewhat misleading with respect to other books dedicated to the statistical theory of turbulence (e.g. Monin and Yaglom). In the present book, emphasis is placed on modelling (engineering closures) for computational fluid dynamics. The probabilistic (pdf) approach is applied to the local scalar field, motivated first by the nonlinearity of chemical source terms which appear in the transport equations of reacting species. The probabilistic and stochastic approaches are also used for the velocity field and particle position; nevertheless they are essentially limited to Lagrangian models for a local vector, with only single-point statistics, as for the scalar. Accordingly, conventional techniques, such as single-point closures for RANS (Reynolds-averaged Navier-Stokes) and subgrid-scale models for LES (large-eddy simulations), are described and in some cases reformulated using underlying Langevin models and filtered pdfs. Even if the theoretical approach to turbulence is not discussed in general, the essentials of probabilistic and stochastic-processes methods are described, with a useful reminder concerning statistics at the molecular level. The book comprises 7 chapters. Chapter 1 briefly states the goals and contents, with a very clear synoptic scheme on page 2. Chapter 2 presents definitions and examples of pdfs and related statistical moments. Chapter 3 deals with stochastic processes, pdf transport equations, from Kramer-Moyal to Fokker-Planck (for Markov processes), and moments equations. Stochastic differential equations are introduced and their relationship to pdfs described. This chapter ends with a discussion of stochastic modelling. The equations of fluid mechanics and thermodynamics are addressed in chapter 4. Classical conservation equations (mass, velocity, internal energy) are derived from their counterparts at the molecular level. In addition, equations are given for multicomponent reacting systems. The chapter ends with miscellaneous topics, including DNS, (idea of) the energy cascade, and RANS. Chapter 5 is devoted to stochastic models for the large scales of turbulence. Langevin-type models for velocity (and particle position) are presented, and their various consequences for second-order single-point corelations (Reynolds stress components, Kolmogorov constant) are discussed. These models are then presented for the scalar. The chapter ends with compressible high-speed flows and various models, ranging from k-epsilon to hybrid RANS-pdf. Stochastic models for small-scale turbulence are addressed in chapter 6. These models are based on the concept of a filter density function (FDF) for the scalar, and a more conventional SGS (sub-grid-scale model) for the velocity in LES. The final chapter, chapter 7, is entitled `The unification of turbulence models' and aims at reconciling large-scale and small-scale modelling. This book offers a timely survey of techniques in modern computational fluid mechanics for turbulent flows with reacting scalars. It should be of interest to engineers, while the discussion of the underlying tools, namely pdfs, stochastic and statistical equations should also be attractive to applied mathematicians and physicists. The book's emphasis on local pdfs and stochastic Langevin models gives a consistent structure to the book and allows the author to cover almost the whole spectrum of practical modelling in turbulent CFD. On the other hand, one might regret that non-local issues are not mentioned explicitly, or even briefly. These problems range from the presence of pressure-strain correlations in the Reynolds stress transport equations to the presence of two-point pdfs in the single-point pdf equation derived from the Navier--Stokes equations. (One may recall that, even without scalar transport, a general closure problem for turbulence statistics results from both non-linearity and non-locality of Navier-Stokes equations, the latter coming from, e.g., the nonlocal relationship of velocity and pressure in the quasi-incompressible case. These two aspects are often intricately linked. It is well known that non-linearity alone is not responsible for the `problem', as evidenced by 1D turbulence without pressure (`Burgulence' from the Burgers equation) and probably 3D (cosmological gas). A local description in terms of pdf for the velocity can resolve the `non-linear' problem, which instead yields an infinite hierarchy of equations in terms of moments. On the other hand, non-locality yields a hierarchy of unclosed equations, with the single-point pdf equation for velocity derived from NS incompressible equations involving a two-point pdf, and so on. The general relationship was given by Lundgren (1967, Phys. Fluids 10 (5), 969-975), with the equation for pdf at n points involving the pdf at n+1 points. The nonlocal problem appears in various statistical models which are not discussed in the book. The simplest example is full RST or ASM models, in which the closure of pressure-strain correlations is pivotal (their counterpart ought to be identified and discussed in equations (5-21) and the following ones). The book does not address more sophisticated non-local approaches, such as two-point (or spectral) non-linear closure theories and models, `rapid distortion theory' for linear regimes, not to mention scaling and intermittency based on two-point structure functions, etc. The book sometimes mixes theoretical modelling and pure empirical relationships, the empirical character coming from the lack of a nonlocal (two-point) approach.) In short, the book is orientated more towards applications than towards turbulence theory; it is written clearly and concisely and should be useful to a large community, interested either in the underlying stochastic formalism or in CFD applications.

Modelling of subgrid-scale phenomena in supercritical transitional mixing layers: an a priori study

NASA Astrophysics Data System (ADS)

Selle, Laurent C.; Okong'o, Nora A.; Bellan, Josette; Harstad, Kenneth G.

A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour.

Evaluation of a Consistent LES/PDF Method Using a Series of Experimental Spray Flames

NASA Astrophysics Data System (ADS)

Heye, Colin; Raman, Venkat

2012-11-01

A consistent method for the evolution of the joint-scalar probability density function (PDF) transport equation is proposed for application to large eddy simulation (LES) of turbulent reacting flows containing evaporating spray droplets. PDF transport equations provide the benefit of including the chemical source term in closed form, however, additional terms describing LES subfilter mixing must be modeled. The recent availability of detailed experimental measurements provide model validation data for a wide range of evaporation rates and combustion regimes, as is well-known to occur in spray flames. In this work, the experimental data will used to investigate the impact of droplet mass loading and evaporation rates on the subfilter scalar PDF shape in comparison with conventional flamelet models. In addition, existing model term closures in the PDF transport equations are evaluated with a focus on their validity in the presence of regime changes.

Four-fluid MHD Simulations of the Plasma and Neutral Gas Environment of Comet Churyumov-Gerasimenko Near Perihelio

NASA Astrophysics Data System (ADS)

Huang, Z.; Toth, G.; Gombosi, T. I.; Jia, X.; Rubin, M.; Hansen, K. C.; Fougere, N.; Bieler, A. M.; Shou, Y.; Altwegg, K.; Combi, M. R.; Tenishev, V.

2015-12-01

The neutral and plasma environment is critical in understanding the interaction of comet Churyumov-Gerasimenko (CG), the target of the Rosetta mission, and the solar wind. To serve this need and support the Rosetta mission, we develop a 3-D four fluid model, which is based on BATS-R-US within the SWMF (Space Weather Modeling Framework) that solves the governing multi-fluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates different mass loading processes, including photo and electron impact ionization, charge exchange, dissociative ion-electron recombination, and collisional interactions between different fluids. We simulate the near nucleus plasma and neutral gas environment near perihelion with a realistic shape model of CG and compare our simulation results with Rosetta observations.

An unstructured grid, three-dimensional model based on the shallow water equations

USGS Publications Warehouse

Casulli, V.; Walters, R.A.

2000-01-01

A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids. There are obvious advantages in using unstructured grids in problems with a complicated geometry. In this development, the concept of unstructured orthogonal grids is introduced and applied to this model. The governing differential equations are discretized by means of a semi-implicit algorithm that is robust, stable and very efficient. The resulting model is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest. Moreover, the simulation of the flooding and drying is included in a natural and straightforward manner. These features are illustrated by a test case for studies of convergence rates and by examples of flooding on a river plain and flow in a shallow estuary. Copyright ?? 2000 John Wiley & Sons, Ltd.

Analysis performance of proton exchange membrane fuel cell (PEMFC)

NASA Astrophysics Data System (ADS)

Mubin, A. N. A.; Bahrom, M. H.; Azri, M.; Ibrahim, Z.; Rahim, N. A.; Raihan, S. R. S.

2017-06-01

Recently, the proton exchange membrane fuel cell (PEMFC) has gained much attention to the technology of renewable energy due to its mechanically ideal and zero emission power source. PEMFC performance reflects from the surroundings such as temperature and pressure. This paper presents an analysis of the performance of the PEMFC by developing the mathematical thermodynamic modelling using Matlab/Simulink. Apart from that, the differential equation of the thermodynamic model of the PEMFC is used to explain the contribution of heat to the performance of the output voltage of the PEMFC. On the other hand, the partial pressure equation of the hydrogen is included in the PEMFC mathematical modeling to study the PEMFC voltage behaviour related to the input variable input hydrogen pressure. The efficiency of the model is 33.8% which calculated by applying the energy conversion device equations on the thermal efficiency. PEMFC’s voltage output performance is increased by increasing the hydrogen input pressure and temperature.

Progress in high-lift aerodynamic calculations

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1993-01-01

The current work presents progress in the effort to numerically simulate the flow over high-lift aerodynamic components, namely, multi-element airfoils and wings in either a take-off or a landing configuration. The computational approach utilizes an incompressible flow solver and an overlaid chimera grid approach. A detailed grid resolution study is presented for flow over a three-element airfoil. Two turbulence models, a one-equation Baldwin-Barth model and a two equation k-omega model are compared. Excellent agreement with experiment is obtained for the lift coefficient at all angles of attack, including the prediction of maximum lift when using the two-equation model. Results for two other flap riggings are shown. Three-dimensional results are presented for a wing with a square wing-tip as a validation case. Grid generation and topology is discussed for computing the flow over a T-39 Sabreliner wing with flap deployed and the initial calculations for this geometry are presented.

Modeling of outgassing and matrix decomposition in carbon-phenolic composites

NASA Technical Reports Server (NTRS)

Mcmanus, Hugh L.

1994-01-01

Work done in the period Jan. - June 1994 is summarized. Two threads of research have been followed. First, the thermodynamics approach was used to model the chemical and mechanical responses of composites exposed to high temperatures. The thermodynamics approach lends itself easily to the usage of variational principles. This thermodynamic-variational approach has been applied to the transpiration cooling problem. The second thread is the development of a better algorithm to solve the governing equations resulting from the modeling. Explicit finite difference method is explored for solving the governing nonlinear, partial differential equations. The method allows detailed material models to be included and solution on massively parallel supercomputers. To demonstrate the feasibility of the explicit scheme in solving nonlinear partial differential equations, a transpiration cooling problem was solved. Some interesting transient behaviors were captured such as stress waves and small spatial oscillations of transient pressure distribution.

Derivation of Hunt equation for suspension distribution using Shannon entropy theory

NASA Astrophysics Data System (ADS)

Kundu, Snehasis

2017-12-01

In this study, the Hunt equation for computing suspension concentration in sediment-laden flows is derived using Shannon entropy theory. Considering the inverse of the void ratio as a random variable and using principle of maximum entropy, probability density function and cumulative distribution function of suspension concentration is derived. A new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of CDF reported in literature. This general form of cumulative distribution function also helps to derive the Rouse equation. The entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory. Finally model parameters in the entropy based model are also expressed as functions of the Rouse number to establish a link between the parameters of the deterministic and probabilistic approaches.

Probing the Interiors of the Ice Giants: Shock Compression of Water to 700 GPa and 3.8 g/cm³

DOE PAGES

Knudson, M. D.; Desjarlais, M. P.; Lemke, R. W.; ...

2012-02-27

Recently, there has been a tremendous increase in the number of identified extrasolar planetary systems. Our understanding of their formation is tied to exoplanet internal structure models, which rely upon equations of state of light elements and compounds such as water. Here, we present shock compression data for water with unprecedented accuracy that show that water equations of state commonly used in planetary modeling significantly overestimate the compressibility at conditions relevant to planetary interiors. Furthermore, we show that its behavior at these conditions, including reflectivity and isentropic response, is well-described by a recent first-principles based equation of state. These findingsmore » advocate that this water model be used as the standard for modeling Neptune, Uranus, and “hot Neptune” exoplanets and should improve our understanding of these types of planets.« less

Neighboring extremal optimal control design including model mismatch errors

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

Kim, T.J.; Hull, D.G.

1994-11-01

The mismatch control technique that is used to simplify model equations of motion in order to determine analytic optimal control laws is extended using neighboring extremal theory. The first variation optimal control equations are linearized about the extremal path to account for perturbations in the initial state and the final constraint manifold. A numerical example demonstrates that the tuning procedure inherent in the mismatch control method increases the performance of the controls to the level of a numerically-determined piecewise-linear controller.

A higher-order split-step Fourier parabolic-equation sound propagation solution scheme.

PubMed

Lin, Ying-Tsong; Duda, Timothy F

2012-08-01

A three-dimensional Cartesian parabolic-equation model with a higher-order approximation to the square-root Helmholtz operator is presented for simulating underwater sound propagation in ocean waveguides. The higher-order approximation includes cross terms with the free-space square-root Helmholtz operator and the medium phase speed anomaly. It can be implemented with a split-step Fourier algorithm to solve for sound pressure in the model. Two idealized ocean waveguide examples are presented to demonstrate the performance of this numerical technique.

The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics

NASA Technical Reports Server (NTRS)

Bayliss, A.; Goldstein, C. I.; Turkel, E.

1984-01-01

The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner.

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

NASA Technical Reports Server (NTRS)

Reese, O. W.

1972-01-01

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Single and Double ITCZ in Aqua-Planet Models with Globally and Temporally Uniform Sea Surface Temperature and Solar Insolation: An Interpretation

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode; Lau, William K. M. (Technical Monitor)

2002-01-01

Previous studies (Chao 2000, Chao and Chen 2001, Kirtman and Schneider 2000, Sumi 1992) have shown that, by means of one of several model design changes, the structure of the ITCZ in an aqua-planet model with globally uniform SST and solar angle (U-SST-SA) can change between a single ITCZ at the equator and a double ITCZ straddling the equator. These model design changes include switching to a different cumulus parameterization scheme (e.g., from relaxed Arakawa Schubert scheme (RAS) to moist convective adjustment scheme (MCA)), changes within the cumulus parameterization scheme, and changes in other aspects of the model, such as horizontal resolution. Sometimes only one component of the double ITCZ shows up; but still this is an ITCZ away from the equator, quite distinct from a single ITCZ over the equator. Since these model results were obtained by different investigators using different models which have yielded reasonable general circulation, they are considered as reliable. Chao and Chen (2001; hereafter CC01) have made an initial attempt to interpret these findings based on the concept of rotational ITCZ attractors that they introduced. The purpose of this paper is to offer a more complete interpretation.

MHD Modeling of the Solar Wind with Turbulence Transport and Heating

NASA Technical Reports Server (NTRS)

Goldstein, M. L.; Usmanov, A. V.; Matthaeus, W. H.; Breech, B.

2009-01-01

We have developed a magnetohydrodynamic model that describes the global axisymmetric steady-state structure of the solar wind near solar minimum with account for transport of small-scale turbulence associated heating. The Reynolds-averaged mass, momentum, induction, and energy equations for the large-scale solar wind flow are solved simultaneously with the turbulence transport equations in the region from 0.3 to 100 AU. The large-scale equations include subgrid-scale terms due to turbulence and the turbulence (small-scale) equations describe the effects of transport and (phenomenologically) dissipation of the MHD turbulence based on a few statistical parameters (turbulence energy, normalized cross-helicity, and correlation scale). The coupled set of equations is integrated numerically for a source dipole field on the Sun by a time-relaxation method in the corotating frame of reference. We present results on the plasma, magnetic field, and turbulence distributions throughout the heliosphere and on the role of the turbulence in the large-scale structure and temperature distribution in the solar wind.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Calculation of the flow field including boundary layer effects for supersonic mixed compression inlets at angles of attack

NASA Technical Reports Server (NTRS)

Vadyak, J.; Hoffman, J. D.

1982-01-01

The flow field in supersonic mixed compression aircraft inlets at angle of attack is calculated. A zonal modeling technique is employed to obtain the solution which divides the flow field into different computational regions. The computational regions consist of a supersonic core flow, boundary layer flows adjacent to both the forebody/centerbody and cowl contours, and flow in the shock wave boundary layer interaction regions. The zonal modeling analysis is described and some computational results are presented. The governing equations for the supersonic core flow form a hyperbolic system of partial differential equations. The equations for the characteristic surfaces and the compatibility equations applicable along these surfaces are derived. The characteristic surfaces are the stream surfaces, which are surfaces composed of streamlines, and the wave surfaces, which are surfaces tangent to a Mach conoid. The compatibility equations are expressed as directional derivatives along streamlines and bicharacteristics, which are the lines of tangency between a wave surface and a Mach conoid.

A theoretical study of radar return and radiometric emission from the sea

NASA Technical Reports Server (NTRS)

Peake, W. H.

1972-01-01

The applicability of the various electromagnetic models of scattering from the ocean are reviewed. These models include the small perturbation method, the geometric optics solution, the composite model, and the exact integral equation solution. The restrictions on the electromagnetic models are discussed.

Model parameter uncertainty analysis for an annual field-scale P loss model

NASA Astrophysics Data System (ADS)

Bolster, Carl H.; Vadas, Peter A.; Boykin, Debbie

2016-08-01

Phosphorous (P) fate and transport models are important tools for developing and evaluating conservation practices aimed at reducing P losses from agricultural fields. Because all models are simplifications of complex systems, there will exist an inherent amount of uncertainty associated with their predictions. It is therefore important that efforts be directed at identifying, quantifying, and communicating the different sources of model uncertainties. In this study, we conducted an uncertainty analysis with the Annual P Loss Estimator (APLE) model. Our analysis included calculating parameter uncertainties and confidence and prediction intervals for five internal regression equations in APLE. We also estimated uncertainties of the model input variables based on values reported in the literature. We then predicted P loss for a suite of fields under different management and climatic conditions while accounting for uncertainties in the model parameters and inputs and compared the relative contributions of these two sources of uncertainty to the overall uncertainty associated with predictions of P loss. Both the overall magnitude of the prediction uncertainties and the relative contributions of the two sources of uncertainty varied depending on management practices and field characteristics. This was due to differences in the number of model input variables and the uncertainties in the regression equations associated with each P loss pathway. Inspection of the uncertainties in the five regression equations brought attention to a previously unrecognized limitation with the equation used to partition surface-applied fertilizer P between leaching and runoff losses. As a result, an alternate equation was identified that provided similar predictions with much less uncertainty. Our results demonstrate how a thorough uncertainty and model residual analysis can be used to identify limitations with a model. Such insight can then be used to guide future data collection and model development and evaluation efforts.

Design of driving control strategy of torque distribution for two - wheel independent drive electric vehicle

NASA Astrophysics Data System (ADS)

Zhang, Chuanwei; Zhang, Dongsheng; Wen, Jianping

2018-02-01

In order to coordinately control the torque distribution of existing two-wheel independent drive electric vehicle, and improve the energy efficiency and control stability of the whole vehicle, the control strategies based on fuzzy control were designed which adopt the direct yaw moment control as the main line. For realizing the torque coordination simulation of the two-wheel independent drive vehicle, the vehicle model, motor model and tire model were built, including the vehicle 7 - DOF dynamics model, motion equation, torque equation. Finally, in the Carsim - Simulink joint simulation platform, the feasibility of the drive control strategy was verified.

Analysis and synthesis of distributed-lumped-active networks by digital computer

NASA Technical Reports Server (NTRS)

1973-01-01

The use of digital computational techniques in the analysis and synthesis of DLA (distributed lumped active) networks is considered. This class of networks consists of three distinct types of elements, namely, distributed elements (modeled by partial differential equations), lumped elements (modeled by algebraic relations and ordinary differential equations), and active elements (modeled by algebraic relations). Such a characterization is applicable to a broad class of circuits, especially including those usually referred to as linear integrated circuits, since the fabrication techniques for such circuits readily produce elements which may be modeled as distributed, as well as the more conventional lumped and active ones.

Computer model of one-dimensional equilibrium controlled sorption processes

USGS Publications Warehouse

Grove, D.B.; Stollenwerk, K.G.

1984-01-01

A numerical solution to the one-dimensional solute-transport equation with equilibrium-controlled sorption and a first-order irreversible-rate reaction is presented. The computer code is written in FORTRAN language, with a variety of options for input and output for user ease. Sorption reactions include Langmuir, Freundlich, and ion-exchange, with or without equal valance. General equations describing transport and reaction processes are solved by finite-difference methods, with nonlinearities accounted for by iteration. Complete documentation of the code, with examples, is included. (USGS)

The ABC model: a non-hydrostatic toy model for use in convective-scale data assimilation investigations

NASA Astrophysics Data System (ADS)

Petrie, Ruth Elizabeth; Bannister, Ross Noel; Priestley Cullen, Michael John

2017-12-01

In developing methods for convective-scale data assimilation (DA), it is necessary to consider the full range of motions governed by the compressible Navier-Stokes equations (including non-hydrostatic and ageostrophic flow). These equations describe motion on a wide range of timescales with non-linear coupling. For the purpose of developing new DA techniques that suit the convective-scale problem, it is helpful to use so-called toy models that are easy to run and contain the same types of motion as the full equation set. Such a model needs to permit hydrostatic and geostrophic balance at large scales but allow imbalance at small scales, and in particular, it needs to exhibit intermittent convection-like behaviour. Existing toy models are not always sufficient for investigating these issues. A simplified system of intermediate complexity derived from the Euler equations is presented, which supports dispersive gravity and acoustic modes. In this system, the separation of timescales can be greatly reduced by changing the physical parameters. Unlike in existing toy models, this allows the acoustic modes to be treated explicitly and hence inexpensively. In addition, the non-linear coupling induced by the equation of state is simplified. This means that the gravity and acoustic modes are less coupled than in conventional models. A vertical slice formulation is used which contains only dry dynamics. The model is shown to give physically reasonable results, and convective behaviour is generated by localised compressible effects. This model provides an affordable and flexible framework within which some of the complex issues of convective-scale DA can later be investigated. The model is called the ABC model after the three tunable parameters introduced: A (the pure gravity wave frequency), B (the modulation of the divergent term in the continuity equation), and C (defining the compressibility).

Development of the Galaxy Chronic Obstructive Pulmonary Disease (COPD) Model Using Data from ECLIPSE: Internal Validation of a Linked-Equations Cohort Model.

PubMed

Briggs, Andrew H; Baker, Timothy; Risebrough, Nancy A; Chambers, Mike; Gonzalez-McQuire, Sebastian; Ismaila, Afisi S; Exuzides, Alex; Colby, Chris; Tabberer, Maggie; Muellerova, Hana; Locantore, Nicholas; Rutten van Mölken, Maureen P M H; Lomas, David A

2017-05-01

The recent joint International Society for Pharmacoeconomics and Outcomes Research / Society for Medical Decision Making Modeling Good Research Practices Task Force emphasized the importance of conceptualizing and validating models. We report a new model of chronic obstructive pulmonary disease (COPD) (part of the Galaxy project) founded on a conceptual model, implemented using a novel linked-equation approach, and internally validated. An expert panel developed a conceptual model including causal relationships between disease attributes, progression, and final outcomes. Risk equations describing these relationships were estimated using data from the Evaluation of COPD Longitudinally to Identify Predictive Surrogate Endpoints (ECLIPSE) study, with costs estimated from the TOwards a Revolution in COPD Health (TORCH) study. Implementation as a linked-equation model enabled direct estimation of health service costs and quality-adjusted life years (QALYs) for COPD patients over their lifetimes. Internal validation compared 3 years of predicted cohort experience with ECLIPSE results. At 3 years, the Galaxy COPD model predictions of annual exacerbation rate and annual decline in forced expiratory volume in 1 second fell within the ECLIPSE data confidence limits, although 3-year overall survival was outside the observed confidence limits. Projections of the risk equations over time permitted extrapolation to patient lifetimes. Averaging the predicted cost/QALY outcomes for the different patients within the ECLIPSE cohort gives an estimated lifetime cost of £25,214 (undiscounted)/£20,318 (discounted) and lifetime QALYs of 6.45 (undiscounted/5.24 [discounted]) per ECLIPSE patient. A new form of model for COPD was conceptualized, implemented, and internally validated, based on a series of linked equations using epidemiological data (ECLIPSE) and cost data (TORCH). This Galaxy model predicts COPD outcomes from treatment effects on disease attributes such as lung function, exacerbations, symptoms, or exercise capacity; further external validation is required.

One-Dimensional Transport with Inflow and Storage (OTIS): A Solute Transport Model for Streams and Rivers

USGS Publications Warehouse

Runkel, Robert L.

1998-01-01

OTIS is a mathematical simulation model used to characterize the fate and transport of water-borne solutes in streams and rivers. The governing equation underlying the model is the advection-dispersion equation with additional terms to account for transient storage, lateral inflow, first-order decay, and sorption. This equation and the associated equations describing transient storage and sorption are solved using a Crank-Nicolson finite-difference solution. OTIS may be used in conjunction with data from field-scale tracer experiments to quantify the hydrologic parameters affecting solute transport. This application typically involves a trial-and-error approach wherein parameter estimates are adjusted to obtain an acceptable match between simulated and observed tracer concentrations. Additional applications include analyses of nonconservative solutes that are subject to sorption processes or first-order decay. OTIS-P, a modified version of OTIS, couples the solution of the governing equation with a nonlinear regression package. OTIS-P determines an optimal set of parameter estimates that minimize the squared differences between the simulated and observed concentrations, thereby automating the parameter estimation process. This report details the development and application of OTIS and OTIS-P. Sections of the report describe model theory, input/output specifications, sample applications, and installation instructions.

A quadrature based method of moments for nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin L.; Vedula, Prakash

2011-09-01

Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

Fortran Programs for Weapon Systems Analysis

DTIC Science & Technology

1990-06-01

interested in ballistics and related work. The programs include skeletal combat models , a set of discrete-event timing routines, mathematical and...32 4.3 LinEqs: Solve Linear Equations Like a Textbook ........................................................................... 34...military applications as it is of computer science. This crisis occurs in all fields, including the modeling of logistics, mobility, ballistics, and combat

A New Reynolds Stress Algebraic Equation Model

NASA Technical Reports Server (NTRS)

Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

1994-01-01

A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

Initialization and assimilation of cloud and rainwater in a regional model

NASA Technical Reports Server (NTRS)

Raymond, William H.; Olson, William S.

1990-01-01

The initialization and assimilation of cloud and rainwater quantities in a mesoscale regional model was examined. Forecasts of explicit cloud and rainwater are made using conservation equations. The physical processes include condensation, evaporation, autoconversion, accretion, and the removal of rainwater by fallout. These physical processes, some of which are parameterized, represent source and sink in terms in the conservation equations. The question of how to initialize the explicit liquid water calculations in numerical models and how to retain information about precipitation processes during the 4-D assimilation cycle are important issues that are addressed.

Combustion-acoustic stability analysis for premixed gas turbine combustors

NASA Technical Reports Server (NTRS)

Darling, Douglas; Radhakrishnan, Krishnan; Oyediran, Ayo; Cowan, Lizabeth

1995-01-01

Lean, prevaporized, premixed combustors are susceptible to combustion-acoustic instabilities. A model was developed to predict eigenvalues of axial modes for combustion-acoustic interactions in a premixed combustor. This work extends previous work by including variable area and detailed chemical kinetics mechanisms, using the code LSENS. Thus the acoustic equations could be integrated through the flame zone. Linear perturbations were made of the continuity, momentum, energy, chemical species, and state equations. The qualitative accuracy of our approach was checked by examining its predictions for various unsteady heat release rate models. Perturbations in fuel flow rate are currently being added to the model.

Factors Affecting the Latitudinal Location of the Intertropical Convergence Zone in a GCM

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode

2002-01-01

The dominant role of the latitudinal peak of the sea surface temperature (SST) in determining the latitudinal location of the intertropical convergence zone (ITCZ) is well-known. However, the roles of the other factors are less well-known and are the topic of this study. These other factors include the inertial stability, the interaction between convection and surface fluxes and the interaction between convection and radiation. Since these interactions involve convection, in a model they involve the cumulus parameterization scheme. These factors are studied with a general circulation model with uniform SST and solar angle. Under the aforementioned model settings, the latitudinal location of the ITCZ is the latitude where the balance of two types of attraction on the ITCZ, both due to earth's rotation, exists. Directly related to the Coriolis parameter, the first type pulls the ITCZ toward the equator and is not sensitive to model design changes. Related to the convective circulation, the second type pulls the ITCZ poleward and is sensitive to model design changes. Due to the shape and the magnitude of the attractors, the balance of the two types of attractions is reached either at the equator or more than 10 degrees away from the equator. The former case results in a single ITCZ over the equator and the latter case a double ITCZ straddling the equator.

A model for simulation of flow in singular and interconnected channels

USGS Publications Warehouse

Schaffranek, Raymond W.; Baltzer, R.A.; Goldberg, D.E.

1981-01-01

A one-dimensional numerical model is presented for simulating the unsteady flow in singular riverine or estuarine reaches and in networks of reaches composed of interconnected channels. The model is both general and flexible in that it can be used to simulate a wide range of flow conditions for various channel configurations. The channel geometry of the network to be modeled should be sufficiently simple so as to lend itself to characterization in one spatial dimension. The flow must be substantially homogenous in density, and hydrostatic pressure must prevail everywhere in the network channels. The slope of each channel bottom ought to be mild and reasonably constant over its length so that the flow remains subcritical. The model accommodates tributary inflows and diversions and includes the effects of wind shear on the water surface as a forcing function in the flow equations. Water-surface elevations and flow discharges are computed at channel junctions, as well as at specified intermediate locations within the network channels. The one-dimensional branch-network flow model uses a four-point, implicit, finite-difference approximation of the unsteady-flow equations. The flow equations are linearized over a time step, and branch transformations are formulated that describe the relationship between the unknowns at the end points of the channels. The resultant matrix of branch-transformation equations and required boundary-condition equations is solved by Gaussian elimination using maximum pivot strategy. Five example applications of the flow model are illustrated. The applications cover such diverse conditions as a singular upland river reach in which unsteady flow results from hydropower regulations, coastal rivers composed of sequentially connected reaches subject to unsteady tide-driven flow, and a multiply connected network of channels whose flow is principally governed by wind tides and seiches in adjoining lakes. The report includes a listing of the FORTRAN IV computer program and a description of the input data requirements. Model supporting programs for the processing and input of initial and boundary-value data are identified, various model output formats are illustrated, and instructions are given to permit the production of graphical output using the line printer, electromechanical pen plotters, cathode-ray-tube display units, or microfilm recorders.

A critical evaluation of two-equation models for near wall turbulence

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Abid, Ridha; Anderson, E. Clay

1990-01-01

A variety of two-equation turbulence models,including several versions of the K-epsilon model as well as the K-omega model, are analyzed critically for near wall turbulent flows from a theoretical and computational standpoint. It is shown that the K-epsilon model has two major problems associated with it: the lack of natural boundary conditions for the dissipation rate and the appearance of higher-order correlations in the balance of terms for the dissipation rate at the wall. In so far as the former problem is concerned, either physically inconsistent boundary conditions have been used or the boundary conditions for the dissipation rate have been tied to higher-order derivatives of the turbulent kinetic energy which leads to numerical stiffness. The K-omega model can alleviate these problems since the asymptotic behavior of omega is known in more detail and since its near wall balance involves only exact viscous terms. However, the modeled form of the omega equation that is used in the literature is incomplete-an exact viscous term is missing which causes the model to behave in an asymptotically inconsistent manner. By including this viscous term and by introducing new wall damping functions with improved asymptotic behavior, a new K-tau model (where tau is identical with 1/omega is turbulent time scale) is developed. It is demonstrated that this new model is computationally robust and yields improved predictions for turbulent boundary layers.

HYDRODYNAMIC SIMULATION OF THE UPPER POTOMAC ESTUARY.

USGS Publications Warehouse

Schaffranck, Raymond W.

1986-01-01

Hydrodynamics of the upper extent of the Potomac Estuary between Indian Head and Morgantown, Md. , are simulated using a two-dimensional model. The model computes water-surface elevations and depth-averaged velocities by numerically integrating finite-difference forms of the equations of mass and momentum conservation using the alternating direction implicit method. The fundamental, non-linear, unsteady-flow equations, upon which the model is formulated, include additional terms to account for Coriolis acceleration and meteorological influences. Preliminary model/prototype data comparisons show agreement to within 9% for tidal flow volumes and phase differences within the measured-data-recording interval. Use of the model to investigate the hydrodynamics and certain aspects of transport within this Potomac Estuary reach is demonstrated. Refs.

Anisotropic constitutive modeling for nickel base single crystal superalloys using a crystallographic approach

NASA Technical Reports Server (NTRS)

Stouffer, D. C.; Sheh, M. Y.

1988-01-01

A micromechanical model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the effect of back stress in single crystals. The results showed that (1) the back stress is orientation dependent; and (2) the back stress state variable in the inelastic flow equation is necessary for predicting anelastic behavior of the material. The model also demonstrated improved fatigue predictive capability. Model predictions and experimental data are presented for single crystal superalloy Rene N4 at 982 C.

Theoretical Analysis of Fas Ligand-Induced Apoptosis with an Ordinary Differential Equation Model.

PubMed

Shi, Zhimin; Li, Yan; Liu, Zhihai; Mi, Jun; Wang, Renxiao

2012-12-01

Upon the treatment of Fas ligand, different types of cells exhibit different apoptotic mechanisms, which are determined by a complex network of biological pathways. In order to derive a quantitative interpretation of the cell sensitivity and apoptosis pathways, we have developed an ordinary differential equation model. Our model is intended to include all of the known major components in apoptosis pathways mediated by Fas receptor. It is composed of 29 equations using a total of 49 rate constants and 13 protein concentrations. All parameters used in our model were derived through nonlinear fitting to experimentally measured concentrations of four selected proteins in Jurkat T-cells, including caspase-3, caspase-8, caspase-9, and Bid. Our model is able to correctly interpret the role of kinetic parameters and protein concentrations in cell sensitivity to FasL. It reveals the possible reasons for the transition between type-I and type-II pathways and also provides some interesting predictions, such as the more decisive role of Fas over Bax in apoptosis pathway and a possible feedback mechanism between type-I and type-II pathways. But our model failed in predicting FasL-induced apoptotic mechanism of NCI-60 cells from their gene-expression levels. Limitations in our model are also discussed. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

NASA Technical Reports Server (NTRS)

Jongen, T.; Gatski, T. B.

1997-01-01

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

On the Connection Between One-and Two-Equation Models of Turbulence

NASA Technical Reports Server (NTRS)

Menter, F. R.; Rai, Man Mohan (Technical Monitor)

1994-01-01

A formalism will be presented that allows the transformation of two-equation eddy viscosity turbulence models into one-equation models. The transformation is based on an assumption that is widely accepted over a large range of boundary layer flows and that has been shown to actually improve predictions when incorporated into two-equation models of turbulence. Based on that assumption, a new one-equation turbulence model will be derived. The new model will be tested in great detail against a previously introduced one-equation model and against its parent two-equation model.

Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations.

PubMed

Feng, Bao-Feng; Malomed, Boris A; Kawahara, Takuji

2002-11-01

We present a two-dimensional (2D) generalization of the stabilized Kuramoto-Sivashinsky system, based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic [Newell-Whitehead-Segel (NWS)] type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear media, combining the weakly 2D dispersion of the KP type with gain and NWS dissipation. Other applications are internal waves in multilayer fluids flowing down an inclined plane, double-front flames in gaseous mixtures, etc. Parallel to this weakly 2D model, we also introduce and study a semiphenomenological one, whose dissipative terms are isotropic, rather than of the NWS type, in order to check if qualitative results are sensitive to the exact form of the lossy terms. The models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, thus opening a way for the existence of stable localized pulses. We focus on the most interesting case, when the dispersive part of the system is of the KP-I type, which corresponds, e.g., to capillary waves, and makes the existence of completely localized 2D pulses possible. Treating the losses and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two steady-state solitons from their continuous family existing in the absence of the dissipative terms (the latter family is found in an exact analytical form, and is numerically demonstrated to be stable). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions, for both the physical and phenomenological models.

Hydrodynamic model for expansion and collisional relaxation of x-ray laser-excited multi-component nanoplasma

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

Saxena, Vikrant, E-mail: vikrant.saxena@desy.de; Hamburg Center for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg; Ziaja, Beata, E-mail: ziaja@mail.desy.de

The irradiation of an atomic cluster with a femtosecond x-ray free-electron laser pulse results in a nanoplasma formation. This typically occurs within a few hundred femtoseconds. By this time the x-ray pulse is over, and the direct photoinduced processes no longer contributing. All created electrons within the nanoplasma are thermalized. The nanoplasma thus formed is a mixture of atoms, electrons, and ions of various charges. While expanding, it is undergoing electron impact ionization and three-body recombination. Below we present a hydrodynamic model to describe the dynamics of such multi-component nanoplasmas. The model equations are derived by taking the moments ofmore » the corresponding Boltzmann kinetic equations. We include the equations obtained, together with the source terms due to electron impact ionization and three-body recombination, in our hydrodynamic solver. Model predictions for a test case, expanding spherical Ar nanoplasma, are obtained. With this model, we complete the two-step approach to simulate x-ray created nanoplasmas, enabling computationally efficient simulations of their picosecond dynamics. Moreover, the hydrodynamic framework including collisional processes can be easily extended for other source terms and then applied to follow relaxation of any finite non-isothermal multi-component nanoplasma with its components relaxed into local thermodynamic equilibrium.« less

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli

1997-01-01

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Water resources planning for rivers draining into mobile bay

NASA Technical Reports Server (NTRS)

Ng, S.; April, G. C.

1976-01-01

A hydrodynamic model describing water movement and tidal elevation is formulated, computed, and used to provide basic data about water quality in natural systems. The hydrodynamic model is based on two-dimensional, unsteady flow equations. The water mass is considered to be reasonably mixed such that integration (averaging) in the depth direction is a valid restriction. Convective acceleration, the Coriolis force, wind and bottom interactions are included as contributing terms in the momentum equations. The solution of the equations is applied to Mobile Bay, and used to investigate the influence that river discharge rate, wind direction and speed, and tidal condition have on water circulation and holdup within the bay. Storm surge conditions, oil spill transport, artificial island construction, dredging, and areas subject to flooding are other topics which could be investigated using the mathematical modeling approach.

Self-energy-modified Poisson-Nernst-Planck equations: WKB approximation and finite-difference approaches.

PubMed

Xu, Zhenli; Ma, Manman; Liu, Pei

2014-07-01

We propose a modified Poisson-Nernst-Planck (PNP) model to investigate charge transport in electrolytes of inhomogeneous dielectric environment. The model includes the ionic polarization due to the dielectric inhomogeneity and the ion-ion correlation. This is achieved by the self energy of test ions through solving a generalized Debye-Hückel (DH) equation. We develop numerical methods for the system composed of the PNP and DH equations. Particularly, toward the numerical challenge of solving the high-dimensional DH equation, we developed an analytical WKB approximation and a numerical approach based on the selective inversion of sparse matrices. The model and numerical methods are validated by simulating the charge diffusion in electrolytes between two electrodes, for which effects of dielectrics and correlation are investigated by comparing the results with the prediction by the classical PNP theory. We find that, at the length scale of the interface separation comparable to the Bjerrum length, the results of the modified equations are significantly different from the classical PNP predictions mostly due to the dielectric effect. It is also shown that when the ion self energy is in weak or mediate strength, the WKB approximation presents a high accuracy, compared to precise finite-difference results.

Enhanced Modeling of First-Order Plant Equations of Motion for Aeroelastic and Aeroservoelastic Applications

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S.

2010-01-01

A methodology is described for generating first-order plant equations of motion for aeroelastic and aeroservoelastic applications. The description begins with the process of generating data files representing specialized mode-shapes, such as rigid-body and control surface modes, using both PATRAN and NASTRAN analysis. NASTRAN executes the 146 solution sequence using numerous Direct Matrix Abstraction Program (DMAP) calls to import the mode-shape files and to perform the aeroelastic response analysis. The aeroelastic response analysis calculates and extracts structural frequencies, generalized masses, frequency-dependent generalized aerodynamic force (GAF) coefficients, sensor deflections and load coefficients data as text-formatted data files. The data files are then re-sequenced and re-formatted using a custom written FORTRAN program. The text-formatted data files are stored and coefficients for s-plane equations are fitted to the frequency-dependent GAF coefficients using two Interactions of Structures, Aerodynamics and Controls (ISAC) programs. With tabular files from stored data created by ISAC, MATLAB generates the first-order aeroservoelastic plant equations of motion. These equations include control-surface actuator, turbulence, sensor and load modeling. Altitude varying root-locus plot and PSD plot results for a model of the F-18 aircraft are presented to demonstrate the capability.

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Osmotic Transport across Cell Membranes in Nondilute Solutions: A New Nondilute Solute Transport Equation

PubMed Central

Elmoazzen, Heidi Y.; Elliott, Janet A.W.; McGann, Locksley E.

2009-01-01

The fundamental physical mechanisms of water and solute transport across cell membranes have long been studied in the field of cell membrane biophysics. Cryobiology is a discipline that requires an understanding of osmotic transport across cell membranes under nondilute solution conditions, yet many of the currently-used transport formalisms make limiting dilute solution assumptions. While dilute solution assumptions are often appropriate under physiological conditions, they are rarely appropriate in cryobiology. The first objective of this article is to review commonly-used transport equations, and the explicit and implicit assumptions made when using the two-parameter and the Kedem-Katchalsky formalisms. The second objective of this article is to describe a set of transport equations that do not make the previous dilute solution or near-equilibrium assumptions. Specifically, a new nondilute solute transport equation is presented. Such nondilute equations are applicable to many fields including cryobiology where dilute solution conditions are not often met. An illustrative example is provided. Utilizing suitable transport equations that fit for two permeability coefficients, fits were as good as with the previous three-parameter model (which includes the reflection coefficient, σ). There is less unexpected concentration dependence with the nondilute transport equations, suggesting that some of the unexpected concentration dependence of permeability is due to the use of inappropriate transport equations. PMID:19348741

Rayleigh-Plesset equation of the bubble stable cavitation in water: A nonequilibrium all-atom molecular dynamics simulation study

NASA Astrophysics Data System (ADS)

Man, Viet Hoang; Li, Mai Suan; Derreumaux, Philippe; Nguyen, Phuong H.

2018-03-01

The Rayleigh-Plesset (RP) equation was derived from the first principles to describe the bubble cavitation in liquids in terms of macroscopic hydrodynamics. A number of nonequilibrium molecular dynamics studies have been carried out to validate this equation in describing the bubble inertial cavitation, but their results are contradictory and the applicability of the RP equation still remains to be examined, especially for the stable cavitation. In this work, we carry out nonequilibrium all-atom simulation to validate the applicability of the RP equation in the description of the stable cavitation of nano-sized bubbles in water. We show that although microscopic effects are not explicitly included, this equation still describes the dynamics of subnano-bubbles quite well as long as the contributions of various terms including inertial, surface tension, and viscosity are correctly taken into account. These terms are directly and inversely proportional to the amplitude and period of the cavitation, respectively. Thus, their contributions to the RP equation depend on these two parameters. This may explain the discrepancy between the current results obtained using different parameters. Finally, the accuracy of the RP equation in the current mathematical modeling studies of the ultrasound-induced blood-brain-barrier experiments is discussed in some detail.

Revisions to the Wharton EFA Automobile Demand Model : The Wharton EFA Motor Vehicle Demand Model (Mark I)

DOT National Transportation Integrated Search

1980-12-01

The report documents revisions made to the Wharton EFA Automobile Demand Model to produce the Wharton EFA Motor Vehicle Demand Model (Mark I). Equations are reestimated for the total desired stock of autos and for desired shares by size class, includ...

3-Dimensional Modeling of Capacitively and Inductively Coupled Plasma Etching Systems

NASA Astrophysics Data System (ADS)

Rauf, Shahid

2008-10-01

Low temperature plasmas are widely used for thin film etching during micro and nano-electronic device fabrication. Fluid and hybrid plasma models were developed 15-20 years ago to understand the fundamentals of these plasmas and plasma etching. These models have significantly evolved since then, and are now a major tool used for new plasma hardware design and problem resolution. Plasma etching is a complex physical phenomenon, where inter-coupled plasma, electromagnetic, fluid dynamics, and thermal effects all have a major influence. The next frontier in the evolution of fluid-based plasma models is where these models are able to self-consistently treat the inter-coupling of plasma physics with fluid dynamics, electromagnetics, heat transfer and magnetostatics. We describe one such model in this paper and illustrate its use in solving engineering problems of interest for next generation plasma etcher design. Our 3-dimensional plasma model includes the full set of Maxwell equations, transport equations for all charged and neutral species in the plasma, the Navier-Stokes equation for fluid flow, and Kirchhoff's equations for the lumped external circuit. This model also includes Monte Carlo based kinetic models for secondary electrons and stochastic heating, and can take account of plasma chemistry. This modeling formalism allows us to self-consistently treat the dynamics in commercial inductively and capacitively coupled plasma etching reactors with realistic plasma chemistries, magnetic fields, and reactor geometries. We are also able to investigate the influence of the distributed electromagnetic circuit at very high frequencies (VHF) on the plasma dynamics. The model is used to assess the impact of azimuthal asymmetries in plasma reactor design (e.g., off-center pump, 3D magnetic field, slit valve, flow restrictor) on plasma characteristics at frequencies from 2 -- 180 MHz. With Jason Kenney, Ankur Agarwal, Ajit Balakrishna, Kallol Bera, and Ken Collins.

Trends of Abutment-Scour Prediction Equations Applied to 144 Field Sites in South Carolina

USGS Publications Warehouse

Benedict, Stephen T.; Deshpande, Nikhil; Aziz, Nadim M.; Conrads, Paul

2006-01-01

The U.S. Geological Survey conducted a study in cooperation with the Federal Highway Administration in which predicted abutment-scour depths computed with selected predictive equations were compared with field measurements of abutment-scour depth made at 144 bridges in South Carolina. The assessment used five equations published in the Fourth Edition of 'Evaluating Scour at Bridges,' (Hydraulic Engineering Circular 18), including the original Froehlich, the modified Froehlich, the Sturm, the Maryland, and the HIRE equations. An additional unpublished equation also was assessed. Comparisons between predicted and observed scour depths are intended to illustrate general trends and order-of-magnitude differences for the prediction equations. Field measurements were taken during non-flood conditions when the hydraulic conditions that caused the scour generally are unknown. The predicted scour depths are based on hydraulic conditions associated with the 100-year flow at all sites and the flood of record for 35 sites. Comparisons showed that predicted scour depths frequently overpredict observed scour and at times were excessive. The comparison also showed that underprediction occurred, but with less frequency. The performance of these equations indicates that they are poor predictors of abutment-scour depth in South Carolina, and it is probable that poor performance will occur when the equations are applied in other geographic regions. Extensive data and graphs used to compare predicted and observed scour depths in this study were compiled into spreadsheets and are included in digital format with this report. In addition to the equation-comparison data, Water-Surface Profile Model tube-velocity data, soil-boring data, and selected abutment-scour data are included in digital format with this report. The digital database was developed as a resource for future researchers and is especially valuable for evaluating the reasonableness of future equations that may be developed.

GVE-Based Dynamics and Control for Formation Flying Spacecraft

NASA Technical Reports Server (NTRS)

Breger, Louis; How, Jonathan P.

2004-01-01

Formation flying is an enabling technology for many future space missions. This paper presents extensions to the equations of relative motion expressed in Keplerian orbital elements, including new initialization techniques for general formation configurations. A new linear time-varying form of the equations of relative motion is developed from Gauss Variational Equations and used in a model predictive controller. The linearizing assumptions for these equations are shown to be consistent with typical formation flying scenarios. Several linear, convex initialization techniques are presented, as well as a general, decentralized method for coordinating a tetrahedral formation using differential orbital elements. Control methods are validated using a commercial numerical propagator.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-10-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ω_i while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev, , Dr.

2017-09-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Analysis of high-speed rotating flow inside gas centrifuge casing

NASA Astrophysics Data System (ADS)

Pradhan, Sahadev

2017-11-01

The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity Ωi while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential (χ) , which is derived from the equations of motion in an axisymmetric (r - z) plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solid-body rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15%) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified.

Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

NASA Technical Reports Server (NTRS)

Egolfopoulos, Fokion N.; Campbell, Charles S.

1999-01-01

A detailed numerical study was conducted on the dynamics and thermal response of inert, spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport, For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.

Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

NASA Technical Reports Server (NTRS)

Egolfopoulos, Fokion N.; Campbell, Charles S.; Wu, Ming-Shin (Technical Monitor)

1999-01-01

A detailed numerical study was conducted on the dynamics and thermal response of inert spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport. For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.; Hendy, A. S.; De Staelen, R. H.

2018-03-01

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein-Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein-Gordon equations driven by a harmonic perturbation at the boundary.

Horizontal density-gradient effects on simulation of flow and transport in the Potomac Estuary

USGS Publications Warehouse

Schaffranek, Raymond W.; Baltzer, Robert A.; ,

1990-01-01

A two-dimensional, depth-integrated, hydrodynamic/transport model of the Potomac Estuary between Indian Head and Morgantown, Md., has been extended to include treatment of baroclinic forcing due to horizontal density gradients. The finite-difference model numerically integrates equations of mass and momentum conservation in conjunction with a transport equation for heat, salt, and constituent fluxes. Lateral and longitudinal density gradients are determined from salinity distributions computed from the convection-diffusion equation and an equation of state that expresses density as a function of temperature and salinity; thus, the hydrodynamic and transport computations are directly coupled. Horizontal density variations are shown to contribute significantly to momentum fluxes determined in the hydrodynamic computation. These fluxes lead to enchanced tidal pumping, and consequently greater dispersion, as is evidenced by numerical simulations. Density gradient effects on tidal propagation and transport behavior are discussed and demonstrated.

Numerical simulation of an oxygen-fed wire-to-cylinder negative corona discharge in the glow regime

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Castellanos, A.

2011-02-01

Negative glow corona discharge in flowing oxygen has been numerically simulated for a wire-to-cylinder electrode geometry. The corona discharge is modelled using a fluid approximation. The radial and axial distributions of charged and neutral species are obtained by solving the corresponding continuity equations, which include the relevant plasma-chemical kinetics. Continuity equations are coupled with Poisson's equation and the energy conservation equation, since the reaction rate constants may depend on the electric field and temperature. The experimental values of the current-voltage characteristic are used as input data into the numerical calculations. The role played by different reactions and chemical species is analysed, and the effect of electrical and geometrical parameters on ozone generation is investigated. The reliability of the numerical model is verified by the reasonable agreement between the numerical predictions of ozone concentration and the experimental measurements.

Incompressible Navier-Stokes Computations with Heat Transfer

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan; Rogers, Stuart; Kutler, Paul (Technical Monitor)

1994-01-01

The existing pseudocompressibility method for the system of incompressible Navier-Stokes equations is extended to heat transfer problems by including the energy equation. The solution method is based on the pseudo compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. Both forced and natural convection problems are examined. Numerical results from turbulent reattaching flow behind a backward-facing step will be compared against experimental measurements for the forced convection case. The validity of Boussinesq approximation to simplify the buoyancy force term will be investigated. The natural convective flow structure generated by heat transfer in a vertical rectangular cavity will be studied. The numerical results will be compared by experimental measurements by Morrison and Tran.

Kinetic modeling of Nernst effect in magnetized hohlraums.

PubMed

Joglekar, A S; Ridgers, C P; Kingham, R J; Thomas, A G R

2016-04-01

We present nanosecond time-scale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's law, including Nernst advection of magnetic fields. In addition to showing the prevalence of nonlocal behavior, we demonstrate that effects such as anomalous heat flow are induced by inverse bremsstrahlung heating. We show magnetic field amplification up to a factor of 3 from Nernst compression into the hohlraum wall. The magnetic field is also expelled towards the hohlraum axis due to Nernst advection faster than frozen-in flux would suggest. Nonlocality contributes to the heat flow towards the hohlraum axis and results in an augmented Nernst advection mechanism that is included self-consistently through kinetic modeling.

A Bayesian Nonparametric Approach to Test Equating

ERIC Educational Resources Information Center

Karabatsos, George; Walker, Stephen G.

2009-01-01

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

a Study of Dynamic Powder Consolidation Based on a Particle-Level Mathematical Model.

NASA Astrophysics Data System (ADS)

Williamson, Richard L.

A mathematical model is developed to investigate the effects of large amplitude shock waves on powder materials during dynamic consolidation. The model is constructed at the particle level, focusing on a region containing a few powder particles and the surrounding interstices. The general equations of continuum mechanics are solved over this region, using initial and boundary conditions appropriate for the consolidation process. Closure of the equation system is obtained using an analytical equation of state; relations are included to account for solid to liquid phase changes. An elastic, perfectly-plastic constitutive law, specifically modified to describe material behavior at high-strain-rates, is applied to the solid materials. To reduce complexity, the model is restricted to two dimensions, therefore individual particles are approximated as infinitely long cylinders rather than spheres. The equation system is solved using standard finite-difference numerical techniques. It is demonstrated that for typical consolidation conditions, energy diffusion mechanisms are insignificant during the rapid densification phase of consolidation. Using type 304 stainless steel powder material, the particle-level model is used to investigate the mechanisms responsible for particle surface heating and metallurgical bonding during consolidation. It is demonstrated that energy deposition near particle surfaces results both from rapid particle deformation during interstitial filling and large localized impacts occurring at the final instant of interstitial closure; particle interior regions remain at sufficiently low temperatures to avoid microstructural modification. Nonuniform metallurgical bonding is predicted around the particle periphery, ranging from complete fusion to mechanical abutment. Simulation results are used to investigate the detailed wave propagation phenomena at the particle level, providing an improved understanding of this complex behavior. A variety of parametric studies are conducted including investigations of the effects of stress wave amplitude and rise time, the role of interstitial gases during consolidation, and various geometric aspects including the importance of initial void fraction. The model is applied to a metal matrix composite system to investigate the consolidation of mixtures of differing materials; results of a two-dimensional experiment are included. Available experimental data are compared with simulation results. In general, very good agreement between simulation results and data is obtained.

A fluidized bed technique for estimating soil critical shear stress

USDA-ARS?s Scientific Manuscript database

Soil erosion models, depending on how they are formulated, always have erodibilitiy parameters in the erosion equations. For a process-based model like the Water Erosion Prediction Project (WEPP) model, the erodibility parameters include rill and interrill erodibility and critical shear stress. Thes...

Comparison of experiment with calculations using curvature-corrected zero and two equation turbulence models for a two-dimensional U-duct

NASA Astrophysics Data System (ADS)

Monson, D. J.; Seegmiller, H. L.; McConnaughey, P. K.

1990-06-01

In this paper experimental measurements are compared with Navier-Stokes calculations using seven different turbulence models for the internal flow in a two-dimensional U-duct. The configuration is representative of many internal flows of engineering interst that experience strong curvature. In an effort to improve agreement, this paper tests several versions of the two-equation k-epsilon turbulence model including the standard version, an extended version with a production range time scale, and a version that includes curvature time scales. Each is tested in its high and low Reynolds number formulations. Calculations using these new models and the original mixing length model are compared here with measurements of mean and turbulence velocities, static pressure and skin friction in the U-duct at two Reynolds numbers. The comparisons show that only the low Reynolds number version of the extended k-epsilon model does a reasonable job of predicting the important features of this flow at both Reynolds numbers tested.

Prediction of Broadband Shock-Associated Noise Including Propagation Effects Originating NASA

NASA Technical Reports Server (NTRS)

Miller, Steven; Morris, Philip J.

2012-01-01

An acoustic analogy is developed based on the Euler equations for broadband shock-associated noise (BBSAN) that directly incorporates the vector Green s function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) to describe the mean flow. The vector Green s function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation rate. An adjoint vector Green s function solver is implemented to determine the vector Green s function based on a locally parallel mean flow at different streamwise locations. The newly developed acoustic analogy can be simplified to one that uses the Green s function associated with the Helmholtz equation, which is consistent with a previous formulation by the authors. A large number of predictions are generated using three different nozzles over a wide range of fully-expanded jet Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise experimental facilities. In addition, two models for the so-called fine-scale mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include propagation effects.

Causal discovery and inference: concepts and recent methodological advances.

PubMed

Spirtes, Peter; Zhang, Kun

This paper aims to give a broad coverage of central concepts and principles involved in automated causal inference and emerging approaches to causal discovery from i.i.d data and from time series. After reviewing concepts including manipulations, causal models, sample predictive modeling, causal predictive modeling, and structural equation models, we present the constraint-based approach to causal discovery, which relies on the conditional independence relationships in the data, and discuss the assumptions underlying its validity. We then focus on causal discovery based on structural equations models, in which a key issue is the identifiability of the causal structure implied by appropriately defined structural equation models: in the two-variable case, under what conditions (and why) is the causal direction between the two variables identifiable? We show that the independence between the error term and causes, together with appropriate structural constraints on the structural equation, makes it possible. Next, we report some recent advances in causal discovery from time series. Assuming that the causal relations are linear with nonGaussian noise, we mention two problems which are traditionally difficult to solve, namely causal discovery from subsampled data and that in the presence of confounding time series. Finally, we list a number of open questions in the field of causal discovery and inference.

Poisson-Boltzmann-Nernst-Planck model

NASA Astrophysics Data System (ADS)

Zheng, Qiong; Wei, Guo-Wei

2011-05-01

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.

Poisson-Boltzmann-Nernst-Planck model

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

Zheng Qiong; Wei Guowei; Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species inmore » the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time.« less

Poisson–Boltzmann–Nernst–Planck model

PubMed Central

Zheng, Qiong; Wei, Guo-Wei

2011-01-01

The Poisson–Nernst–Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst–Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst–Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst–Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson–Boltzmann and Nernst–Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current–voltage (I–V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I–V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. PMID:21599038

Poisson-Boltzmann-Nernst-Planck model.

PubMed

Zheng, Qiong; Wei, Guo-Wei

2011-05-21

The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. © 2011 American Institute of Physics.

Anyons in an electromagnetic field and the Bargmann-Michel-Telegdi equation

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

Ghosh, S.

1995-05-15

The Lagrangian model for anyons, presented earlier, is extended to include interactions with an external, homogeneous electromagnetic field. Explicit electric and magnetic moment terms for the anyon are introduced in the Lagrangian. The (2+1)-dimensional Bargmann-Michel-Telegdi equation as well as the correct value (2) of the gyromagnetic ratio is rederived, in the Hamiltonian framework.

The Relationship between the Amount of Learning and Time (The Example of Equations)

ERIC Educational Resources Information Center

Kesan, Cenk; Kaya, Deniz; Ok, Gokce; Erkus, Yusuf

2016-01-01

The main purpose of this study is to determine the amount of time-dependent learning of "solving problems that require establishing of single variable equations of the first order" of the seventh grade students. The study, adopting the screening model, consisted of a total of 84 students, including 42 female and 42 male students at the…

Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons.

PubMed

Ratas, Irmantas; Pyragas, Kestutis

2017-10-01

We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of nonsymmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, and chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.

Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons

NASA Astrophysics Data System (ADS)

Ratas, Irmantas; Pyragas, Kestutis

2017-10-01

We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of nonsymmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, and chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.

The mimetic finite difference method for the Landau–Lifshitz equation

DOE PAGES

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

2017-01-01

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

Slew maneuvers of Spacecraft Control Laboratory Experiment (SCOLE)

NASA Technical Reports Server (NTRS)

Kakad, Yogendra P.

1992-01-01

This is the final report on the dynamics and control of slew maneuvers of the Spacecraft Control Laboratory Experiment (SCOLE) test facility. The report documents the basic dynamical equation derivations for an arbitrary large angle slew maneuver as well as the basic decentralized slew maneuver control algorithm. The set of dynamical equations incorporate rigid body slew maneuver and three dimensional vibrations of the complete assembly comprising the rigid shuttle, the flexible beam, and the reflector with an offset mass. The analysis also includes kinematic nonlinearities of the entire assembly during the maneuver and the dynamics of the interactions between the rigid shuttle and the flexible appendage. The equations are simplified and evaluated numerically to include the first ten flexible modes to yield a model for designing control systems to perform slew maneuvers. The control problem incorporates the nonlinear dynamical equations and is expressed in terms of a two point boundary value problem.

The mimetic finite difference method for the Landau–Lifshitz equation

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

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

A Viscoelastic Hybrid Shell Finite Element

NASA Technical Reports Server (NTRS)

Johnson, Arthur

1999-01-01

An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

An evaluation of the accuracy and precision of methane prediction equations for beef cattle fed high-forage and high-grain diets.

PubMed

Escobar-Bahamondes, P; Oba, M; Beauchemin, K A

2017-01-01

The study determined the performance of equations to predict enteric methane (CH4) from beef cattle fed forage- and grain-based diets. Many equations are available to predict CH4 from beef cattle and the predictions vary substantially among equations. The aims were to (1) construct a database of CH4 emissions for beef cattle from published literature, and (2) identify the most precise and accurate extant CH4 prediction models for beef cattle fed diets varying in forage content. The database was comprised of treatment means of CH4 production from in vivo beef studies published from 2000 to 2015. Criteria to include data in the database were as follows: animal description, intakes, diet composition and CH4 production. In all, 54 published equations that predict CH4 production from diet composition were evaluated. Precision and accuracy of the equations were evaluated using the concordance correlation coefficient (r c ), root mean square prediction error (RMSPE), model efficiency and analysis of errors. Equations were ranked using a combined index of the various statistical assessments based on principal component analysis. The final database contained 53 studies and 207 treatment means that were divided into two data sets: diets containing ⩾400 g/kg dry matter (DM) forage (n=116) and diets containing ⩽200 g/kg DM forage (n=42). Diets containing between ⩽400 and ⩾200 g/kg DM forage were not included in the analysis because of their limited numbers (n=6). Outliers, treatment means where feed was fed restrictively and diets with CH4 mitigation additives were omitted (n=43). Using the high-forage dataset the best-fit equations were the International Panel on Climate Change Tier 2 method, 3 equations for steers that considered gross energy intake (GEI) and body weight and an equation that considered dry matter intake and starch:neutral detergent fiber with r c ranging from 0.60 to 0.73 and RMSPE from 35.6 to 45.9 g/day. For the high-grain diets, the 5 best-fit equations considered intakes of metabolisable energy, cellulose, hemicellulose and fat, or for steers GEI and body weight, with r c ranging from 0.35 to 0.52 and RMSPE from 47.4 to 62.9 g/day. Ranking of extant CH4 prediction equations for their accuracy and precision differed with forage content of the diet. When used for cattle fed high-grain diets, extant CH4 prediction models were generally imprecise and lacked accuracy.

Section 1. Simulation of surface-water integrated flow and transport in two-dimensions: SWIFT2D user's manual

USGS Publications Warehouse

Schaffranek, Raymond W.

2004-01-01

A numerical model for simulation of surface-water integrated flow and transport in two (horizontal-space) dimensions is documented. The model solves vertically integrated forms of the equations of mass and momentum conservation and solute transport equations for heat, salt, and constituent fluxes. An equation of state for salt balance directly couples solution of the hydrodynamic and transport equations to account for the horizontal density gradient effects of salt concentrations on flow. The model can be used to simulate the hydrodynamics, transport, and water quality of well-mixed bodies of water, such as estuaries, coastal seas, harbors, lakes, rivers, and inland waterways. The finite-difference model can be applied to geographical areas bounded by any combination of closed land or open water boundaries. The simulation program accounts for sources of internal discharges (such as tributary rivers or hydraulic outfalls), tidal flats, islands, dams, and movable flow barriers or sluices. Water-quality computations can treat reactive and (or) conservative constituents simultaneously. Input requirements include bathymetric and topographic data defining land-surface elevations, time-varying water level or flow conditions at open boundaries, and hydraulic coefficients. Optional input includes the geometry of hydraulic barriers and constituent concentrations at open boundaries. Time-dependent water level, flow, and constituent-concentration data are required for model calibration and verification. Model output consists of printed reports and digital files of numerical results in forms suitable for postprocessing by graphical software programs and (or) scientific visualization packages. The model is compatible with most mainframe, workstation, mini- and micro-computer operating systems and FORTRAN compilers. This report defines the mathematical formulation and computational features of the model, explains the solution technique and related model constraints, describes the model framework, documents the type and format of inputs required, and identifies the type and format of output available.

Hybrid simulations of magnetic reconnection with kinetic ions and fluid electron pressure anisotropy

DOE PAGES

Le, A.; Daughton, W.; Karimabadi, H.; ...

2016-03-16

We present the first hybrid simulations with kinetic ions and recently developed equations of state for the electron fluid appropriate for reconnection with a guide field. The equations of state account for the main anisotropy of the electron pressure tensor.Magnetic reconnection is studied in two systems, an initially force-free current sheet and a Harris sheet. The hybrid model with the equations of state is compared to two other models, hybrid simulations with isothermal electrons and fully kinetic simulations. Including the anisotropicequations of state in the hybrid model provides a better match to the fully kinetic model. In agreement with fullymore » kinetic results, the main feature captured is the formation of an electron current sheet that extends several ion inertial lengths. This electron current sheet modifies the Hall magnetic field structure near the X-line, and it is not observed in the standard hybrid model with isotropic electrons. The saturated reconnection rate in this regime nevertheless remains similar in all three models. Here, implications for global modeling are discussed.« less

Modeling the impact behavior of high strength ceramics. Final report

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

Rajendran, A.M.

1993-12-01

An advanced constitutive model is used to describe the shock and high strain rate behaviors of silicon carbide (SC), boron carbide B4C, and titanium diboride (TiB2) under impact loading conditions. The model's governing equations utilize a set of microphysically-based constitutive relationships to model the deformation and damage processes in a ceramic. The total strain is decomposed into elastic, plastic, and microcracking components. The plastic strain component was calculated using conventional viscoplastic equations. The strain components due to microcracking utilized relationships derived for a penny-shaped crack containing elastic solids. The main features of the model include degradation of strength and stiffnessmore » under both compressive and tensile loading conditions. When loaded above the Hugoniot elastic limit (HEL), the strength is limited by the strain rate dependent strength equation. However, below the HEL, the strength variation with respect to strain rate and pressure is modeled through microcracking relationships assuming no plastic flow. The ceramic model parameters were determined using a set of VISAR data from the plate impact experiments.« less

Revisiting Turbulence Model Validation for High-Mach Number Axisymmetric Compression Corner Flows

NASA Technical Reports Server (NTRS)

Georgiadis, Nicholas J.; Rumsey, Christopher L.; Huang, George P.

2015-01-01

Two axisymmetric shock-wave/boundary-layer interaction (SWBLI) cases are used to benchmark one- and two-equation Reynolds-averaged Navier-Stokes (RANS) turbulence models. This validation exercise was executed in the philosophy of the NASA Turbulence Modeling Resource and the AIAA Turbulence Model Benchmarking Working Group. Both SWBLI cases are from the experiments of Kussoy and Horstman for axisymmetric compression corner geometries with SWBLI inducing flares of 20 and 30 degrees, respectively. The freestream Mach number was approximately 7. The RANS closures examined are the Spalart-Allmaras one-equation model and the Menter family of kappa - omega two equation models including the Baseline and Shear Stress Transport formulations. The Wind-US and CFL3D RANS solvers are employed to simulate the SWBLI cases. Comparisons of RANS solutions to experimental data are made for a boundary layer survey plane just upstream of the SWBLI region. In the SWBLI region, comparisons of surface pressure and heat transfer are made. The effects of inflow modeling strategy, grid resolution, grid orthogonality, turbulent Prandtl number, and code-to-code variations are also addressed.

Integrable Semi-discrete Kundu-Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong; Yuan, Jinyun; Zhu, Zuo-nong

2018-02-01

To get more insight into the relation between discrete model and continuous counterpart, a new integrable semi-discrete Kundu-Eckhaus equation is derived from the reduction in an extended Ablowitz-Ladik hierarchy. The integrability of the semi-discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The dynamic characteristics of the breather and rational solutions have been analyzed in detail for our semi-discrete Kundu-Eckhaus equation to reveal some new interesting phenomena which was not found in continuous one. It is shown that the theory of the discrete system including Lax pair, Darboux transformation and explicit solutions systematically yields their continuous counterparts in the continuous limit.

Analytical and numerical solution for wave reflection from a porous wave absorber

NASA Astrophysics Data System (ADS)

Magdalena, Ikha; Roque, Marian P.

2018-03-01

In this paper, wave reflection from a porous wave absorber is investigated theoretically and numerically. The equations that we used are based on shallow water type model. Modification of motion inside the absorber is by including linearized friction term in momentum equation and introducing a filtered velocity. Here, an analytical solution for wave reflection coefficient from a porous wave absorber over a flat bottom is derived. Numerically, we solve the equations using the finite volume method on a staggered grid. To validate our numerical model, comparison of the numerical reflection coefficient is made against the analytical solution. Further, we implement our numerical scheme to study the evolution of surface waves pass through a porous absorber over varied bottom topography.

Beyond linear fields: the Lie–Taylor expansion

PubMed Central

2017-01-01

The work extends the linear fields’ solution of compressible nonlinear magnetohydrodynamics (MHD) to the case where the magnetic field depends on superlinear powers of position vector, usually, but not always, expressed in Cartesian components. Implications of the resulting Lie–Taylor series expansion for physical applicability of the Dolzhansky–Kirchhoff (D–K) equations are found to be positive. It is demonstrated how resistivity may be included in the D–K model. Arguments are put forward that the D–K equations may be regarded as illustrating properties of nonlinear MHD in the same sense that the Lorenz equations inform about the onset of convective turbulence. It is suggested that the Lie–Taylor series approach may lead to valuable insights into other fluid models. PMID:28265187

Stochastic differential equations and turbulent dispersion

NASA Technical Reports Server (NTRS)

Durbin, P. A.

1983-01-01

Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

Variational objective analysis for cyclone studies

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.

1989-01-01

Significant accomplishments during 1987 to 1988 are summarized with regard to each of the major project components. Model 1 requires satisfaction of two nonlinear horizontal momentum equations, the integrated continuity equation, and the hydrostatic equation. Model 2 requires satisfaction of model 1 plus the thermodynamic equation for a dry atmosphere. Model 3 requires satisfaction of model 2 plus the radiative transfer equation. Model 4 requires satisfaction of model 3 plus a moisture conservation equation and a parameterization for moist processes.

A unique set of micromechanics equations for high temperature metal matrix composites

NASA Technical Reports Server (NTRS)

Hopkins, D. A.; Chamis, C. C.

1985-01-01

A unique set of micromechanic equations is presented for high temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Simulating Donnan equilibria based on the Nernst-Planck equation

NASA Astrophysics Data System (ADS)

Gimmi, Thomas; Alt-Epping, Peter

2018-07-01

Understanding ion transport through clays and clay membranes is important for many geochemical and environmental applications. Ion transport is affected by electrostatic forces exerted by charged clay surfaces. Anions are partly excluded from pore water near these surfaces, whereas cations are enriched. Such effects can be modeled by the Donnan approach. Here we introduce a new, comparatively simple way to represent Donnan equilibria in transport simulations. We include charged surfaces as immobile ions in the balance equation and calculate coupled transport of all components, including the immobile charges, with the Nernst-Planck equation. This results in an additional diffusion potential that influences ion transport, leading to Donnan ion distributions while maintaining local charge balance. The validity of our new approach was demonstrated by comparing Nernst-Planck simulations using the reactive transport code Flotran with analytical solutions available for simple Donnan systems. Attention has to be paid to the numerical evaluation of the electrochemical migration term in the Nernst-Planck equation to obtain correct results for asymmetric electrolytes. Sensitivity simulations demonstrate the influence of various Donnan model parameters on simulated anion accessible porosities. It is furthermore shown that the salt diffusion coefficient in a Donnan pore depends on local concentrations, in contrast to the aqueous salt diffusion coefficient. Our approach can be easily implemented into other transport codes. It is versatile and facilitates, for instance, assessing the implications of different activity models for the Donnan porosity.

Transport of water and ions in partially water-saturated porous media. Part 1. Constitutive equations

NASA Astrophysics Data System (ADS)

Revil, A.

2017-05-01

I developed a model of cross-coupled flow in partially saturated porous media based on electrokinetic coupling including the effect of ion filtration (normal and reverse osmosis) and the multi-component nature of the pore water (wetting) phase. The model also handles diffusion and membrane polarization but is valid only for saturations above the irreducible water saturation. I start with the local Nernst-Planck and Stokes equations and I use a volume-averaging procedure to obtain the generalized Ohm, Fick, and Darcy equations with cross-coupling terms at the scale of a representative elementary volume of the porous rock. These coupling terms obey Onsager's reciprocity, which is a required condition, at the macroscale, to keep the total dissipation function of the system positive. Rather than writing the electrokinetic terms in terms of zeta potential (the double layer electrical potential on the slipping plane located in the pore water), I developed the model in terms of an effective charge density dragged by the flow of the pore water. This effective charge density is found to be strongly controlled by the permeability and the water saturation. I also developed an electrical conductivity equation including the effect of saturation on both bulk and surface conductivities, the surface conductivity being associated with electromigration in the electrical diffuse layer coating the grains. This surface conductivity depends on the CEC of the porous material.

Differential morphology and image processing.

PubMed

Maragos, P

1996-01-01

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.

Nonlocal theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-09-01

New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

A compressible near-wall turbulence model for boundary layer calculations

NASA Technical Reports Server (NTRS)

So, R. M. C.; Zhang, H. S.; Lai, Y. G.

1992-01-01

A compressible near-wall two-equation model is derived by relaxing the assumption of dynamical field similarity between compressible and incompressible flows. This requires justifications for extending the incompressible models to compressible flows and the formulation of the turbulent kinetic energy equation in a form similar to its incompressible counterpart. As a result, the compressible dissipation function has to be split into a solenoidal part, which is not sensitive to changes of compressibility indicators, and a dilational part, which is directly affected by these changes. This approach isolates terms with explicit dependence on compressibility so that they can be modeled accordingly. An equation that governs the transport of the solenoidal dissipation rate with additional terms that are explicitly dependent on the compressibility effects is derived similarly. A model with an explicit dependence on the turbulent Mach number is proposed for the dilational dissipation rate. Thus formulated, all near-wall incompressible flow models could be expressed in terms of the solenoidal dissipation rate and straight-forwardly extended to compressible flows. Therefore, the incompressible equations are recovered correctly in the limit of constant density. The two-equation model and the assumption of constant turbulent Prandtl number are used to calculate compressible boundary layers on a flat plate with different wall thermal boundary conditions and free-stream Mach numbers. The calculated results, including the near-wall distributions of turbulence statistics and their limiting behavior, are in good agreement with measurements. In particular, the near-wall asymptotic properties are found to be consistent with incompressible behavior; thus suggesting that turbulent flows in the viscous sublayer are not much affected by compressibility effects.

Tidal, Residual, Intertidal Mudflat (TRIM) Model and its Applications to San Francisco Bay, California

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; Gartner, J.W.

1993-01-01

A numerical model using a semi-implicit finite-difference method for solving the two-dimensional shallow-water equations is presented. The gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation are finite-differenced implicitly, the remaining terms are finite-differenced explicitly. The convective terms are treated using an Eulerian-Lagrangian method. The combination of the semi-implicit finite-difference solution for the gravity wave propagation, and the Eulerian-Lagrangian treatment of the convective terms renders the numerical model unconditionally stable. When the baroclinic forcing is included, a salt transport equation is coupled to the momentum equations, and the numerical method is subject to a weak stability condition. The method of solution and the properties of the numerical model are given. This numerical model is particularly suitable for applications to coastal plain estuaries and tidal embayments in which tidal currents are dominant, and tidally generated residual currents are important. The model is applied to San Francisco Bay, California where extensive historical tides and current-meter data are available. The model calibration is considered by comparing time-series of the field data and of the model results. Alternatively, and perhaps more meaningfully, the model is calibrated by comparing the harmonic constants of tides and tidal currents derived from field data with those derived from the model. The model is further verified by comparing the model results with an independent data set representing the wet season. The strengths and the weaknesses of the model are assessed based on the results of model calibration and verification. Using the model results, the properties of tides and tidal currents in San Francisco Bay are characterized and discussed. Furthermore, using the numerical model, estimates of San Francisco Bay's volume, surface area, mean water depth, tidal prisms, and tidal excursions at spring and neap tides are computed. Additional applications of the model reveal, qualitatively the spatial distribution of residual variables. ?? 1993 Academic Press. All rights reserved.

Numerical Modeling of Interstitial Fluid Flow Coupled with Blood Flow through a Remodeled Solid Tumor Microvascular Network

PubMed Central

Soltani, M.; Chen, P.

2013-01-01

Modeling of interstitial fluid flow involves processes such as fluid diffusion, convective transport in extracellular matrix, and extravasation from blood vessels. To date, majority of microvascular flow modeling has been done at different levels and scales mostly on simple tumor shapes with their capillaries. However, with our proposed numerical model, more complex and realistic tumor shapes and capillary networks can be studied. Both blood flow through a capillary network, which is induced by a solid tumor, and fluid flow in tumor’s surrounding tissue are formulated. First, governing equations of angiogenesis are implemented to specify the different domains for the network and interstitium. Then, governing equations for flow modeling are introduced for different domains. The conservation laws for mass and momentum (including continuity equation, Darcy’s law for tissue, and simplified Navier–Stokes equation for blood flow through capillaries) are used for simulating interstitial and intravascular flows and Starling’s law is used for closing this system of equations and coupling the intravascular and extravascular flows. This is the first study of flow modeling in solid tumors to naturalistically couple intravascular and extravascular flow through a network. This network is generated by sprouting angiogenesis and consisting of one parent vessel connected to the network while taking into account the non-continuous behavior of blood, adaptability of capillary diameter to hemodynamics and metabolic stimuli, non-Newtonian blood flow, and phase separation of blood flow in capillary bifurcation. The incorporation of the outlined components beyond the previous models provides a more realistic prediction of interstitial fluid flow pattern in solid tumors and surrounding tissues. Results predict higher interstitial pressure, almost two times, for realistic model compared to the simplified model. PMID:23840579

Differential equations with applications in cancer diseases.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2013-01-01

Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

PyR@TE. Renormalization group equations for general gauge theories

NASA Astrophysics Data System (ADS)

Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.

2014-03-01

Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer: Personal computer. Operating system: Tested on Fedora 15, MacOS 10 and 11, Ubuntu 12. Classification: 11.1. External routines: SymPy, PyYAML, NumPy, IPython, SciPy Nature of problem: Deriving the renormalization group equations for a general quantum field theory. Solution method: Group theory, tensor algebra Running time: Tens of seconds per model (one-loop), tens of minutes (two-loop)

A Multivariate Model of Physics Problem Solving

ERIC Educational Resources Information Center

Taasoobshirazi, Gita; Farley, John

2013-01-01

A model of expertise in physics problem solving was tested on undergraduate science, physics, and engineering majors enrolled in an introductory-level physics course. Structural equation modeling was used to test hypothesized relationships among variables linked to expertise in physics problem solving including motivation, metacognitive planning,…

[A Structural Equation Model on Family Strength of Married Working Women].

PubMed

Hong, Yeong Seon; Han, Kuem Sun

2015-12-01

The purpose of this study was to identify the effect of predictive factors related to family strength and develop a structural equation model that explains family strength among married working women. A hypothesized model was developed based on literature reviews and predictors of family strength by Yoo. This constructed model was built of an eight pathway form. Two exogenous variables included in this model were ego-resilience and family support. Three endogenous variables included in this model were functional couple communication, family stress and family strength. Data were collected using a self-report questionnaire from 319 married working women who were 30~40 of age and lived in cities of Chungnam province in Korea. Data were analyzed with PASW/WIN 18.0 and AMOS 18.0 programs. Family support had a positive direct, indirect and total effect on family strength. Family stress had a negative direct, indirect and total effect on family strength. Functional couple communication had a positive direct and total effect on family strength. These predictive variables of family strength explained 61.8% of model. The results of the study show a structural equation model for family strength of married working women and that predicting factors for family strength are family support, family stress, and functional couple communication. To improve family strength of married working women, the results of this study suggest nursing access and mediative programs to improve family support and functional couple communication, and reduce family stress.

Theoretical study of the tunnel-boundary lift interference due to slotted walls in the presence of the trailing-vortex system of a lifting model

NASA Technical Reports Server (NTRS)

Matthews, Clarence W

1955-01-01

The equations presented in this report give the interference on the trailing-vortex system of a uniformly loaded finite-span wing in a circular tunnel containing partly open and partly closed walls, with special reference to symmetrical arrangements of the open and closed portions. Methods are given for extending the equations to include tunnel shapes other than circular. The rectangular tunnel is used to demonstrate these methods. The equations are also extended to nonuniformly loaded wings.

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Prediction of Airfoil Characteristics With Higher Order Turbulence Models

NASA Technical Reports Server (NTRS)

Gatski, Thomas B.

1996-01-01

This study focuses on the prediction of airfoil characteristics, including lift and drag over a range of Reynolds numbers. Two different turbulence models, which represent two different types of models, are tested. The first is a standard isotropic eddy-viscosity two-equation model, and the second is an explicit algebraic stress model (EASM). The turbulent flow field over a general-aviation airfoil (GA(W)-2) at three Reynolds numbers is studied. At each Reynolds number, predicted lift and drag values at different angles of attack are compared with experimental results, and predicted variations of stall locations with Reynolds number are compared with experimental data. Finally, the size of the separation zone predicted by each model is analyzed, and correlated with the behavior of the lift coefficient near stall. In summary, the EASM model is able to predict the lift and drag coefficients over a wider range of angles of attack than the two-equation model for the three Reynolds numbers studied. However, both models are unable to predict the correct lift and drag behavior near the stall angle, and for the lowest Reynolds number case, the two-equation model did not predict separation on the airfoil near stall.

Assessment of turbulent models for scramjet flowfields

NASA Technical Reports Server (NTRS)

Sindir, M. M.; Harsha, P. T.

1982-01-01

The behavior of several turbulence models applied to the prediction of scramjet combustor flows is described. These models include the basic two equation model, the multiple dissipation length scale variant of the two equation model, and the algebraic stress model (ASM). Predictions were made of planar backward facing step flows and axisymmetric sudden expansion flows using each of these approaches. The formulation of each of these models are discussed, and the application of the different approaches to supersonic flows is described. A modified version of the ASM is found to provide the best prediction of the planar backward facing step flow in the region near the recirculation zone, while the basic ASM provides the best results downstream of the recirculation. Aspects of the interaction of numerica modeling and turbulences modeling as they affect the assessment of turbulence models are discussed.

Numerical model for learning concepts of streamflow simulation

USGS Publications Warehouse

DeLong, L.L.; ,

1993-01-01

Numerical models are useful for demonstrating principles of open-channel flow. Such models can allow experimentation with cause-and-effect relations, testing concepts of physics and numerical techniques. Four PT is a numerical model written primarily as a teaching supplement for a course in one-dimensional stream-flow modeling. Four PT options particularly useful in training include selection of governing equations, boundary-value perturbation, and user-programmable constraint equations. The model can simulate non-trivial concepts such as flow in complex interconnected channel networks, meandering channels with variable effective flow lengths, hydraulic structures defined by unique three-parameter relations, and density-driven flow.The model is coded in FORTRAN 77, and data encapsulation is used extensively to simplify maintenance and modification and to enhance the use of Four PT modules by other programs and programmers.

Three-dimensional simulation of beam propagation and heat transfer in static gas Cs DPALs using wave optics and fluid dynamics models

NASA Astrophysics Data System (ADS)

Waichman, Karol; Barmashenko, Boris D.; Rosenwaks, Salman

2017-10-01

Analysis of beam propagation, kinetic and fluid dynamic processes in Cs diode pumped alkali lasers (DPALs), using wave optics model and gasdynamic code, is reported. The analysis is based on a three-dimensional, time-dependent computational fluid dynamics (3D CFD) model. The Navier-Stokes equations for momentum, heat and mass transfer are solved by a commercial Ansys FLUENT solver based on the finite volume discretization technique. The CFD code which solves the gas conservation equations includes effects of natural convection and temperature diffusion of the species in the DPAL mixture. The DPAL kinetic processes in the Cs/He/C2H6 gas mixture dealt with in this paper involve the three lowest energy levels of Cs, (1) 62S1/2, (2) 62P1/2 and (3) 62P3/2. The kinetic processes include absorption due to the 1->3 D2 transition followed by relaxation the 3 to 2 fine structure levels and stimulated emission due to the 2->1 D1 transition. Collisional quenching of levels 2 and 3 and spontaneous emission from these levels are also considered. The gas flow conservation equations are coupled to fast-Fourier-transform algorithm for transverse mode propagation to obtain a solution of the scalar paraxial propagation equation for the laser beam. The wave propagation equation is solved by the split-step beam propagation method where the gain and refractive index in the DPAL medium affect the wave amplitude and phase. Using the CFD and beam propagation models, the gas flow pattern and spatial distributions of the pump and laser intensities in the resonator were calculated for end-pumped Cs DPAL. The laser power, DPAL medium temperature and the laser beam quality were calculated as a function of pump power. The results of the theoretical model for laser power were compared to experimental results of Cs DPAL.

Efecto de la difusión y la velocidad en la ionización del átomo de Carbono

NASA Astrophysics Data System (ADS)

Rovira, M. G.; Fontenla, J. M.

The equations of statistical equilibrium for all ionization states of the atom are solved. The effects of diffusion and center of mass velocity are included. In order to estimate the modifications of the ionization curves, they were applied to the Carbon atom. To solve these equations, solar prominences' models obtained in a previous paper were adopted. They were extended to reach a temperature of 1.5 × 106 K and the complete model of the prominence was calculated. Ionization curves for different values of velocity, diffusion and medium models were obtained. The different models represent structures with different densities. Considerable modifications due to these effects are found.

Reactions to Stress During the Persian Gulf War: The Use of Structural Equations for Testing the Horowitz Model

PubMed

Koslowsky; Solomon; Bleich; Laor

1994-06-01

In one of the few models specific to victims' reactions to traumatic events, it has been proposed that consequences typically include alternating patterns of intrusive and avoidance symptoms. The present exploratory investigation examined the responses of 120 victims who had been evacuated to a hotel after a SCUD missile attack on their home. Analyses using structural equation modeling showed that both psychological states follow stressful stimuli and perceived threat. In addition, results were found to be consistent with a model that posits intrusion as antecedent to anxiety which, in turn, was found to precede a latent outcome measure consisting of psychological, physical, and work functioning.

A crystallographic model for the tensile and fatigue response for Rene N4 at 982 C

NASA Technical Reports Server (NTRS)

Sheh, M. Y.; Stouffer, D. C.

1990-01-01

An anisotropic constitutive model based on crystallographic slip theory was formulated for nickel-base single-crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the existence of back stress in single crystals. The results showed that the back stress effect of reverse inelastic flow on the unloading stress is orientation-dependent, and a back stress state variable in the inelastic flow equation is necessary for predicting inelastic behavior. Model correlations and predictions of experimental data are presented for the single crystal superalloy Rene N4 at 982 C.

Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling

PubMed Central

Ye, Hao; Beamish, Richard J.; Glaser, Sarah M.; Grant, Sue C. H.; Hsieh, Chih-hao; Richards, Laura J.; Schnute, Jon T.; Sugihara, George

2015-01-01

It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equivalent EDM formulations that explicitly use spawning stock and environmental variables to forecast recruitment. We find that EDM models produce more accurate and precise forecasts, and unlike extensions of the classic Ricker spawner–recruit equation, they show significant improvements when environmental factors are included. Our analysis demonstrates the strategic utility of EDM for incorporating environmental influences into fisheries forecasts and, more generally, for providing insight into how environmental factors can operate in forecast models, thus paving the way for equation-free mechanistic forecasting to be applied in management contexts. PMID:25733874

Reciprocity theory of homogeneous reactions

NASA Astrophysics Data System (ADS)

Agbormbai, Adolf A.

1990-03-01

The reciprocity formalism is applied to the homogeneous gaseous reactions in which the structure of the participating molecules changes upon collision with one another, resulting in a change in the composition of the gas. The approach is applied to various classes of dissociation, recombination, rearrangement, ionizing, and photochemical reactions. It is shown that for the principle of reciprocity to be satisfied it is necessary that all chemical reactions exist in complementary pairs which consist of the forward and backward reactions. The backward reaction may be described by either the reverse or inverse process. The forward and backward processes must satisfy the same reciprocity equation. Because the number of dynamical variables is usually unbalanced on both sides of a chemical equation, it is necessary that this balance be established by including as many of the dynamical variables as needed before the reciprocity equation can be formulated. Statistical transformation models of the reactions are formulated. The models are classified under the titles free exchange, restricted exchange and simplified restricted exchange. The special equations for the forward and backward processes are obtained. The models are consistent with the H theorem and Le Chatelier's principle. The models are also formulated in the context of the direct simulation Monte Carlo method.

Modeling mass transfer and reaction of dilute solutes in a ternary phase system by the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Fu, Yu-Hang; Bai, Lin; Luo, Kai-Hong; Jin, Yong; Cheng, Yi

2017-04-01

In this work, we propose a general approach for modeling mass transfer and reaction of dilute solute(s) in incompressible three-phase flows by introducing a collision operator in lattice Boltzmann (LB) method. An LB equation was used to simulate the solute dynamics among three different fluids, in which the newly expanded collision operator was used to depict the interface behavior of dilute solute(s). The multiscale analysis showed that the presented model can recover the macroscopic transport equations derived from the Maxwell-Stefan equation for dilute solutes in three-phase systems. Compared with the analytical equation of state of solute and dynamic behavior, these results are proven to constitute a generalized framework to simulate solute distributions in three-phase flows, including compound soluble in one phase, compound adsorbed on single-interface, compound in two phases, and solute soluble in three phases. Moreover, numerical simulations of benchmark cases, such as phase decomposition, multilayered planar interfaces, and liquid lens, were performed to test the stability and efficiency of the model. Finally, the multiphase mass transfer and reaction in Janus droplet transport in a straight microchannel were well reproduced.

Three-Fluid Magnetohydrodynamic Modeling of the Solar Wind in the Outer Heliosphere

NASA Technical Reports Server (NTRS)

Usmanov, Arcadi V.; Goldstein, Melvyn L.; Matthaeus, William H.

2011-01-01

We have developed a three-fluid, fully three-dimensional magnetohydrodynamic model of the solar wind plasma in the outer heliosphere as a co-moving system of solar wind protons, electrons, and interstellar pickup protons, with separate energy equations for each species. Our approach takes into account the effects of electron heat conduction and dissipation of Alfvenic turbulence on the spatial evolution of the solar wind plasma and interplanetary magnetic fields. The turbulence transport model is based on the Reynolds decomposition of physical variables into mean and fluctuating components and uses the turbulent phenomenologies that describe the conversion of fluctuation energy into heat due to a turbulent cascade. We solve the coupled set of the three-fluid equations for the mean-field solar wind and the turbulence equations for the turbulence energy, cross helicity, and correlation length. The equations are written in the rotating frame of reference and include heating by turbulent dissipation, energy transfer from interstellar pickup protons to solar wind protons, and solar wind deceleration due to the interaction with the interstellar hydrogen. The numerical solution is constructed by the time relaxation method in the region from 0.3 to 100 AU. Initial results from the novel model are presented.

A molecular model for cohesive slip at polymer melt/solid interfaces.

PubMed

Tchesnokov, M A; Molenaar, J; Slot, J J M; Stepanyan, R

2005-06-01

A molecular model is proposed which predicts wall slip by disentanglement of polymer chains adsorbed on a wall from those in the polymer bulk. The dynamics of the near-wall boundary layer is found to be governed by a nonlinear equation of motion, which accounts for such mechanisms on surface chains as convection, retraction, constraint release, and thermal fluctuations. This equation is valid over a wide range of grafting regimes, including those in which interactions between neighboring adsorbed molecules become essential. It is not closed since the dynamics of adsorbed chains is shown to be coupled to that of polymer chains in the bulk via constraint release. The constitutive equations for the layer and bulk, together with continuity of stress and velocity, are found to form a closed system of equations which governs the dynamics of the whole "bulk+boundary layer" ensemble. Its solution provides a stick-slip law in terms of the molecular parameters and extruder geometry. The model is quantitative and contains only those parameters that can be measured directly, or extracted from independent rheological measurements. The model predictions show a good agreement with available experimental data.

Dynamical modeling and experiment for an intra-cavity optical parametric oscillator pumped by a Q-switched self-mode-locking laser

NASA Astrophysics Data System (ADS)

Wang, Jing; Liu, Nianqiao; Song, Peng; Zhang, Haikun

2016-11-01

The rate-equation-based model for the Q-switched mode-locking (QML) intra-cavity OPO (IOPO) is developed, which includes the behavior of the fundamental laser. The intensity fluctuation mechanism of the fundamental laser is first introduced into the dynamics of a mode-locking OPO. In the derived model, the OPO nonlinear conversion is considered as a loss for the fundamental laser and thus the QML signal profile originates from the QML fundamental laser. The rate equations are solved by a digital computer for the case of an IOPO pumped by an electro-optic (EO) Q-switched self-mode-locking fundamental laser. The simulated results for the temporal shape with 20 kHz EO repetition and 11.25 W pump power, the signal average power, the Q-switched pulsewidth and the Q-switched pulse energy are obtained from the rate equations. The signal trace and output power from an EO QML Nd3+: GdVO4/KTA IOPO are experimentally measured. The theoretical values from the rate equations agree with the experimental results well. The developed model explains the behavior, which is helpful to system optimization.

Explicit integration of Friedmann's equation with nonlinear equations of state

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

Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong, E-mail: chensx@henu.edu.cn, E-mail: gwg1@damtp.cam.ac.uk, E-mail: yisongyang@nyu.edu

2015-05-01

In this paper we study the integrability of the Friedmann equations, when the equation of state for the perfect-fluid universe is nonlinear, in the light of the Chebyshev theorem. A series of important, yet not previously touched, problems will be worked out which include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born-Infeld, two-fluid models, and Chern-Simons modified gravity theory models. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution which may also offer clues to a profound understanding of the problems in generalmore » settings. For example, in the Chaplygin gas universe, a few integrable cases lead us to derive a universal formula for the asymptotic exponential growth rate of the scale factor, of an explicit form, whether the Friedmann equation is integrable or not, which reveals the coupled roles played by various physical sectors and it is seen that, as far as there is a tiny presence of nonlinear matter, conventional linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied.« less

A Multiple Deficit Model of Reading Disability and Attention-Deficit/Hyperactivity Disorder: Searching for Shared Cognitive Deficits

ERIC Educational Resources Information Center

McGrath, Lauren M.; Pennington, Bruce F.; Shanahan, Michelle A.; Santerre-Lemmon, Laura E.; Barnard, Holly D.; Willcutt, Erik G.; DeFries, John C.; Olson, Richard K.

2011-01-01

Background: This study tests a multiple cognitive deficit model of reading disability (RD), attention-deficit/hyperactivity disorder (ADHD), and their comorbidity. Methods: A structural equation model (SEM) of multiple cognitive risk factors and symptom outcome variables was constructed. The model included phonological awareness as a unique…

Estimation of fat-free mass in Asian neonates using bioelectrical impedance analysis

PubMed Central

Tint, Mya-Thway; Ward, Leigh C; Soh, Shu E; Aris, Izzuddin M; Chinnadurai, Amutha; Saw, Seang Mei; Gluckman, Peter D; Godfrey, Keith M; Chong, Yap-Seng; Kramer, Michael S; Yap, Fabian; Lingwood, Barbara; Lee, Yung Seng

2016-01-01

The aims of this study were to develop and validate a prediction equation of fat-free mass (FFM) based on bioelectrical impedance analysis (BIA) and anthropometry using air displacement plethysmography (ADP) as a reference in Asian neonates and to test the applicability of the prediction equations in independent Western cohort. A total of 173 neonates at birth and 140 at week-2 of age were included. Multiple linear regression analysis was performed to develop the prediction equations in a two-third randomly selected subset and validated on the remaining one-third subset at each time point and in an independent Queensland cohort. FFM measured by ADP was the dependent variable and anthropometric measures, sex and impedance quotient (L2/R50) were independent variables in the model. Accuracy of prediction equations were assessed using intra-class correlation and Bland-Altman analyses. L2/R50 was the significant predictor of FFM at week-2 but not at birth. Compared to the model using weight, sex and length, including L2/R50 slightly improved the prediction with a bias of 0.01kg with 2SD limits of agreement (LOA) (0.18, −0.20). Prediction explained 88.9% of variation but not beyond that of anthropometry. Applying these equations to Queensland cohort provided similar performance at the appropriate age. However, when the Queensland equations were applied to our cohort, the bias increased slightly but with similar LOA. BIA appears to have limited use in predicting FFM in the first few weeks of life compared to simple anthropometry in Asian populations. There is a need for population and age appropriate FFM prediction equations. PMID:26856420

Estimation of fat-free mass in Asian neonates using bioelectrical impedance analysis.

PubMed

Tint, Mya-Thway; Ward, Leigh C; Soh, Shu E; Aris, Izzuddin M; Chinnadurai, Amutha; Saw, Seang Mei; Gluckman, Peter D; Godfrey, Keith M; Chong, Yap-Seng; Kramer, Michael S; Yap, Fabian; Lingwood, Barbara; Lee, Yung Seng

2016-03-28

The aims of this study were to develop and validate a prediction equation of fat-free mass (FFM) based on bioelectrical impedance analysis (BIA) and anthropometry using air-displacement plethysmography (ADP) as a reference in Asian neonates and to test the applicability of the prediction equations in an independent Western cohort. A total of 173 neonates at birth and 140 at two weeks of age were included. Multiple linear regression analysis was performed to develop the prediction equations in a two-third randomly selected subset and validated on the remaining one-third subset at each time point and in an independent Queensland cohort. FFM measured by ADP was the dependent variable, and anthropometric measures, sex and impedance quotient (L2/R50) were independent variables in the model. Accuracy of prediction equations was assessed using intra-class correlation and Bland-Altman analyses. L2/R50 was the significant predictor of FFM at week two but not at birth. Compared with the model using weight, sex and length, including L2/R50 slightly improved the prediction with a bias of 0·01 kg with 2 sd limits of agreement (LOA) (0·18, -0·20). Prediction explained 88·9 % of variation but not beyond that of anthropometry. Applying these equations to the Queensland cohort provided similar performance at the appropriate age. However, when the Queensland equations were applied to our cohort, the bias increased slightly but with similar LOA. BIA appears to have limited use in predicting FFM in the first few weeks of life compared with simple anthropometry in Asian populations. There is a need for population- and age-appropriate FFM prediction equations.

Predictive equations for total lung capacity and residual volume calculated from radiographs in a random sample of the Michigan population.

PubMed Central

Kilburn, K H; Warshaw, R H; Thornton, J C; Thornton, K; Miller, A

1992-01-01

BACKGROUND: Published predicted values for total lung capacity and residual volume are often based on a small number of subjects and derive from different populations from predicted spirometric values. Equations from the only two large studies gave smaller predicted values for total lung capacity than the smaller studies. A large number of subjects have been studied from a population which has already provided predicted values for spirometry and transfer factor for carbon monoxide. METHODS: Total lung capacity was measured from standard posteroanterior and lateral chest radiographs and forced vital capacity by spirometry in a population sample of 771 subjects. Prediction equations were developed for total lung capacity (TLC), residual volume (RV) and RV/TLC in two groups--normal and total. Subjects with signs or symptoms of cardiopulmonary disease were combined with the normal subjects and equations for all subjects were also modelled. RESULTS: Prediction equations for TLC and RV in non-smoking normal men and women were square root transformations which included height and weight but not age. They included a coefficient for duration of smoking in current smokers. The predictive equation for RV/TLC included weight, age, age and duration of smoking for current smokers and ex-smokers of both sexes. For the total population the equations took the same form but the height coefficients and constants were slightly different. CONCLUSION: These population based prediction equations for TLC, RV and RV/TLC provide reference standards in a population that has provided reference standards for spirometry and single breath transfer factor for carbon monoxide. PMID:1412094

Development of helicopter attitude axes controlled hover flight without pilot assistance and vehicle crashes

NASA Astrophysics Data System (ADS)

Simon, Miguel

In this work, we show how to computerize a helicopter to fly attitude axes controlled hover flight without the assistance of a pilot and without ever crashing. We start by developing a helicopter research test bed system including all hardware, software, and means for testing and training the helicopter to fly by computer. We select a Remote Controlled helicopter with a 5 ft. diameter rotor and 2.2 hp engine. We equip the helicopter with a payload of sensors, computers, navigation and telemetry equipment, and batteries. We develop a differential GPS system with cm accuracy and a ground computerized navigation system for six degrees of freedom (6-DoF) free flight while tracking navigation commands. We design feedback control loops with yet-to-be-determined gains for the five control "knobs" available to a flying radio-controlled (RC) miniature helicopter: engine throttle, main rotor collective pitch, longitudinal cyclic pitch, lateral cyclic pitch, and tail rotor collective pitch. We develop helicopter flight equations using fundamental dynamics, helicopter momentum theory and blade element theory. The helicopter flight equations include helicopter rotor equations of motions, helicopter rotor forces and moments, helicopter trim equations, helicopter stability derivatives, and a coupled fuselage-rotor helicopter 6-DoF model. The helicopter simulation also includes helicopter engine control equations, a helicopter aerodynamic model, and finally helicopter stability and control equations. The derivation of a set of non-linear equations of motion for the main rotor is a contribution of this thesis work. We design and build two special test stands for training and testing the helicopter to fly attitude axes controlled hover flight, starting with one axis at a time and progressing to multiple axes. The first test stand is built for teaching and testing controlled flight of elevation and yaw (i.e., directional control). The second test stand is built for teaching and testing any one or combination of the following attitude axes controlled flight: (1) pitch, (2) roll and (3) yaw. The subsequent development of a novel method to decouple, stabilize and teach the helicopter hover flight is a primary contribution of this thesis. The novel method included the development of a non-linear modeling technique for linearizing the RPM state equation dynamics so that a simple but accurate transfer function is derivable between the "available torque of the engine" and RPM. Specifically, the main rotor and tail rotor torques are modeled accurately with a bias term plus a nonlinear term involving the product of RPM squared times the main rotor blade pitch angle raised to the three-halves power. Application of this non-linear modeling technique resulted in a simple, representative and accurate transfer function model of the open-loop plant for the entire helicopter system so that all the feedback control laws for autonomous flight purposes could be derived easily using classical control theory. This is one of the contributions of this dissertation work. After discussing the integration of hardware and software elements of our helicopter research test bed system, we perform a number of experiments and tests using the two specially built test stands. Feedback gains are derived for controlling the following: (1) engine throttle to maintain prescribed main rotor angular speed, (2) main rotor collective pitch to maintain constant elevation, (3) longitudinal cyclic pitch to maintain prescribed pitch angle, (4) lateral cyclic pitch to maintain prescribed roll angle, and (5) yaw axis to maintain prescribed compass direction. (Abstract shortened by UMI.)

Hybrid discrete-time neural networks.

PubMed

Cao, Hongjun; Ibarz, Borja

2010-11-13

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.

Structural equation modeling of the associations between the home environment and obesity-related cardiovascular fitness and insulin resistance among Hispanic children.

PubMed

Santiago-Torres, Margarita; Cui, Yuchen; Adams, Alexandra K; Allen, David B; Carrel, Aaron L; Guo, Jessica Y; LaRowe, Tara L; Schoeller, Dale A

2016-06-01

Hispanic children are disproportionally affected by obesity-related risk of metabolic disease. We used the structural equation modeling to examine the associations between specific diet and physical activity (PA) behaviors at home and Hispanic children's metabolic health. A total of 187 Hispanic children and their parents from an urban community in Wisconsin participated in the study. Exposure variables included, children's daily intake of sugar-sweetened beverages (SSB) and PA; home availability of SSB and PA areas/equipment; and parents' intake of SSB and PA, assessed through self-administered questionnaires. Outcome variables for children's metabolic health included, measured anthropometrics; cardiovascular fitness assessed using the Progressive Aerobic Cardiovascular Endurance Run (PACER); and insulin resistance determined with the homeostasis model assessment of insulin resistance (HOMAIR). We found that children's daily intake of SSB was positively associated with BMI z-score, which in turn, was positively associated with HOMAIR (P < 0.05). Specific diet behaviors at home associated with children's intake of SSB, included home availability of SSB, which mediated the association between parents' and children's intake of SSB (P < 0.05). Children's PA was positively associated with PACER z-score, which in turn, was inversely associated with HOMAIR (P < 0.05). Specific PA behaviors at home associated with children's PA, included home availability of PA areas/equipment, which mediated the association between parents' and children's PA (P < 0.05). The structural equation model indices suggested a satisfactory model fit (Chi-square, X(2) = 53.1, comparative fix index = 0.92, root-mean-squared error associated = 0.04). The findings confirm the need for interventions at the family level that promotes healthier home environments by targeting poor diet and low levels of PA in all family members. Published by Elsevier Ltd.

The Gassmann-Burgers Model to Simulate Seismic Waves at the Earth Crust And Mantle

NASA Astrophysics Data System (ADS)

Carcione, José M.; Poletto, Flavio; Farina, Biancamaria; Craglietto, Aronne

2017-03-01

The upper part of the crust shows generally brittle behaviour while deeper zones, including the mantle, may present ductile behaviour, depending on the pressure-temperature conditions; moreover, some parts are melted. Seismic waves can be used to detect these conditions on the basis of reflection and transmission events. Basically, from the elastic-plastic point of view the seismic properties (seismic velocity and density) depend on effective pressure and temperature. Confining and pore pressures have opposite effects on these properties, such that very small effective pressures (the presence of overpressured fluids) may substantially decrease the P- and S-wave velocities, mainly the latter, by opening of cracks and weakening of grain contacts. Similarly, high temperatures induce the same effect by partial melting. To model these effects, we consider a poro-viscoelastic model based on Gassmann equations and Burgers mechanical model to represent the properties of the rock frame and describe ductility in which deformation takes place by shear plastic flow. The Burgers elements allow us to model the effects of seismic attenuation, velocity dispersion and steady-state creep flow, respectively. The stiffness components of the brittle and ductile media depend on stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. Effective pressure effects are taken into account in the dry-rock moduli using exponential functions whose parameters are obtained by fitting experimental data as a function of confining pressure. Since fluid effects are important, the density and bulk modulus of the saturating fluids (water and steam) are modeled using the equations provided by the NIST website, including supercritical behaviour. The theory allows us to obtain the phase velocity and quality factor as a function of depth and geological pressure and temperature as well as time frequency. We then obtain the PS and SH equations of motion recast in the velocity-stress formulation, including memory variables to avoid the computation of time convolutions. The equations correspond to isotropic anelastic and inhomogeneous media and are solved by a direct grid method based on the Runge-Kutta time stepping technique and the Fourier pseudospectral method. The algorithm is tested with success against known analytical solutions for different shear viscosities. An example shows how anomalous conditions of pressure and temperature can in principle be detected with seismic waves.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Carbon solids in oxygen-deficient explosives (LA-UR-13-21151)

NASA Astrophysics Data System (ADS)

Peery, Travis

2013-06-01

The phase behavior of excess carbon in oxygen-deficient explosives has a significant effect on detonation properties and product equations of state. Mixtures of fuel oil in ammonium nitrate (ANFO) above a stoichiometric ratio demonstrate that even small amounts of graphite, on the order of 5% by mole fraction, can substantially alter the Chapman-Jouget (CJ) state properties, a central ingredient in modeling the products equation of state. Similar effects can be seen for Composition B, which borders the carbon phase boundary between graphite and diamond. Nano-diamond formation adds complexity to the product modeling because of surface adsorption effects. I will discuss these carbon phase issues in our equation of state modeling of detonation products, including our statistical mechanics description of carbon clustering and surface chemistry to properly treat solid carbon formation. This work is supported by the Advanced Simulation and Computing Program, under the NNSA.

Numerical Simulation and Quantitative Uncertainty Assessment of Microchannel Flow

NASA Astrophysics Data System (ADS)

Debusschere, Bert; Najm, Habib; Knio, Omar; Matta, Alain; Ghanem, Roger; Le Maitre, Olivier

2002-11-01

This study investigates the effect of uncertainty in physical model parameters on computed electrokinetic flow of proteins in a microchannel with a potassium phosphate buffer. The coupled momentum, species transport, and electrostatic field equations give a detailed representation of electroosmotic and pressure-driven flow, including sample dispersion mechanisms. The chemistry model accounts for pH-dependent protein labeling reactions as well as detailed buffer electrochemistry in a mixed finite-rate/equilibrium formulation. To quantify uncertainty, the governing equations are reformulated using a pseudo-spectral stochastic methodology, which uses polynomial chaos expansions to describe uncertain/stochastic model parameters, boundary conditions, and flow quantities. Integration of the resulting equations for the spectral mode strengths gives the evolution of all stochastic modes for all variables. Results show the spatiotemporal evolution of uncertainties in predicted quantities and highlight the dominant parameters contributing to these uncertainties during various flow phases. This work is supported by DARPA.

A model of rotationally-sampled wind turbulence for predicting fatigue loads in wind turbines

NASA Technical Reports Server (NTRS)

Spera, David A.

1995-01-01

Empirical equations are presented with which to model rotationally-sampled (R-S) turbulence for input to structural-dynamic computer codes and the calculation of wind turbine fatigue loads. These equations are derived from R-S turbulence data which were measured at the vertical-plane array in Clayton, New Mexico. For validation, the equations are applied to the calculation of cyclic flapwise blade loads for the NASA/DOE Mod-2 2.5-MW experimental HAWT's (horizontal-axis wind turbines), and the results compared to measured cyclic loads. Good correlation is achieved, indicating that the R-S turbulence model developed in this study contains the characteristics of the wind which produce many of the fatigue loads sustained by wind turbines. Empirical factors are included which permit the prediction of load levels at specified percentiles of occurrence, which is required for the generation of fatigue load spectra and the prediction of the fatigue lifetime of structures.

Generalized two-temperature model for coupled phonon-magnon diffusion.

PubMed

Liao, Bolin; Zhou, Jiawei; Chen, Gang

2014-07-11

We generalize the two-temperature model [Sanders and Walton, Phys. Rev. B 15, 1489 (1977)] for coupled phonon-magnon diffusion to include the effect of the concurrent magnetization flow, with a particular emphasis on the thermal consequence of the magnon flow driven by a nonuniform magnetic field. Working within the framework of the Boltzmann transport equation, we derive the constitutive equations for coupled phonon-magnon transport driven by gradients of both temperature and external magnetic fields, and the corresponding conservation laws. Our equations reduce to the original Sanders-Walton two-temperature model under a uniform external field, but predict a new magnon cooling effect driven by a nonuniform magnetic field in a homogeneous single-domain ferromagnet. We estimate the magnitude of the cooling effect in an yttrium iron garnet, and show it is within current experimental reach. With properly optimized materials, the predicted cooling effect can potentially supplement the conventional magnetocaloric effect in cryogenic applications in the future.

On a Multiphase Multicomponent Model of Biofilm Growth

NASA Astrophysics Data System (ADS)

Friedman, Avner; Hu, Bei; Xue, Chuan

2014-01-01

Biofilms are formed when free-floating bacteria attach to a surface and secrete polysaccharide to form an extracellular polymeric matrix (EPS). A general model of biofilm growth needs to include the bacteria, the EPS, and the solvent within the biofilm region Ω( t), and the solvent in the surrounding region D( t). The interface between the two regions, Γ( t), is a free boundary. In this paper, we consider a mathematical model that consists of a Stokes equation for the EPS with bacteria attached to it, a Stokes equation for the solvent in Ω( t) and another for the solvent in D( t). The volume fraction of the EPS is another unknown satisfying a reaction-diffusion equation. The entire system is coupled nonlinearly within Ω( t) and across the free surface Γ( t). We prove the existence and uniqueness of a solution, with a smooth surface Γ( t), for a small time interval.

Effect of surface bilayer charges on the magnetic field around ionic channels

NASA Astrophysics Data System (ADS)

Gomes Soares, Marília Amável; Cortez, Celia Martins; Oliveira Cruz, Frederico Alan de; Silva, Dilson

2017-01-01

In this work, we present a physic-mathematical model for representing the ion transport through membrane channels, in special Na+ and K+-channels, and discuss the influence of surface bilayer charges on the magnetic field behavior around the ionic current. The model was composed of a set of equations, including: a nonlinear differential Poisson-Boltzmann equation which usually allows to estimate the surface potentials and electric potential profile across membrane; equations for the ionic flux through channel and the ionic current density based on Armstrong's model for Na+ and K+ permeability and other Physics concepts; and a magnetic field expression derived from the classical Ampère equation. Results from computational simulations using the finite element method suggest that the ionic permeability is strongly dependent of surface bilayer charges, the current density through a K+-channel is very less sensible to temperature changes than the current density through a Na+- channel, active Na+-channels do not directly interfere with the K+-channels around, and vice-versa, since the magnetic perturbation generated by an active channel is of short-range.

Hierarchical coarse-graining model for photosystem II including electron and excitation-energy transfer processes.

PubMed

Matsuoka, Takeshi; Tanaka, Shigenori; Ebina, Kuniyoshi

2014-03-01

We propose a hierarchical reduction scheme to cope with coupled rate equations that describe the dynamics of multi-time-scale photosynthetic reactions. To numerically solve nonlinear dynamical equations containing a wide temporal range of rate constants, we first study a prototypical three-variable model. Using a separation of the time scale of rate constants combined with identified slow variables as (quasi-)conserved quantities in the fast process, we achieve a coarse-graining of the dynamical equations reduced to those at a slower time scale. By iteratively employing this reduction method, the coarse-graining of broadly multi-scale dynamical equations can be performed in a hierarchical manner. We then apply this scheme to the reaction dynamics analysis of a simplified model for an illuminated photosystem II, which involves many processes of electron and excitation-energy transfers with a wide range of rate constants. We thus confirm a good agreement between the coarse-grained and fully (finely) integrated results for the population dynamics. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.