A near-wall turbulence model and its application to fully developed turbulent channel and pipe flows

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1988-01-01

A near wall turbulence model and its incorporation into a multiple-time-scale turbulence model are presented. In the method, the conservation of mass, momentum, and the turbulent kinetic energy equations are integrated up to the wall; and the energy transfer rate and the dissipation rate inside the near wall layer are obtained from algebraic equations. The algebraic equations for the energy transfer rate and the dissipation rate inside the near wall layer were obtained from a k-equation turbulence model and the near wall analysis. A fully developed turbulent channel flow and fully developed turbulent pipe flows were solved using a finite element method to test the predictive capability of the turbulence model. The computational results compared favorably with experimental data. It is also shown that the present turbulence model could resolve the over shoot phenomena of the turbulent kinetic energy and the dissipation rate in the region very close to the wall.

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

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

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

Method of controlling a resin curing process. [for fiber reinforced composites

NASA Technical Reports Server (NTRS)

Webster, Charles Neal (Inventor); Scott, Robert O. (Inventor)

1989-01-01

The invention relates to an analytical technique for controlling the curing process of fiber-reinforced composite materials that are formed using thermosetting resins. The technique is the percent gel method and involves development of a time-to-gel equation as a function of temperature. From this equation a rate-of-gel equation is then determined, and a percent gel is calculated which is the product of rate-of-gel times time. Percent gel accounting is used to control the proper pressure application point in an autoclave cure process to achieve desired properties in a production composite part.

High Strain Rate Deformation Modeling of a Polymer Matrix Composite. Part 1; Matrix Constitutive Equations

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Stouffer, Donald C.

1998-01-01

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Development and application of an observation-based light attenuation equation for northern Gulf of Mexico

EPA Science Inventory

Solar radiation is one of the main factors controlling the rate of primary production on the Louisiana Shelf in the northern Gulf of Mexico. This work seeks to improve on previously published empirical equations through the use of statistical data transformation and the incorpora...

Flow stress equations for type 304 stainless and AISI 1055 steels

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

Dadras, P.

A model for stress-strain behavior under hot working conditions has been proposed. Based on experimental data, equations for the dependence of flow stress on strain, strain rate, and temperature have been developed. Application to type 304 stainless steel and AISI 1055 steel has been demonstrated.

Effect of picric acid and enzymatic creatinine on the efficiency of the glomerular filtration rate predicator formula.

PubMed

Qiu, Ling; Guo, Xiuzhi; Zhu, Yan; Shou, Weilin; Gong, Mengchun; Zhang, Lin; Han, Huijuan; Quan, Guoqiang; Xu, Tao; Li, Hang; Li, Xuewang

2013-01-01

To investigate the impact of serum creatinine measurement on the applicability of glomerular filtration rate (GFR) evaluation equations. 99mTc-DTPA plasma clearance rate was used as GFR reference (rGFR) in patients with chronic kidney disease (CKD). Serum creatinine was measureded using enzymatic or picric acid creatinine reagent. The GFR of the patients were estimated using the Cockcroft-Gault equation corrected for body surface area, simplified Modification of Diet in Renal Disease (MDRD) equation, simplified MDRD equation corrected to isotopes dilution mass spectrometry, the CKD epidemiology collaborative research equation, and two Chinese simplified MDRD equations. Significant differences in the eGFR results estimated through enzymatic and picric acid methods were observed for the same evaluation equation. The intraclass correlation coefficient (ICC) of eGFR when the creatinine was measured by the picric acid method was significantly lower than that of the enzymatic method. The assessment accuracy of every equation using the enzymatic method to measure creatinine was significantly higher than that measured by the picric acid method when rGFR was > or = 60 mL/min/1.73m2. A significant difference was demonstrated in the same GFR evaluation equation using the picric acid and enzymatic methods. The enzymatic creatinine method was better than the picric acid method.

Simulation of a steady-state integrated human thermal system.

NASA Technical Reports Server (NTRS)

Hsu, F. T.; Fan, L. T.; Hwang, C. L.

1972-01-01

The mathematical model of an integrated human thermal system is formulated. The system consists of an external thermal regulation device on the human body. The purpose of the device (a network of cooling tubes held in contact with the surface of the skin) is to maintain the human body in a state of thermoneutrality. The device is controlled by varying the inlet coolant temperature and coolant mass flow rate. The differential equations of the model are approximated by a set of algebraic equations which result from the application of the explicit forward finite difference method to the differential equations. The integrated human thermal system is simulated for a variety of combinations of the inlet coolant temperature, coolant mass flow rate, and metabolic rates.

Dissolution of solid dosage form. II. Equations for the dissolution of nondisintegrating tablet under the sink condition.

PubMed

Yonezawa, Y; Shirakura, K; Otsuka, A; Sunada, H

1991-03-01

An equation for dissolution from the whole surface of a nondisintegrating single component tablet under the sink condition was derived. Also, equations for several dissolution manners of the tablet under the sink condition were derived in the postulation of the dominant dissolution rate constant which determines the dissolution manner. The applicability or validity of these equations were examined by the dissolution measurements with nondisintegrating single component tablets. About one-tenth the amount of the amount needed to saturate the solution was used to prepare a tablet, and dissolution measurements were carried out with the tablet whose flat or side surface was masked with an adhesive tape in accordance with the conditions for derivation of equations. Among the derived equations, dissolution from the whole surface of a tablet was expressed by a form similar to the cube root law equation for particles. Hence, a single component tablet compressed by the use of a suitable amount was thought to behave like a single crystal. Also, equations derived for several dissolution manners were thought to be applicable for the dissolution of a nonspherical particle and crystal concerning the crystal's habit and its dissolution property, and the extended applicability was examined by converting the crystal into a simplified or idealized form, i.e., rectangle or plate.

Relationships between thermal maturity indices calculated using Arrhenius equation and Lopatin method: implications for petroleum exploration

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

Wood, D.A.

1988-02-01

Thermal maturity can be calculated with time-temperature indices (TTI) based on the Arrhenius equation using kinetics applicable to a range of Types II and III kerogens. These TTIs are compared with TTI calculations based on the Lopatin method and are related theoretically (and empirically via vitrinite reflectance) to the petroleum-generation window. The TTIs for both methods are expressed mathematically as integrals of temperature combined with variable linear heating rates for selected temperature intervals. Heating rates control the thermal-maturation trends of buried sediments. Relative to Arrhenius TTIs, Lopatin TTIs tend to underestimate thermal maturity at high heating rates and overestimate itmore » as low heating rates. Complex burial histories applicable to a range of tectonic environments illustrate the different exploration decisions that might be made on the basis of independent results of these two thermal-maturation models. 15 figures, 8 tables.« less

Parallel multigrid smoothing: polynomial versus Gauss-Seidel

NASA Astrophysics Data System (ADS)

Adams, Mark; Brezina, Marian; Hu, Jonathan; Tuminaro, Ray

2003-07-01

Gauss-Seidel is often the smoother of choice within multigrid applications. In the context of unstructured meshes, however, maintaining good parallel efficiency is difficult with multiplicative iterative methods such as Gauss-Seidel. This leads us to consider alternative smoothers. We discuss the computational advantages of polynomial smoothers within parallel multigrid algorithms for positive definite symmetric systems. Two particular polynomials are considered: Chebyshev and a multilevel specific polynomial. The advantages of polynomial smoothing over traditional smoothers such as Gauss-Seidel are illustrated on several applications: Poisson's equation, thin-body elasticity, and eddy current approximations to Maxwell's equations. While parallelizing the Gauss-Seidel method typically involves a compromise between a scalable convergence rate and maintaining high flop rates, polynomial smoothers achieve parallel scalable multigrid convergence rates without sacrificing flop rates. We show that, although parallel computers are the main motivation, polynomial smoothers are often surprisingly competitive with Gauss-Seidel smoothers on serial machines.

On conforming mixed finite element methods for incompressible viscous flow problems

NASA Technical Reports Server (NTRS)

Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.

1982-01-01

The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.

Semiempirical equations for modeling solid-state kinetics based on a Maxwell-Boltzmann distribution of activation energies: applications to a polymorphic transformation under crystallization slurry conditions and to the thermal decomposition of AgMnO4 crystals.

PubMed

Skrdla, Peter J; Robertson, Rebecca T

2005-06-02

Many solid-state reactions and phase transformations performed under isothermal conditions give rise to asymmetric, sigmoidally shaped conversion-time (x-t) profiles. The mathematical treatment of such curves, as well as their physical interpretation, is often challenging. In this work, the functional form of a Maxwell-Boltzmann (M-B) distribution is used to describe the distribution of activation energies for the reagent solids, which, when coupled with an integrated first-order rate expression, yields a novel semiempirical equation that may offer better success in the modeling of solid-state kinetics. In this approach, the Arrhenius equation is used to relate the distribution of activation energies to a corresponding distribution of rate constants for the individual molecules in the reagent solids. This distribution of molecular rate constants is then correlated to the (observable) reaction time in the derivation of the model equation. In addition to providing a versatile treatment for asymmetric, sigmoidal reaction curves, another key advantage of our equation over other models is that the start time of conversion is uniquely defined at t = 0. We demonstrate the ability of our simple, two-parameter equation to successfully model the experimental x-t data for the polymorphic transformation of a pharmaceutical compound under crystallization slurry (i.e., heterogeneous) conditions. Additionally, we use a modification of this equation to model the kinetics of a historically significant, homogeneous solid-state reaction: the thermal decomposition of AgMnO4 crystals. The potential broad applicability of our statistical (i.e., dispersive) kinetic approach makes it a potentially attractive alternative to existing models/approaches.

Fracture simulation of elastomer blended polypropylene based on elastoviscoplastic constitutive equation with craze and tensile softening law

NASA Astrophysics Data System (ADS)

Mae, H.

2006-08-01

The strong strain-rate dependence, neck propagation and craze evolution characterize the large plastic deformation and fracture behavior of polymer. In the latest study, Kobayashi, Tomii and Shizawa suggested the elastoviscoplastic constitutive equation based on craze evolution and annihilation and then applied it to the plane strain issue of polymer. In the previous study, the author applied their suggested elastoviscoplastic constitutive equation with craze effect to the three dimensional shell and then showed that the load displacement history was in good agreement with the experimental result including only microscopic crack such as crazes. For the future industrial applications, the macroscopic crack has to be taken into account. Thus, the main objective of this study is to propose the tensile softening equation and then add it to the elastoviscoplastic constitutive equation with craze effect so that the load displacement history can be roughly simulated during the macroscopic crack propagation. The tested material in this study is the elastomer blended polypropylene used in the interior and exterior of automobiles. First, the material properties are obtained based on the tensile test results at wide range of strain rates: 10 - 4-102 (1/sec). Next, the compact tension test is conducted and then the tensile softening parameters are fixed. Then, the dart impact test is carried out in order to obtain the load displacement history and also observe the macroscopic crack propagation at high strain rate. Finally, the fracture behavior is simulated and then compared with the experimental results. It is shown that the predictions of the constitutive equation with the proposed tensile softening equation are in good agreement with the experimental results for the future industrial applications.

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.

An optimal resolved rate law for kindematically redundant manipulators

NASA Technical Reports Server (NTRS)

Bourgeois, B. J.

1987-01-01

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution was found to cause large joint rates in some case. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to nonplanar manipulators.

Application of Stochastic and Deterministic Approaches to Modeling Interstellar Chemistry

NASA Astrophysics Data System (ADS)

Pei, Yezhe

This work is about simulations of interstellar chemistry using the deterministic rate equation (RE) method and the stochastic moment equation (ME) method. Primordial metal-poor interstellar medium (ISM) is of our interest and the socalled “Population-II” stars could have been formed in this environment during the “Epoch of Reionization” in the baby universe. We build a gas phase model using the RE scheme to describe the ionization-powered interstellar chemistry. We demonstrate that OH replaces CO as the most abundant metal-bearing molecule in such interstellar clouds of the early universe. Grain surface reactions play an important role in the studies of astrochemistry. But the lack of an accurate yet effective simulation method still presents a challenge, especially for large, practical gas-grain system. We develop a hybrid scheme of moment equations and rate equations (HMR) for large gas-grain network to model astrochemical reactions in the interstellar clouds. Specifically, we have used a large chemical gas-grain model, with stochastic moment equations to treat the surface chemistry and deterministic rate equations to treat the gas phase chemistry, to simulate astrochemical systems as of the ISM in the Milky Way, the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC). We compare the results to those of pure rate equations and modified rate equations and present a discussion about how moment equations improve our theoretical modeling and how the abundances of the assorted species are changed by varied metallicity. We also model the observed composition of H2O, CO and CO2 ices toward Young Stellar Objects in the LMC and show that the HMR method gives a better match to the observation than the pure RE method.

Approximate convective heating equations for hypersonic flows

NASA Technical Reports Server (NTRS)

Zoby, E. V.; Moss, J. N.; Sutton, K.

1979-01-01

Laminar and turbulent heating-rate equations appropriate for engineering predictions of the convective heating rates about blunt reentry spacecraft at hypersonic conditions are developed. The approximate methods are applicable to both nonreacting and reacting gas mixtures for either constant or variable-entropy edge conditions. A procedure which accounts for variable-entropy effects and is not based on mass balancing is presented. Results of the approximate heating methods are in good agreement with existing experimental results as well as boundary-layer and viscous-shock-layer solutions.

Development of a new model for batch sedimentation and application to secondary settling tanks design.

PubMed

Karamisheva, Ralica D; Islam, M A

2005-01-01

Assuming that settling takes place in two zones (a constant rate zone and a variable rate zone), a model using four parameters accounting for the nature of the water-suspension system has been proposed for describing batch sedimentation processes. The sludge volume index (SVI) has been expressed in terms of these parameters. Some disadvantages of the SVI application as a design parameter have been pointed out, and it has been shown that a relationship between zone settling velocity and sludge concentration is more consistent for describing the settling behavior and for design of settling tanks. The permissible overflow rate has been related to the technological parameters of secondary settling tank by simple working equations. The graphical representations of these equations could be used to optimize the design and operation of secondary settling tanks.

Concurrent Reinforcement Schedules for Problem Behavior and Appropriate Behavior: Experimental Applications of the Matching Law

ERIC Educational Resources Information Center

Borrero, Carrie S. W.; Vollmer, Timothy R.; Borrero, John C.; Bourret, Jason C.; Sloman, Kimberly N.; Samaha, Andrew L.; Dallery, Jesse

2010-01-01

This study evaluated how children who exhibited functionally equivalent problem and appropriate behavior allocate responding to experimentally arranged reinforcer rates. Relative reinforcer rates were arranged on concurrent variable-interval schedules and effects on relative response rates were interpreted using the generalized matching equation.…

Illness-death model: statistical perspective and differential equations.

PubMed

Brinks, Ralph; Hoyer, Annika

2018-01-27

The aim of this work is to relate the theory of stochastic processes with the differential equations associated with multistate (compartment) models. We show that the Kolmogorov Forward Differential Equations can be used to derive a relation between the prevalence and the transition rates in the illness-death model. Then, we prove mathematical well-definedness and epidemiological meaningfulness of the prevalence of the disease. As an application, we derive the incidence of diabetes from a series of cross-sections.

Strain Rate Dependent Deformation and Strength Modeling of a Polymer Matrix Composite Utilizing a Micromechanics Approach. Degree awarded by Cincinnati Univ.

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.

1999-01-01

Potential gas turbine applications will expose polymer matrix composites to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under extreme conditions. Specifically, analytical methods designed for these applications must have the capability of properly capturing the strain rate sensitivities and nonlinearities that are present in the material response. The Ramaswamy-Stouffer constitutive equations, originally developed to analyze the viscoplastic deformation of metals, have been modified to simulate the nonlinear deformation response of ductile, crystalline polymers. The constitutive model is characterized and correlated for two representative ductile polymers. Fiberite 977-2 and PEEK, and the computed results correlate well with experimental values. The polymer constitutive equations are implemented in a mechanics of materials based composite micromechanics model to predict the nonlinear, rate dependent deformation response of a composite ply. Uniform stress and uniform strain assumptions are applied to compute the effective stresses of a composite unit cell from the applied strains. The micromechanics equations are successfully verified for two polymer matrix composites. IM7/977-2 and AS4/PEEK. The ultimate strength of a composite ply is predicted with the Hashin failure criteria that were implemented in the composite micromechanics model. The failure stresses of the two composite material systems are accurately predicted for a variety of fiber orientations and strain rates. The composite deformation model is implemented in LS-DYNA, a commercially available transient dynamic explicit finite element code. The matrix constitutive equations are converted into an incremental form, and the model is implemented into LS-DYNA through the use of a user defined material subroutine. The deformation response of a bulk polymer and a polymer matrix composite are predicted by finite element analyses. The results compare reasonably well to experimental values, with some discrepancies. The discrepancies are at least partially caused by the method used to integrate the rate equations in the polymer constitutive model.

Apparatus and method for determining solids circulation rate

DOEpatents

Ludlow, J Christopher [Morgantown, WV; Spenik, James L [Morgantown, WV

2012-02-14

The invention relates to a method of determining bed velocity and solids circulation rate in a standpipe experiencing a moving packed bed flow, such as the in the standpipe section of a circulating bed fluidized reactor The method utilizes in-situ measurement of differential pressure over known axial lengths of the standpipe in conjunction with in-situ gas velocity measurement for a novel application of Ergun equations allowing determination of standpipe void fraction and moving packed bed velocity. The method takes advantage of the moving packed bed property of constant void fraction in order to integrate measured parameters into simultaneous solution of Ergun-based equations and conservation of mass equations across multiple sections of the standpipe.

Basal metabolic rate studies in humans: measurement and development of new equations.

PubMed

Henry, C J K

2005-10-01

To facilitate the Food and Agriculture Organization/World Health Organization/United Nations University Joint (FAO/WHO/UNU) Expert Consultation on Energy and Protein Requirements which met in Rome in 1981, Schofield et al. reviewed the literature and produced predictive equations for both sexes for the following ages: 0-3, 3-10, 10-18, 18-30, 30-60 and >60 years. These formed the basis for the equations used in 1985 FAO/WHO/UNU document, Energy and Protein Requirements. While Schofield's analysis has served a significant role in re-establishing the importance of using basal metabolic rate (BMR) to predict human energy requirements, recent workers have subsequently queried the universal validity and application of these equations. A survey of the most recent studies (1980-2000) in BMR suggests that in most cases the current FAO/WHO/UNU predictive equations overestimate BMR in many communities. The FAO/WHO/UNU equations to predict BMR were developed using a database that contained a disproportionate number--3388 out of 7173 (47%)--of Italian subjects. The Schofield database contained relatively few subjects from the tropical region. The objective here is to review the historical development in the measurement and application of BMR and to critically review the Schofield et al. BMR database presenting a series of new equations to predict BMR. This division, while arbitrary, will enable readers who wish to omit the historical review of BMR to concentrate on the evolution of the new BMR equations. BMR data collected from published and measured values. A series of new equations (Oxford equations) have been developed using a data set of 10,552 BMR values that (1) excluded all the Italian subjects and (2) included a much larger number (4018) of people from the tropics. In general, the Oxford equations tend to produce lower BMR values than the current FAO/WHO/UNU equations in 18-30 and 30-60 year old males and in all females over 18 years of age. This is an opportune moment to re-examine the role and place of BMR measurements in estimating total energy requirements today. The Oxford equations' future use and application will surely depend on their ability to predict more accurately the BMR in contemporary populations.

Numerical simulations of microwave heating of liquids: enhancements using Krylov subspace methods

NASA Astrophysics Data System (ADS)

Lollchund, M. R.; Dookhitram, K.; Sunhaloo, M. S.; Boojhawon, R.

2013-04-01

In this paper, we compare the performances of three iterative solvers for large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes (NS) equations. These equations are employed mainly in the simulation of microwave heating of liquids. The emphasis of this work is on the application of Krylov projection techniques such as Generalized Minimal Residual (GMRES) to solve the Pressure Poisson Equations that result from discretisation of the NS equations. The performance of the GMRES method is compared with the traditional Gauss-Seidel (GS) and point successive over relaxation (PSOR) techniques through their application to simulate the dynamics of water housed inside a vertical cylindrical vessel which is subjected to microwave radiation. It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of computational times and number of iterations.

Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river

USGS Publications Warehouse

Gaeuman, David; Andrews, E.D.; Krause, Andreas; Smith, Wes

2009-01-01

Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock‐Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (τ*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between τ*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock‐Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock‐Crowe equations nonetheless consistently under‐predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of τ*rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock‐Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock‐Crowe equation for determining τ*rm and the hiding function used to scale τ*rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.

Virtual Levels and Role Models: N-Level Structural Equations Model of Reciprocal Ratings Data.

PubMed

Mehta, Paras D

2018-01-01

A general latent variable modeling framework called n-Level Structural Equations Modeling (NL-SEM) for dependent data-structures is introduced. NL-SEM is applicable to a wide range of complex multilevel data-structures (e.g., cross-classified, switching membership, etc.). Reciprocal dyadic ratings obtained in round-robin design involve complex set of dependencies that cannot be modeled within Multilevel Modeling (MLM) or Structural Equations Modeling (SEM) frameworks. The Social Relations Model (SRM) for round robin data is used as an example to illustrate key aspects of the NL-SEM framework. NL-SEM introduces novel constructs such as 'virtual levels' that allows a natural specification of latent variable SRMs. An empirical application of an explanatory SRM for personality using xxM, a software package implementing NL-SEM is presented. Results show that person perceptions are an integral aspect of personality. Methodological implications of NL-SEM for the analyses of an emerging class of contextual- and relational-SEMs are discussed.

An optimal resolved rate law for kinematically redundant manipulators

NASA Technical Reports Server (NTRS)

Bourgeois, B. J.

1987-01-01

The resolved rate law for a manipulator provides the instantaneous joint rates required to satisfy a given instantaneous hand motion. When the joint space has more degrees of freedom than the task space, the manipulator is kinematically redundant and the kinematic rate equations are underdetermined. These equations can be locally optimized, but the resulting pseudo-inverse solution has been found to cause large joint rates in some cases. A weighting matrix in the locally optimized (pseudo-inverse) solution is dynamically adjusted to control the joint motion as desired. Joint reach limit avoidance is demonstrated in a kinematically redundant planar arm model. The treatment is applicable to redundant manipulators with any number of revolute joints and to non-planar manipulators.

Application of Eyring's thermal activation theory to constitutive equations for polymers

NASA Astrophysics Data System (ADS)

Zerilli, Frank J.; Armstrong, Ronald W.

2000-04-01

The application of a constitutive model based on the thermal activation theory of Eyring to the yield stress of polymethylmethacrylate at various temperatures and strain rates, as measured by Bauwens-Crowet, shows that the yield stress may reasonably well be described by a thermal activation equation in which the volume of activation is inversely proportional to the yield stress. It is found that, to obtain an accurate model, the dependence of the cold (T=0 K) yield stress on the shear modulus must be taken into account.

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

NASA Technical Reports Server (NTRS)

Ito, K.

1983-01-01

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

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.

How electronic dynamics with Pauli exclusion produces Fermi-Dirac statistics.

PubMed

Nguyen, Triet S; Nanguneri, Ravindra; Parkhill, John

2015-04-07

It is important that any dynamics method approaches the correct population distribution at long times. In this paper, we derive a one-body reduced density matrix dynamics for electrons in energetic contact with a bath. We obtain a remarkable equation of motion which shows that in order to reach equilibrium properly, rates of electron transitions depend on the density matrix. Even though the bath drives the electrons towards a Boltzmann distribution, hole blocking factors in our equation of motion cause the electronic populations to relax to a Fermi-Dirac distribution. These factors are an old concept, but we show how they can be derived with a combination of time-dependent perturbation theory and the extended normal ordering of Mukherjee and Kutzelnigg for a general electronic state. The resulting non-equilibrium kinetic equations generalize the usual Redfield theory to many-electron systems, while ensuring that the orbital occupations remain between zero and one. In numerical applications of our equations, we show that relaxation rates of molecules are not constant because of the blocking effect. Other applications to model atomic chains are also presented which highlight the importance of treating both dephasing and relaxation. Finally, we show how the bath localizes the electron density matrix.

Evaluation of the pentose phosphate pathway from 14CO2 data. Fallibility of a classic equation when applied to non-homogeneous tissues.

PubMed

Larrabee, M G

1990-11-15

A classic equation that has frequently been used to estimate the fraction of glucose metabolized by the pentose phosphate pathway, using 14CO2 data, is more simply re-derived with careful consideration of the assumptions involved and the conditions under which it is applicable. The equation is shown to be unreliable for non-homogeneous tissues, depending on the fraction of triose phosphate converted to CO2. The formula in question is as follows: ([1]CO2/G-[6]CO2/G)/(1-[6]CO2/G) = 3Fmet./(1 + 2Fmet.) where [1]CO2 and [6]CO2 are output rates of carbons 1 and 6 of glucose respectively to CO2, G is the rate of glucose uptake and Fmet. is the fraction of the glucose that is metabolized to CO2 and triose phosphate by the pentose phosphate pathway, allowing for recycling of an appropriate fraction of the fructose-6-phosphate produced by the pathway. This analysis illustrates the importance of suitably testing any equation that assumes homogeneity before application to non-homogeneous tissues.

Proof-of-Concept Application of Tier 2 Modeling Approach within the Training Range Environmental Evaluation And Characterization System

DTIC Science & Technology

2011-08-01

Topographic factor, LS, in USLE (U.S. Department of Agriculture (USDA) Soil Conservation Service (SCS) 1983...0.000221 m/yr) based on the Universal Soil Loss Equation ( USLE ) as de- scribed by Dortch et al. (2010). This erosion rate includes use of a sedi...area of 0.619 m2 results in an erosion rate of 4.43 E-4 m/yr. The Universal Soil Loss Equation ( USLE ) was applied within the Hydro-Geo- ERDC/EL TR-11

Multigrid and Krylov Subspace Methods for the Discrete Stokes Equations

NASA Technical Reports Server (NTRS)

Elman, Howard C.

1996-01-01

Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizations, a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the discretization. In this paper, we compare the performance of four such methods: variants of the Uzawa, preconditioned conjugate gradient, preconditioned conjugate residual, and multigrid methods, for solving several two-dimensional model problems. The results indicate that where it is applicable, multigrid with smoothing based on incomplete factorization is more efficient than the other methods, but typically by no more than a factor of two. The conjugate residual method has the advantage of being both independent of iteration parameters and widely applicable.

E. coli survival in waters: applicability of the Arrhenius equation

USDA-ARS?s Scientific Manuscript database

E. coli is an important microorganism indicator used to show the presence of pathogens and fecal contamination in waters. Knowing E. coli survival rates is important for assessing the severity of contamination that has occurred and making appropriate management evaluations. E. coli survival rates ...

3D optical digitation applied to orthodontics: analysis of unilateral cleft lip and palate in newborn infants

NASA Astrophysics Data System (ADS)

Canal, Fernando; Garcia-Mateos, Jorge; Rodriguez-Larena, Jorge; Rivera, Alejandro; Aparicio, E.

2000-12-01

Medical therapeutic applications using lasers involves understanding the light tissue interaction, in particular the rate ofphotochemical and thermal reactions. Tissue is composed ofa mix ofturbid media. Light propagation in turbid media can be described by the so-called Equation of Radiative Transfer, an integro-differential equation where scattering, absorption and internal reflection are significant factors in determining the light distribution in tissue. The Equation of Radiative Transfer however can not commonly be solved analytically.' In order to visualize and simulate the effects of laser light on heart tissues (myocardium) in relation to the treatment of irregular heart rates or so called arrhythmias, a fast interactive computer program has been developed in Java.

A Potential Function Derivation of a Constitutive Equation for Inelastic Material Response

NASA Technical Reports Server (NTRS)

Stouffer, D. C.; Elfoutouh, N. A.

1983-01-01

Physical and thermodynamic concepts are used to develop a potential function for application to high temperature polycrystalline material response. Inherent in the formulation is a differential relationship between the potential function and constitutive equation in terms of the state variables. Integration of the differential relationship produces a state variable evolution equation that requires specification of the initial value of the state variable and its time derivative. It is shown that the initial loading rate, which is directly related to the initial hardening rate, can significantly influence subsequent material response. This effect is consistent with observed material behavior on the macroscopic and microscopic levels, and may explain the wide scatter in response often found in creep testing.

Applicability of geomechanical classifications for estimation of strength properties in Brazilian rock masses.

PubMed

Santos, Tatiana B; Lana, Milene S; Santos, Allan E M; Silveira, Larissa R C

2017-01-01

Many authors have been proposed several correlation equations between geomechanical classifications and strength parameters. However, these correlation equations have been based in rock masses with different characteristics when compared to Brazilian rock masses. This paper aims to study the applicability of the geomechanical classifications to obtain strength parameters of three Brazilian rock masses. Four classification systems have been used; the Rock Mass Rating (RMR), the Rock Mass Quality (Q), the Geological Strength Index (GSI) and the Rock Mass Index (RMi). A strong rock mass and two soft rock masses with different degrees of weathering located in the cities of Ouro Preto and Mariana, Brazil; were selected for the study. Correlation equations were used to estimate the strength properties of these rock masses. However, such correlations do not always provide compatible results with the rock mass behavior. For the calibration of the strength values obtained through the use of classification systems, ​​stability analyses of failures in these rock masses have been done. After calibration of these parameters, the applicability of the various correlation equations found in the literature have been discussed. According to the results presented in this paper, some of these equations are not suitable for the studied rock masses.

Birth-jump processes and application to forest fire spotting.

PubMed

Hillen, T; Greese, B; Martin, J; de Vries, G

2015-01-01

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Rate and time dependent behavior of structural adhesives. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Renieri, M. P.; Herakovich, C. T.; Brinson, H. F.

1976-01-01

Studies on two adhesives (Metlbond 1113 and 1113-2) identified as having applications in the bonding of composite materials are presented. Constitutive equations capable of describing changes in material behavior with strain rate are derived from various theoretical approaches. It is shown that certain unique relationships exist between these approaches. It is also shown that the constitutive equation derived from mechanical models can be used for creep and relaxation loading. A creep to failure phenomenon is shown to exist and is correlated with a delayed yield equation proposed by Crochet. Loading-unloading results are presented and are shown to correlate well with the proposed form of the loading-unloading equations for the modified Bingham model. Experimental results obtained for relaxation tests above and below the glass transition temperature are presented. It is shown that the adhesives obey the time-temperature superposition principle.

Calculating the True and Observed Rates of Complex Heterogeneous Catalytic Reactions

NASA Astrophysics Data System (ADS)

Avetisov, A. K.; Zyskin, A. G.

2018-06-01

Equations of the theory of steady-state complex reactions are considered in matrix form. A set of stage stationarity equations is given, and an algorithm is described for deriving the canonic set of stationarity equations with appropriate corrections for the existence of fast stages in a mechanism. A formula for calculating the number of key compounds is presented. The applicability of the Gibbs rule to estimating the number of independent compounds in a complex reaction is analyzed. Some matrix equations relating the rates of dependent and key substances are derived. They are used as a basis to determine the general diffusion stoichiometry relationships between temperature, the concentrations of dependent reaction participants, and the concentrations of key reaction participants in a catalyst grain. An algorithm is described for calculating heat and mass transfer in a catalyst grain with respect to arbitrary complex heterogeneous catalytic reactions.

A New Method for 3D Radiative Transfer with Adaptive Grids

NASA Astrophysics Data System (ADS)

Folini, D.; Walder, R.; Psarros, M.; Desboeufs, A.

2003-01-01

We present a new method for 3D NLTE radiative transfer in moving media, including an adaptive grid, along with some test examples and first applications. The central features of our approach we briefly outline in the following. For the solution of the radiative transfer equation, we make use of a generalized mean intensity approach. In this approach, the transfer eqation is solved directly, instead of using the moments of the transfer equation, thus avoiding the associated closure problem. In a first step, a system of equations for the transfer of each directed intensity is set up, using short characteristics. Next, the entity of systems of equations for each directed intensity is re-formulated in the form of one system of equations for the angle-integrated mean intensity. This system then is solved by a modern, fast BiCGStab iterative solver. An additional advantage of this procedure is that convergence rates barely depend on the spatial discretization. For the solution of the rate equations we use Housholder transformations. Lines are treated by a 3D generalization of the well-known Sobolev-approximation. The two parts, solution of the transfer equation and solution of the rate equations, are iteratively coupled. We recently have implemented an adaptive grid, which allows for recursive refinement on a cell-by-cell basis. The spatial resolution, which is always a problematic issue in 3D simulations, we can thus locally reduce or augment, depending on the problem to be solved.

A deterministic method for estimating free energy genetic network landscapes with applications to cell commitment and reprogramming paths.

PubMed

Olariu, Victor; Manesso, Erica; Peterson, Carsten

2017-06-01

Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis-Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming.

A deterministic method for estimating free energy genetic network landscapes with applications to cell commitment and reprogramming paths

PubMed Central

Olariu, Victor; Manesso, Erica

2017-01-01

Depicting developmental processes as movements in free energy genetic landscapes is an illustrative tool. However, exploring such landscapes to obtain quantitative or even qualitative predictions is hampered by the lack of free energy functions corresponding to the biochemical Michaelis–Menten or Hill rate equations for the dynamics. Being armed with energy landscapes defined by a network and its interactions would open up the possibility of swiftly identifying cell states and computing optimal paths, including those of cell reprogramming, thereby avoiding exhaustive trial-and-error simulations with rate equations for different parameter sets. It turns out that sigmoidal rate equations do have approximate free energy associations. With this replacement of rate equations, we develop a deterministic method for estimating the free energy surfaces of systems of interacting genes at different noise levels or temperatures. Once such free energy landscape estimates have been established, we adapt a shortest path algorithm to determine optimal routes in the landscapes. We explore the method on three circuits for haematopoiesis and embryonic stem cell development for commitment and reprogramming scenarios and illustrate how the method can be used to determine sequential steps for onsets of external factors, essential for efficient reprogramming. PMID:28680655

Towards a unified theory for morphomechanics

PubMed Central

Taber, Larry A.

2009-01-01

Mechanical forces are closely involved in the construction of an embryo. Experiments have suggested that mechanical feedback plays a role in regulating these forces, but the nature of this feedback is poorly understood. Here, we propose a general principle for the mechanics of morphogenesis, as governed by a pair of evolution equations based on feedback from tissue stress. In one equation, the rate of growth (or contraction) depends on the difference between the current tissue stress and a target (homeostatic) stress. In the other equation, the target stress changes at a rate that depends on the same stress difference. The parameters in these morphomechanical laws are assumed to depend on stress rate. Computational models are used to illustrate how these equations can capture a relatively wide range of behaviours observed in developing embryos, as well as show the limitations of this theory. Specific applications include growth of pressure vessels (e.g. the heart, arteries and brain), wound healing and sea urchin gastrulation. Understanding the fundamental principles of tissue construction can help engineers design new strategies for creating replacement tissues and organs in vitro. PMID:19657011

Microscopic modeling of gas-surface scattering. I. A combined molecular dynamics-rate equation approach

NASA Astrophysics Data System (ADS)

Filinov, A.; Bonitz, M.; Loffhagen, D.

2018-06-01

A combination of first principle molecular dynamics (MD) simulations with a rate equation model (MD-RE approach) is presented to study the trapping and the scattering of rare gas atoms from metal surfaces. The temporal evolution of the atom fractions that are either adsorbed or scattered into the continuum is investigated in detail. We demonstrate that for this description one has to consider trapped, quasi-trapped and scattering states, and present an energetic definition of these states. The rate equations contain the transition probabilities between the states. We demonstrate how these rate equations can be derived from kinetic theory. Moreover, we present a rigorous way to determine the transition probabilities from a microscopic analysis of the particle trajectories generated by MD simulations. Once the system reaches quasi-equilibrium, the rates converge to stationary values, and the subsequent thermal adsorption/desorption dynamics is completely described by the rate equations without the need to perform further time-consuming MD simulations. As a proof of concept of our approach, MD simulations for argon atoms interacting with a platinum (111) surface are presented. A detailed deterministic trajectory analysis is performed, and the transition rates are constructed. The dependence of the rates on the incidence conditions and the lattice temperature is analyzed. Based on this example, we analyze the time scale of the gas-surface system to approach the quasi-stationary state. The MD-RE model has great relevance for the plasma-surface modeling as it makes an extension of accurate simulations to long, experimentally relevant time scales possible. Its application to the computation of atomic sticking probabilities is given in the second part (paper II).

Textbook Multigrid Efficiency for the Steady Euler Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.

Near-wall turbulence model and its application to fully developed turbulent channel and pipe flows

NASA Technical Reports Server (NTRS)

Kim, S.-W.

1990-01-01

A near-wall turbulence model and its incorporation into a multiple-timescale turbulence model are presented. The near-wall turbulence model is obtained from a k-equation turbulence model and a near-wall analysis. In the method, the equations for the conservation of mass, momentum, and turbulent kinetic energy are integrated up to the wall, and the energy transfer and the dissipation rates inside the near-wall layer are obtained from algebraic equations. Fully developed turbulent channel and pipe flows are solved using a finite element method. The computational results compare favorably with experimental data. It is also shown that the turbulence model can resolve the overshoot phenomena of the turbulent kinetic energy and the dissipation rate in the region very close to the wall.

Gas Atomization of Molten Metal: Part II. Applications

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

Abu-Lebdeh, Taher M.; Leon, Genaro Perez-de; Hamoush, Sameer A.

A numerical model was derived to obtain results for two alloys during the Gas Atomization (GA) method. The model equations and governing equations were implemented through the application of part I data. Aspects such as heat transfer, fluid mechanics, thermodynamics and law of motions were taken into account for the formulation of equations that take gas dynamics, droplet dynamics and energy balance or conservation into consideration. The inputs of the model include: Processing parameters such as the size of the droplets, characteristics of the metal alloy, initial temperature of the molten metal, properties and fractions of the atomization gas andmore » the gas pressure. The outputs include velocity and thermal profiles of the droplet and gas. Velocity profiles illustrate the velocity of both droplet and gas, while thermal profiles illustrate cooling rate and the rate of temperature change of the droplets. The alloys are gamma-Titanium Aluminide (γ-TiAl) and Al-3003-O. These alloys were selected due to the vast amount of applications both can have in several industries. Certain processing parameters were held constant, while others were altered. Furthermore, the main focus of this study was to gain insight into which optimal parameters should be utilized within the GA method for these alloys and to provide insight into the behavior of these alloys« less

Gas Atomization of Molten Metal: Part II. Applications

DOE PAGES

Abu-Lebdeh, Taher M.; Leon, Genaro Perez-de; Hamoush, Sameer A.; ...

2016-02-01

A numerical model was derived to obtain results for two alloys during the Gas Atomization (GA) method. The model equations and governing equations were implemented through the application of part I data. Aspects such as heat transfer, fluid mechanics, thermodynamics and law of motions were taken into account for the formulation of equations that take gas dynamics, droplet dynamics and energy balance or conservation into consideration. The inputs of the model include: Processing parameters such as the size of the droplets, characteristics of the metal alloy, initial temperature of the molten metal, properties and fractions of the atomization gas andmore » the gas pressure. The outputs include velocity and thermal profiles of the droplet and gas. Velocity profiles illustrate the velocity of both droplet and gas, while thermal profiles illustrate cooling rate and the rate of temperature change of the droplets. The alloys are gamma-Titanium Aluminide (γ-TiAl) and Al-3003-O. These alloys were selected due to the vast amount of applications both can have in several industries. Certain processing parameters were held constant, while others were altered. Furthermore, the main focus of this study was to gain insight into which optimal parameters should be utilized within the GA method for these alloys and to provide insight into the behavior of these alloys« less

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.

Application of the compensated Arrhenius formalism to explain the dielectric constant dependence of rates for Menschutkin reactions.

PubMed

Petrowsky, Matt; Glatzhofer, Daniel T; Frech, Roger

2013-11-21

The dependence of the reaction rate on solvent dielectric constant is examined for the reaction of trihexylamine with 1-bromohexane in a series of 2-ketones over the temperature range 25-80 °C. The rate constant data are analyzed using the compensated Arrhenius formalism (CAF), where the rate constant assumes an Arrhenius-like equation that also contains a dielectric constant dependence in the exponential prefactor. The CAF activation energies are substantially higher than those obtained using the simple Arrhenius equation. A master curve of the data is observed by plotting the prefactors against the solvent dielectric constant. The master curve shows that the reaction rate has a weak dependence on dielectric constant for values approximately less than 10 and increases more rapidly for dielectric constant values greater than 10.

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smooth particle hydrodynamics

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

Pan, Wenxiao; Daily, Michael D.; Baker, Nathan A.

2015-12-01

We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. The numerical method is first verified in simple systems and then applied to the calculation of ligand binding to an acetylcholinesterase monomer. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) boundary condition, is considered on the reactive boundaries. This new boundary condition treatment allows for the analysis of enzymes with "imperfect" reaction rates. Rates for inhibitor binding to mAChE are calculated atmore » various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

Rate kernel theory for pseudo-first-order kinetics of diffusion-influenced reactions and application to fluorescence quenching kinetics.

PubMed

Yang, Mino

2007-06-07

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived.

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

NASA Astrophysics Data System (ADS)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

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

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

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

Determining the spill flow discharge of combined sewer overflows using rating curves based on computational fluid dynamics instead of the standard weir equation.

PubMed

Fach, S; Sitzenfrei, R; Rauch, W

2009-01-01

It is state of the art to evaluate and optimise sewer systems with urban drainage models. Since spill flow data is essential in the calibration process of conceptual models it is important to enhance the quality of such data. A wide spread approach is to calculate the spill flow volume by using standard weir equations together with measured water levels. However, these equations are only applicable to combined sewer overflow (CSO) structures, whose weir constructions correspond with the standard weir layout. The objective of this work is to outline an alternative approach to obtain spill flow discharge data based on measurements with a sonic depth finder. The idea is to determine the relation between water level and rate of spill flow by running a detailed 3D computational fluid dynamics (CFD) model. Two real world CSO structures have been chosen due to their complex structure, especially with respect to the weir construction. In a first step the simulation results were analysed to identify flow conditions for discrete steady states. It will be shown that the flow conditions in the CSO structure change after the spill flow pipe acts as a controlled outflow and therefore the spill flow discharge cannot be described with a standard weir equation. In a second step the CFD results will be used to derive rating curves which can be easily applied in everyday practice. Therefore the rating curves are developed on basis of the standard weir equation and the equation for orifice-type outlets. Because the intersection of both equations is not known, the coefficients of discharge are regressed from CFD simulation results. Furthermore, the regression of the CFD simulation results are compared with the one of the standard weir equation by using historic water levels and hydrographs generated with a hydrodynamic model. The uncertainties resulting of the wide spread use of the standard weir equation are demonstrated.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.

2004-01-01

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

A general integral form of the boundary-layer equation for incompressible flow with an application to the calculation of the separation point of turbulent boundary layers

NASA Technical Reports Server (NTRS)

Tetervin, Neal; Lin, Chia Chiao

1951-01-01

A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.

Resting metabolic rate in elite rowers and canoeists: difference between indirect calorimetry and prediction.

PubMed

Carlsohn, Anja; Scharhag-Rosenberger, Friederike; Cassel, Michael; Mayer, Frank

2011-01-01

Athletes may differ in their resting metabolic rate (RMR) from the general population. However, to estimate the RMR in athletes, prediction equations that have not been validated in athletes are often used. The purpose of this study was therefore to verify the applicability of commonly used RMR predictions for use in athletes. The RMR was measured by indirect calorimetry in 17 highly trained rowers and canoeists of the German national teams (BMI 24 ± 2 kg/m(2), fat-free mass 69 ± 15 kg). In addition, the RMR was predicted using Cunningham (CUN) and Harris-Benedict (HB) equations. A two-way repeated measures ANOVA was calculated to test for differences between predicted and measured RMR (α = 0.05). The root mean square percentage error (RMSPE) was calculated and the Bland-Altman procedure was used to quantify the bias for each prediction. Prediction equations significantly underestimated the RMR in males (p < 0.001). The RMSPE was calculated to be 18.4% (CUN) and 20.9% (HB) in the entire group. The bias was 133 kcal/24 h for CUN and 202 kcal/24 h for HB. Predictions significantly underestimate the RMR in male heavyweight endurance athletes but not in females. In athletes with a high fat-free mass, prediction equations might therefore not be applicable to estimate energy requirements. Instead, measurement of the resting energy expenditure or specific prediction equations might be needed for the individual heavyweight athlete. Copyright © 2011 S. Karger AG, Basel.

Order-of-magnitude estimates of latency (time to appearance) and refill time of a cancer from a single cancer 'stem' cell compared by an exponential and a logistic equation.

PubMed

Anderson, Ken M; Rubenstein, Marvin; Guinan, Patrick; Patel, Minu

2012-01-01

The time required before a mass of cancer cells considered to have originated from a single malignantly transformed cancer 'stem' cell reaches a certain number has not been studied. Applications might include determination of the time the cell mass reaches a size that can be detected by X-rays or physical examination or modeling growth rates in vitro in order to compare with other models or established data. We employed a simple logarithmic equation and a common logistic equation incorporating 'feedback' for unknown variables of cell birth, growth, division, and death that can be used to model cell proliferation. It can be used in association with free or commercial statistical software. Results with these two equations, varying the proliferation rate, nominally reduced by generational cell loss, are presented in two tables. The resulting equation, instructions, examples, and necessary mathematical software are available in the online appendix, where several parameters of interest can be modified by the reader www.uic.edu/nursing/publicationsupplements/tobillion_Anderson_Rubenstein_Guinan_Patel1.pdf. Reducing the proliferation rate by whatever alterations employed, markedly increases the time to reach 10(9) cells originating from an initial progenitor. In thinking about multistep oncogenesis, it is useful to consider the profound effect that variations in the effective proliferation rate may have during cancer development. This can be approached with the proposed equation, which is easy to use and available to further peer fine-tuning to be used in future modeling of cell growth.

Continuum Fatigue Damage Modeling for Use in Life Extending Control

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.

1994-01-01

This paper develops a simplified continuum (continuous wrp to time, stress, etc.) fatigue damage model for use in Life Extending Controls (LEC) studies. The work is based on zero mean stress local strain cyclic damage modeling. New nonlinear explicit equation forms of cyclic damage in terms of stress amplitude are derived to facilitate the continuum modeling. Stress based continuum models are derived. Extension to plastic strain-strain rate models are also presented. Application of these models to LEC applications is considered. Progress toward a nonzero mean stress based continuum model is presented. Also, new nonlinear explicit equation forms in terms of stress amplitude are also derived for this case.

Using Mathematical Algorithms to Modify Glomerular Filtration Rate Estimation Equations

PubMed Central

Zhu, Bei; Wu, Jianqing; Zhu, Jin; Zhao, Weihong

2013-01-01

Background The equations provide a rapid and low-cost method of evaluating glomerular filtration rate (GFR). Previous studies indicated that the Modification of Diet in Renal Disease (MDRD), Chronic Kidney Disease-Epidemiology (CKD-EPI) and MacIsaac equations need further modification for application in Chinese population. Thus, this study was designed to modify the three equations, and compare the diagnostic accuracy of the equations modified before and after. Methodology With the use of 99 mTc-DTPA renal dynamic imaging as the reference GFR (rGFR), the MDRD, CKD-EPI and MacIsaac equations were modified by two mathematical algorithms: the hill-climbing and the simulated-annealing algorithms. Results A total of 703 Chinese subjects were recruited, with the average rGFR 77.14±25.93 ml/min. The entire modification process was based on a random sample of 80% of subjects in each GFR level as a training sample set, the rest of 20% of subjects as a validation sample set. After modification, the three equations performed significant improvement in slop, intercept, correlated coefficient, root mean square error (RMSE), total deviation index (TDI), and the proportion of estimated GFR (eGFR) within 10% and 30% deviation of rGFR (P10 and P30). Of the three modified equations, the modified CKD-EPI equation showed the best accuracy. Conclusions Mathematical algorithms could be a considerable tool to modify the GFR equations. Accuracy of all the three modified equations was significantly improved in which the modified CKD-EPI equation could be the optimal one. PMID:23472113

A review of near-wall Reynolds-stress

NASA Technical Reports Server (NTRS)

So, R. M. C.; Lai, Y. G.; Zhang, H. S.; Hwang, B. C.

1991-01-01

The advances made in second-order near-wall turbulence closures are summarized. All closures examined are based on some form of high Reynolds number models for the Reynolds stress and the turbulent kinetic energy dissipation rate equations. Consequently, most near-wall closures proposed to data attempt to modify the high Reynolds number models for the dissipation rate equation so that the resultant models are applicable all the way to the wall. The near-wall closures are examined for their asymptotic behavior so that they can be compared with the proper near-wall behavior of the exact equations. A comparison of the closure's performance in the calculation of a low Reynolds number plane channel flow is carried out. In addition, the closures are evaluated for their ability to predict the turbulence statistics and the limiting behavior of the structure parameters compared to direct simulation data.

The equations of motion for moist atmospheric air

NASA Astrophysics Data System (ADS)

Makarieva, Anastassia M.; Gorshkov, Victor G.; Nefiodov, Andrei V.; Sheil, Douglas; Nobre, Antonio Donato; Bunyard, Peter; Nobre, Paulo; Li, Bai-Lian

2017-07-01

How phase transitions affect the motion of moist atmospheric air remains controversial. In the early 2000s two distinct differential equations of motion were proposed. Besides their contrasting formulations for the acceleration of condensate, the equations differ concerning the presence/absence of a term equal to the rate of phase transitions multiplied by the difference in velocity between condensate and air. This term was interpreted in the literature as the "reactive motion" associated with condensation. The reasoning behind this reactive motion was that when water vapor condenses and droplets begin to fall the remaining gas must move upward to conserve momentum. Here we show that the two contrasting formulations imply distinct assumptions about how gaseous air and condensate particles interact. We show that these assumptions cannot be simultaneously applicable to condensation and evaporation. Reactive motion leading to an upward acceleration of air during condensation does not exist. The reactive motion term can be justified for evaporation only; it describes the downward acceleration of air. We emphasize the difference between the equations of motion (i.e., equations constraining velocity) and those constraining momentum (i.e., equations of motion and continuity combined). We show that owing to the imprecise nature of the continuity equations, consideration of total momentum can be misleading and that this led to the reactive motion controversy. Finally, we provide a revised and generally applicable equation for the motion of moist air.

Models for nearly every occasion: Part III - One box decreasing emission models.

PubMed

Hewett, Paul; Ganser, Gary H

2017-11-01

New one box "well-mixed room" decreasing emission (DE) models are introduced that allow for local exhaust or local exhaust with filtered return, as well the recirculation of a filtered (or cleaned) portion of the general room ventilation. For each control device scenario, a steady state and transient model is presented. The transient equations predict the concentration at any time t after the application of a known mass of a volatile substance to a surface, and can be used to predict the task exposure profile, the average task exposure, as well as peak and short-term exposures. The steady state equations can be used to predict the "average concentration per application" that is reached whenever the substance is repeatedly applied. Whenever the beginning and end concentrations are expected to be zero (or near zero) the steady state equations can also be used to predict the average concentration for a single task with multiple applications during the task, or even a series of such tasks. The transient equations should be used whenever these criteria cannot be met. A structured calibration procedure is proposed that utilizes a mass balance approach. Depending upon the DE model selected, one or more calibration measurements are collected. Using rearranged versions of the steady state equations, estimates of the model variables-e.g., the mass of the substance applied during each application, local exhaust capture efficiency, and the various cleaning or filtration efficiencies-can be calculated. A new procedure is proposed for estimating the emission rate constant.

Multimode VCSEL model for wide frequency-range RIN simulation

NASA Astrophysics Data System (ADS)

Perchoux, Julien; Rissons, Angélique; Mollier, Jean-Claude

2008-01-01

In this paper, we present an equivalent circuit model for oxide-confined AlGaAs/GaAs VCSEL with the noise contribution adapted to optomicrowave links applications. This model is derived from the multimode rate equations. In order to understand the modal competition process, we restrain our description to a two-modes rate equations system affected by the spectral hole-burning. The relative intensity noise (RIN) measurements which were achieved on a prober in Faraday cage confirm the low frequency enhancement described by the model. We validate our model for a wide frequency-range [1 MHz-10 GHz] and high bias level up to six times the threshold current.

Method to monitor HC-SCR catalyst NOx reduction performance for lean exhaust applications

DOEpatents

Viola, Michael B [Macomb Township, MI; Schmieg, Steven J [Troy, MI; Sloane, Thompson M [Oxford, MI; Hilden, David L [Shelby Township, MI; Mulawa, Patricia A [Clinton Township, MI; Lee, Jong H [Rochester Hills, MI; Cheng, Shi-Wai S [Troy, MI

2012-05-29

A method for initiating a regeneration mode in selective catalytic reduction device utilizing hydrocarbons as a reductant includes monitoring a temperature within the aftertreatment system, monitoring a fuel dosing rate to the selective catalytic reduction device, monitoring an initial conversion efficiency, selecting a determined equation to estimate changes in a conversion efficiency of the selective catalytic reduction device based upon the monitored temperature and the monitored fuel dosing rate, estimating changes in the conversion efficiency based upon the determined equation and the initial conversion efficiency, and initiating a regeneration mode for the selective catalytic reduction device based upon the estimated changes in conversion efficiency.

The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

NASA Astrophysics Data System (ADS)

Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

2017-08-01

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

Numerical Modeling of Conjugate Heat Transfer in Fluid Network

NASA Technical Reports Server (NTRS)

Majumdar, Alok

2004-01-01

Fluid network modeling with conjugate heat transfer has many applications in Aerospace engineering. In modeling unsteady flow with heat transfer, it is important to know the variation of wall temperature in time and space to calculate heat transfer between solid to fluid. Since wall temperature is a function of flow, a coupled analysis of temperature of solid and fluid is necessary. In cryogenic applications, modeling of conjugate heat transfer is of great importance to correctly predict boil-off rate in propellant tanks and chill down of transfer lines. In TFAWS 2003, the present author delivered a paper to describe a general-purpose computer program, GFSSP (Generalized Fluid System Simulation Program). GFSSP calculates flow distribution in complex flow circuit for compressible/incompressible, with or without heat transfer or phase change in all real fluids or mixtures. The flow circuit constitutes of fluid nodes and branches. The mass, energy and specie conservation equations are solved at the nodes where as momentum conservation equations are solved at the branches. The proposed paper describes the extension of GFSSP to model conjugate heat transfer. The network also includes solid nodes and conductors in addition to fluid nodes and branches. The energy conservation equations for solid nodes solves to determine the temperatures of the solid nodes simultaneously with all conservation equations governing fluid flow. The numerical scheme accounts for conduction, convection and radiation heat transfer. The paper will also describe the applications of the code to predict chill down of cryogenic transfer line and boil-off rate of cryogenic propellant storage tank.

Calculation of prevalence estimates through differential equations: application to stroke-related disability.

PubMed

Mar, Javier; Sainz-Ezkerra, María; Moler-Cuiral, Jose Antonio

2008-01-01

Neurological diseases now make up 6.3% of the global burden of disease mainly because they cause disability. To assess disability, prevalence estimates are needed. The objective of this study is to apply a method based on differential equations to calculate the prevalence of stroke-related disability. On the basis of a flow diagram, a set of differential equations for each age group was constructed. The linear system was solved analytically and numerically. The parameters of the system were obtained from the literature. The model was validated and calibrated by comparison with previous results. The stroke prevalence rate per 100,000 men was 828, and the rate for stroke-related disability was 331. The rates steadily rose with age, but the group between the ages of 65 and 74 years had the highest total number of individuals. Differential equations are useful to represent the natural history of neurological diseases and to make possible the calculation of the prevalence for the various states of disability. In our experience, when compared with the results obtained by Markov models, the benefit of the continuous use of time outweighs the mathematical requirements of our model. (c) 2008 S. Karger AG, Basel.

Kinetic study on the isothermal and nonisothermal crystallization of monoglyceride organogels.

PubMed

Meng, Zong; Yang, Lijun; Geng, Wenxin; Yao, Yubo; Wang, Xingguo; Liu, Yuanfa

2014-01-01

The isothermal and nonisothermal crystallization kinetics of monoglyceride (MAG) organogels were studied by pulsed nuclear magnetic resonance (pNMR) and differential scanning calorimetry (DSC), respectively. The Avrami equation was used to describe the isothermal crystallization kinetics and experimental data fitted the equation fairly well. Results showed that the crystal growth of MAG organogels was a rod-like growth of instantaneous nuclei at higher degrees of supercooling and a plate-like form with high nucleation rate at lower degrees of supercooling. The exothermic peak in nonisothermal DSC curves for the MAG organogels became wider and shifted to lower temperature when the cooling rate increased, and nonisothermal crystallization was analyzed by Mo equation. Results indicated that at the same crystallization time, to get a higher degree of relative crystallinity, a higher cooling rate was necessary. The activation energy of nonisothermal crystallization was calculated as 739.59 kJ/mol according to the Kissinger method. Therefore, as the results of the isothermal and nonisothermal crystallization kinetics for the MAG organogels obtained, the crystallization rate, crystal nucleation, and growth during the crystallization process could be preliminarily monitored through temperature and cooling rate regulation, which laid the foundation for the real industrial manufacture and application of the MAG organogels.

Solution of weakly compressible isothermal flow in landfill gas collection networks

NASA Astrophysics Data System (ADS)

Nec, Y.; Huculak, G.

2017-12-01

Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy-Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein.

Expanded prediction equations of human sweat loss and water needs.

PubMed

Gonzalez, R R; Cheuvront, S N; Montain, S J; Goodman, D A; Blanchard, L A; Berglund, L G; Sawka, M N

2009-08-01

The Institute of Medicine expressed a need for improved sweating rate (msw) prediction models that calculate hourly and daily water needs based on metabolic rate, clothing, and environment. More than 25 years ago, the original Shapiro prediction equation (OSE) was formulated as msw (g.m(-2).h(-1))=27.9.Ereq.(Emax)(-0.455), where Ereq is required evaporative heat loss and Emax is maximum evaporative power of the environment; OSE was developed for a limited set of environments, exposures times, and clothing systems. Recent evidence shows that OSE often overpredicts fluid needs. Our study developed a corrected OSE and a new msw prediction equation by using independent data sets from a wide range of environmental conditions, metabolic rates (rest to 500 observations) by using a variety of metabolic rates over a range of environmental conditions (ambient temperature, 15-46 degrees C; water vapor pressure, 0.27-4.45 kPa; wind speed, 0.4-2.5 m/s), clothing, and equipment combinations and durations (2-8 h). Data are expressed as grams per square meter per hour and were analyzed using fuzzy piecewise regression. OSE overpredicted sweating rates (P<0.003) compared with observed msw. Both the correction equation (OSEC), msw=147.exp (0.0012.OSE), and a new piecewise (PW) equation, msw=147+1.527.Ereq-0.87.Emax were derived, compared with OSE, and then cross-validated against independent data (21 males and 9 females; >200 observations). OSEC and PW were more accurate predictors of sweating rate (58 and 65% more accurate, P<0.01) and produced minimal error (standard error estimate<100 g.m(-2).h(-1)) for conditions both within and outside the original OSE domain of validity. The new equations provide for more accurate sweat predictions over a broader range of conditions with applications to public health, military, occupational, and sports medicine settings.

Entropy production and nonlinear Fokker-Planck equations.

PubMed

Casas, G A; Nobre, F D; Curado, E M F

2012-12-01

The entropy time rate of systems described by nonlinear Fokker-Planck equations--which are directly related to generalized entropic forms--is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.

Steady-state equation of water vapor sorption for CaCl2-based chemical sorbents and its application

PubMed Central

Zhang, Haiquan; Yuan, Yanping; Sun, Qingrong; Cao, Xiaoling; Sun, Liangliang

2016-01-01

Green CaCl2-based chemical sorbent has been widely used in sorption refrigeration, air purification and air desiccation. Methods to improve the sorption rate have been extensively investigated, but the corresponding theoretical formulations have not been reported. In this paper, a sorption system of solid-liquid coexistence is established based on the hypothesis of steady-state sorption. The combination of theoretical analysis and experimental results indicates that the system can be described by steady-state sorption process. The steady-state sorption equation, μ = (η − γT) , was obtained in consideration of humidity, temperature and the surface area. Based on engineering applications and this equation, two methods including an increase of specific surface area and adjustment of the critical relative humidity (γ) for chemical sorbents, have been proposed to increase the sorption rate. The results indicate that the CaCl2/CNTs composite with a large specific surface area can be obtained by coating CaCl2 powder on the surface of carbon nanotubes (CNTs). The composite reached sorption equilibrium within only 4 h, and the sorption capacity was improved by 75% compared with pure CaCl2 powder. Furthermore, the addition of NaCl powder to saturated CaCl2 solution could significantly lower the solution’s γ. The sorption rate was improved by 30% under the same environment. PMID:27682811

Steady-state equation of water vapor sorption for CaCl2-based chemical sorbents and its application

NASA Astrophysics Data System (ADS)

Zhang, Haiquan; Yuan, Yanping; Sun, Qingrong; Cao, Xiaoling; Sun, Liangliang

2016-09-01

Green CaCl2-based chemical sorbent has been widely used in sorption refrigeration, air purification and air desiccation. Methods to improve the sorption rate have been extensively investigated, but the corresponding theoretical formulations have not been reported. In this paper, a sorption system of solid-liquid coexistence is established based on the hypothesis of steady-state sorption. The combination of theoretical analysis and experimental results indicates that the system can be described by steady-state sorption process. The steady-state sorption equation, μ = (η - γT) , was obtained in consideration of humidity, temperature and the surface area. Based on engineering applications and this equation, two methods including an increase of specific surface area and adjustment of the critical relative humidity (γ) for chemical sorbents, have been proposed to increase the sorption rate. The results indicate that the CaCl2/CNTs composite with a large specific surface area can be obtained by coating CaCl2 powder on the surface of carbon nanotubes (CNTs). The composite reached sorption equilibrium within only 4 h, and the sorption capacity was improved by 75% compared with pure CaCl2 powder. Furthermore, the addition of NaCl powder to saturated CaCl2 solution could significantly lower the solution’s γ. The sorption rate was improved by 30% under the same environment.

A matlab framework for estimation of NLME models using stochastic differential equations: applications for estimation of insulin secretion rates.

PubMed

Mortensen, Stig B; Klim, Søren; Dammann, Bernd; Kristensen, Niels R; Madsen, Henrik; Overgaard, Rune V

2007-10-01

The non-linear mixed-effects model based on stochastic differential equations (SDEs) provides an attractive residual error model, that is able to handle serially correlated residuals typically arising from structural mis-specification of the true underlying model. The use of SDEs also opens up for new tools for model development and easily allows for tracking of unknown inputs and parameters over time. An algorithm for maximum likelihood estimation of the model has earlier been proposed, and the present paper presents the first general implementation of this algorithm. The implementation is done in Matlab and also demonstrates the use of parallel computing for improved estimation times. The use of the implementation is illustrated by two examples of application which focus on the ability of the model to estimate unknown inputs facilitated by the extension to SDEs. The first application is a deconvolution-type estimation of the insulin secretion rate based on a linear two-compartment model for C-peptide measurements. In the second application the model is extended to also give an estimate of the time varying liver extraction based on both C-peptide and insulin measurements.

Computational Flow Analysis of Ultra High Pressure Firefighting Technology with Application to Long Range Nozzle Design

DTIC Science & Technology

2010-03-01

release; distribution unlimited. Ref AFRL/RXQ Public Affairs Case # 10-100. Document contains color images . Although aqueous fire fighting agent...in conjunction with the standard Eulerian multiphase flow model. The two- equation k- model was selected due to its wide industrial application in...energy (k) and its dissipation rate (). Because of their heuristic development, RANS models have applicable limitations and in general must be

Reacting gas mixtures in the state-to-state approach: The chemical reaction rates

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

Kustova, Elena V.; Kremer, Gilberto M.

2014-12-09

In this work chemically reacting mixtures of viscous flows are analyzed within the framework of Boltzmann equation. By applying a modified Chapman-Enskog method to the system of Boltzmann equations general expressions for the rates of chemical reactions and vibrational energy transitions are determined as functions of two thermodynamic forces: the velocity divergence and the affinity. As an application chemically reacting mixtures of N{sub 2} across a shock wave are studied, where the first lowest vibrational states are taken into account. Here we consider only the contributions from the first four single quantum vibrational-translational energy transitions. It is shown that themore » contribution to the chemical reaction rate related to the affinity is much larger than that of the velocity divergence.« less

Evaluation of total energy-rate feedback for glidescope tracking in wind shear

NASA Technical Reports Server (NTRS)

Belcastro, C. M.; Ostroff, A. J.

1986-01-01

Low-altitude wind shear is recognized as an infrequent but significant hazard to all aircraft during take-off and landing. A total energy-rate sensor, which is potentially applicable to this problem, has been developed for measuring specific total energy-rate of an airplane with respect to the air mass. This paper presents control system designs, with and without energy-rate feedback, for the approach to landing of a transport airplane through severe wind shear and gusts to evaluate application of this sensor. A system model is developed which incorporates wind shear dynamics equations with the airplance equations of motion, thus allowing the control systems to be analyzed under various wind shears. The control systems are designed using optimal output feedback and are analyzed using frequency domain control theory techniques. Control system performance is evaluated using a complete nonlinear simulation of the airplane and a severe wind shear and gust data package. The analysis and simulation results indicate very similar stability and performance characteristics for the two designs. An implementation technique for distributing the velocity gains between airspeed and ground speed in the simulation is also presented, and this technique is shown to improve the performance characteristics of both designs.

Predictive Variables of Half-Marathon Performance for Male Runners

PubMed Central

Gómez-Molina, Josué; Ogueta-Alday, Ana; Camara, Jesus; Stickley, Christoper; Rodríguez-Marroyo, José A.; García-López, Juan

2017-01-01

The aims of this study were to establish and validate various predictive equations of half-marathon performance. Seventy-eight half-marathon male runners participated in two different phases. Phase 1 (n = 48) was used to establish the equations for estimating half-marathon performance, and Phase 2 (n = 30) to validate these equations. Apart from half-marathon performance, training-related and anthropometric variables were recorded, and an incremental test on a treadmill was performed, in which physiological (VO2max, speed at the anaerobic threshold, peak speed) and biomechanical variables (contact and flight times, step length and step rate) were registered. In Phase 1, half-marathon performance could be predicted to 90.3% by variables related to training and anthropometry (Equation 1), 94.9% by physiological variables (Equation 2), 93.7% by biomechanical parameters (Equation 3) and 96.2% by a general equation (Equation 4). Using these equations, in Phase 2 the predicted time was significantly correlated with performance (r = 0.78, 0.92, 0.90 and 0.95, respectively). The proposed equations and their validation showed a high prediction of half-marathon performance in long distance male runners, considered from different approaches. Furthermore, they improved the prediction performance of previous studies, which makes them a highly practical application in the field of training and performance. Key points The present study obtained four equations involving anthropometric, training, physiological and biomechanical variables to estimate half-marathon performance. These equations were validated in a different population, demonstrating narrows ranges of prediction than previous studies and also their consistency. As a novelty, some biomechanical variables (i.e. step length and step rate at RCT, and maximal step length) have been related to half-marathon performance. PMID:28630571

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.

Solution of the comoving-frame equation of transfer in spherically symmetric flows. V - Multilevel atoms. [in early star atmospheres

NASA Technical Reports Server (NTRS)

Mihalas, D.; Kunasz, P. B.

1978-01-01

The coupled radiative transfer and statistical equilibrium equations for multilevel ionic structures in the atmospheres of early-type stars are solved. Both lines and continua are treated consistently; the treatment is applicable throughout a transonic wind, and allows for the presence of background continuum sources and sinks in the transfer. An equivalent-two-level-atoms approach provides the solution for the equations. Calculations for simplified He (+)-like model atoms in parameterized isothermal wind models indicate that subordinate line profiles are sensitive to the assumed mass-loss rate, and to the assumed structure of the velocity law in the atmospheres.

Constitutive Equation with Varying Parameters for Superplastic Flow Behavior

NASA Astrophysics Data System (ADS)

Guan, Zhiping; Ren, Mingwen; Jia, Hongjie; Zhao, Po; Ma, Pinkui

2014-03-01

In this study, constitutive equations for superplastic materials with an extra large elongation were investigated through mechanical analysis. From the view of phenomenology, firstly, some traditional empirical constitutive relations were standardized by restricting some strain paths and parameter conditions, and the coefficients in these relations were strictly given new mechanical definitions. Subsequently, a new, general constitutive equation with varying parameters was theoretically deduced based on the general mechanical equation of state. The superplastic tension test data of Zn-5%Al alloy at 340 °C under strain rates, velocities, and loads were employed for building a new constitutive equation and examining its validity. Analysis results indicated that the constitutive equation with varying parameters could characterize superplastic flow behavior in practical superplastic forming with high prediction accuracy and without any restriction of strain path or deformation condition, showing good industrial or scientific interest. On the contrary, those empirical equations have low prediction capabilities due to constant parameters and poor applicability because of the limit of special strain path or parameter conditions based on strict phenomenology.

Unsteady density-current equations for highly curved terrain

NASA Technical Reports Server (NTRS)

Sivakumaran, N. S.; Dressler, R. F.

1989-01-01

New nonlinear partial differential equations containing terrain curvature and its rate of change are derived that describe the flow of an atmospheric density current. Unlike the classical hydraulic-type equations for density currents, the new equations are valid for two-dimensional, gradually varied flow over highly curved terrain, hence suitable for computing unsteady (or steady) flows over arbitrary mountain/valley profiles. The model assumes the atmosphere above the density current exerts a known arbitrary variable pressure upon the unknown interface. Later this is specialized to the varying hydrostatic pressure of the atmosphere above. The new equations yield the variable velocity distribution, the interface position, and the pressure distribution that contains a centrifugal component, often significantly larger than its hydrostatic component. These partial differential equations are hyperbolic, and the characteristic equations and characteristic directions are derived. Using these to form a characteristic mesh, a hypothetical unsteady curved-flow problem is calculated, not based upon observed data, merely as an example to illustrate the simplicity of their application to unsteady flows over mountains.

Application of TVD schemes for the Euler equations of gas dynamics. [total variation diminishing for nonlinear hyperbolic systems

NASA Technical Reports Server (NTRS)

Yee, H. C.; Warming, R. F.; Harten, A.

1985-01-01

First-order, second-order, and implicit total variation diminishing (TVD) schemes are reviewed using the modified flux approach. Some transient and steady-state calculations are then carried out to illustrate the applicability of these schemes to the Euler equations. It is shown that the second-order explicit TVD schemes generate good shock resolution for both transient and steady-state one-dimensional and two-dimensional problems. Numerical experiments for a quasi-one-dimensional nozzle problem show that the second-order implicit TVD scheme produces a fairly rapid convergence rate and remains stable even when running with a Courant number of 10 to the 6th.

Calculation of free turbulent mixing by interaction approach.

NASA Technical Reports Server (NTRS)

Morel, T.; Torda, T. P.

1973-01-01

The applicability of Bradshaw's interaction hypothesis to two-dimensional free shear flows was investigated. According to it, flows with velocity extrema may be considered to consist of several interacting layers. The hypothesis leads to a new expression for the shear stress which removes the usual restriction that shear stress vanishes at the velocity extremum. The approach is based on kinetic energy and the length scale equations. The compressible flow equations are simplified by restriction to low Mach numbers, and the range of their applicability is discussed. The empirical functions of the turbulence model are found here to be correlated with the spreading rate of the shear layer. The analysis demonstrates that the interaction hypothesis is a workable concept.

Linear constraint relations in biochemical reaction systems: I. Classification of the calculability and the balanceability of conversion rates.

PubMed

van der Heijden, R T; Heijnen, J J; Hellinga, C; Romein, B; Luyben, K C

1994-01-05

Measurements provide the basis for process monitoring and control as well as for model development and validation. Systematic approaches to increase the accuracy and credibility of the empirical data set are therefore of great value. In (bio)chemical conversions, linear conservation relations such as the balance equations for charge, enthalpy, and/or chemical elements, can be employed to relate conversion rates. In a pactical situation, some of these rates will be measured (in effect, be calculated directly from primary measurements of, e.g., concentrations and flow rates), as others can or cannot be calculated from the measured ones. When certain measured rates can also be calculated from other measured rates, the set of equations, the accuracy and credibility of the measured rates can indeed be improved by, respectively, balancing and gross error diagnosis. The balanced conversion rates are more accurate, and form a consistent set of data, which is more suitable for further application (e.g., to calculate nonmeasured rates) than the raw measurements. Such an approach has drawn attention in previous studies. The current study deals mainly with the problem of mathematically classifying the conversion rates into balanceable and calculable rates, given the subset of measured rates. The significance of this problem is illustrated with some examples. It is shown that a simple matrix equation can be derived that contains the vector of measured conversion rates and the redundancy matrix R. Matrix R plays a predominant role in the classification problem. In supplementary articles, significance of the redundancy matrix R for an improved gross error diagnosis approach will be shown. In addition, efficient equations have been derived to calculate the balanceable and/or calculable rates. The method is completely based on matrix algebra (principally different from the graph-theoretical approach), and it is easily implemented into a computer program. (c) 1994 John Wiley & Sons, Inc.

Growth monitoring and control in complex medium: a case study employing fed-batch penicillin fermentation and computer-aided on-line mass balancing.

PubMed

Mou, D G; Cooney, C L

1983-01-01

To broaden the practicality of on-line growth monitoring and control, its application in fedbatch penicillin fermentation using high corn steep liquor (CSL) concentration (53 g/L) is demonstrated. By employing a calculation method that considers the vagaries of CSL consumption, overall and instantaneous carbon-balancing equations are successfully used to calculate, on-line, the cell concentration and instantaneous specific growth rate in the penicillin production phase. As a consequence, these equations, together with a feedback control strategy, enable the computer control of glucose feed and maintenance of the preselected production-phase growth rate with error less than 0.002 h(-1).

Numerical calculation of protein-ligand binding rates through solution of the Smoluchowski equation using smoothed particle hydrodynamics

DOE PAGES

Pan, Wenxiao; Daily, Michael; Baker, Nathan A.

2015-05-07

Background: The calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors. Methods: We demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with “imperfect” reaction rates. Results: The numerical method is first verified in simple systems and thenmore » applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates. Conclusions: Although this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.« less

Angular-Rate Estimation Using Delayed Quaternion Measurements

NASA Technical Reports Server (NTRS)

Azor, R.; Bar-Itzhack, I. Y.; Harman, R. R.

1999-01-01

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared one that uses differentiated quaternion measurements to yield coarse rate measurements, which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear part of the rotas rotational dynamics equation of a body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This non unique decomposition, enables the treatment of the nonlinear spacecraft (SC) dynamics model as a linear one and, thus, the application of a PseudoLinear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the gain matrix and thus eliminates the need to compute recursively the filter covariance matrix. The replacement of the rotational dynamics by a simple Markov model is also examined. In this paper special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results are presented.

Evaluation of HYDRUS-1D for Estimating Evapotranspiration of Bell Pepper Regulated by Cloud-based Fertigation System in Greenhouse

NASA Astrophysics Data System (ADS)

Ito, Y.; Honda, R.; Takesako, H.; Ozawa, K.; Kita, E.; Kanno, M.; Noborio, K.

2017-12-01

A fertile surface layer, contaminated with radiocesium resulting from the accident of the Fukushima Daiichi Nuclear Power Plant in 2011, was removed and replaced by non-fertile soil in Fukushima farmlands. In a greenhouse, we used a commercially-available cloud-based fertigation system (CBFS) for regulating an application rate of liquid fertilizer to bell pepper grown in the non-fertile soil. Although the CBFS regulates the application rate based on a weekly trend of volumetric water content (Θw) remotely measured at the soil surface using a soil moisture sensor if all applied water being consumed by plants in a greenhouse is not known. Evapotranspiration of green pepper grown with the CBFS was estimated by HYDRUS-1D. Experiments in a greenhouse were conducted in Fukushima, Japan, from September 1st to October 31st in 2016. Bell pepper plants were transplanted in the begging of June in 2016. The Penman-Monteith equation was used to estimate evapotranspiration, representing transpiration since the soil surface was covered with plastic mulch. Time domain reflectometry (TDR) probes were horizontally installed to monitor changes in Θw at 5, 10, 20, and 30 cm deep from the soil surface. The van Genuchten-Mualem hydraulic model for water and heat flow in soil was used for HYDRUS-1D. A precipitation rate for the upper boundary condition was given as an irrigation rate. We assumed wind speed was always 0.6 m s-1 for the Penman-Monteith equation. The amount of evapotranspiration estimated with the Penman-Monteith equation agreed well with the amount of irrigated water measured. The evapotranspiration simulated with HYDRUS-1D agreed well with that estimated with the Penman-Monteith equation. However, Θw at all depth were underestimated with Hydrus-1D by approximately 0.05 m3 m-3 and differences of Θw between measured and estimated with HYDRYS-1D became larger at deeper the soil depths. This might be attributed to larger water flow occurred because of a free drainage used for the lower boundary condition. Although transpiration from plants should be measured directly to properly evaluate irrigation rate regulated by the CBFS, HYDRUS-1D was found to estimate evapotranspiration with enough accuracy. We will further evaluate the applicability of HYDRUS-1D to estimate evapotranspiration throughout a growing period.

Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

NASA Astrophysics Data System (ADS)

Zhou, Yajun

This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of compact operators, we outline the geometric and physical conditions that guarantee a robust solution to the light scattering problem, and devise an asymptotic solution to the Born equation of electromagnetic scattering for arbitrarily shaped dielectric in a non-perturbative manner.

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

NASA Astrophysics Data System (ADS)

Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

2017-01-01

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

DEVELOPMENT OF SPLIT-OPERATOR, PETROV-GALERKIN METHODS TO SIMULATE TRANSPORT AND DIFFUSION PROBLEMS

EPA Science Inventory

The rate at which contaminants in groundwater undergo sorption and desorption is routinely described using diffusion models. Such approaches, when incorporated into transport models, lead to large systems of coupled equations, often nonlinear. This has restricted applications of ...

Solving Kinetic Equations for the Laser Flash Photolysis Experiment on Nitric Oxide Synthases: Effect of Conformational Dynamics on the Interdomain Electron Transfer.

PubMed

Astashkin, Andrei V; Feng, Changjian

2015-11-12

The production of nitric oxide by the nitric oxide synthase (NOS) enzyme depends on the interdomain electron transfer (IET) between the flavin mononucleotide (FMN) and heme domains. Although the rate of this IET has been measured by laser flash photolysis (LFP) for various NOS proteins, no rigorous analysis of the relevant kinetic equations was performed so far. In this work, we provide an analytical solution of the kinetic equations underlying the LFP approach. The derived expressions reveal that the bulk IET rate is significantly affected by the conformational dynamics that determines the formation and dissociation rates of the docking complex between the FMN and heme domains. We show that in order to informatively study the electron transfer across the NOS enzyme, LFP should be used in combination with other spectroscopic methods that could directly probe the docking equilibrium and the conformational change rate constants. The implications of the obtained analytical expressions for the interpretation of the LFP results from various native and modified NOS proteins are discussed. The mathematical formulas derived in this work should also be applicable for interpreting the IET kinetics in other modular redox enzymes.

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Bar-Itzhack, Itzhack Y.; Markley, F. Landis

1990-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Minimal parameter solution of the orthogonal matrix differential equation

NASA Technical Reports Server (NTRS)

Baritzhack, Itzhack Y.; Markley, F. Landis

1988-01-01

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed employing the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Dimensional analysis of detrimental ozone generation by positive wire-to-plate corona discharge in air

NASA Astrophysics Data System (ADS)

Bo, Z.; Chen, J. H.

2010-02-01

The dimensional analysis technique is used to formulate a correlation between ozone generation rate and various parameters that are important in the design and operation of positive wire-to-plate corona discharges in indoor air. The dimensionless relation is determined by linear regression analysis based on the results from 36 laboratory-scale experiments. The derived equation is validated by experimental data and a numerical model published in the literature. Applications of such derived equation are illustrated through an example selection of the appropriate set of operating conditions in the design/operation of a photocopier to follow the federal regulations of ozone emission. Finally, a new current-voltage characteristic equation is proposed for positive wire-to-plate corona discharges based on the derived dimensionless equation.

Analytic descriptions of stochastic bistable systems under force ramp

DOE PAGES

Friddle, Raymond W.

2016-05-13

Solving the two-state master equation with time-dependent rates, the ubiquitous driven bistable system, is a long-standing problem that does not permit a complete solution for all driving rates. We show an accurate approximation to this problem by considering the system in the control parameter regime. Moreover, the results are immediately applicable to a diverse range of bistable systems including single-molecule mechanics.

Iothalamate versus estimated GFR in a Hispanic-dominant pediatric renal transplant population.

PubMed

Papez, Karen E; Barletta, Gina-Marie; Hsieh, Stephanie; Joseph, Mark; Morgenstern, Bruce Z

2013-12-01

Accurate knowledge of glomerular filtration rate (GFR) is essential to the practice of nephrology. Routine surveillance of GFR is most commonly executed using estimated GFR (eGFR) calculations, most often from serum creatinine measurements. However, cystatin C-based equations have demonstrated earlier sensitivity to decline in renal function. The literature regarding eGFR from cystatin C has few references that include transplant recipients. Additionally, for most of the published eGFR equations, patients of Hispanic ethnicity have not been enrolled in sufficient numbers. The applicability of several eGFR equations to the pediatric kidney transplant population at our center were compared in the context of determining whether Hispanic ethnicity was associated with equation performance. Updated Schwartz, CKiD, and Zappitelli eGFR estimation equations demonstrated the highest correlations. The authors recommend further prospective investigations to validate and identify factors contributing to these findings.

A two-equation model for heat transport in wall turbulent shear flows

NASA Astrophysics Data System (ADS)

Nagano, Y.; Kim, C.

1988-08-01

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modeling. The eddy diffusivity concept is used in modeling. However, just as the eddy viscosity is determined from solutions of the k and epsilon equations, so the eddy diffusivity for heat is given as functions of temperature variance, and the dissipation rate of temperature fluctuations, together with k and epsilon. Thus, the proposed model does not require any questionable assumptions for the 'turbulent Prandtl number'. Modeled forms of the equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat-plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with the experiment is generally very satisfactory.

Angular-Rate Estimation Using Star Tracker Measurements

NASA Technical Reports Server (NTRS)

Azor, R.; Bar-Itzhack, I.; Deutschmann, Julie K.; Harman, Richard R.

1999-01-01

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quatemion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quatemion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quatemion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.

Angular-Rate Estimation using Star Tracker Measurements

NASA Technical Reports Server (NTRS)

Azor, R.; Bar-Itzhack, Itzhack Y.; Deutschmann, Julie K.; Harman, Richard R.

1999-01-01

This paper presents algorithms for estimating the angular-rate vector of satellites using quaternion measurements. Two approaches are compared, one that uses differentiated quaternion measurements to yield coarse rate measurements which are then fed into two different estimators. In the other approach the raw quaternion measurements themselves are fed directly into the two estimators. The two estimators rely on the ability to decompose the non-linear rate dependent part of the rotational dynamics equation of a rigid body into a product of an angular-rate dependent matrix and the angular-rate vector itself. This decomposition, which is not unique, enables the treatment of the nonlinear spacecraft dynamics model as a linear one and, consequently, the application of a Pseudo-Linear Kalman Filter (PSELIKA). It also enables the application of a special Kalman filter which is based on the use of the solution of the State Dependent Algebraic Riccati Equation (SDARE) in order to compute the Kalman gain matrix and thus eliminates the need to propagate and update the filter covariance matrix. The replacement of the elaborate rotational dynamics by a simple first order Markov model is also examined. In this paper a special consideration is given to the problem of delayed quaternion measurements. Two solutions to this problem are suggested and tested. Real Rossi X-Ray Timing Explorer (RXTE) data is used to test these algorithms, and results of these tests are presented.

Simulation of a steady-state integrated human thermal system.

NASA Technical Reports Server (NTRS)

Hsu, F. T.; Fan, L. T.; Hwang, C. L.

1972-01-01

The mathematical model of an integrated human thermal system is formulated. The system consists of an external thermal regulation device on the human body. The purpose of the device (a network of cooling tubes held in contact with the surface of the skin) is to maintain the human body in a state of thermoneutrality. The device is controlled by varying the inlet coolant temperature and coolant mass flow rate. The differential equations of the model are approximated by a set of algebraic equations which result from the application of the explicit forward finite difference method to the differential equations. The integrated human thermal system is simulated for a variety of combinations of the inlet coolant temperature, coolant mass flow rate, and metabolic rates. Two specific cases are considered: (1) the external thermal regulation device is placed only on the head and (2) the devices are placed on the head and the torso. The results of the simulation indicate that when the human body is exposed to hot environment, thermoneutrality can be attained by localized cooling if the operating variables of the external regulation device(s) are properly controlled.

A thermomechanical anisotropic model for shock loading of elastic-plastic and elastic-viscoplastic materials with application to jointed rock

DOE PAGES

Rubin, M. B.; Vorobiev, O.; Vitali, E.

2016-04-21

Here, a large deformation thermomechanical model is developed for shock loading of a material that can exhibit elastic and inelastic anisotropy. Use is made of evolution equations for a triad of microstructural vectors m i(i=1,2,3) which model elastic deformations and directions of anisotropy. Specific constitutive equations are presented for a material with orthotropic elastic response. The rate of inelasticity depends on an orthotropic yield function that can be used to model weak fault planes with failure in shear and which exhibits a smooth transition to isotropic response at high compression. Moreover, a robust, strongly objective numerical algorithm is proposed formore » both rate-independent and rate-dependent response. The predictions of the continuum model are examined by comparison with exact steady-state solutions. Also, the constitutive equations are used to obtain a simplified continuum model of jointed rock which is compared with high fidelity numerical solutions that model a persistent system of joints explicitly in the rock medium.« less

On the modelling of non-reactive and reactive turbulent combustor flows

NASA Technical Reports Server (NTRS)

Nikjooy, Mohammad; So, Ronald M. C.

1987-01-01

A study of non-reactive and reactive axisymmetric combustor flows with and without swirl is presented. Closure of the Reynolds equations is achieved by three models: kappa-epsilon, algebraic stress and Reynolds stress closure. Performance of two locally nonequilibrium and one equilibrium algebraic stress models is analyzed assuming four pressure strain models. A comparison is also made of the performance of a high and a low Reynolds number model for combustor flow calculations using Reynolds stress closures. Effects of diffusion and pressure-strain models on these closures are also investigated. Two models for the scalar transport are presented. One employs the second-moment closure which solves the transport equations for the scalar fluxes, while the other solves the algebraic equations for the scalar fluxes. In addition, two cases of non-premixed and one case of premixed combustion are considered. Fast- and finite-rate chemistry models are applied to non-premixed combustion. Both show promise for application in gas turbine combustors. However, finite rate chemistry models need to be examined to establish a suitable coupling of the heat release effects on turbulence field and rate constants.

Kinetic Study on the Isothermal and Nonisothermal Crystallization of Monoglyceride Organogels

PubMed Central

Meng, Zong; Yang, Lijun; Geng, Wenxin; Yao, Yubo; Wang, Xingguo; Liu, Yuanfa

2014-01-01

The isothermal and nonisothermal crystallization kinetics of monoglyceride (MAG) organogels were studied by pulsed nuclear magnetic resonance (pNMR) and differential scanning calorimetry (DSC), respectively. The Avrami equation was used to describe the isothermal crystallization kinetics and experimental data fitted the equation fairly well. Results showed that the crystal growth of MAG organogels was a rod-like growth of instantaneous nuclei at higher degrees of supercooling and a plate-like form with high nucleation rate at lower degrees of supercooling. The exothermic peak in nonisothermal DSC curves for the MAG organogels became wider and shifted to lower temperature when the cooling rate increased, and nonisothermal crystallization was analyzed by Mo equation. Results indicated that at the same crystallization time, to get a higher degree of relative crystallinity, a higher cooling rate was necessary. The activation energy of nonisothermal crystallization was calculated as 739.59 kJ/mol according to the Kissinger method. Therefore, as the results of the isothermal and nonisothermal crystallization kinetics for the MAG organogels obtained, the crystallization rate, crystal nucleation, and growth during the crystallization process could be preliminarily monitored through temperature and cooling rate regulation, which laid the foundation for the real industrial manufacture and application of the MAG organogels. PMID:24701138

Application of fault factor method to fault detection and diagnosis for space shuttle main engine

NASA Astrophysics Data System (ADS)

Cha, Jihyoung; Ha, Chulsu; Ko, Sangho; Koo, Jaye

2016-09-01

This paper deals with an application of the multiple linear regression algorithm to fault detection and diagnosis for the space shuttle main engine (SSME) during a steady state. In order to develop the algorithm, the energy balance equations, which balances the relation among pressure, mass flow rate and power at various locations within the SSME, are obtained. Then using the measurement data of some important parameters of the engine, fault factors which reflects the deviation of each equation from the normal state are estimated. The probable location of each fault and the levels of severity can be obtained from the estimated fault factors. This process is numerically demonstrated for the SSME at 104% Rated Propulsion Level (RPL) by using the simulated measurement data from the mathematical models of the engine. The result of the current study is particularly important considering that the recently developed reusable Liquid Rocket Engines (LREs) have staged-combustion cycles similarly to the SSME.

Derivation and application of the energy dissipation factor in the design of fishways

USGS Publications Warehouse

Towler, Brett; Mulligan, Kevin; Haro, Alexander J.

2015-01-01

Reducing turbulence and associated air entrainment is generally considered advantageous in the engineering design of fish passage facilities. The well-known energy dissipation factor, or EDF, correlates with observations of the phenomena. However, inconsistencies in EDF forms exist and the bases for volumetric energy dissipation rate criteria are often misunderstood. A comprehensive survey of EDF criteria is presented. Clarity in the application of the EDF and resolutions to these inconsistencies are provided through formal derivations; it is demonstrated that kinetic energy represents only 1/3 of the total energy input for the special case of a broad-crested weir. Specific errors in published design manuals are identified and resolved. New, fundamentally sound, design equations for culvert outlet pools and standard Denil Fishway resting pools are developed. The findings underscore the utility of EDF equations, demonstrate the transferability of volumetric energy dissipation rates, and provide a foundation for future refinement of component-, species-, and life-stage-specific EDF criteria.

Variance reduction through robust design of boundary conditions for stochastic hyperbolic systems of equations

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

Nordström, Jan, E-mail: jan.nordstrom@liu.se; Wahlsten, Markus, E-mail: markus.wahlsten@liu.se

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is to show that different boundary conditions give different convergence rates of the variance of the solution. This means that we can with the same knowledge of data get a more or less accurate description of the uncertainty in the solution. A variety of boundary conditions are compared and both analytical and numerical estimates of the variance of the solution are presented. As an application, we study the effect of this technique on Maxwell's equations as well as on a subsonic outflow boundary for themore » Euler equations.« less

bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport

DOE PAGES

Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.

2015-06-25

We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and tomore » a slowly accreting Kerr black hole in axisymmetry.« less

The development of an explicit thermochemical nonequilibrium algorithm and its application to compute three dimensional AFE flowfields

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

This study presents a three-dimensional explicit, finite-difference, shock-capturing numerical algorithm applied to viscous hypersonic flows in thermochemical nonequilibrium. The algorithm employs a two-temperature physical model. Equations governing the finite-rate chemical reactions are fully-coupled to the gas dynamic equations using a novel coupling technique. The new coupling method maintains stability in the explicit, finite-rate formulation while allowing relatively large global time steps. The code uses flux-vector accuracy. Comparisons with experimental data and other numerical computations verify the accuracy of the present method. The code is used to compute the three-dimensional flowfield over the Aeroassist Flight Experiment (AFE) vehicle at one of its trajectory points.

40 CFR 63.1564 - What are my requirements for metal HAP emissions from catalytic cracking units?

Code of Federal Regulations, 2013 CFR

2013-07-01

... coke burn-off emission limit (Option 4). (2) Comply with each operating limit in Table 2 of this... the PM emission rate (lb/1,000 lbs of coke burn-off) for each run using Equations 1, 2, and 3 (if applicable) of this section as follows: ER11AP02.000 Where: Rc = Coke burn-off rate, kg/hr (lb/hr); Qr...

40 CFR 63.1564 - What are my requirements for metal HAP emissions from catalytic cracking units?

Code of Federal Regulations, 2014 CFR

2014-07-01

... coke burn-off emission limit (Option 4). (2) Comply with each operating limit in Table 2 of this... the PM emission rate (lb/1,000 lbs of coke burn-off) for each run using Equations 1, 2, and 3 (if applicable) of this section as follows: ER11AP02.000 Where: Rc = Coke burn-off rate, kg/hr (lb/hr); Qr...

40 CFR 63.1564 - What are my requirements for metal HAP emissions from catalytic cracking units?

Code of Federal Regulations, 2012 CFR

2012-07-01

... coke burn-off emission limit (Option 4). (2) Comply with each operating limit in Table 2 of this... the PM emission rate (lb/1,000 lbs of coke burn-off) for each run using Equations 1, 2, and 3 (if applicable) of this section as follows: ER11AP02.000 Where: Rc = Coke burn-off rate, kg/hr (lb/hr); Qr...

Applications of MMPBSA to Membrane Proteins I: Efficient Numerical Solutions of Periodic Poisson-Boltzmann Equation

PubMed Central

Botello-Smith, Wesley M.; Luo, Ray

2016-01-01

Continuum solvent models have been widely used in biomolecular modeling applications. Recently much attention has been given to inclusion of implicit membrane into existing continuum Poisson-Boltzmann solvent models to extend their applications to membrane systems. Inclusion of an implicit membrane complicates numerical solutions of the underlining Poisson-Boltzmann equation due to the dielectric inhomogeneity on the boundary surfaces of a computation grid. This can be alleviated by the use of the periodic boundary condition, a common practice in electrostatic computations in particle simulations. The conjugate gradient and successive over-relaxation methods are relatively straightforward to be adapted to periodic calculations, but their convergence rates are quite low, limiting their applications to free energy simulations that require a large number of conformations to be processed. To accelerate convergence, the Incomplete Cholesky preconditioning and the geometric multi-grid methods have been extended to incorporate periodicity for biomolecular applications. Impressive convergence behaviors were found as in the previous applications of these numerical methods to tested biomolecules and MMPBSA calculations. PMID:26389966

The allometric relationship between resting metabolic rate and body mass in wild waterfowl (Anatidae) and an application to estimation of winter habitat requirements

USGS Publications Warehouse

Miller, M.R.; Eadie, J. McA

2006-01-01

We examined the allometric relationship between resting metabolic rate (RMR; kJ day-1) and body mass (kg) in wild waterfowl (Anatidae) by regressing RMR on body mass using species means from data obtained from published literature (18 sources, 54 measurements, 24 species; all data from captive birds). There was no significant difference among measurements from the rest (night; n = 37), active (day; n = 14), and unspecified (n = 3) phases of the daily cycle (P > 0.10), and we pooled these measurements for analysis. The resulting power function (aMassb) for all waterfowl (swans, geese, and ducks) had an exponent (b; slope of the regression) of 0.74, indistinguishable from that determined with commonly used general equations for nonpasserine birds (0.72-0.73). In contrast, the mass proportionality coefficient (b; y-intercept at mass = 1 kg) of 422 exceeded that obtained from the nonpasserine equations by 29%-37%. Analyses using independent contrasts correcting for phylogeny did not substantially alter the equation. Our results suggest the waterfowl equation provides a more appropriate estimate of RMR for bioenergetics analyses of waterfowl than do the general nonpasserine equations. When adjusted with a multiple to account for energy costs of free living, the waterfowl equation better estimates daily energy expenditure. Using this equation, we estimated that the extent of wetland habitat required to support wintering waterfowl populations could be 37%-50% higher than previously predicted using general nonpasserine equations. ?? The Cooper Ornithological Society 2006.

Inertially Stabilized Platforms for SATCOM On-The-Move Applications: A Hybrid Open/Closed-Loop Antenna Pointing Strategy

DTIC Science & Technology

2008-06-01

Photo courtesy of www.mathworks.com. Next, Equation (3.16) translates the aircraft disturbance rates through the de - sired local azimuth and elevation...Hessian matrix of the assumed quadratic cost function [34–36]. Equation (4.11) exactly de - termines the minimum of a quadratic function in a single...according to: Bkpk = −gk (4.21) Bk+1 = Bk +Qk (4.22) where Bk in some way approximates Gk from (4.12), and Qk is an update matrix de - pendent upon xk

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1976-01-01

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Applications of tribology to determine attrition by wear of particulate solids in CFB systems

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

Bayham, Samuel C.; Breault, Ronald; Monazam, Esmail

In recent years, much attention has been focused on the development of novel technologies for carbon capture and chemicals production that utilize a circulating fluidized bed (CFB) configuration; examples include chemical looping combustion and circulation of temperature swing adsorbents in a CFB configuration for CO 2 capture. A major uncertainty in determining the economic feasibility of these technologies is the required solids makeup rate, which, among other factors, is due to impact and wear attrition at various locations, including standpipes, cyclones, and the gas jets in fluid beds. While correlations have been developed that estimate the attrition rates at thesemore » areas, these correlations are dependent on constants that are uncertain without extensive experiment in the corresponding unit operation. Thus, it is difficult to determine the attrition rate a priori without performing extensive experiments on the materials or scaling up entirely. In this work, the authors outline a methodology for predictive attrition based on fundamental material properties from fields of tribology—specifically, the study of wear—to the knowledge of forces and sliding distances determined from hydrodynamic models to develop basic attrition models for novel CFB systems. The equations are derived for the standpipe and cyclone, which are common components found in CFBs, and the cyclone equation is compared to experimental data of attrition in the literature. The cyclone equation derived in this work results in an abrasion rate based on (1) material properties such as particle density and hardness, (2) inlet velocity, and (3) cyclone geometry. According to this equation, increasing the diameter of the cyclone and the solids inlet velocity tends to increase the rate of abrasion of the catalyst, while decreasing the hardness increases the abrasion rate. The functionality of the increasing attrition rate with velocity increase implies that increasing the efficiency of the cyclone may also increase the attrition rate via abrasion. With modifications to the severity coefficient term to include the solids loading, the cyclone equation derived in this work fits data from Reppenhagen and Werther with a coefficient of determination (R2) of 92%.« less

Applications of tribology to determine attrition by wear of particulate solids in CFB systems

DOE PAGES

Bayham, Samuel C.; Breault, Ronald; Monazam, Esmail

2016-11-03

In recent years, much attention has been focused on the development of novel technologies for carbon capture and chemicals production that utilize a circulating fluidized bed (CFB) configuration; examples include chemical looping combustion and circulation of temperature swing adsorbents in a CFB configuration for CO 2 capture. A major uncertainty in determining the economic feasibility of these technologies is the required solids makeup rate, which, among other factors, is due to impact and wear attrition at various locations, including standpipes, cyclones, and the gas jets in fluid beds. While correlations have been developed that estimate the attrition rates at thesemore » areas, these correlations are dependent on constants that are uncertain without extensive experiment in the corresponding unit operation. Thus, it is difficult to determine the attrition rate a priori without performing extensive experiments on the materials or scaling up entirely. In this work, the authors outline a methodology for predictive attrition based on fundamental material properties from fields of tribology—specifically, the study of wear—to the knowledge of forces and sliding distances determined from hydrodynamic models to develop basic attrition models for novel CFB systems. The equations are derived for the standpipe and cyclone, which are common components found in CFBs, and the cyclone equation is compared to experimental data of attrition in the literature. The cyclone equation derived in this work results in an abrasion rate based on (1) material properties such as particle density and hardness, (2) inlet velocity, and (3) cyclone geometry. According to this equation, increasing the diameter of the cyclone and the solids inlet velocity tends to increase the rate of abrasion of the catalyst, while decreasing the hardness increases the abrasion rate. The functionality of the increasing attrition rate with velocity increase implies that increasing the efficiency of the cyclone may also increase the attrition rate via abrasion. With modifications to the severity coefficient term to include the solids loading, the cyclone equation derived in this work fits data from Reppenhagen and Werther with a coefficient of determination (R2) of 92%.« less

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.

The effect of capturing the correct turbulence dissipation rate in BHR

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

Schwarzkopf, John Dennis; Ristorcelli, Raymond

In this manuscript, we discuss the shortcoming of a quasi-equilibrium assumption made in the BHR closure model. Turbulence closure models generally assume fully developed turbulence, which is not applicable to 1) non-equilibrium turbulence (e.g. change in mean pressure gradient) or 2) laminar-turbulence transition flows. Based on DNS data, we show that the current BHR dissipation equation [modeled based on the fully developed turbulence phenomenology] does not capture important features of nonequilibrium flows. To demonstrate our thesis, we use the BHR equations to predict a non-equilibrium flow both with the BHR dissipation and the dissipation from DNS. We find that themore » prediction can be substantially improved, both qualitatively and quantitatively, with the correct dissipation rate. We conclude that a new set of nonequilibrium phenomenological assumptions must be used to develop a new model equation for the dissipation to accurately predict the turbulence time scale used by other models.« less

The solution of linear systems of equations with a structural analysis code on the NAS CRAY-2

NASA Technical Reports Server (NTRS)

Poole, Eugene L.; Overman, Andrea L.

1988-01-01

Two methods for solving linear systems of equations on the NAS Cray-2 are described. One is a direct method; the other is an iterative method. Both methods exploit the architecture of the Cray-2, particularly the vectorization, and are aimed at structural analysis applications. To demonstrate and evaluate the methods, they were installed in a finite element structural analysis code denoted the Computational Structural Mechanics (CSM) Testbed. A description of the techniques used to integrate the two solvers into the Testbed is given. Storage schemes, memory requirements, operation counts, and reformatting procedures are discussed. Finally, results from the new methods are compared with results from the initial Testbed sparse Choleski equation solver for three structural analysis problems. The new direct solvers described achieve the highest computational rates of the methods compared. The new iterative methods are not able to achieve as high computation rates as the vectorized direct solvers but are best for well conditioned problems which require fewer iterations to converge to the solution.

Probabilistic Determination of Green Infrastructure Pollutant Removal Rates from the International Stormwater BMP Database

NASA Astrophysics Data System (ADS)

Gilliom, R.; Hogue, T. S.; McCray, J. E.

2017-12-01

There is a need for improved parameterization of stormwater best management practices (BMP) performance estimates to improve modeling of urban hydrology, planning and design of green infrastructure projects, and water quality crediting for stormwater management. Percent removal is commonly used to estimate BMP pollutant removal efficiency, but there is general agreement that this approach has significant uncertainties and is easily affected by site-specific factors. Additionally, some fraction of monitored BMPs have negative percent removal, so it is important to understand the probability that a BMP will provide the desired water quality function versus exacerbating water quality problems. The widely used k-C* equation has shown to provide a more adaptable and accurate method to model BMP contaminant attenuation, and previous work has begun to evaluate the strengths and weaknesses of the k-C* method. However, no systematic method exists for obtaining first-order removal rate constants needed to use the k-C* equation for stormwater BMPs; thus there is minimal application of the method. The current research analyzes existing water quality data in the International Stormwater BMP Database to provide screening-level parameterization of the k-C* equation for selected BMP types and analysis of factors that skew the distribution of efficiency estimates from the database. Results illustrate that while certain BMPs are more likely to provide desired contaminant removal than others, site- and design-specific factors strongly influence performance. For example, bioretention systems show both the highest and lowest removal rates of dissolved copper, total phosphorous, and total nitrogen. Exploration and discussion of this and other findings will inform the application of the probabilistic pollutant removal rate constants. Though data limitations exist, this research will facilitate improved accuracy of BMP modeling and ultimately aid decision-making for stormwater quality management in urban systems.

An internal variable constitutive model for the large deformation of metals at high temperatures

NASA Technical Reports Server (NTRS)

Brown, Stuart; Anand, Lallit

1988-01-01

The advent of large deformation finite element methodologies is beginning to permit the numerical simulation of hot working processes whose design until recently has been based on prior industrial experience. Proper application of such finite element techniques requires realistic constitutive equations which more accurately model material behavior during hot working. A simple constitutive model for hot working is the single scalar internal variable model for isotropic thermal elastoplasticity proposed by Anand. The model is recalled and the specific scalar functions, for the equivalent plastic strain rate and the evolution equation for the internal variable, presented are slight modifications of those proposed by Anand. The modified functions are better able to represent high temperature material behavior. The monotonic constant true strain rate and strain rate jump compression experiments on a 2 percent silicon iron is briefly described. The model is implemented in the general purpose finite element program ABAQUS.

Calculation of State Specific Rate Coefficients for Non-Equilibrium Hypersonics Applications: from H(Psi) = E(Psi) to k(T) = A *exp(-E(sub a)/RT)

NASA Technical Reports Server (NTRS)

Jaffe, Richard; Schwenke, David; Chaban, Galina; Panesi, Marco

2014-01-01

Development of High-Fidelity Physics-Based Models to describe hypersonic flight through the atmospheres of Earth and Mars is underway at NASA Ames Research Center. The goal is to construct chemistry models of the collisional and radiative processes that occur in the bow shock and boundary layers of spacecraft during atmospheric entry that are free of empiricism. In this talk I will discuss our philosophy and describe some of our progress. Topics to be covered include thermochemistry, internal energy relaxation, collisional dissociation and radiative emission and absorption. For this work we start by solving the Schrodinger equation to obtain accurate interaction potentials and radiative properties. Then we invoke classical mechanics to compute state-specific heavy particle collision cross sections and reaction rate coefficients. Finally, phenomenological rate coefficients and relaxation times are determined from master equation solutions.

An Application of Calculus to Cinematography.

ERIC Educational Resources Information Center

Sworder, Steven C.

This paper presents a laboratory exercise in which an integration problem is applied to cinematography, without the need for apparatus. The problem situation is about the oscillation control of a camera platform to attain the contrast angular rate of objects. Wave equations for describing the oscillations are presented and an expression for…

A Least-Squares Transport Equation Compatible with Voids

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

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Predictive Variables of Half-Marathon Performance for Male Runners.

PubMed

Gómez-Molina, Josué; Ogueta-Alday, Ana; Camara, Jesus; Stickley, Christoper; Rodríguez-Marroyo, José A; García-López, Juan

2017-06-01

The aims of this study were to establish and validate various predictive equations of half-marathon performance. Seventy-eight half-marathon male runners participated in two different phases. Phase 1 (n = 48) was used to establish the equations for estimating half-marathon performance, and Phase 2 (n = 30) to validate these equations. Apart from half-marathon performance, training-related and anthropometric variables were recorded, and an incremental test on a treadmill was performed, in which physiological (VO 2max , speed at the anaerobic threshold, peak speed) and biomechanical variables (contact and flight times, step length and step rate) were registered. In Phase 1, half-marathon performance could be predicted to 90.3% by variables related to training and anthropometry (Equation 1), 94.9% by physiological variables (Equation 2), 93.7% by biomechanical parameters (Equation 3) and 96.2% by a general equation (Equation 4). Using these equations, in Phase 2 the predicted time was significantly correlated with performance (r = 0.78, 0.92, 0.90 and 0.95, respectively). The proposed equations and their validation showed a high prediction of half-marathon performance in long distance male runners, considered from different approaches. Furthermore, they improved the prediction performance of previous studies, which makes them a highly practical application in the field of training and performance.

On multigrid solution of the implicit equations of hydrodynamics. Experiments for the compressible Euler equations in general coordinates

NASA Astrophysics Data System (ADS)

Kifonidis, K.; Müller, E.

2012-08-01

Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a Courant number of nine thousand, even complete multigrid breakdown is observed. Local Fourier analysis indicates that the degradation of the convergence rate is associated with the coarse-grid correction algorithm. An implicit scheme for the Euler equations that makes use of the present method was, nevertheless, able to outperform a standard explicit scheme on a time-dependent problem with a Courant number of order 1000. Conclusions: For steady-state problems, the described approach enables the construction of parallelizable, efficient, and robust implicit hydrodynamics solvers. The applicability of the method to time-dependent problems is presently restricted to cases with moderately high Courant numbers. This is due to an insufficient coarse-grid correction of the employed multigrid algorithm for large time steps. Further research will be required to help us to understand and overcome the observed multigrid convergence difficulties for time-dependent problems.

Microscopic modeling of gas-surface scattering: II. Application to argon atom adsorption on a platinum (111) surface

NASA Astrophysics Data System (ADS)

Filinov, A.; Bonitz, M.; Loffhagen, D.

2018-06-01

A new combination of first principle molecular dynamics (MD) simulations with a rate equation model presented in the preceding paper (paper I) is applied to analyze in detail the scattering of argon atoms from a platinum (111) surface. The combined model is based on a classification of all atom trajectories according to their energies into trapped, quasi-trapped and scattering states. The number of particles in each of the three classes obeys coupled rate equations. The coefficients in the rate equations are the transition probabilities between these states which are obtained from MD simulations. While these rates are generally time-dependent, after a characteristic time scale t E of several tens of picoseconds they become stationary allowing for a rather simple analysis. Here, we investigate this time scale by analyzing in detail the temporal evolution of the energy distribution functions of the adsorbate atoms. We separately study the energy loss distribution function of the atoms and the distribution function of in-plane and perpendicular energy components. Further, we compute the sticking probability of argon atoms as a function of incident energy, angle and lattice temperature. Our model is important for plasma-surface modeling as it allows to extend accurate simulations to longer time scales.

Application of a Reynolds stress turbulence model to the compressible shear layer

NASA Technical Reports Server (NTRS)

Sarkar, S.; Balakrishnan, L.

1990-01-01

Theoretically based turbulence models have had success in predicting many features of incompressible, free shear layers. However, attempts to extend these models to the high-speed, compressible shear layer have been less effective. In the present work, the compressible shear layer was studied with a second-order turbulence closure, which initially used only variable density extensions of incompressible models for the Reynolds stress transport equation and the dissipation rate transport equation. The quasi-incompressible closure was unsuccessful; the predicted effect of the convective Mach number on the shear layer growth rate was significantly smaller than that observed in experiments. Having thus confirmed that compressibility effects have to be explicitly considered, a new model for the compressible dissipation was introduced into the closure. This model is based on a low Mach number, asymptotic analysis of the Navier-Stokes equations, and on direct numerical simulation of compressible, isotropic turbulence. The use of the new model for the compressible dissipation led to good agreement of the computed growth rates with the experimental data. Both the computations and the experiments indicate a dramatic reduction in the growth rate when the convective Mach number is increased. Experimental data on the normalized maximum turbulence intensities and shear stress also show a reduction with increasing Mach number.

Status of rates and rate equations for thermal leptogenesis

NASA Astrophysics Data System (ADS)

Biondini, S.; Bödeker, D.; Brambilla, N.; Garny, M.; Ghiglieri, J.; Hohenegger, A.; Laine, M.; Mendizabal, S.; Millington, P.; Salvio, A.; Vairo, A.

2018-02-01

In many realizations of leptogenesis, heavy right-handed neutrinos play the main role in the generation of an imbalance between matter and antimatter in the early Universe. Hence, it is relevant to address quantitatively their dynamics in a hot and dense environment by taking into account the various thermal aspects of the problem at hand. The strong washout regime offers an interesting framework to carry out calculations systematically and reduce theoretical uncertainties. Indeed, any matter-antimatter asymmetry generated when the temperature of the hot plasma T exceeds the right-handed neutrino mass scale M is efficiently erased, and one can focus on the temperature window T ≪ M. We review recent progress in the thermal field theoretic derivation of the key ingredients for the leptogenesis mechanism: the right-handed neutrino production rate, the CP asymmetry in the heavy-neutrino decays and the washout rates. The derivation of evolution equations for the heavy-neutrino and lepton-asymmetry number densities, their rigorous formulation and applicability are also discussed.

Explicit bounds for the positive root of classes of polynomials with applications

NASA Astrophysics Data System (ADS)

Herzberger, Jürgen

2003-03-01

We consider a certain type of polynomial equations for which there exists--according to Descartes' rule of signs--only one simple positive root. These equations are occurring in Numerical Analysis when calculating or estimating the R-order or Q-order of convergence of certain iterative processes with an error-recursion of special form. On the other hand, these polynomial equations are very common as defining equations for the effective rate of return for certain cashflows like bonds or annuities in finance. The effective rate of interest i* for those cashflows is i*=q*-1, where q* is the unique positive root of such polynomial. We construct bounds for i* for a special problem concerning an ordinary simple annuity which is obtained by changing the conditions of such an annuity with given data applying the German rule (Preisangabeverordnung or short PAngV). Moreover, we consider a number of results for such polynomial roots in Numerical Analysis showing that by a simple variable transformation we can derive several formulas out of earlier results by applying this transformation. The same is possible in finance in order to generalize results to more complicated cashflows.

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

NASA Technical Reports Server (NTRS)

Eckert, E.R.G.; Livingood, John N.B.

1951-01-01

An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.

Computation of turbulent high speed mixing layers using a two-equation turbulence model

NASA Technical Reports Server (NTRS)

Narayan, J. R.; Sekar, B.

1991-01-01

A two-equation turbulence model was extended to be applicable for compressible flows. A compressibility correction based on modelling the dilational terms in the Reynolds stress equations were included in the model. The model is used in conjunction with the SPARK code for the computation of high speed mixing layers. The observed trend of decreasing growth rate with increasing convective Mach number in compressible mixing layers is well predicted by the model. The predictions agree well with the experimental data and the results from a compressible Reynolds stress model. The present model appears to be well suited for the study of compressible free shear flows. Preliminary results obtained for the reacting mixing layers are included.

On the use temperature parameterized rate coefficients in the estimation of non-equilibrium reaction rates

NASA Astrophysics Data System (ADS)

Shizgal, Bernie D.; Chikhaoui, Aziz

2006-06-01

The present paper considers a detailed analysis of the nonequilibrium effects for a model reactive system with the Chapman-Eskog (CE) solution of the Boltzmann equation as well as an explicit time dependent solution. The elastic cross sections employed are a hard sphere cross section and the Maxwell molecule cross section. Reactive cross sections which model reactions with and without activation energy are used. A detailed comparison is carried out with these solutions of the Boltzmann equation and the approximation introduced by Cukrowski and coworkers [J. Chem. Phys. 97 (1992) 9086; Chem. Phys. 89 (1992) 159; Physica A 188 (1992) 344; Chem. Phys. Lett. A 297 (1998) 402; Physica A 275 (2000) 134; Chem. Phys. Lett. 341 (2001) 585; Acta Phys. Polonica B 334 (2003) 3607.] based on the temperature of the reactive particles. We show that the Cukrowski approximation has limited applicability for the large class of reactive systems studied in this paper. The explicit time dependent solutions of the Boltzmann equation demonstrate that the CE approach is valid only for very slow reactions for which the corrections to the equilibrium rate coefficient are very small.

Application of a data reconciliation method to the stoichiometric analysis of Fibrobacter succinogenes growth.

PubMed

Guiavarch, Erell; Pons, Agnes; Creuly, Catherine; Dussap, Claude-Gilles

2008-12-01

Fibrobacter succinogenes S85, a strictly anaerobic Gram-negative bacterium, was grown in continuous culture in a bioreactor at different dilution rates (0.02 to 0.092 h(-1)) on a fully synthetic culture medium with glucose as carbon source. Glucose and ammonium sulfate consumption, as well as biomass, succinate, acetate, formate, and carbohydrate production were regularly measured. The relevant biomass elemental compositions were established for each dilution rate. Robustness of the experimental information was checked by C and N mass balances estimation, which were satisfactory. A detailed overall stoichiometry analysis of the process, including all substrates and products of the culture, was proposed. Online and off-line parameters measured during the culture brought a large number of data which were weighted by their respective variance associated to the measured value. The material balance resulted in an overdetermined linear system of equations made of weighted relationships including experimental data, elemental balances (C, H, O, N, S, Na), and an additional constraint. The mass balances involved in stoichiometric equations were solved using data reconciliation and linear algebra methods to take into account error measurements. This methodology allowed to establish the overall stoichiometric equation for each dilution rate studied.

A rain splash transport equation assimilating field and laboratory measurements

USGS Publications Warehouse

Dunne, T.; Malmon, D.V.; Mudd, S.M.

2010-01-01

Process-based models of hillslope evolution require transport equations relating sediment flux to its major controls. An equation for rain splash transport in the absence of overland flow was constructed by modifying an approach developed by Reeve (1982) and parameterizing it with measurements from single-drop laboratory experiments and simulated rainfall on a grassland in East Africa. The equation relates rain splash to hillslope gradient, the median raindrop diameter of a storm, and ground cover density; the effect of soil texture on detachability can be incorporated from other published results. The spatial and temporal applicability of such an equation for rain splash transport in the absence of overland flow on uncultivated hillslopes can be estimated from hydrological calculations. The predicted transport is lower than landscape-averaged geologic erosion rates from Kenya but is large enough to modify short, slowly eroding natural hillslopes as well as microtopographic interrill surfaces between which overland flow transports the mobilized sediment. Copyright 2010 by the American Geophysical Union. Copyright 2010 by the American Geophysical Union.

Reformulation and solution of the master equation for multiple-well chemical reactions.

PubMed

Georgievskii, Yuri; Miller, James A; Burke, Michael P; Klippenstein, Stephen J

2013-11-21

We consider an alternative formulation of the master equation for complex-forming chemical reactions with multiple wells and bimolecular products. Within this formulation the dynamical phase space consists of only the microscopic populations of the various isomers making up the reactive complex, while the bimolecular reactants and products are treated equally as sources and sinks. This reformulation yields compact expressions for the phenomenological rate coefficients describing all chemical processes, i.e., internal isomerization reactions, bimolecular-to-bimolecular reactions, isomer-to-bimolecular reactions, and bimolecular-to-isomer reactions. The applicability of the detailed balance condition is discussed and confirmed. We also consider the situation where some of the chemical eigenvalues approach the energy relaxation time scale and show how to modify the phenomenological rate coefficients so that they retain their validity.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

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.

Numerical modeling of a vortex stabilized arcjet

NASA Astrophysics Data System (ADS)

Pawlas, Gary Edward

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Satellite station-keeping is an example of a maneuvering application requiring the low thrust, high specific impulse of an arcjet. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity and swirling flow. Arcjet geometries are large area ratio converging-diverging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown a swirl or circumferential velocity component stabilizes a constricted arc. The equations are described which governs the flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is used in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and redial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split and Gauss-Seidel line relaxation is used to accelerate convergence. 'Converging diverging' nozzles with exit-to-throat area ratios up to 100:1 and annual nozzles were examined. Comparisons with experimental data and previous numerical results were in excellent agreement. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures.

The Rangeland Hydrology and Erosion Model

NASA Astrophysics Data System (ADS)

Nearing, M. A.

2016-12-01

The Rangeland Hydrology and Erosion Model (RHEM) is a process-based model that was designed to address rangelands conditions. RHEM is designed for government agencies, land managers and conservationists who need sound, science-based technology to model, assess, and predict runoff and erosion rates on rangelands and to assist in evaluating rangeland conservation practices effects. RHEM is an event-based model that estimates runoff, erosion, and sediment delivery rates and volumes at the spatial scale of the hillslope and the temporal scale of as single rainfall event. It represents erosion processes under normal and fire-impacted rangeland conditions. Moreover, it adopts a new splash erosion and thin sheet-flow transport equation developed from rangeland data, and it links the model hydrologic and erosion parameters with rangeland plant community by providing a new system of parameter estimation equations based on 204 plots at 49 rangeland sites distributed across 15 western U.S. states. A dynamic partial differential sediment continuity equation is used to model the total detachment rate of concentrated flow and rain splash and sheet flow. RHEM is also designed to be used as a calculator, or "engine", within other watershed scale models. From the research perspective RHEM acts as a vehicle for incorporating new scientific findings from rangeland infiltration, runoff, and erosion studies. Current applications of the model include: 1) a web site for general use (conservation planning, research, etc.), 2) National Resource Inventory reports to Congress, 3) as a computational engine within watershed scale models (e.g., KINEROS, HEC), 4) Ecological Site & State and Transition Descriptions, 5) proposed in 2015 to become part of the NRCS Desktop applications for field offices.

Accurate D-bar Reconstructions of Conductivity Images Based on a Method of Moment with Sinc Basis.

PubMed

Abbasi, Mahdi

2014-01-01

Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N (2)log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR.

Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

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

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2014-03-14

The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Reduced Equations for Calculating the Combustion Rates of Jet-A and Methane Fuel

NASA Technical Reports Server (NTRS)

Molnar, Melissa; Marek, C. John

2003-01-01

Simplified kinetic schemes for Jet-A and methane fuels were developed to be used in numerical combustion codes, such as the National Combustor Code (NCC) that is being developed at Glenn. These kinetic schemes presented here result in a correlation that gives the chemical kinetic time as a function of initial overall cell fuel/air ratio, pressure, and temperature. The correlations would then be used with the turbulent mixing times to determine the limiting properties and progress of the reaction. A similar correlation was also developed using data from NASA's Chemical Equilibrium Applications (CEA) code to determine the equilibrium concentration of carbon monoxide as a function of fuel air ratio, pressure, and temperature. The NASA Glenn GLSENS kinetics code calculates the reaction rates and rate constants for each species in a kinetic scheme for finite kinetic rates. These reaction rates and the values obtained from the equilibrium correlations were then used to calculate the necessary chemical kinetic times. Chemical kinetic time equations for fuel, carbon monoxide, and NOx were obtained for both Jet-A fuel and methane.

Generalized Bregman distances and convergence rates for non-convex regularization methods

NASA Astrophysics Data System (ADS)

Grasmair, Markus

2010-11-01

We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ1/p holds, if the regularization term has a slightly faster growth at zero than |t|p.

Threshold analysis of pulsed lasers with application to a room-temperature Co:MgF2 laser

NASA Technical Reports Server (NTRS)

Harrison, James; Welford, David; Moulton, Peter F.

1989-01-01

Rate-equation calculations are used to model accurately the near-threshold behavior of a Co:MgF2 laser operating at room temperature. The results demonstrate the limitations of the conventional threshold analysis in cases of practical interest. This conclusion is applicable to pulsed solid-state lasers in general. The calculations, together with experimental data, are used to determine emission cross sections for the Co:MgF2 laser.

Kinematic equations for resolved-rate control of an industrial robot arm

NASA Technical Reports Server (NTRS)

Barker, L. K.

1983-01-01

An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.

Decreasing Nitrogen Fertilizer Input Had Little Effect on Microbial Communities in Three Types of Soils

PubMed Central

Yu, Hailing; Gao, Qiang; Shao, Zeqiang; Ying, Anning; Sun, Yuyang; Liu, Jingwei; Mao, Wei; Zhang, Bin

2016-01-01

In this study, we examined the influence of different nitrogen (N) application rates (0, 168, 240, 270 and 312 kg N ha-1) on soil properties, maize (Zea mays L.) yields and microbial communities of three types of soils (clay, alluvial and sandy soils). Phospholipid fatty acid analysis was used to characterize soil microbial communities. Results indicated that N fertilization significantly decreased microbial biomass in both clay and sandy soils regardless of application rate. These decreases were more likely a result of soil pH decreases induced by N fertilization, especially in the sandy soils. This is supported by structural equation modeling and redundancy analysis results. Nitrogen fertilization also led to significant changes in soil microbial community composition. However, the change differences were gradually dismissed with increase in N application rate. We also observed that N fertilization increased maize yields to the same level regardless of application rate. This suggests that farmers could apply N fertilizers at a lower rate (i.e. 168 kg N ha-1), which could achieve high maize yield on one hand while maintain soil microbial functions on the other hand. PMID:26992097

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

Berman, P. R.

1972-01-01

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Integral-equation based methods for parameter estimation in output pulses of radiation detectors: Application in nuclear medicine and spectroscopy

NASA Astrophysics Data System (ADS)

Mohammadian-Behbahani, Mohammad-Reza; Saramad, Shahyar

2018-04-01

Model based analysis methods are relatively new approaches for processing the output data of radiation detectors in nuclear medicine imaging and spectroscopy. A class of such methods requires fast algorithms for fitting pulse models to experimental data. In order to apply integral-equation based methods for processing the preamplifier output pulses, this article proposes a fast and simple method for estimating the parameters of the well-known bi-exponential pulse model by solving an integral equation. The proposed method needs samples from only three points of the recorded pulse as well as its first and second order integrals. After optimizing the sampling points, the estimation results were calculated and compared with two traditional integration-based methods. Different noise levels (signal-to-noise ratios from 10 to 3000) were simulated for testing the functionality of the proposed method, then it was applied to a set of experimental pulses. Finally, the effect of quantization noise was assessed by studying different sampling rates. Promising results by the proposed method endorse it for future real-time applications.

Stochastic theory of nonequilibrium steady states and its applications. Part I

NASA Astrophysics Data System (ADS)

Zhang, Xue-Juan; Qian, Hong; Qian, Min

2012-01-01

The concepts of equilibrium and nonequilibrium steady states are introduced in the present review as mathematical concepts associated with stationary Markov processes. For both discrete stochastic systems with master equations and continuous diffusion processes with Fokker-Planck equations, the nonequilibrium steady state (NESS) is characterized in terms of several key notions which are originated from nonequilibrium physics: time irreversibility, breakdown of detailed balance, free energy dissipation, and positive entropy production rate. After presenting this NESS theory in pedagogically accessible mathematical terms that require only a minimal amount of prerequisites in nonlinear differential equations and the theory of probability, it is applied, in Part I, to two widely studied problems: the stochastic resonance (also known as coherent resonance) and molecular motors (also known as Brownian ratchet). Although both areas have advanced rapidly on their own with a vast amount of literature, the theory of NESS provides them with a unifying mathematical foundation. Part II of this review contains applications of the NESS theory to processes from cellular biochemistry, ranging from enzyme catalyzed reactions, kinetic proofreading, to zeroth-order ultrasensitivity.

Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

NASA Technical Reports Server (NTRS)

Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming

1996-01-01

We develop a methodology to ensure that the stress tensor, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds stress transport equation.

High strain rate behavior of a SiC particulate reinforced Al{sub 2}O{sub 3} ceramic matrix composite

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

Hall, I.W.; Guden, M.

The high strain rate deformation behavior of composite materials is important for several reasons. First, knowledge of the mechanical properties of composites at high strain rates is needed for designing with these materials in applications where sudden changes in loading rates are likely to occur. Second, knowledge of both the dynamic and quasi-static mechanical responses can be used to establish the constitutive equations which are necessary to increase the confidence limits of these materials, particularly if they are to be used in critical structural applications. Moreover, dynamic studies and the knowledge gained form them are essential for the further developmentmore » of new material systems for impact applications. In this study, the high strain rate compressive deformation behavior of a ceramic matrix composite (CMC) consisting of SiC particles and an Al{sub 2}O{sub 3} matrix was studied and compared with its quasi-static behavior. Microscopic observations were conducted to investigate the deformation and fracture mechanism of the composite.« less

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.

Computer modeling of electromagnetic and thermal effects in microwave soft tissue ablation (Invited Paper)

NASA Astrophysics Data System (ADS)

Cronin, Nigel J.; Clegg, Peter J.

2005-04-01

Microwave Endometrial Ablation (MEA) is a technique that can be used for the treatment of abnormal uterine bleeding. The procedure involves sweeping a specially designed microwave applicator throughout the uterine cavity to achieve an ideally uniform depth of tissue necrosis of between 5 and 6mm. We have performed a computer analysis of the MEA procedure in which finite element analysis was used to determine the SAR pattern around the applicator. This was followed by a Green Function based solution of the Bioheat equation to determine the resulting induced temperatures. The method developed is applicable to situations involving a moving microwave source, as used in MEA. The validity of the simulation was verified by measurements in a tissue phantom material using a purpose built applicator and a calibrated pulling device. From the calculated temperatures the depth of necrosis was assessed through integration of the resulting rates of cell death estimated using the Arrhenius equation. The Arrhenius parameters used were derived from published data on BHK cells. Good agreement was seen between the calculated depths of cell necrosis and those found in human in-vivo testing.

Tensile stress-strain and work hardening behaviour of P9 steel for wrapper application in sodium cooled fast reactors

NASA Astrophysics Data System (ADS)

Christopher, J.; Choudhary, B. K.; Isaac Samuel, E.; Mathew, M. D.; Jayakumar, T.

2012-01-01

Tensile flow behaviour of P9 steel with different silicon content has been examined in the framework of Hollomon, Ludwik, Swift, Ludwigson and Voce relationships for a wide temperature range (300-873 K) at a strain rate of 1.3 × 10 -3 s -1. Ludwigson equation described true stress ( σ)-true plastic strain ( ɛ) data most accurately in the range 300-723 K. At high temperatures (773-873 K), Ludwigson equation reduces to Hollomon equation. The variations of instantaneous work hardening rate ( θ = dσ/ dɛ) and θσ with stress indicated two-stage work hardening behaviour. True stress-true plastic strain, flow parameters, θ vs. σ and θσ vs. σ with respect to temperature exhibited three distinct temperature regimes and displayed anomalous behaviour due to dynamic strain ageing at intermediate temperatures. Rapid decrease in flow stress and flow parameters, and rapid shift in θ- σ and θσ- σ towards lower stresses with increase in temperature indicated dominance of dynamic recovery at high temperatures.

A kinetic theory for age-structured stochastic birth-death processes

NASA Astrophysics Data System (ADS)

Chou, Tom; Greenman, Chris

Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) 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 BBGKY-like hierarchy. 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. NSF.

Calculation of equivalent friction coefficient for castor seed by single screw press

NASA Astrophysics Data System (ADS)

Liu, R.; Xiao, Z.; Li, C.; Zhang, L.; Li, P.; Li, H.; Zhang, A.; Tang, S.; Sun, F.

2017-08-01

Based on the traction angle and transportation rate equation, castor beans were pressed by application of single screw under different cake diameter and different screw speed. The results showed that the greater the cake diameter and screw rotation speed, the greater the actual transmission rate was. The equivalent friction coefficient was defined and calculated as 0.4136, and the friction coefficients between press material and screw, bar cage were less than the equivalent friction coefficient value.

Phase coupling in the cardiorespiratory interaction.

PubMed

Bahraminasab, A; Kenwright, D; Stefanovska, A; Ghasemi, F; McClintock, P V E

2008-01-01

Markovian analysis is applied to derive nonlinear stochastic equations for the reconstruction of heart rate and respiration rate variability data. A model of their 'phase' interactions is obtained for the first time, thereby gaining new insights into the strength and direction of the cardiorespiratory phase coupling. The reconstructed model can reproduce synchronisation phenomena between the cardiac and the respiratory systems, including switches in synchronisation ratio. The technique is equally applicable to the extraction of the multi-dimensional couplings between many interacting subsystems.

The development of structure in the expanding universe

NASA Technical Reports Server (NTRS)

Silk, J.; White, S. D.

1978-01-01

A model for clustering in an expanding universe is developed based on an application of the coagulation equation to the collision and aggregation of bound condensations. While the growth rate of clustering is determined by the rate at which density fluctuations reach the nonlinear regime and therefore depends on the initial fluctuation spectrum, the mass spectrum rapidly approaches a self-similar limiting form. This form is determined by the tidal processes which lead to the merging of condensations, and is not dependent on initial conditions.

Damage Identification of Piles Based on Vibration Characteristics

PubMed Central

Zhang, Xiaozhong; Yao, Wenjuan; Chen, Bo; Liu, Dewen

2014-01-01

A method of damage identification of piles was established by using vibration characteristics. The approach focused on the application of the element strain energy and sensitive modals. A damage identification equation of piles was deduced using the structural vibration equation. The equation contained three major factors: change rate of element modal strain energy, damage factor of pile, and sensitivity factor of modal damage. The sensitive modals of damage identification were selected by using sensitivity factor of modal damage firstly. Subsequently, the indexes for early-warning of pile damage were established by applying the change rate of strain energy. Then the technology of computational analysis of wavelet transform was used to damage identification for pile. The identification of small damage of pile was completely achieved, including the location of damage and the extent of damage. In the process of identifying the extent of damage of pile, the equation of damage identification was used in many times. Finally, a stadium project was used as an example to demonstrate the effectiveness of the proposed method of damage identification for piles. The correctness and practicability of the proposed method were verified by comparing the results of damage identification with that of low strain test. The research provided a new way for damage identification of piles. PMID:25506062

Thermal radiation heat transfer in participating media by finite volume discretization using collimated beam incidence

NASA Astrophysics Data System (ADS)

Harijishnu, R.; Jayakumar, J. S.

2017-09-01

The main objective of this paper is to study the heat transfer rate of thermal radiation in participating media. For that, a generated collimated beam has been passed through a two dimensional slab model of flint glass with a refractive index 2. Both Polar and azimuthal angle have been varied to generate such a beam. The Temperature of the slab and Snells law has been validated by Radiation Transfer Equation (RTE) in OpenFOAM (Open Field Operation and Manipulation), a CFD software which is the major computational tool used in Industry and research applications where the source code is modified in which radiation heat transfer equation is added to the case and different radiation heat transfer models are utilized. This work concentrates on the numerical strategies involving both transparent and participating media. Since Radiation Transfer Equation (RTE) is difficult to solve, the purpose of this paper is to use existing solver buoyantSimlpeFoam to solve radiation model in the participating media by compiling the source code to obtain the heat transfer rate inside the slab by varying the Intensity of radiation. The Finite Volume Method (FVM) is applied to solve the Radiation Transfer Equation (RTE) governing the above said physical phenomena.

The thermodynamic and transport properties of GdCl3 in molten eutectic LiCl-KCl derived from the analysis of cyclic voltammetry signals

NASA Astrophysics Data System (ADS)

Samin, Adib; Wu, Evan; Zhang, Jinsuo

2017-02-01

Pyroprocessing technology is a promising tool for recycling nuclear fuel and producing high purity gadolinium for industrial applications. An efficient implementation of pyroprocessing entails a careful characterization of the electrochemical and transport properties of lanthanides in high temperature molten salts. In this work, the cyclic voltammetry signals of Gd in molten LiCl-KCl salt were recorded for a combination of three temperatures (723 K, 773 K, and 823 K) and three concentration levels (3 wt. %, 6 wt. %, and 9 wt. %) including concentration levels higher than previously reported and relevant for a realistic application of pyroprocessing for molten salt recycle, and the concentration effects were investigated. Four scan rates (200 mV/s to 500 mV/s) were used for each condition, and the signals were examined using conventional Cyclic Voltammetry (CV) analysis equations and by utilizing a two-plate Brunauer, Emmett, and Teller (BET) model accounting for mass diffusion, kinetics, adsorption, and the evolution of electrode morphology via a nonlinear least squares procedure for fitting the model to the experimental signals. It was determined that the redox process is quasi-reversible for the scan rates being used. Furthermore, the applicability of the conventional equations for CV analysis was shown to be problematic for the conditions used, and this is thought to be due to the fact that these equations were derived under the assumption of reversible conditions. The model-derived values for diffusivity are consistent with the literature and are shown to decrease with increasing concentration. This may be due to increased interactions at higher concentration levels. It was also shown that the formal redox potential increased with a concentration and was slightly more positive on the covered electrode.

Application of the Grunwald-Winstein Equations to Studies of Solvolytic Reactions of Chloroformate and Fluoroformate Esters

PubMed Central

D’Souza, Malcolm J.; Kevill, Dennis N.

2014-01-01

Chloroformates are important laboratory and industrial chemicals with almost one hundred listed in the catalogs of leading suppliers. They are, for example, of prime importance as protecting groups in peptide synthesis. In some instances, the more stable fluoroformate is preferred. In recent years, the specific rates of solvolysis (k) for chloroformates and fluoroformates in solvents of widely ranging nucleophilicity and ionizing power have been studied. Analysis of these rates using the extended (two-term) Grunwald-Winstein equation has led to important information concerning reaction mechanism. Also assisting in this effort have been studies of kinetic solvent isotope effects (KSIE), of leaving group effects (especially kF/kCl ratios), and of entropies of activation from studies of specific rate variations with temperature. For solvolyses of chloroformate esters, two mechanisms (addition-elimination and ionization) are commonly encountered. For solvolyses of fluoroformates, mainly because of a strong C–F bond, the ionization pathway is rare and the addition-elimination pathway is in most situations the one encountered. PMID:25364780

Measurement of a linear free energy relationship one molecule at a time

PubMed Central

Rao, B. V.; Kwon, K.-Y.; Liu, A.; Bartels, L.

2004-01-01

A systematic study of the dehydrogenation of substituted thiophenols by controlled charge injection from the tip of a scanning tunneling microscope (STM) reveals a pronounced dependence of the reaction yield on the position and the chemical nature of the substituent. We evaluate the dehydrogenation rate of para-halo-substituted species within a linear free energy relationship, namely the Hammett equation. The resultant ρ value of 1.4 can faithfully predict the reaction rates of molecules that are meta-halo-substituted or para-methyl-substituted. The positive sign of ρ suggests a negatively charged transition state at the core of the STM-induced process, and the magnitude of the ρ value indicates that the presence of the substrate does not preclude substantial substituent effects. The applicability of the Hammett equation to single-molecule chemistry offers facile prediction of the rate of STM-based single-molecule chemistry in a field, which so far has been addressed by focusing on involved quantum-mechanical modeling of its underlying processes. PMID:15601774

Measurement of a linear free energy relationship one molecule at a time.

PubMed

Rao, B V; Kwon, K-Y; Liu, A; Bartels, L

2004-12-28

A systematic study of the dehydrogenation of substituted thiophenols by controlled charge injection from the tip of a scanning tunneling microscope (STM) reveals a pronounced dependence of the reaction yield on the position and the chemical nature of the substituent. We evaluate the dehydrogenation rate of para-halo-substituted species within a linear free energy relationship, namely the Hammett equation. The resultant rho value of 1.4 can faithfully predict the reaction rates of molecules that are meta-halo-substituted or para-methyl-substituted. The positive sign of rho suggests a negatively charged transition state at the core of the STM-induced process, and the magnitude of the rho value indicates that the presence of the substrate does not preclude substantial substituent effects. The applicability of the Hammett equation to single-molecule chemistry offers facile prediction of the rate of STM-based single-molecule chemistry in a field, which so far has been addressed by focusing on involved quantum-mechanical modeling of its underlying processes.

Application of balancing methods in modeling the penicillin fermentation.

PubMed

Heijnen, J J; Roels, J A; Stouthamer, A H

1979-12-01

This paper shows the application of elementary balancing methods in combination with simple kinetic equations in the formulation of an unstructured model for the fed-batch process for the production of penicillin. The rate of substrate uptake is modeled with a Monod-type relationship. The specific penicillin production rate is assumed to be a function of growth rate. Hydrolysis of penicillin to penicilloic acid is assumed to be first order in penicillin. In simulations with the present model it is shown that the model, although assuming a strict relationship between specific growth rate and penicillin productivity, allows for the commonly observed lag phase in the penicillin concentration curve and the apparent separation between growth and production phase (idiophase-trophophase concept). Furthermore it is shown that the feed rate profile during fermentation is of vital importance in the realization of a high production rate throughout the duration of the fermentation. It is emphasized that the method of modeling presented may also prove rewarding for an analysis of fermentation processes other than the penicillin fermentation.

A study of the rate-controlled constrained-equilibrium dimension reduction method and its different implementations

NASA Astrophysics Data System (ADS)

Hiremath, Varun; Pope, Stephen B.

2013-04-01

The Rate-Controlled Constrained-Equilibrium (RCCE) method is a thermodynamic based dimension reduction method which enables representation of chemistry involving n s species in terms of fewer n r constraints. Here we focus on the application of the RCCE method to Lagrangian particle probability density function based computations. In these computations, at every reaction fractional step, given the initial particle composition (represented using RCCE), we need to compute the reaction mapping, i.e. the particle composition at the end of the time step. In this work we study three different implementations of RCCE for computing this reaction mapping, and compare their relative accuracy and efficiency. These implementations include: (1) RCCE/TIFS (Trajectory In Full Space): this involves solving a system of n s rate-equations for all the species in the full composition space to obtain the reaction mapping. The other two implementations obtain the reaction mapping by solving a reduced system of n r rate-equations obtained by projecting the n s rate-equations for species evaluated in the full space onto the constrained subspace. These implementations include (2) RCCE: this is the classical implementation of RCCE which uses a direct projection of the rate-equations for species onto the constrained subspace; and (3) RCCE/RAMP (Reaction-mixing Attracting Manifold Projector): this is a new implementation introduced here which uses an alternative projector obtained using the RAMP approach. We test these three implementations of RCCE for methane/air premixed combustion in the partially-stirred reactor with chemistry represented using the n s=31 species GRI-Mech 1.2 mechanism with n r=13 to 19 constraints. We show that: (a) the classical RCCE implementation involves an inaccurate projector which yields large errors (over 50%) in the reaction mapping; (b) both RCCE/RAMP and RCCE/TIFS approaches yield significantly lower errors (less than 2%); and (c) overall the RCCE/TIFS approach is the most accurate, efficient (by orders of magnitude) and robust implementation.

Reaction rate constants and mean population percentage for nitrifiers in an alternating oxidation ditch system.

PubMed

Mantziaras, I D; Katsiri, A

2011-01-01

This paper presents a methodology for the determination of reaction rate constants for nitrifying bacteria and their mean population percentage in biomass in an alternating oxidation ditch system. The method used is based on the growth rate equations of the ASM1 model (IWA) (Henze et al. in Activated sludge models ASM1, ASM2, ASM2d, and ASM3. IWA Scientific and Technical Report no. 9, IWA Publishing, London, UK, 2000) and the application of mass balance equations for nitrifiers and ammonium nitrogen in an operational cycle of the ditch system. The system consists of two ditches operating in four phases. Data from a large-scale oxidation ditch pilot plant with a total volume of 120 m(3) within an experimental period of 8 months was used. Maximum specific growth rate for autotrophs (μ(A)) and the half-saturation constant for ammonium nitrogen (K(NH)) were found to be 0.36 day(-1) and 0.65 mgNH(4)-N/l, respectively. Additionally, the average population percentage of the nitrifiers in the biomass was estimated to be around 3%.

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

NASA Technical Reports Server (NTRS)

Radhadrishnan, Krishnan

1993-01-01

A detailed analysis of the accuracy of several techniques recently developed for integrating stiff ordinary differential equations is presented. The techniques include two general-purpose codes EPISODE and LSODE developed for an arbitrary system of ordinary differential equations, and three specialized codes CHEMEQ, CREK1D, and GCKP4 developed specifically to solve chemical kinetic rate equations. The accuracy study is made by application of these codes to two practical combustion kinetics problems. Both problems describe adiabatic, homogeneous, gas-phase chemical reactions at constant pressure, and include all three combustion regimes: induction, heat release, and equilibration. To illustrate the error variation in the different combustion regimes the species are divided into three types (reactants, intermediates, and products), and error versus time plots are presented for each species type and the temperature. These plots show that CHEMEQ is the most accurate code during induction and early heat release. During late heat release and equilibration, however, the other codes are more accurate. A single global quantity, a mean integrated root-mean-square error, that measures the average error incurred in solving the complete problem is used to compare the accuracy of the codes. Among the codes examined, LSODE is the most accurate for solving chemical kinetics problems. It is also the most efficient code, in the sense that it requires the least computational work to attain a specified accuracy level. An important finding is that use of the algebraic enthalpy conservation equation to compute the temperature can be more accurate and efficient than integrating the temperature differential equation.

GFR Estimation: From Physiology to Public Health

PubMed Central

Levey, Andrew S.; Inker, Lesley A.; Coresh, Josef

2014-01-01

Estimating glomerular filtration rate (GFR) is essential for clinical practice, research, and public health. Appropriate interpretation of estimated GFR (eGFR) requires understanding the principles of physiology, laboratory medicine, epidemiology and biostatistics used in the development and validation of GFR estimating equations. Equations developed in diverse populations are less biased at higher GFR than equations developed in CKD populations and are more appropriate for general use. Equations that include multiple endogenous filtration markers are more precise than equations including a single filtration marker. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations are the most accurate GFR estimating equations that have been evaluated in large, diverse populations and are applicable for general clinical use. The 2009 CKD-EPI creatinine equation is more accurate in estimating GFR and prognosis than the 2006 Modification of Diet in Renal Disease (MDRD) Study equation and provides lower estimates of prevalence of decreased eGFR. It is useful as a “first” test for decreased eGFR and should replace the MDRD Study equation for routine reporting of serum creatinine–based eGFR by clinical laboratories. The 2012 CKD-EPI cystatin C equation is as accurate as the 2009 CKD-EPI creatinine equation in estimating eGFR, does not require specification of race, and may be more accurate in patients with decreased muscle mass. The 2012 CKD-EPI creatinine–cystatin C equation is more accurate than the 2009 CKD-EPI creatinine and 2012 CKD-EPI cystatin C equations and is useful as a confirmatory test for decreased eGFR as determined by an equation based on serum creatinine. Further improvement in GFR estimating equations will require development in more broadly representative populations, including diverse racial and ethnic groups, use of multiple filtration markers, and evaluation using statistical techniques to compare eGFR to “true GFR”. PMID:24485147

Receptor binding kinetics equations: Derivation using the Laplace transform method.

PubMed

Hoare, Sam R J

Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time-dependent pharmacological activities. Copyright © 2017 Elsevier Inc. All rights reserved.

Exact solutions to the Mo-Papas and Landau-Lifshitz equations

NASA Astrophysics Data System (ADS)

Rivera, R.; Villarroel, D.

2002-10-01

Two exact solutions of the Mo-Papas and Landau-Lifshitz equations for a point charge in classical electrodynamics are presented here. Both equations admit as an exact solution the motion of a charge rotating with constant speed in a circular orbit. These equations also admit as an exact solution the motion of two identical charges rotating with constant speed at the opposite ends of a diameter. These exact solutions allow one to obtain, starting from the equation of motion, a definite formula for the rate of radiation. In both cases the rate of radiation can also be obtained, with independence of the equation of motion, from the well known fields of a point charge, that is, from the Maxwell equations. The rate of radiation obtained from the Mo-Papas equation in the one-charge case coincides with the rate of radiation that comes from the Maxwell equations; but in the two-charge case the results do not coincide. On the other hand, the rate of radiation obtained from the Landau-Lifshitz equation differs from the one that follows from the Maxwell equations in both the one-charge and two-charge cases. This last result does not support a recent statement by Rohrlich in favor of considering the Landau-Lifshitz equation as the correct and exact equation of motion for a point charge in classical electrodynamics.

Critical spaces for quasilinear parabolic evolution equations and applications

NASA Astrophysics Data System (ADS)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Reference equation for prediction of a total distance during six-minute walk test using Indonesian anthropometrics.

PubMed

Nusdwinuringtyas, Nury; Widjajalaksmi; Yunus, Faisal; Alwi, Idrus

2014-04-01

to develop a reference equation for prediction of the total distance walk using Indonesian anthropometrics of sedentary healthy subjects. Subsequently, the prediction obtained was compared to those calculated by the Caucasian-based Enright prediction equation. the cross-sectional study was conducted among 123 healthy Indonesian adults with sedentary life style (58 male and 65 female subjects in an age range between 18 and 50 years). Heart rate was recorded using Polar with expectation in the sub-maximal zone (120-170 beats per minute). The subjects performed two six-minute walk tests, the first one on a 15-meter track according to the protocol developed by the investigator. The second walk was carried out on Biodex®gait trainer as gold standard. an average total distance of 547±54.24 m was found, not significantly different from the gold standard of 544.72±54.11 m (p>0.05). Multiple regression analysis was performed to develop the new equation. the reference equation for prediction of the total distance using Indonesian anthropometrics is more applicable in Indonesia.

Application of linear multifrequency-grey acceleration to preconditioned Krylov iterations for thermal radiation transport

DOE PAGES

Till, Andrew T.; Warsa, James S.; Morel, Jim E.

2018-06-15

The thermal radiative transfer (TRT) equations comprise a radiation equation coupled to the material internal energy equation. Linearization of these equations produces effective, thermally-redistributed scattering through absorption-reemission. In this paper, we investigate the effectiveness and efficiency of Linear-Multi-Frequency-Grey (LMFG) acceleration that has been reformulated for use as a preconditioner to Krylov iterative solution methods. We introduce two general frameworks, the scalar flux formulation (SFF) and the absorption rate formulation (ARF), and investigate their iterative properties in the absence and presence of true scattering. SFF has a group-dependent state size but may be formulated without inner iterations in the presence ofmore » scattering, while ARF has a group-independent state size but requires inner iterations when scattering is present. We compare and evaluate the computational cost and efficiency of LMFG applied to these two formulations using a direct solver for the preconditioners. Finally, this work is novel because the use of LMFG for the radiation transport equation, in conjunction with Krylov methods, involves special considerations not required for radiation diffusion.« less

A method for predicting optimized processing parameters for surfacing

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

Dupont, J.N.; Marder, A.R.

1994-12-31

Welding is used extensively for surfacing applications. To operate a surfacing process efficiently, the variables must be optimized to produce low levels of dilution with the substrate while maintaining high deposition rates. An equation for dilution in terms of the welding variables, thermal efficiency factors, and thermophysical properties of the overlay and substrate was developed by balancing energy and mass terms across the welding arc. To test the validity of the resultant dilution equation, the PAW, GTAW, GMAW, and SAW processes were used to deposit austenitic stainless steel onto carbon steel over a wide range of parameters. Arc efficiency measurementsmore » were conducted using a Seebeck arc welding calorimeter. Melting efficiency was determined based on knowledge of the arc efficiency. Dilution was determined for each set of processing parameters using a quantitative image analysis system. The pertinent equations indicate dilution is a function of arc power (corrected for arc efficiency), filler metal feed rate, melting efficiency, and thermophysical properties of the overlay and substrate. With the aid of the dilution equation, the effect of processing parameters on dilution is presented by a new processing diagram. A new method is proposed for determining dilution from welding variables. Dilution is shown to depend on the arc power, filler metal feed rate, arc and melting efficiency, and the thermophysical properties of the overlay and substrate. Calculated dilution levels were compared with measured values over a large range of processing parameters and good agreement was obtained. The results have been applied to generate a processing diagram which can be used to: (1) predict the maximum deposition rate for a given arc power while maintaining adequate fusion with the substrate, and (2) predict the resultant level of dilution with the substrate.« less

Trade-off between linewidth and slip rate in a mode-locked laser model.

PubMed

Moore, Richard O

2014-05-15

We demonstrate a trade-off between linewidth and loss-of-lock rate in a mode-locked laser employing active feedback to control the carrier-envelope offset phase difference. In frequency metrology applications, the linewidth translates directly to uncertainty in the measured frequency, whereas the impact of lock loss and recovery on the measured frequency is less well understood. We reduce the dynamics to stochastic differential equations, specifically diffusion processes, and compare the linearized linewidth to the rate of lock loss determined by the mean time to exit, as calculated from large deviation theory.

Simple taper: Taper equations for the field forester

Treesearch

David R. Larsen

2017-01-01

"Simple taper" is set of linear equations that are based on stem taper rates; the intent is to provide taper equation functionality to field foresters. The equation parameters are two taper rates based on differences in diameter outside bark at two points on a tree. The simple taper equations are statistically equivalent to more complex equations. The linear...

Utility of Equations to Estimate Peak Oxygen Uptake and Work Rate From a 6-Minute Walk Test in Patients With COPD in a Clinical Setting.

PubMed

Kirkham, Amy A; Pauhl, Katherine E; Elliott, Robyn M; Scott, Jen A; Doria, Silvana C; Davidson, Hanan K; Neil-Sztramko, Sarah E; Campbell, Kristin L; Camp, Pat G

2015-01-01

To determine the utility of equations that use the 6-minute walk test (6MWT) results to estimate peak oxygen uptake ((Equation is included in full-text article.)o2) and peak work rate with chronic obstructive pulmonary disease (COPD) patients in a clinical setting. This study included a systematic review to identify published equations estimating peak (Equation is included in full-text article.)o2 and peak work rate in watts in COPD patients and a retrospective chart review of data from a hospital-based pulmonary rehabilitation program. The following variables were abstracted from the records of 42 consecutively enrolled COPD patients: measured peak (Equation is included in full-text article.)o2 and peak work rate achieved during a cycle ergometer cardiopulmonary exercise test, 6MWT distance, age, sex, weight, height, forced expiratory volume in 1 second, forced vital capacity, and lung diffusion capacity. Estimated peak (Equation is included in full-text article.)o2 and peak work rate were estimated from 6MWT distance using published equations. The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work to prescribe aerobic exercise intensities of 60% and 80% was calculated. Eleven equations from 6 studies were identified. Agreement between estimated and measured values was poor to moderate (intraclass correlation coefficients = 0.11-0.63). The error associated with using estimated peak (Equation is included in full-text article.)o2 or peak work rate to prescribe exercise intensities of 60% and 80% of measured values ranged from mean differences of 12 to 35 and 16 to 47 percentage points, respectively. There is poor to moderate agreement between measured peak (Equation is included in full-text article.)o2 and peak work rate and estimations from equations that use 6MWT distance, and the use of the estimated values for prescription of aerobic exercise intensity would result in large error. Equations estimating peak (Equation is included in full-text article.)o2 and peak work rate are of low utility for prescribing exercise intensity in pulmonary rehabilitation programs.

PRODUCTION OF SOUND BY UNSTEADY THROTTLING OF FLOW INTO A RESONANT CAVITY, WITH APPLICATION TO VOICED SPEECH

PubMed Central

Howe, M. S.; McGowan, R. S.

2011-01-01

An analysis is made of the sound generated by the time-dependent throttling of a nominally steady stream of air through a small orifice into a flow-through resonant cavity. This is exemplified by the production of voiced speech, where air from the lungs enters the vocal tract through the glottis at a time variable volume flow rate Q(t) controlled by oscillations of the glottis cross-section. Voicing theory has hitherto determined Q from a heuristic, reduced complexity ‘Fant’ differential equation (G. Fant, Acoustic Theory of Speech Production, 1960). A new self-consistent, integro-differential form of this equation is derived in this paper using the theory of aerodynamic sound, with full account taken of the back-reaction of the resonant tract on the glottal flux Q. The theory involves an aeroacoustic Green’s function (G) for flow-surface interactions in a time-dependent glottis, so making the problem non-self-adjoint. In complex problems of this type it is not usually possible to obtain G in an explicit analytic form. The principal objective of the paper is to show how the Fant equation can still be derived in such cases from a consideration of the equation of aerodynamic sound and from the adjoint of the equation governing G in the neighbourhood of the ‘throttle’. The theory is illustrated by application to the canonical problem of throttled flow into a Helmholtz resonator. PMID:21666824

Classical Coset Hamiltonian for the Electronic Motion and its Application to Anderson Localization and Hammett Equation

NASA Astrophysics Data System (ADS)

Xing, Guan; Wu, Guo-Zhen

2001-02-01

A classical coset Hamiltonian is introduced for the system of one electron in multi-sites. By this Hamiltonian, the dynamical behaviour of the electronic motion can be readily simulated. The simulation reproduces the retardation of the electron density decay in a lattice with site energies randomly distributed - an analogy with Anderson localization. This algorithm is also applied to reproduce the Hammett equation which relates the reaction rate with the property of the substitutions in the organic chemical reactions. The advantages and shortcomings of this algorithm, as contrasted with traditional quantum methods such as the molecular orbital theory, are also discussed.

One-equation near-wall turbulence modeling with the aid of direct simulation data

NASA Technical Reports Server (NTRS)

Rodi, W.; Mansour, N. N.; Michelassi, V.

1993-01-01

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

A Brief Historical Introduction to Determinants with Applications

ERIC Educational Resources Information Center

Debnath, L.

2013-01-01

This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…

Associative Flow Rule Used to Include Hydrostatic Stress Effects in Analysis of Strain-Rate-Dependent Deformation of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.

2004-01-01

designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.

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.

Stochastic lumping analysis for linear kinetics and its application to the fluctuation relations between hierarchical kinetic networks.

PubMed

Deng, De-Ming; Chang, Cheng-Hung

2015-05-14

Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal the same experimentally measured fluctuating behaviors and unique fluctuation related physical properties. To clarify these questions, we introduce stochasticity into the traditional lumping analysis, generalize it from rate equations to chemical master equations and stochastic differential equations, and extract the fluctuation relations between kinetically and thermodynamically equivalent networks under intrinsic and extrinsic noises. The results provide a theoretical basis for the legitimate use of low-dimensional models in the studies of macromolecular fluctuations and, more generally, for exploring stochastic features in different levels of contracted networks in chemical and biological kinetic systems.

Sampling errors in the measurement of rain and hail parameters

NASA Technical Reports Server (NTRS)

Gertzman, H. S.; Atlas, D.

1977-01-01

Attention is given to a general derivation of the fractional standard deviation (FSD) of any integrated property X such that X(D) = cD to the n. This work extends that of Joss and Waldvogel (1969). The equation is applicable to measuring integrated properties of cloud, rain or hail populations (such as water content, precipitation rate, kinetic energy, or radar reflectivity) which are subject to statistical sampling errors due to the Poisson distributed fluctuations of particles sampled in each particle size interval and the weighted sum of the associated variances in proportion to their contribution to the integral parameter to be measured. Universal curves are presented which are applicable to the exponential size distribution permitting FSD estimation of any parameters from n = 0 to n = 6. The equations and curves also permit corrections for finite upper limits in the size spectrum and a realistic fall speed law.

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

BDflex: A method for efficient treatment of molecular flexibility in calculating protein-ligand binding rate constants from Brownian dynamics simulations

PubMed Central

Greives, Nicholas; Zhou, Huan-Xiang

2012-01-01

A method developed by Northrup [J. Chem. Phys. 80, 1517 (1984)]10.1063/1.446900 for calculating protein-ligand binding rate constants (ka) from Brownian dynamics (BD) simulations has been widely used for rigid molecules. Application to flexible molecules is limited by the formidable computational cost to treat conformational fluctuations during the long BD simulations necessary for ka calculation. Here, we propose a new method called BDflex for ka calculation that circumvents this problem. The basic idea is to separate the whole space into an outer region and an inner region, and formulate ka as the product of kE and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}\\bar \\eta _{\\rm d}\\end{equation*} \\end{document}η¯d, which are obtained by separately solving exterior and interior problems. kE is the diffusion-controlled rate constant for the ligand in the outer region to reach the dividing surface between the outer and inner regions; in this exterior problem conformational fluctuations can be neglected. \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}\\bar \\eta _{\\rm d}\\end{equation*} \\end{document}η¯d is the probability that the ligand, starting from the dividing surface, will react at the binding site rather than escape to infinity. The crucial step in reducing the determination of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{upgreek} \\usepackage{mathrsfs} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} \\begin{equation*}\\bar \\eta _{\\rm d}\\end{equation*} \\end{document}η¯d to a problem confined to the inner region is a radiation boundary condition imposed on the dividing surface; the reactivity on this boundary is proportional to kE. By confining the ligand to the inner region and imposing the radiation boundary condition, we avoid multiple-crossing of the dividing surface before reaction at the binding site and hence dramatically cut down the total simulation time, making the treatment of conformational fluctuations affordable. BDflex is expected to have wide applications in problems where conformational fluctuations of the molecules are crucial for productive ligand binding, such as in cases where transient widening of a bottleneck allows the ligand to access the binding pocket, or the binding site is properly formed only after ligand entrance induces the closure of a lid. PMID:23039617

Double stratification effects in chemically reactive squeezed Sutterby fluid flow with thermal radiation and mixed convection

NASA Astrophysics Data System (ADS)

Ahmad, S.; Farooq, M.; Javed, M.; Anjum, Aisha

2018-03-01

A current analysis is carried out to study theoretically the mixed convection characteristics in squeezing flow of Sutterby fluid in squeezed channel. The constitutive equation of Sutterby model is utilized to characterize the rheology of squeezing phenomenon. Flow characteristics are explored with dual stratification. In flowing fluid which contains heat and mass transport, the first order chemical reaction and radiative heat flux affect the transport phenomenon. The systems of non-linear governing equations have been modulating which then solved by mean of convergent approach (Homotopy Analysis Method). The graphs are reported and illustrated for emerging parameters. Through graphical explanations, drag force, rate of heat and mass transport are conversed for different pertinent parameters. It is found that heat and mass transport rate decays with dominant double stratified parameters and chemical reaction parameter. The present two-dimensional examination is applicable in some of the engineering processes and industrial fluid mechanics.

Optimal growth trajectories with finite carrying capacity.

PubMed

Caravelli, F; Sindoni, L; Caccioli, F; Ududec, C

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Method for estimating spatially variable seepage loss and hydraulic conductivity in intermittent and ephemeral streams

USGS Publications Warehouse

Niswonger, R.G.; Prudic, David E.; Fogg, G.E.; Stonestrom, David A.; Buckland, E.M.

2008-01-01

A method is presented for estimating seepage loss and streambed hydraulic conductivity along intermittent and ephemeral streams using streamflow front velocities in initially dry channels. The method uses the kinematic wave equation for routing streamflow in channels coupled to Philip's equation for infiltration. The coupled model considers variations in seepage loss both across and along the channel. Water redistribution in the unsaturated zone is also represented in the model. Sensitivity of the streamflow front velocity to parameters used for calculating seepage loss and for routing streamflow shows that the streambed hydraulic conductivity has the greatest sensitivity for moderate to large seepage loss rates. Channel roughness, geometry, and slope are most important for low seepage loss rates; however, streambed hydraulic conductivity is still important for values greater than 0.008 m/d. Two example applications are presented to demonstrate the utility of the method.

The effect of viscous flow and thermal flux on the rate of chemical reaction in dilute gases

NASA Astrophysics Data System (ADS)

Cukrowski, A. S.; Popielawski, J.

1986-11-01

Expression for the corrections describing the effect of viscous flow and thermal flux on the rate of chemical reaction have been derived for the reaction A + A = B + C described by Prigogine-Xhrouet and Present. These corrections are calculated for the velocity distribution function up to the second-order approximation for the Chapman-Enskog solution of the Boltzmann equation. These corrections are shown to be the same as those which would follow after application of the method of linearized-moments equations described by Eu and Li. The effects of viscous flow and thermal flux are presented as functions of activation energy of chemical reaction, temperature, density, coefficients of shear viscosity of thermal conductivity, and relevant gradients of mean molecular velocity or temperature. It is pointed out that for very slow reactions and for very large gradients (e.g. in shock waves) these effects can be quite significant.

Nucleophilic Participation in the Solvolyses of (Arylthio)methyl Chlorides and Derivatives: Application of Simple and Extended Forms of the Grunwald-Winstein Equations

PubMed Central

Kevill, Dennis N.; Park, Young Hoon; Park, Byoung-Chun; D’Souza, Malcolm J.

2012-01-01

The specific rates of solvolysis of chloromethyl phenyl sulfide [(phenylthio)methyl chloride] and its p-chloro-derivative have been determined at 0.0 °C in a wide range of hydroxylic solvents, including several containing a fluroalcohol. Treatment in terms of a two-term Grunwald-Winstein equation, incorporating terms based on solvent ionizing power (YCl) and solvent nucleophilicity (NT) suggest a mechanism similar to that for the solvolyses of tert-butyl chloride, involving in the rate-determining step a nucleophilic solvation of the incipient carbocation in an ionization process. A previous suggestion, that a third-term governed by the aromatic ring parameter (I) is required, is shown both for the new and for the previously studied related substrates to be an artifact, resulting from an appreciable degree of multicollinearity between I values and a linear combination of NT and YCl values. PMID:22711999

Optimal growth trajectories with finite carrying capacity

NASA Astrophysics Data System (ADS)

Caravelli, F.; Sindoni, L.; Caccioli, F.; Ududec, C.

2016-08-01

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Exoatmospheric Applications of Obscurants and Smokes.

DTIC Science & Technology

1985-09-01

field equations (.14)-(19) with substra- tum and their Galilei transformation (24)-(28) represent a field theory in terms of absolute or Galilean space r...of Scientific Research (AFOSR) c ntrat-is-concerned with experimental and theoretical investigations on electrically conducting aerosols for...Another method of reducing the decay rate of ferromagnetic aerosols is to spray the ferromagnetic particles with electric charges. The resulting

Silicon Isotopes doping experiments to measure quartz dissolution and precipitation rates at equilibrium and test the principle of detailed balance

NASA Astrophysics Data System (ADS)

Zhu, C.; Rimstidt, J. D.; Liu, Z.; Yuan, H.

2016-12-01

The principle of detailed balance (PDB) has been a cornerstone for irreversible thermodynamics and chemical kinetics for a long time, and its wide application in geochemistry has mostly been implicit and without experimental testing of its applicability. Nevertheless, many extrapolations based on PDB without experimental validation have far reaching impacts on society's mega environmental enterprises. Here we report an isotope doping method that independently measures simultaneous dissolution and precipitation rates and can test this principle. The technique reacts a solution enriched in a rare isotope of an element with a solid having natural isotopic abundances (Beck et al., 1992; Gaillardet, 2008; Gruber et al., 2013). Dissolution and precipitation rates are found from the changing isotopic ratios. Our quartz experiment doped with 29Si showed that the equilibrium dissolution rate remains unchanged at all degrees of undersaturation. We recommend this approach to test the validity of using the detailed balance relationship in rate equations for other substances.

Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems

NASA Astrophysics Data System (ADS)

Skinner, Thomas E.

2018-01-01

The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which provides information towards control of the dissipative process. The Bloch equation also describes a system of three coupled harmonic oscillators, providing additional perspective on dissipative systems.

Quick and Easy Rate Equations for Multistep Reactions

ERIC Educational Resources Information Center

Savage, Phillip E.

2008-01-01

Students rarely see closed-form analytical rate equations derived from underlying chemical mechanisms that contain more than a few steps unless restrictive simplifying assumptions (e.g., existence of a rate-determining step) are made. Yet, work published decades ago allows closed-form analytical rate equations to be written quickly and easily for…

Representing Rate Equations for Enzyme-Catalyzed Reactions

ERIC Educational Resources Information Center

Ault, Addison

2011-01-01

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

Speaking rate effects on locus equation slope.

PubMed

Berry, Jeff; Weismer, Gary

2013-11-01

A locus equation describes a 1st order regression fit to a scatter of vowel steady-state frequency values predicting vowel onset frequency values. Locus equation coefficients are often interpreted as indices of coarticulation. Speaking rate variations with a constant consonant-vowel form are thought to induce changes in the degree of coarticulation. In the current work, the hypothesis that locus slope is a transparent index of coarticulation is examined through the analysis of acoustic samples of large-scale, nearly continuous variations in speaking rate. Following the methodological conventions for locus equation derivation, data pooled across ten vowels yield locus equation slopes that are mostly consistent with the hypothesis that locus equations vary systematically with coarticulation. Comparable analyses between different four-vowel pools reveal variations in the locus slope range and changes in locus slope sensitivity to rate change. Analyses across rate but within vowels are substantially less consistent with the locus hypothesis. Taken together, these findings suggest that the practice of vowel pooling exerts a non-negligible influence on locus outcomes. Results are discussed within the context of articulatory accounts of locus equations and the effects of speaking rate change.

A feedback linearization approach to spacecraft control using momentum exchange devices. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Dzielski, John Edward

1988-01-01

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

Bernoulli-Langevin Wind Speed Model for Simulation of Storm Events

NASA Astrophysics Data System (ADS)

Fürstenau, Norbert; Mittendorf, Monika

2016-12-01

We present a simple nonlinear dynamics Langevin model for predicting the instationary wind speed profile during storm events typically accompanying extreme low-pressure situations. It is based on a second-degree Bernoulli equation with δ-correlated Gaussian noise and may complement stationary stochastic wind models. Transition between increasing and decreasing wind speed and (quasi) stationary normal wind and storm states are induced by the sign change of the controlling time-dependent rate parameter k(t). This approach corresponds to the simplified nonlinear laser dynamics for the incoherent to coherent transition of light emission that can be understood by a phase transition analogy within equilibrium thermodynamics [H. Haken, Synergetics, 3rd ed., Springer, Berlin, Heidelberg, New York 1983/2004.]. Evidence for the nonlinear dynamics two-state approach is generated by fitting of two historical wind speed profiles (low-pressure situations "Xaver" and "Christian", 2013) taken from Meteorological Terminal Air Report weather data, with a logistic approximation (i.e. constant rate coefficients k) to the solution of our dynamical model using a sum of sigmoid functions. The analytical solution of our dynamical two-state Bernoulli equation as obtained with a sinusoidal rate ansatz k(t) of period T (=storm duration) exhibits reasonable agreement with the logistic fit to the empirical data. Noise parameter estimates of speed fluctuations are derived from empirical fit residuals and by means of a stationary solution of the corresponding Fokker-Planck equation. Numerical simulations with the Bernoulli-Langevin equation demonstrate the potential for stochastic wind speed profile modeling and predictive filtering under extreme storm events that is suggested for applications in anticipative air traffic management.

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 2, Part 2: Appendixes B, C, D and E

NASA Technical Reports Server (NTRS)

Lowrie, J. W.; Fermelia, A. J.; Haley, D. C.; Gremban, K. D.; Vanbaalen, J.; Walsh, R. W.

1982-01-01

The derivation of the equations is presented, the rate control algorithm described, and simulation methodologies summarized. A set of dynamics equations that can be used recursively to calculate forces and torques acting at the joints of an n link manipulator given the manipulator joint rates are derived. The equations are valid for any n link manipulator system with any kind of joints connected in any sequence. The equations of motion for the class of manipulators consisting of n rigid links interconnected by rotary joints are derived. A technique is outlined for reducing the system of equations to eliminate contraint torques. The linearized dynamics equations for an n link manipulator system are derived. The general n link linearized equations are then applied to a two link configuration. The coordinated rate control algorithm used to compute individual joint rates when given end effector rates is described. A short discussion of simulation methodologies is presented.

Relationship between supersaturation ratio and supply rate of solute in the growth process of monodisperse colloidal particles and application to AgBr systems.

PubMed

Shiba, Fumiyuki; Okawa, Yusuke

2005-11-24

Supersaturation ratio, S, has been theoretically related to the supply rate of solute, Q, from growth rate and mass-balance equations in the quasi-steady state in the growth process of isotropic monodisperse particles. The derived equation, (S - 1) = (1/D + 1/kr)(Q/betaC(0)nr) + 2V(m)gamma/rRT, suggests a linear dependence of S on Q under constant n and r, where D is the diffusion coefficient, k is the rate constant for surface-reaction, C(0) is the solubility, n and r are the number and radius of growing particles, respectively, V(m) is the molar volume of particles, R is the gas constant, T is the absolute temperature, and beta is the shape factor defined by beta identical with (1/r(2)) dupsilon/dr, where upsilon is the volume of an individual particle. The equation was applied to the analysis of growth kinetics and determinations of critical supersaturation ratio in monodisperse AgBr particles in the controlled double-jet system with the assistance of a potentiometric supersaturation measurement. In both cubic and octahedral particles, growth rates were completely limited by diffusion and surface-reaction at pBr ( identical with -log[Br(-)]) 3.0 and 1.0, respectively, while the growths were intermediate of them at pBr 2.0 and 4.0. The growth parameters, DC(0) and kC(0), were experimentally determined. Also, critical supersaturation ratio was estimated as 1.28 as an average in the present study.

A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry

NASA Astrophysics Data System (ADS)

Pei, Y.; Herbst, E.

2011-05-01

Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod 2008), which partially takes into account the stochastic effect for surface reactions, and (3) the master equation approach solved using a Monte Carlo technique. At 10 K and standard grain sizes, our model results agree well with the above three methods, while discrepancies appear at higher temperatures and smaller grain sizes.

Study of transient behavior of finned coil heat exchangers

NASA Technical Reports Server (NTRS)

Rooke, S. P.; Elissa, M. G.

1993-01-01

The status of research on the transient behavior of finned coil cross-flow heat exchangers using single phase fluids is reviewed. Applications with available analytical or numerical solutions are discussed. Investigation of water-to-air type cross-flow finned tube heat exchangers is examined through the use of simplified governing equations and an up-wind finite difference scheme. The degenerate case of zero air-side capacitance rate is compared with available exact solution. Generalization of the numerical model is discussed for application to multi-row multi-circuit heat exchangers.

Performance of bed-load transport equations relative to geomorphic significance: Predicting effective discharge and its transport rate

Treesearch

Jeffrey J. Barry; John M. Buffington; Peter Goodwin; John .G. King; William W. Emmett

2008-01-01

Previous studies assessing the accuracy of bed-load transport equations have considered equation performance statistically based on paired observations of measured and predicted bed-load transport rates. However, transport measurements were typically taken during low flows, biasing the assessment of equation performance toward low discharges, and because equation...

Dry season mean monthly flow and harmonic mean flow regression equations for selected ungaged basins in Arkansas

USGS Publications Warehouse

Breaker, Brian K.

2015-01-01

Equations for two regions were found to be statistically significant for developing regression equations for estimating harmonic mean flows at ungaged basins; thus, equations are applicable only to streams in those respective regions in Arkansas. Regression equations for dry season mean monthly flows are applicable only to streams located throughout Arkansas. All regression equations are applicable only to unaltered streams where flows were not significantly affected by regulation, diversion, or urbanization. The median number of years used for dry season mean monthly flow calculation was 43, and the median number of years used for harmonic mean flow calculations was 34 for region 1 and 43 for region 2.

How "Hot Precursors" Modify Island Nucleation: A Rate-Equation Model

NASA Astrophysics Data System (ADS)

Morales-Cifuentes, Josue R.; Einstein, T. L.; Pimpinelli, A.

2014-12-01

We propose a novel island nucleation and growth model explicitly including transient (ballistic) mobility of the monomers deposited at rate F , assumed to be in a hot precursor state before thermalizing. In limiting regimes, corresponding to fast (diffusive) and slow (ballistic) thermalization, the island density N obeys scaling N ∝Fα . In between is found a rich, complex behavior, with various distinctive scaling regimes, characterized by effective exponents αeff and activation energies that we compute exactly. Application to N (F ,T ) of recent organic-molecule deposition experiments yields an excellent fit.

Development of braided rope seals for hypersonic engine applications. Part 2: Flow modeling

NASA Technical Reports Server (NTRS)

Mutharasan, Rajakkannu; Steinetz, Bruce M.; Tao, Xiaoming; Ko, Frank

1991-01-01

Two models based on the Kozeny-Carmen equation were developed to analyze the fluid flow through a new class of braided rope seals under development for advanced hypersonic engines. A hybrid seal geometry consisting of a braided sleeve and a substantial amount of longitudinal fibers with high packing density was selected for development based on its low leakage rates. The models developed allow prediction of the gas leakage rate as a function of fiber diameter, fiber packing density, gas properties, and pressure drop across the seal.

Optimal Assignment Problem Applications of Finite Mathematics to Business and Economics. [and] Difference Equations with Applications. Applications of Difference Equations to Economics and Social Sciences. [and] Selected Applications of Mathematics to Finance and Investment. Applications of Elementary Algebra to Finance. [and] Force of Interest. Applications of Calculus to Finance. UMAP Units 317, 322, 381, 382.

ERIC Educational Resources Information Center

Gale, David; And Others

Four units make up the contents of this document. The first examines applications of finite mathematics to business and economies. The user is expected to learn the method of optimization in optimal assignment problems. The second module presents applications of difference equations to economics and social sciences, and shows how to: 1) interpret…

An explicit predictor-corrector solver with applications to Burgers' equation

NASA Technical Reports Server (NTRS)

Dey, S. K.; Dey, C.

1983-01-01

Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.

Rapid-Equilibrium Enzyme Kinetics

ERIC Educational Resources Information Center

Alberty, Robert A.

2008-01-01

Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful because if experimental data can be fit by these simpler rate equations, the Michaelis constants can be interpreted as equilibrium constants. However, for some reactions it is necessary to use the more complicated steady-state rate equations. Thermodynamics is…

Equations for obtaining melting points for the ternary system ethylene glycol/sodium chloride/water and their application to cryopreservation.

PubMed

Woods, E J; Zieger, M A; Gao, D Y; Critser, J K

1999-06-01

The present study describes the H(2)O-NaCl-ethylene glycol ternary system by using a differential scanning calorimeter to measure melting points (T(m)) of four different ratios (R) of ethylene glycol to NaCl and then devising equations to fit the experimental measurements. Ultimately an equation is derived which characterizes the liquidus surface above the eutectic for any R value in the system. This study focuses on ethylene glycol in part because of recent evidence indicating it may be less toxic to pancreatic islets than Me(2)SO, which is currently used routinely for islet cryopreservation. The resulting physical data and previously determined information regarding the osmotic characteristics of canine pancreatic islets are combined in a mathematical model to describe the volumetric response to equilibrium-rate freezing in varying initial concentrations of ethylene glycol. Copyright 1999 Academic Press.

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

NASA Astrophysics Data System (ADS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

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

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

NASA Astrophysics Data System (ADS)

Gupta, Diksha; Kumar, Lokendra; Bég, O. Anwar; Singh, Bani

2017-10-01

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has applications in polymer processing.

A general multiple-compartment model for the transport of trace elements through animals

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

Assimakopoulos, P.A.; Ioannides, K.G.; Pakou, A.A.

1991-08-01

Multiple-compartment models employed in the analysis of trace element transport in animals are often based on linear differential equations which relate the rate of change of contaminant (or contaminant concentration) in each compartment to the amount of contaminant (or contaminant concentration) in every other compartment in the system. This has the serious disadvantage of mixing intrinsic physiological properties with the geometry of the animal. The basic equations on which the model presented here is developed are derived from the actual physical process under way and are capable of separating intrinsic physiological properties from geometry. It is thus expected that ratemore » coefficients determined through this model will be applicable to a wider category of physiologically similar animals. A specific application of the model for the study of contamination of sheep--or indeed for any ruminant--is presented, and the temporal evolution of contaminant concentration in the various compartments of the animal is calculated. The application of this model to a system of compartments with changing geometry is also presented.« less

Wave Turbulence

NASA Astrophysics Data System (ADS)

Newell, Alan C.; Rumpf, Benno

2011-01-01

In this article, we state and review the premises on which a successful asymptotic closure of the moment equations of wave turbulence is based, describe how and why this closure obtains, and examine the nature of solutions of the kinetic equation. We discuss obstacles that limit the theory's validity and suggest how the theory might then be modified. We also compare the experimental evidence with the theory's predictions in a range of applications. Finally, and most importantly, we suggest open challenges and encourage the reader to apply and explore wave turbulence with confidence. The narrative is terse but, we hope, delivered at a speed more akin to the crisp pace of a Hemingway story than the wordjumblingtumbling rate of a Joycean novel.

Double diffusive conjugate heat transfer: Part II

NASA Astrophysics Data System (ADS)

Azeem, Soudagar, Manzoor Elahi M.

2018-05-01

Conjugate heat transfer in porous medium is an important study involved in many practical applications. The current study is aimed to investigate the double diffusive flow in a square porous cavity subjected to left vertical surface heating and right vertical surface cooling respectively along with left and right surfaces maintained at high and low concentration. The three governing equations are converted into algebraic form of equations by applying finite element method and solved in iterative manner. The study is focused to investigate the effect of presence of solid inside the cavity with respect to varying buoyancy ratio. It is found that the local heat and mass transfer rate decreases along the height of cavity.

Application of nano filter for organic pollutant degradation

NASA Astrophysics Data System (ADS)

Qandalee, Mohammad; Hatami, Mehdi; Majedi, Ali; Bateni, Mohsen; Vahdat, Seyed Mohammad

2012-12-01

In this study, the possibility of using a novel nanocomposite structure based on nanoscale titanium dioxide as a filter toward elimination of organic pollutant was investigated. Methyl Orange (MO) was selected as a typical organic pollutant and effect of lamp intensity, addition of hydrogen peroxide and MO concentration were investigated. The photocatalytic degradation of MO was modeled using Langmuir-Hinshelwood equation and the removal rates were simulated.

Estimation and application of a growth and yield model for uneven-aged mixed conifer stands in California.

Treesearch

Jingjing Liang; J. Buongiorno; R.A. Monserud

2005-01-01

A growth model for uneven-aged mixed-conifer stands in California was developed with data from 205 permanent plots. The model predicts the number of softwood and hardwood trees in nineteen diameter classes, based on equations for diameter growth rates, mortality arid recruitment. The model gave unbiased predictions of the expected number of trees by diameter class and...

Computational method for analysis of polyethylene biodegradation

NASA Astrophysics Data System (ADS)

Watanabe, Masaji; Kawai, Fusako; Shibata, Masaru; Yokoyama, Shigeo; Sudate, Yasuhiro

2003-12-01

In a previous study concerning the biodegradation of polyethylene, we proposed a mathematical model based on two primary factors: the direct consumption or absorption of small molecules and the successive weight loss of large molecules due to β-oxidation. Our model is an initial value problem consisting of a differential equation whose independent variable is time. Its unknown variable represents the total weight of all the polyethylene molecules that belong to a molecular-weight class specified by a parameter. In this paper, we describe a numerical technique to introduce experimental results into analysis of our model. We first establish its mathematical foundation in order to guarantee its validity, by showing that the initial value problem associated with the differential equation has a unique solution. Our computational technique is based on a linear system of differential equations derived from the original problem. We introduce some numerical results to illustrate our technique as a practical application of the linear approximation. In particular, we show how to solve the inverse problem to determine the consumption rate and the β-oxidation rate numerically, and illustrate our numerical technique by analyzing the GPC patterns of polyethylene wax obtained before and after 5 weeks cultivation of a fungus, Aspergillus sp. AK-3. A numerical simulation based on these degradation rates confirms that the primary factors of the polyethylene biodegradation posed in modeling are indeed appropriate.

Application of turbulence modeling to predict surface heat transfer in stagnation flow region of circular cylinder

NASA Technical Reports Server (NTRS)

Wang, Chi R.; Yeh, Frederick C.

1987-01-01

A theoretical analysis and numerical calculations for the turbulent flow field and for the effect of free-stream turbulence on the surface heat transfer rate of a stagnation flow are presented. The emphasis is on the modeling of turbulence and its augmentation of surface heat transfer rate. The flow field considered is the region near the forward stagnation point of a circular cylinder in a uniform turbulent mean flow. The free stream is steady and incompressible with a Reynolds number of the order of 10 to the 5th power and turbulence intensity of less than 5 percent. For this analysis, the flow field is divided into three regions: (1) a uniform free-stream region where the turbulence is homogeneous and isotropic; (2) an external viscid flow region where the turbulence is distorted by the variation of the mean flow velocity; and, (3) an anisotropic turbulent boundary layer region over the cylinder surface. The turbulence modeling techniques used are the kappa-epsilon two-equation model in the external flow region and the time-averaged turbulence transport equation in the boundary layer region. The turbulence double correlations, the mean velocity, and the mean temperature within the boundary layer are solved numerically from the transport equations. The surface heat transfer rate is calculated as functions of the free-stream turbulence longitudinal microlength scale, the turbulence intensity, and the Reynolds number.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Nonlinear Boltzmann equation for the homogeneous isotropic case: Some improvements to deterministic methods and applications to relaxation towards local equilibrium

NASA Astrophysics Data System (ADS)

Asinari, P.

2011-03-01

Boltzmann equation is one the most powerful paradigms for explaining transport phenomena in fluids. Since early fifties, it received a lot of attention due to aerodynamic requirements for high altitude vehicles, vacuum technology requirements and nowadays, micro-electro-mechanical systems (MEMs). Because of the intrinsic mathematical complexity of the problem, Boltzmann himself started his work by considering first the case when the distribution function does not depend on space (homogeneous case), but only on time and the magnitude of the molecular velocity (isotropic collisional integral). The interest with regards to the homogeneous isotropic Boltzmann equation goes beyond simple dilute gases. In the so-called econophysics, a Boltzmann type model is sometimes introduced for studying the distribution of wealth in a simple market. Another recent application of the homogeneous isotropic Boltzmann equation is given by opinion formation modeling in quantitative sociology, also called socio-dynamics or sociophysics. The present work [1] aims to improve the deterministic method for solving homogenous isotropic Boltzmann equation proposed by Aristov [2] by two ideas: (a) the homogeneous isotropic problem is reformulated first in terms of particle kinetic energy (this allows one to ensure exact particle number and energy conservation during microscopic collisions) and (b) a DVM-like correction (where DVM stands for Discrete Velocity Model) is adopted for improving the relaxation rates (this allows one to satisfy exactly the conservation laws at macroscopic level, which is particularly important for describing the late dynamics in the relaxation towards the equilibrium).

Simulation of relationship between river discharge and sediment yield in the semi-arid river watersheds

NASA Astrophysics Data System (ADS)

Khaleghi, Mohammad Reza; Varvani, Javad

2018-02-01

Complex and variable nature of the river sediment yield caused many problems in estimating the long-term sediment yield and problems input into the reservoirs. Sediment Rating Curves (SRCs) are generally used to estimate the suspended sediment load of the rivers and drainage watersheds. Since the regression equations of the SRCs are obtained by logarithmic retransformation and have a little independent variable in this equation, they also overestimate or underestimate the true sediment load of the rivers. To evaluate the bias correction factors in Kalshor and Kashafroud watersheds, seven hydrometric stations of this region with suitable upstream watershed and spatial distribution were selected. Investigation of the accuracy index (ratio of estimated sediment yield to observed sediment yield) and the precision index of different bias correction factors of FAO, Quasi-Maximum Likelihood Estimator (QMLE), Smearing, and Minimum-Variance Unbiased Estimator (MVUE) with LSD test showed that FAO coefficient increases the estimated error in all of the stations. Application of MVUE in linear and mean load rating curves has not statistically meaningful effects. QMLE and smearing factors increased the estimated error in mean load rating curve, but that does not have any effect on linear rating curve estimation.

Kinetics of leather dyeing pretreated with enzymes: role of acid protease.

PubMed

Kanth, Swarna Vinodh; Venba, Rajangam; Jayakumar, Gladstone Christopher; Chandrababu, Narasimhan Kannan

2009-04-01

In the present investigation, kinetics of dyeing involving pretreatment with acid protease has been presented. Application of acid protease in dyeing process resulted in increased absorption and diffusion of dye into the leather matrix. Enzyme treatment at 1% concentration, 60 min duration and 50 degrees C resulted in maximum of 98% dye exhaustion and increased absorption rate constants. The final exhaustion (C(infinity)) for the best fit of CI Acid Black 194 dye has been 98.5% with K and r2 values from the modified Cegarra-Puente isotherm as 0.1033 and 0.0631. CI Acid Black 194 being a 2:1 metal complex acid dye exhibited higher absorption rate than the acid dye CI Acid Black 210. A reduction in 50% activation energy calculated from Arrhenius equation has been observed in enzyme assisted dyeing process of both the dyes that substantiates enhanced dye absorption. The absorption rate constant calculated with modified Cegarra-Puente equation confirm higher rate constants and faster kinetics for enzyme assisted dyeing process. Enzyme treated leather exhibited richness of color and shade when compared with control. The present study substantiates the essential role of enzyme pretreatment as an eco-friendly leather dyeing process.

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

Modeling collective behavior of dislocations in crystalline materials

NASA Astrophysics Data System (ADS)

Varadhan, Satya N.

Elastic interaction of dislocations leads to collective behavior and determines plastic response at the mesoscale. Notable characteristics of mesoscale plasticity include the formation of dislocation patterns, propagative instability phenomena due to strain aging such as the Luders and Portevin-Le Chatelier effects, and size-dependence of low stress. This work presents a unified approach to modeling collective behavior based on mesoscale field dislocation mechanics and crystal plasticity, using constitutive models with physical basis. Successful application is made to: compression of a bicrystal, where "smaller is stronger"---the flow stress increases as the specimen size is reduced; torsional creep of ice single crystals, where the plastic strain rate increases with time under constant applied torque; strain aging in a single crystal alloy, where the transition from homogeneous deformation to intermittent bands to continuous band is captured as the applied deformation rate is increased. A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.

A Particle Representation Model for the Deformation of Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Kassinos, S. C.; Reynolds, W. C.

1996-01-01

In simple flows, where the mean deformation rates are mild and the turbulence has time to come to equilibrium with the mean flow, the Reynolds stresses are determined by the applied strain rate. Hence in these flows, it is often adequate to use an eddy-viscosity representation. The modern family of kappa-epsilon models has been very useful in predicting near equilibrium turbulent flows, where the rms deformation rate S is small compared to the reciprocal time scale of the turbulence (epsilon/kappa). In modern engineering applications, turbulence models are quite often required to predict flows with very rapid deformations (large S kappa/epsilon). In these flows, the structure takes some time to respond and eddy viscosity models are inadequate. The response of turbulence to rapid deformations is given by rapid distortion theory (RDT). Under RDT the nonlinear effects due to turbulence-turbulence interactions are neglected in the governing equations, but even when linearized in this fashion, the governing equations are unclosed at the one-point level due to the non-locality of the pressure fluctuations.

Reynolds-number dependence of the dimensionless dissipation rate in homogeneous magnetohydrodynamic turbulence.

PubMed

Linkmann, Moritz; Berera, Arjun; Goldstraw, Erin E

2017-01-01

This paper examines the behavior of the dimensionless dissipation rate C_{ɛ} for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for C_{ɛ} applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote C_{ɛ,∞} lie between 0.193≤C_{ɛ,∞}≤0.268 for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure C_{ɛ,∞}=0.223.

Sizes of nanobubbles from nucleation rate measurements

NASA Astrophysics Data System (ADS)

Wilemski, G.

2003-03-01

In homogeneous bubble nucleation, the critical nucleus typically has nanometer dimensions. The volume V of a critical bubble can be determined from the simple equation (partial W/partial p)_T=V, where W is the reversible work of nucleus formation and p is the ambient pressure of the liquid phase in which bubble formation is occurring. The relation, W/kT=-ln J+ln A, where J is the steady state nucleation rate and A is the weakly pressure-dependent kinetic prefactor, allows V to be determined from rate measurements. The original derivation of this equation for V from the nucleation theorem was limited to one-component, ideal gas bubbles with a gas density much smaller than that of the ambient liquid. [D. Kashchiev, Nucleation: basic theory with applications (Butterworth-Heinemann, Oxford, 2000) p. 226.] The result is actually much more general, and it will be shown that it applies to multi-component, nonideal gas bubbles, provided the same density inequality holds. When the bubble phase and liquid densities are comparable, a more complicated, but also general and rigorous result is found.

Linear free energy study of ring-substituted aniline ozonation for developing treatment of aniline-based pesticide wastes.

PubMed

Pierpoint, A C; Hapeman, C J; Torrents, A

2001-08-01

The relative rate constants for the reaction of ozone were determined for several substituted anilines in aqueous solutions at pH 6.5 and 1.5. At pH 6.5, with the exception of m- and p-nitroaniline, the rate constants obey Hammett's equation: log(k(X)/k(H)) = rho sigma. The departure of m- and p-nitroaniline may be explained by direct conjugation of the reaction center. The commonly used sigma(p)(-) value of 1.27, which extends the range of applicability of the Hammett equation, was insufficient to account for the conjugation effects on ozonation of p-nitroaniline; rho = -1.48 (R = 0.973). Use of amine group atomic charge determinations significantly improved correlations: (k(X)/k(H)) = 48.7 delta - 18.2 (R = 0.996). A linear plot of Hammett constants versus relative rate data at pH 1.5 showed poor correlation: rho = 0.72 (R = 0.572). Poor correlation was similarly observed for amine group atomic charge determinations, suggesting varied reaction mechanisms.

An efficient mode-splitting method for a curvilinear nearshore circulation model

USGS Publications Warehouse

Shi, Fengyan; Kirby, James T.; Hanes, Daniel M.

2007-01-01

A mode-splitting method is applied to the quasi-3D nearshore circulation equations in generalized curvilinear coordinates. The gravity wave mode and the vorticity wave mode of the equations are derived using the two-step projection method. Using an implicit algorithm for the gravity mode and an explicit algorithm for the vorticity mode, we combine the two modes to derive a mixed difference–differential equation with respect to surface elevation. McKee et al.'s [McKee, S., Wall, D.P., and Wilson, S.K., 1996. An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms. J. Comput. Phys., 126, 64–76.] ADI scheme is then used to solve the parabolic-type equation in dealing with the mixed derivative and convective terms from the curvilinear coordinate transformation. Good convergence rates are found in two typical cases which represent respectively the motions dominated by the gravity mode and the vorticity mode. Time step limitations imposed by the vorticity convective Courant number in vorticity-mode-dominant cases are discussed. Model efficiency and accuracy are verified in model application to tidal current simulations in San Francisco Bight.

Influence of heat conducting substrates on explosive crystallization in thin layers

NASA Astrophysics Data System (ADS)

Schneider, Wilhelm

2017-09-01

Crystallization in a thin, initially amorphous layer is considered. The layer is in thermal contact with a substrate of very large dimensions. The energy equation of the layer contains source and sink terms. The source term is due to liberation of latent heat in the crystallization process, while the sink term is due to conduction of heat into the substrate. To determine the latter, the heat diffusion equation for the substrate is solved by applying Duhamel's integral. Thus, the energy equation of the layer becomes a heat diffusion equation with a time integral as an additional term. The latter term indicates that the heat loss due to the substrate depends on the history of the process. To complete the set of equations, the crystallization process is described by a rate equation for the degree of crystallization. The governing equations are then transformed to a moving co-ordinate system in order to analyze crystallization waves that propagate with invariant properties. Dual solutions are found by an asymptotic expansion for large activation energies of molecular diffusion. By introducing suitable variables, the results can be presented in a universal form that comprises the influence of all non-dimensional parameters that govern the process. Of particular interest for applications is the prediction of a critical heat loss parameter for the existence of crystallization waves with invariant properties.

Application of the time-temperature superposition principle to the mechanical characterization of elastomeric adhesives for crash simulation purposes

NASA Astrophysics Data System (ADS)

Rauh, A.; Hinterhölzl, R.; Drechsler, K.

2012-05-01

In the automotive industry, finite element simulation is widely used to ensure crashworthiness. Mechanical material data over wide strain rate and temperature ranges are required as a basis. This work proposes a method reducing the cost of mechanical material characterization by using the time-temperature superposition principle on elastomeric adhesives. The method is based on the time and temperature interdependence which is characteristic for mechanical properties of polymers. Based on the assumption that polymers behave similarly at high strain rates and at low temperatures, a temperature-dominated test program is suggested, which can be used to deduce strain rate dependent material behavior at different reference temperatures. The temperature shift factor is found by means of dynamic mechanical analysis according to the WLF-equation, named after Williams, Landel and Ferry. The principle is applied to the viscoelastic properties as well as to the failure properties of the polymer. The applicability is validated with high strain rate tests.

On the mechanics of continua with boundary energies and growing surfaces

NASA Astrophysics Data System (ADS)

Papastavrou, Areti; Steinmann, Paul; Kuhl, Ellen

2013-06-01

Many biological systems are coated by thin films for protection, selective absorption, or transmembrane transport. A typical example is the mucous membrane covering the airways, the esophagus, and the intestine. Biological surfaces typically display a distinct mechanical behavior from the bulk; in particular, they may grow at different rates. Growth, morphological instabilities, and buckling of biological surfaces have been studied intensely by approximating the surface as a layer of finite thickness; however, growth has never been attributed to the surface itself. Here, we establish a theory of continua with boundary energies and growing surfaces of zero thickness in which the surface is equipped with its own potential energy and is allowed to grow independently of the bulk. In complete analogy to the kinematic equations, the balance equations, and the constitutive equations of a growing solid body, we derive the governing equations for a growing surface. We illustrate their spatial discretization using the finite element method, and discuss their consistent algorithmic linearization. To demonstrate the conceptual differences between volume and surface growth, we simulate the constrained growth of the inner layer of a cylindrical tube. Our novel approach toward continua with growing surfaces is capable of predicting extreme growth of the inner cylindrical surface, which more than doubles its initial area. The underlying algorithmic framework is robust and stable; it allows to predict morphological changes due to surface growth during the onset of buckling and beyond. The modeling of surface growth has immediate biomedical applications in the diagnosis and treatment of asthma, gastritis, obstructive sleep apnoea, and tumor invasion. Beyond biomedical applications, the scientific understanding of growth-induced morphological instabilities and surface wrinkling has important implications in material sciences, manufacturing, and microfabrication, with applications in soft lithography, metrology, and flexible electronics.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation.

PubMed

Augustin, Moritz; Ladenbauer, Josef; Baumann, Fabian; Obermayer, Klaus

2017-06-01

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models.

Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: Comparison and implementation

PubMed Central

Baumann, Fabian; Obermayer, Klaus

2017-01-01

The spiking activity of single neurons can be well described by a nonlinear integrate-and-fire model that includes somatic adaptation. When exposed to fluctuating inputs sparsely coupled populations of these model neurons exhibit stochastic collective dynamics that can be effectively characterized using the Fokker-Planck equation. This approach, however, leads to a model with an infinite-dimensional state space and non-standard boundary conditions. Here we derive from that description four simple models for the spike rate dynamics in terms of low-dimensional ordinary differential equations using two different reduction techniques: one uses the spectral decomposition of the Fokker-Planck operator, the other is based on a cascade of two linear filters and a nonlinearity, which are determined from the Fokker-Planck equation and semi-analytically approximated. We evaluate the reduced models for a wide range of biologically plausible input statistics and find that both approximation approaches lead to spike rate models that accurately reproduce the spiking behavior of the underlying adaptive integrate-and-fire population. Particularly the cascade-based models are overall most accurate and robust, especially in the sensitive region of rapidly changing input. For the mean-driven regime, when input fluctuations are not too strong and fast, however, the best performing model is based on the spectral decomposition. The low-dimensional models also well reproduce stable oscillatory spike rate dynamics that are generated either by recurrent synaptic excitation and neuronal adaptation or through delayed inhibitory synaptic feedback. The computational demands of the reduced models are very low but the implementation complexity differs between the different model variants. Therefore we have made available implementations that allow to numerically integrate the low-dimensional spike rate models as well as the Fokker-Planck partial differential equation in efficient ways for arbitrary model parametrizations as open source software. The derived spike rate descriptions retain a direct link to the properties of single neurons, allow for convenient mathematical analyses of network states, and are well suited for application in neural mass/mean-field based brain network models. PMID:28644841

The wave equation in Friedmann-Robertson-Walker space-times and asymptotics of the intensity and distance relationship of a localised source

NASA Astrophysics Data System (ADS)

Starko, Darij; Craig, Walter

2018-04-01

Variations in redshift measurements of Type 1a supernovae and intensity observations from large sky surveys are an indicator of a component of acceleration in the rate of expansion of space-time. A key factor in the measurements is the intensity-distance relation for Maxwell's equations in Friedmann-Robertson-Walker (FRW) space-times. In view of future measurements of the decay of other fields on astronomical time and spatial scales, we determine the asymptotic behavior of the intensity-distance relationship for the solution of the wave equation in space-times with an FRW metric. This builds on previous work done on initial value problems for the wave equation in FRW space-time [Abbasi, B. and Craig, W., Proc. R. Soc. London, Ser. A 470, 20140361 (2014)]. In this paper, we focus on the precise intensity decay rates of the special cases for curvature k = 0 and k = -1, as well as giving a general derivation of the wave solution for -∞ < k < 0. We choose a Cauchy surface {(t, x) : t = t0 > 0} where t0 represents the time of an initial emission source, relative to the Big Bang singularity at t = 0. The initial data [g(x), h(x)] are assumed to be compactly supported; supp(g, h) ⊆ BR(0) and terms in the expression for the fundamental solution for the wave equation with the slowest decay rate are retained. The intensities calculated for coordinate time {t : t > 0} contain correction terms proportional to the ratio of t0 and the time differences ρ = t - t0. For the case of general curvature k, these expressions for the intensity reduce by scaling to the same form as for k = -1, from which we deduce the general formula. We note that for typical astronomical events such as Type 1a supernovae, the first order correction term for all curvatures -∞ < k < 0 is on the order of 10-4 smaller than the zeroth order term. These correction terms are small but may be significant in applications to alternative observations of cosmological space-time expansion rates.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Computation of a controlled store separation from a cavity

NASA Technical Reports Server (NTRS)

Atwood, Christopher A.

1993-01-01

Coupling of the Reynolds-averaged Navier-Stokes equations, rigid-body dynamics, and a pitch attitude control law is demonstrated in two- and three-dimensions. The application problem was the separation of a canard-controlled store from an open-flow rectangular cavity bay at a freestream Mach number of 1.2. The transient flowfield was computed using a diagonal scheme in an overset mesh framework, with the resultant aerodynamic loads used as the forcing functions in the nonlinear dynamics equations. The proportional and rate gyro sensitivities were computed a priori using pole placement techniques for the linearized dynamical equations. These fixed gain values were used in the controller for the nonlinear simulation. Reasonable comparison between the full and linearized equations for a perturbed two-dimensional missile was found. Also in two-dimensions, a controlled store was found to possess improved separation characteristics over a canard-fixed store. In three-dimensions, trajectory comparisons with wind-tunnel data for the canard-fixed case will be made. In addition, it will be determined if a canard-controlled store is an effective means of improving cavity store separation characteristics.

Validating and Improving Interrill Erosion Equations

PubMed Central

Zhang, Feng-Bao; Wang, Zhan-Li; Yang, Ming-Yi

2014-01-01

Existing interrill erosion equations based on mini-plot experiments have largely ignored the effects of slope length and plot size on interrill erosion rate. This paper describes a series of simulated rainfall experiments which were conducted according to a randomized factorial design for five slope lengths (0.4, 0.8, 1.2, 1.6, and 2 m) at a width of 0.4 m, five slope gradients (17%, 27%, 36%, 47%, and 58%), and five rainfall intensities (48, 62.4, 102, 149, and 170 mm h−1) to perform a systematic validation of existing interrill erosion equations based on mini-plots. The results indicated that the existing interrill erosion equations do not adequately describe the relationships between interrill erosion rate and its influencing factors with increasing slope length and rainfall intensity. Univariate analysis of variance showed that runoff rate, rainfall intensity, slope gradient, and slope length had significant effects on interrill erosion rate and that their interactions were significant at p = 0.01. An improved interrill erosion equation was constructed by analyzing the relationships of sediment concentration with rainfall intensity, slope length, and slope gradient. In the improved interrill erosion equation, the runoff rate and slope factor are the same as in the interrill erosion equation in the Water Erosion Prediction Project (WEPP), with the weight of rainfall intensity adjusted by an exponent of 0.22 and a slope length term added with an exponent of −0.25. Using experimental data from WEPP cropland soil field interrill erodibility experiments, it has been shown that the improved interrill erosion equation describes the relationship between interrill erosion rate and runoff rate, rainfall intensity, slope gradient, and slope length reasonably well and better than existing interrill erosion equations. PMID:24516624

Creatinine Clearance Is Not Equal to Glomerular Filtration Rate and Cockcroft-Gault Equation Is Not Equal to CKD-EPI Collaboration Equation.

PubMed

Fernandez-Prado, Raul; Castillo-Rodriguez, Esmeralda; Velez-Arribas, Fernando Javier; Gracia-Iguacel, Carolina; Ortiz, Alberto

2016-12-01

Direct oral anticoagulants (DOACs) may require dose reduction or avoidance when glomerular filtration rate is low. However, glomerular filtration rate is not usually measured in routine clinical practice. Rather, equations that incorporate different variables use serum creatinine to estimate either creatinine clearance in mL/min or glomerular filtration rate in mL/min/1.73 m 2 . The Cockcroft-Gault equation estimates creatinine clearance and incorporates weight into the equation. By contrast, the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equations estimate glomerular filtration rate and incorporate ethnicity but not weight. As a result, an individual patient may have very different renal function estimates, depending on the equation used. We now highlight these differences and discuss the impact on routine clinical care for anticoagulation to prevent embolization in atrial fibrillation. Pivotal DOAC clinical trials used creatinine clearance as a criterion for patient enrollment, and dose adjustment and Federal Drug Administration recommendations are based on creatinine clearance. However, clinical biochemistry laboratories provide CKD-EPI glomerular filtration rate estimations, resulting in discrepancies between clinical trial and routine use of the drugs. Copyright © 2016 Elsevier Inc. All rights reserved.

Nonlinear optical response and its theoretical modelling of Sb2S3 nanorod

NASA Astrophysics Data System (ADS)

Yadav, Rajesh Kumar; Barik, A. R.; Das, Amlan; Adarsh, K. V.

2018-05-01

Light-matter interaction in nanoscale regime have unprecedented and accelerating demand in optoelectronics, valley electronics and device applications. Such interaction in 1-dimention (1D) metal chalcogenides has emerged as an important research topic because of its possibility to custom design optical properties, implying enormous application including optical computers, communications, bioimaging, and so on. However, understanding of nonlinear optical response of these nanostructures is still lacking, although it constitutes an interesting problem on the light-matter interaction. Here, we have presented the nonlinear optical response in Sb2S3 nanorod using Z-scan technique. Our experimental findings show a strong saturable absorption (SA). In this context, we have numerically simulated the experimental result using two level rate equation. The solutions of these two-level rate equation for a Gaussian shaped pulse exactly replicated the experimental data. From the best numerical fit, we found excited state decay time (τ ≈ 0.15ns) and saturation intensity (IS ≈ 0.01 GW/cm2). Additionally, we have calculated number of career density (N ≈ 5.31 × 10-17 cm-3), ground state absorption cross section (σ1 ≈ 1.63 × 10-17 cm2). Our experimental finding indicates that they can be employed as saturable absorbers.

New fundamental parameters for attitude representation

NASA Astrophysics Data System (ADS)

Patera, Russell P.

2017-08-01

A new attitude parameter set is developed to clarify the geometry of combining finite rotations in a rotational sequence and in combining infinitesimal angular increments generated by angular rate. The resulting parameter set of six Pivot Parameters represents a rotation as a great circle arc on a unit sphere that can be located at any clocking location in the rotation plane. Two rotations are combined by linking their arcs at either of the two intersection points of the respective rotation planes. In a similar fashion, linking rotational increments produced by angular rate is used to derive the associated kinematical equations, which are linear and have no singularities. Included in this paper is the derivation of twelve Pivot Parameter elements that represent all twelve Euler Angle sequences, which enables efficient conversions between Pivot Parameters and any Euler Angle sequence. Applications of this new parameter set include the derivation of quaternions and the quaternion composition rule, as well as, the derivation of the analytical solution to time dependent coning motion. The relationships between Pivot Parameters and traditional parameter sets are included in this work. Pivot Parameters are well suited for a variety of aerospace applications due to their effective composition rule, singularity free kinematic equations, efficient conversion to and from Euler Angle sequences and clarity of their geometrical foundation.

Nanosystem self-assembly pathways discovered via all-atom multiscale analysis.

PubMed

Pankavich, Stephen D; Ortoleva, Peter J

2012-07-26

We consider the self-assembly of composite structures from a group of nanocomponents, each consisting of particles within an N-atom system. Self-assembly pathways and rates for nanocomposites are derived via a multiscale analysis of the classical Liouville equation. From a reduced statistical framework, rigorous stochastic equations for population levels of beginning, intermediate, and final aggregates are also derived. It is shown that the definition of an assembly type is a self-consistency criterion that must strike a balance between precision and the need for population levels to be slowly varying relative to the time scale of atomic motion. The deductive multiscale approach is complemented by a qualitative notion of multicomponent association and the ensemble of exact atomic-level configurations consistent with them. In processes such as viral self-assembly from proteins and RNA or DNA, there are many possible intermediates, so that it is usually difficult to predict the most efficient assembly pathway. However, in the current study, rates of assembly of each possible intermediate can be predicted. This avoids the need, as in a phenomenological approach, for recalibration with each new application. The method accounts for the feedback across scales in space and time that is fundamental to nanosystem self-assembly. The theory has applications to bionanostructures, geomaterials, engineered composites, and nanocapsule therapeutic delivery systems.

Determination of the lead-acid battery's dynamic response using Butler-Volmer equation for advanced battery management systems in automotive applications

NASA Astrophysics Data System (ADS)

Piłatowicz, Grzegorz; Budde-Meiwes, Heide; Kowal, Julia; Sarfert, Christel; Schoch, Eberhard; Königsmann, Martin; Sauer, Dirk Uwe

2016-11-01

Micro-hybrid vehicles (μH) are currently starting to dominate the European market and seize constantly growing share of other leading markets in the world. On the one hand, the additional functionality of μH reduces the CO2 emissions and improves the fuel economy, but, on the other hand, the additional stress imposed on the lead-acid battery reduces significantly its expected service life in comparison to conventional vehicles. Because of that μH require highly accurate battery state detection solutions. They are necessary to ensure the vehicle reliability requirements, prolong service life and reduce warranty costs. This paper presents an electrical model based on Butler-Volmer equation. The main novelty of the presented approach is its ability to predict accurately dynamic response of a battery considering a wide range of discharge current rates, state-of-charges and temperatures. Presented approach is fully implementable and adaptable in state-of-the-art low-cost platforms. Additionally, shown results indicate that it is applicable as a supporting tool for state-of-charge and state-of-health estimation and scalable for the different battery technologies and sizes. Validation using both static pulses and dynamic driving profile resulted in average absolute error of 124 mV regarding cranking current rate of 800 A respectively.

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1983-01-01

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

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...

The application of the least squares finite element method to Abel's integral equation. [with application to glow discharge problem

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Norrie, D. H.; De Vries, G.

1979-01-01

Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the solution of this non-linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions

On implicit abstract neutral nonlinear differential equations

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

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br; O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

Considerations of "Combined Probability of Injury" in the next-generation USA frontal NCAP.

PubMed

Laituri, Tony R; Henry, Scott; Sullivan, Kaye; Nutt, Marvin

2010-08-01

The numerical basis for assigning star ratings in the next-generation USA New Car Assessment Program (NCAP) for frontal impacts was assessed. That basis, the Combined Probability of Injury, or CPI, is the probability of an occupant sustaining an injury to any of the specified body regions. For an NCAP test, a CPI value is computed by (a) using risk curves to convert body-region responses from a test dummy into body-region risks and (b) using a theoretical, overarching CPI equation to convert those separate body-region risks into a single CPI value. Though the general concept of applying a CPI equation to assign star ratings has existed since 1994, there will be numerous changes to the 2011 frontal NCAP: there will be two additional body regions (n = 4 vs. 2), the injury probabilities will be evaluated for lower-severity (more likely) injury levels, and some of the occupant responses will change. These changes could yield more disperse CPIs that could yield more disperse ratings. However, the reasons for this increased dispersion should be consistent with real-world findings. Related assessments were the topic of this two-part study, focused on drivers. In Part 1, the CPI equation was assessed without applying risk curves. Specifically, field injury probabilities for the four body regions were used as inputs to the CPI equation, and the resulting equation-produced CPIs were compared with the field CPIs. In Part 2, subject to analyses of test dummy responses from recent NCAP tests, the effect of risk curve choice on CPIs was assessed. Specifically, dispersion statistics were compared for CPIs based on various underlying risk curves applied to data from 2001-2005 model year vehicles (n = 183). From Part 1, the theoretical CPI equation for four body regions demonstrated acceptable fidelity when provided field injury rates (R(2)= 0.92), with the equation-based CPIs being approximately 12 percent lower than those of ideal correlation. From Part 2, the 2011 NCAP protocol (i.e., application of a four-body-region CPI equation whose inputs were from risk curves) generally increased both the CPIs and their dispersion relative to the current NCAP protocol. However, the CPIs generally increased due to an emphasis on neck injury-an emphasis not observed in real-world crashes. Subject to alternative risk curves for the neck and chest, again there was increased dispersion of the CPIs, but the unrealistic emphasis on the neck was eliminated. However, risk estimates for the knee/thigh/hip (KTH) for NCAP-type events remained understated and did not fall within the confidence bands of the field data. Accordingly, KTH risk estimation is an area for future research.

Evolution of magnetization due to asymmetric dimerization: theoretical considerations and application to aberrant oligomers formed by apoSOD1(2SH).

PubMed

Sekhar, Ashok; Bain, Alex D; Rumfeldt, Jessica A O; Meiering, Elizabeth M; Kay, Lewis E

2016-02-17

A set of coupled differential equations is presented describing the evolution of magnetization due to an exchange reaction whereby a pair of identical monomers form an asymmetric dimer. In their most general form the equations describe a three-site exchange process that reduces to two-site exchange under certain limiting conditions that are discussed. An application to the study of sparsely populated, transiently formed sets of aberrant dimers, symmetric and asymmetric, of superoxide dismutase is presented. Fits of concentration dependent CPMG relaxation dispersion profiles provide measures of the dimer dissociation constants and both on- and off-rates. Dissociation constants on the order of 70 mM are extracted from fits of the data, with dimeric populations of ∼2% and lifetimes of ∼6 and ∼2 ms for the symmetric and asymmetric complexes, respectively. This work emphasizes the important role that NMR relaxation experiments can play in characterizing very weak molecular complexes that remain invisible to most biophysical approaches.

Risk and Vulnerability Analysis of Satellites Due to MM/SD with PIRAT

NASA Astrophysics Data System (ADS)

Kempf, Scott; Schafer, Frank Rudolph, Martin; Welty, Nathan; Donath, Therese; Destefanis, Roberto; Grassi, Lilith; Janovsky, Rolf; Evans, Leanne; Winterboer, Arne

2013-08-01

Until recently, the state-of-the-art assessment of the threat posed to spacecraft by micrometeoroids and space debris was limited to the application of ballistic limit equations to the outer hull of a spacecraft. The probability of no penetration (PNP) is acceptable for assessing the risk and vulnerability of manned space mission, however, for unmanned missions, whereby penetrations of the spacecraft exterior do not necessarily constitute satellite or mission failure, these values are overly conservative. The newly developed software tool PIRAT (Particle Impact Risk and Vulnerability Analysis Tool) has been developed based on the Schäfer-Ryan-Lambert (SRL) triple-wall ballistic limit equation (BLE), applicable for various satellite components. As a result, it has become possible to assess the individual failure rates of satellite components. This paper demonstrates the modeling of an example satellite, the performance of a PIRAT analysis and the potential for subsequent design optimizations with respect of micrometeoroid and space debris (MM/SD) impact risk.

Development of braided fiber seals for engine applications

NASA Technical Reports Server (NTRS)

Cai, Zhong; Mutharasan, Rajakkannu; Ko, Frank K.; Du, Guang-Wu; Steinetz, Bruce M.

1993-01-01

A new type of braided fiber seal was developed for high temperature engine applications. Development work performed includes seal design, fabrication, leakage flow testing, and flow resistance modeling. This new type of seal utilizes the high flow resistance of tightly packed fibers and the conformability of textile structures. The seal contains a core part with aligned fibers, and a sheath with braided fiber layers. Seal samples are made by using the conventional braiding process. Leakage flow measurements are then performed. Mass flow rate versus the simulated engine pressure and preload pressure is recorded. The flow resistance of the seal is analyzed using the Ergun equation for flow through porous media, including both laminar and turbulent effects. The two constants in the Ergun equation are evaluated for the seal structures. Leakage flow of the seal under the test condition is found to be in the transition flow region. The analysis is used to predict the leakage flow performance of the seal with the determined design parameters.

Maneuver Estimation Model for Geostationary Orbit Determination

DTIC Science & Technology

2006-06-01

create a more robust model which would reduce the amount of data needed to make accurate maneuver estimations. The Clohessy - Wiltshire equations were...Applications to Geostationary Satellites...........................................7 2.3.2 Clohessy - Wiltshire Equations...15 3.1.1 Application of Clohessy - Wiltshire Equations ................................15 3.1.2

Methodology and Results of Mathematical Modelling of Complex Technological Processes

NASA Astrophysics Data System (ADS)

Mokrova, Nataliya V.

2018-03-01

The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

Implementing statistical equating for MRCP(UK) Parts 1 and 2.

PubMed

McManus, I C; Chis, Liliana; Fox, Ray; Waller, Derek; Tang, Peter

2014-09-26

The MRCP(UK) exam, in 2008 and 2010, changed the standard-setting of its Part 1 and Part 2 examinations from a hybrid Angoff/Hofstee method to statistical equating using Item Response Theory, the reference group being UK graduates. The present paper considers the implementation of the change, the question of whether the pass rate increased amongst non-UK candidates, any possible role of Differential Item Functioning (DIF), and changes in examination predictive validity after the change. Analysis of data of MRCP(UK) Part 1 exam from 2003 to 2013 and Part 2 exam from 2005 to 2013. Inspection suggested that Part 1 pass rates were stable after the introduction of statistical equating, but showed greater annual variation probably due to stronger candidates taking the examination earlier. Pass rates seemed to have increased in non-UK graduates after equating was introduced, but was not associated with any changes in DIF after statistical equating. Statistical modelling of the pass rates for non-UK graduates found that pass rates, in both Part 1 and Part 2, were increasing year on year, with the changes probably beginning before the introduction of equating. The predictive validity of Part 1 for Part 2 was higher with statistical equating than with the previous hybrid Angoff/Hofstee method, confirming the utility of IRT-based statistical equating. Statistical equating was successfully introduced into the MRCP(UK) Part 1 and Part 2 written examinations, resulting in higher predictive validity than the previous Angoff/Hofstee standard setting. Concerns about an artefactual increase in pass rates for non-UK candidates after equating were shown not to be well-founded. Most likely the changes resulted from a genuine increase in candidate ability, albeit for reasons which remain unclear, coupled with a cognitive illusion giving the impression of a step-change immediately after equating began. Statistical equating provides a robust standard-setting method, with a better theoretical foundation than judgemental techniques such as Angoff, and is more straightforward and requires far less examiner time to provide a more valid result. The present study provides a detailed case study of introducing statistical equating, and issues which may need to be considered with its introduction.

Effects of partial slip boundary condition and radiation on the heat and mass transfer of MHD-nanofluid flow

NASA Astrophysics Data System (ADS)

Abd Elazem, Nader Y.; Ebaid, Abdelhalim

2017-12-01

In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.

Robust numerical solution of the reservoir routing equation

NASA Astrophysics Data System (ADS)

Fiorentini, Marcello; Orlandini, Stefano

2013-09-01

The robustness of numerical methods for the solution of the reservoir routing equation is evaluated. The methods considered in this study are: (1) the Laurenson-Pilgrim method, (2) the fourth-order Runge-Kutta method, and (3) the fixed order Cash-Karp method. Method (1) is unable to handle nonmonotonic outflow rating curves. Method (2) is found to fail under critical conditions occurring, especially at the end of inflow recession limbs, when large time steps (greater than 12 min in this application) are used. Method (3) is computationally intensive and it does not solve the limitations of method (2). The limitations of method (2) can be efficiently overcome by reducing the time step in the critical phases of the simulation so as to ensure that water level remains inside the domains of the storage function and the outflow rating curve. The incorporation of a simple backstepping procedure implementing this control into the method (2) yields a robust and accurate reservoir routing method that can be safely used in distributed time-continuous catchment models.

Enhancement of specific absorption rate in lossy dielectric objects using a slab of left-handed material.

PubMed

Zhao, Lei; Cui, Tie Jun

2005-12-01

An enhancement of the specific absorption rate (SAR) inside a lossy dielectric object has been investigated theoretically based on a slab of left-handed medium (LHM). In order to make an accurate analysis of SAR distribution, a proper Green's function involved in the LHM slab is proposed, from which an integral equation for the electric field inside the dielectric object is derived. Such an integral equation has been solved accurately and efficiently using the conjugate gradient method and the fast Fourier transform. We have made a lot of numerical experiments on the SAR distributions inside the dielectric object excited by a line source with and without the LHM slab. Numerical experiments show that SAR can be enhanced tremendously when the LHM slab is involved due to the proper usage of strong surface waves, which will be helpful in the potential biomedical applications for hyperthermia. The physical insight for such a phenomenon has also been discussed.

An Estimation Theory for Differential Equations and other Problems, with Applications.

DTIC Science & Technology

1981-11-01

order differential -8- operators and M-operators, in particular, the Perron - Frobenius theory and generalizations. Convergence theory for iterative... THEORY FOR DIFFERENTIAL 0EQUATIONS AND OTHER FROBLEMS, WITH APPLICATIONS 0 ,Final Technical Report by Johann Schr6der November, 1981 EUROPEAN RESEARCH...COVERED An estimation theory for differential equations Final Report and other problrms, with app)lications A981 6. PERFORMING ORG. RN,-ORT NUMfFR 7

Stochastic von Bertalanffy models, with applications to fish recruitment.

PubMed

Lv, Qiming; Pitchford, Jonathan W

2007-02-21

We consider three individual-based models describing growth in stochastic environments. Stochastic differential equations (SDEs) with identical von Bertalanffy deterministic parts are formulated, with a stochastic term which decreases, remains constant, or increases with organism size, respectively. Probability density functions for hitting times are evaluated in the context of fish growth and mortality. Solving the hitting time problem analytically or numerically shows that stochasticity can have a large positive impact on fish recruitment probability. It is also demonstrated that the observed mean growth rate of surviving individuals always exceeds the mean population growth rate, which itself exceeds the growth rate of the equivalent deterministic model. The consequences of these results in more general biological situations are discussed.

Cross-validation of resting metabolic rate prediction equations

USDA-ARS?s Scientific Manuscript database

Background: Knowledge of the resting metabolic rate (RMR) is necessary for determining individual total energy requirements. Measurement of RMR is time consuming and requires specialized equipment. Prediction equations provide an easy method to estimate RMR; however, the accuracy of these equations...

Technical note: Use of a simplified equation for estimating glomerular filtration rate in beef cattle.

PubMed

Murayama, I; Miyano, A; Sasaki, Y; Hirata, T; Ichijo, T; Satoh, H; Sato, S; Furuhama, K

2013-11-01

This study was performed to clarify whether a formula (Holstein equation) based on a single blood sample and the isotonic, nonionic, iodine contrast medium iodixanol in Holstein dairy cows can apply to the estimation of glomerular filtration rate (GFR) for beef cattle. To verify the application of iodixanol in beef cattle, instead of the standard tracer inulin, both agents were coadministered as a bolus intravenous injection to identical animals at doses of 10 mg of I/kg of BW and 30 mg/kg. Blood was collected 30, 60, 90, and 120 min after the injection, and the GFR was determined by the conventional multisample strategies. The GFR values from iodixanol were well consistent with those from inulin, and no effects of BW, age, or parity on GFR estimates were noted. However, the GFR in cattle weighing less than 300 kg, aged<1 yr old, largely fluctuated, presumably due to the rapid ruminal growth and dynamic changes in renal function at young adult ages. Using clinically healthy cattle and those with renal failure, the GFR values estimated from the Holstein equation were in good agreement with those by the multisample method using iodixanol (r=0.89, P=0.01). The results indicate that the simplified Holstein equation using iodixanol can be used for estimating the GFR of beef cattle in the same dose regimen as Holstein dairy cows, and provides a practical and ethical alternative.

Optimization of Equation of State and Burn Model Parameters for Explosives

NASA Astrophysics Data System (ADS)

Bergh, Magnus; Wedberg, Rasmus; Lundgren, Jonas

2017-06-01

A reactive burn model implemented in a multi-dimensional hydrocode can be a powerful tool for predicting non-ideal effects as well as initiation phenomena in explosives. Calibration against experiment is, however, critical and non-trivial. Here, a procedure is presented for calibrating the Ignition and Growth Model utilizing hydrocode simulation in conjunction with the optimization program LS-OPT. The model is applied to the explosive PBXN-109. First, a cylinder expansion test is presented together with a new automatic routine for product equation of state calibration. Secondly, rate stick tests and instrumented gap tests are presented. Data from these experiments are used to calibrate burn model parameters. Finally, we discuss the applicability and development of this optimization routine.

Analysis and calculation of macrosegregation in a casting ingot, exhibits C and E

NASA Technical Reports Server (NTRS)

Poirier, D. R.; Maples, A. L.

1984-01-01

A computer model which describes the solidification of a binary metal alloy in an insulated rectangular mold with a temperature gradient is presented. A numerical technique, applicable to a broad class of moving boundary problems, was implemented therein. The solidification model described is used to calculate the macrosegregation within the solidified casting by coupling the equations for liquid flow in the solid/liquid or mushy zone with the energy equation for heat flow throughout the ingot and thermal convection in the bulk liquid portion. The rate of development of the solid can be automatically calculated by the model. Numerical analysis of such solidification parameters as enthalpy and boundary layer flow is displayed. On-line user interface and software documentation are presented.

Numerical Studies of Impurities in Fusion Plasmas

DOE R&D Accomplishments Database

Hulse, R. A.

1982-09-01

The coupled partial differential equations used to describe the behavior of impurity ions in magnetically confined controlled fusion plasmas require numerical solution for cases of practical interest. Computer codes developed for impurity modeling at the Princeton Plasma Physics Laboratory are used as examples of the types of codes employed for this purpose. These codes solve for the impurity ionization state densities and associated radiation rates using atomic physics appropriate for these low-density, high-temperature plasmas. The simpler codes solve local equations in zero spatial dimensions while more complex cases require codes which explicitly include transport of the impurity ions simultaneously with the atomic processes of ionization and recombination. Typical applications are discussed and computational results are presented for selected cases of interest.

A variable turbulent Prandtl and Schmidt number model study for scramjet applications

NASA Astrophysics Data System (ADS)

Keistler, Patrick

A turbulence model that allows for the calculation of the variable turbulent Prandtl (Prt) and Schmidt (Sct) numbers as part of the solution is presented. The model also accounts for the interactions between turbulence and chemistry by modeling the corresponding terms. Four equations are added to the baseline k-zeta turbulence model: two equations for enthalpy variance and its dissipation rate to calculate the turbulent diffusivity, and two equations for the concentrations variance and its dissipation rate to calculate the turbulent diffusion coefficient. The underlying turbulence model already accounts for compressibility effects. The variable Prt /Sct turbulence model is validated and tuned by simulating a wide variety of experiments. Included in the experiments are two-dimensional, axisymmetric, and three-dimensional mixing and combustion cases. The combustion cases involved either hydrogen and air, or hydrogen, ethylene, and air. Two chemical kinetic models are employed for each of these situations. For the hydrogen and air cases, a seven species/seven reaction model where the reaction rates are temperature dependent and a nine species/nineteen reaction model where the reaction rates are dependent on both pressure and temperature are used. For the cases involving ethylene, a 15 species/44 reaction reduced model that is both pressure and temperature dependent is used, along with a 22 species/18 global reaction reduced model that makes use of the quasi-steady-state approximation. In general, fair to good agreement is indicated for all simulated experiments. The turbulence/chemistry interaction terms are found to have a significant impact on flame location for the two-dimensional combustion case, with excellent experimental agreement when the terms are included. In most cases, the hydrogen chemical mechanisms behave nearly identically, but for one case, the pressure dependent model would not auto-ignite at the same conditions as the experiment and the other chemical model. The model was artificially ignited in that case. For the cases involving ethylene combustion, the chemical model has a profound impact on the flame size, shape, and ignition location. However, without quantitative experimental data, it is difficult to determine which one is more suitable for this particular application.

Beyond the Mincer Equation: The Internal Rate of Return to Higher Education in Colombia

ERIC Educational Resources Information Center

García-Suaza, Andrés Felipe; Guataquí, Juan Carlos; Guerra, José Alberto; Maldonado, Darío

2014-01-01

In order to present an estimation of the internal rate of return (IRR) to higher education in Colombia, we take advantage of recent updates on the methodological approach towards earnings equations. In order to overcome the criticism that surrounds interpretations of the education coefficient of Mincer equations as being the rate of return to…

The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Ye, Zhou

1997-01-01

The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.

Application of the Parabolic Approximation to Predict Acoustical Propagation in the Ocean.

ERIC Educational Resources Information Center

McDaniel, Suzanne T.

1979-01-01

A simplified derivation of the parabolic approximation to the acoustical wave equation is presented. Exact solutions to this approximate equation are compared with solutions to the wave equation to demonstrate the applicability of this method to the study of underwater sound propagation. (Author/BB)

Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Wang, Jun; Luo, Ray

2009-01-01

CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

NASA Technical Reports Server (NTRS)

Tseng, K.

1984-01-01

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Synthesis, Characterization, and Sensitivity Analysis of Urea Nitrate (UN)

DTIC Science & Technology

2015-04-01

of the line is the rate of the reaction for the corresponding temperature. The equations for the zero order reaction and half- life equation follow...rate law (k is rate constant; [A] is the concentration of UN) Rate = k[A]n . (1) Eq. 2 shows the half-life (t½) equation for a zero order reaction...MGMT 1 GOVT PRINTG OFC (PDF) A MALHOTRA 2 WEAPONS DEV & (PDF) INTEGRATION DIRCTRT AMRDEC RDMR WDN J NEIDERT G DRAKE

A Hybrid Ground-Motion Prediction Equation for Earthquakes in Western Alberta

NASA Astrophysics Data System (ADS)

Spriggs, N.; Yenier, E.; Law, A.; Moores, A. O.

2015-12-01

Estimation of ground-motion amplitudes that may be produced by future earthquakes constitutes the foundation of seismic hazard assessment and earthquake-resistant structural design. This is typically done by using a prediction equation that quantifies amplitudes as a function of key seismological variables such as magnitude, distance and site condition. In this study, we develop a hybrid empirical prediction equation for earthquakes in western Alberta, where evaluation of seismic hazard associated with induced seismicity is of particular interest. We use peak ground motions and response spectra from recorded seismic events to model the regional source and attenuation attributes. The available empirical data is limited in the magnitude range of engineering interest (M>4). Therefore, we combine empirical data with a simulation-based model in order to obtain seismologically informed predictions for moderate-to-large magnitude events. The methodology is two-fold. First, we investigate the shape of geometrical spreading in Alberta. We supplement the seismic data with ground motions obtained from mining/quarry blasts, in order to gain insights into the regional attenuation over a wide distance range. A comparison of ground-motion amplitudes for earthquakes and mining/quarry blasts show that both event types decay at similar rates with distance and demonstrate a significant Moho-bounce effect. In the second stage, we calibrate the source and attenuation parameters of a simulation-based prediction equation to match the available amplitude data from seismic events. We model the geometrical spreading using a trilinear function with attenuation rates obtained from the first stage, and calculate coefficients of anelastic attenuation and site amplification via regression analysis. This provides a hybrid ground-motion prediction equation that is calibrated for observed motions in western Alberta and is applicable to moderate-to-large magnitude events.

Nonlinear fluctuations-induced rate equations for linear birth-death processes

NASA Astrophysics Data System (ADS)

Honkonen, J.

2008-05-01

The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.

An exact solution on unsteady MHD free convection chemically reacting silver nanofluid flow past an exponentially accelerated vertical plate through porous medium

NASA Astrophysics Data System (ADS)

Kumaresan, E.; Vijaya Kumar, A. G.; Rushi Kumar, B.

2017-11-01

This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.

Second-order variational equations for N-body simulations

NASA Astrophysics Data System (ADS)

Rein, Hanno; Tamayo, Daniel

2016-07-01

First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). In this paper we lay out the theoretical framework to extend the idea of variational equations to higher order. We explicitly derive the differential equations that govern the evolution of second-order variations in the N-body problem. Going to second order opens the door to new applications, including optimization algorithms that require the first and second derivatives of the solution, like the classical Newton's method. Typically, these methods have faster convergence rates than derivative-free methods. Derivatives are also required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods which provide significantly shorter correlation times than standard methods. Such improved optimization methods can be applied to anything from radial-velocity/transit-timing-variation fitting to spacecraft trajectory optimization to asteroid deflection. We provide an implementation of first- and second-order variational equations for the publicly available REBOUND integrator package. Our implementation allows the simultaneous integration of any number of first- and second-order variational equations with the high-accuracy IAS15 integrator. We also provide routines to generate consistent and accurate initial conditions without the need for finite differencing.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M. S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

NASA Astrophysics Data System (ADS)

Moix, Jeremy M.; Cao, Jianshu

2013-10-01

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems.

PubMed

Moix, Jeremy M; Cao, Jianshu

2013-10-07

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

Designing herbicide formulation characteristics to maximize efficacy and minimize rice injury in paddy environments.

PubMed

Cryer, S A; Mann, R K; Erhardt-Zabik, S; Keeney, F N; Handy, P R

2001-06-01

Mathematical descriptors, coupled with experimental observations, are used to quantify differential uptake of an experimental herbicide in Japonica and Indica rice (Oryza sativa, non-target) and barnyardgrass (Echinochloa crus-galli, target). Partitioning, degradation, plant uptake and metabolism are described using mass-balance conservation equations in the form of kinetic approximations. Estimated environmental concentrations, governed by the pesticide formulation, are described using superimposed analytical solutions for the one-dimensional diffusion equation in spherical coordinates and by a finite difference representation of the two-dimensional diffusion equation in Cartesian coordinates. Formulation attributes from granules include active ingredient release rates, particle sizes, pesticide loading, and granule spacing. The diffusion model for pesticide transport is coupled with the compartment model to follow the fate and transport of a pesticide from its initial application location to various environmental matrices of interest. Formulation effects, partitioning and degradation in the various environmental matrices, differential plant uptake and metabolism, and dose-response information for plants are accounted for. This novel model provides a mechanism for selecting formulation delivery systems that optimize specific attributes (such as weed control or the therapeutic index) for risk-assessment procedures. In this report we describe how this methodology was used to explore the factors affecting herbicide efficacy and to define an optimal release rate for a granule formulation.

On the JWKB solution of the uniformly lengthening pendulum via change of independent variable in the Bessel's equation

NASA Astrophysics Data System (ADS)

Deniz, Coşkun

2017-01-01

Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel's equation into the normal form `via the suggested change of independent variable'. JWKB approximation of the first-order Bessel functions ( ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders ( ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.

SU-G-JeP3-09: Tumor Location Prediction Using Natural Respiratory Volume for Respiratory Gated Radiation Therapy (RGRT): System Verification Study

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

Kim, M; Jung, J; Yoon, D

Purpose: Respiratory gated radiation therapy (RGRT) gives accurate results when a patient’s breathing is stable and regular. Thus, the patient should be fully aware during respiratory pattern training before undergoing the RGRT treatment. In order to bypass the process of respiratory pattern training, we propose a target location prediction system for RGRT that uses only natural respiratory volume, and confirm its application. Methods: In order to verify the proposed target location prediction system, an in-house phantom set was used. This set involves a chest phantom including target, external markers, and motion generator. Natural respiratory volume signals were generated using themore » random function in MATLAB code. In the chest phantom, the target takes a linear motion based on the respiratory signal. After a four-dimensional computed tomography (4DCT) scan of the in-house phantom, the motion trajectory was derived as a linear equation. The accuracy of the linear equation was compared with that of the motion algorithm used by the operating motion generator. In addition, we attempted target location prediction using random respiratory volume values. Results: The correspondence rate of the linear equation derived from the 4DCT images with the motion algorithm of the motion generator was 99.41%. In addition, the average error rate of target location prediction was 1.23% for 26 cases. Conclusion: We confirmed the applicability of our proposed target location prediction system for RGRT using natural respiratory volume. If additional clinical studies can be conducted, a more accurate prediction system can be realized without requiring respiratory pattern training.« less

Glass dissolution as a function of pH and its implications for understanding mechanisms and future experiments

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

Strachan, Denis

For years, we have been using a certain form of the glass dissolution rate equation. In this article, I examine the assumptions that have been made and suggest that the rate equation may be more complex than originally thought. Suggestions of experiments that are needed to correct or validate the exisiting form of the rate equation are made.

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

ERIC Educational Resources Information Center

Golicnik, Marko

2011-01-01

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

A relativistic dissipative hydrodynamic description for systems including particle number changing processes

NASA Astrophysics Data System (ADS)

El, Andrej; Muronga, Azwinndini; Xu, Zhe; Greiner, Carsten

2010-12-01

Relativistic dissipative hydrodynamic equations are extended by taking into account particle number changing processes in a gluon system, which expands in one dimension boost-invariantly. Chemical equilibration is treated by a rate equation for the particle number density based on Boltzmann equation and Grad's ansatz for the off-equilibrium particle phase space distribution. We find that not only the particle production, but also the temperature and the momentum spectra of the gluon system, obtained from the hydrodynamic calculations, are sensitive to the rates of particle number changing processes. Comparisons of the hydrodynamic calculations with the transport ones employing the parton cascade BAMPS show the inaccuracy of the rate equation at large shear viscosity to entropy density ratio. To improve the rate equation, Grad's ansatz has to be modified beyond the second moments in momentum.

A Simultaneous Equation Demand Model for Block Rates

NASA Astrophysics Data System (ADS)

Agthe, Donald E.; Billings, R. Bruce; Dobra, John L.; Raffiee, Kambiz

1986-01-01

This paper examines the problem of simultaneous-equations bias in estimation of the water demand function under an increasing block rate structure. The Hausman specification test is used to detect the presence of simultaneous-equations bias arising from correlation of the price measures with the regression error term in the results of a previously published study of water demand in Tucson, Arizona. An alternative simultaneous equation model is proposed for estimating the elasticity of demand in the presence of block rate pricing structures and availability of service charges. This model is used to reestimate the price and rate premium elasticities of demand in Tucson, Arizona for both the usual long-run static model and for a simple short-run demand model. The results from these simultaneous equation models are consistent with a priori expectations and are unbiased.

Morphodynamic Modeling of the Lower Yellow River, China: Flux (Equilibrium) Form or Entrainment (Nonequilibrium) Form of Sediment Mass Conservation?

NASA Astrophysics Data System (ADS)

An, C.; Parker, G.; Ma, H.; Naito, K.; Moodie, A. J.; Fu, X.

2017-12-01

Models of river morphodynamics consist of three elements: (1) a treatment of flow hydraulics, (2) a formulation relating some aspect of sediment transport to flow hydraulics, and (3) a description of sediment conservation. In the case of unidirectional river flow, the Exner equation of sediment conservation is commonly described in terms of a flux-based formulation, in which bed elevation variation is related to the streamwise gradient of sediment transport rate. An alternate formulation of the Exner equation, however, is the entrainment-based formulation in which bed elevation variation is related to the difference between the entrainment rate of bed sediment into suspension and the deposition rate of suspended sediment onto the bed. In the flux-based formulation, sediment transport is regarded to be in a local equilibrium state (i.e., sediment transport rate locally equals sediment transport capacity). However, the entrainment-based formulation does not require this constraint; the sediment transport rate may lag in space and time behind the changing flow conditions. In modeling the fine-grained Lower Yellow River, it is usual to treat sediment conservation in terms of an entrainment-based (nonequilibrium) rather than a flux-based (equilibrium) formulation with the consideration that fine-grained sediment may be entrained at one place but deposited only at some distant location downstream. However, the differences in prediction between the two formulations are still not well known, and the entrainment formulation may not always be necessary for the Lower Yellow River. Here we study this problem by comparing the results of flux-based and entrainment-based morphodynamics under conditions typical of the Yellow River, using sediment transport equations specifically designed for the Lower Yellow River. We find, somewhat unexpectedly, that in a treatment of a 200-km reach using uniform sediment, there is little difference between the two formulations unless the sediment fall velocity is arbitrarily greatly reduced. A consideration of sediment mixtures, however, shows that the two formulations give very different patterns of grain sorting. We explain this in terms of the structures of the two Exner equations for sediment mixtures, and define conditions for applicability of each formulation.

Interactive Macroeconomics

NASA Astrophysics Data System (ADS)

Di Guilmi, Corrado; Gallegati, Mauro; Landini, Simone

2017-04-01

Preface; List of tables; List of figures, 1. Introduction; Part I. Methodological Notes and Tools: 2. The state space notion; 3. The master equation; Part II. Applications to HIA Based Models: 4. Financial fragility and macroeconomic dynamics I: heterogeneity and interaction; 5. Financial fragility and macroeconomic Dynamics II: learning; Part III. Conclusions: 6. Conclusive remarks; Part IV. Appendices and Complements: Appendix A: Complements to Chapter 3; Appendix B: Solving the ME to solve the ABM; Appendix C: Specifying transition rates; Index.

Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

NASA Astrophysics Data System (ADS)

Rasin, Alexander G.

2010-06-01

The application of the Gardner method for the generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely Bäcklund transformations and initial conservation laws, follows from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for the generation of symmetries is developed and applied to the discrete Korteweg-de Vries equation. It can also be applied to all the other ABS equations.

A Biochemist's View of Ecosystem Rates and their Response to Changing Temperature

NASA Astrophysics Data System (ADS)

Arcus, V. L.

2017-12-01

Enzyme kinetics lie at the heart of biochemistry and the Michaelis-Menten equation that defines the relationship between substrate and rate is over 100 years old. About 80 years ago Eyring and Polyani formulated Transistion State Theory (TST) which describes the temperature-dependence of chemical reaction rates and the precise relationship between activation energy and the rate. TST provided a robust theoretical foundation for the Arrhenius equation and together, these equations are the foundation equations for the biochemist. Can these equations provide any insights into rates at larger scales, such as organism growth rates and those rates that interest ecosystem scientists (e.g. heterotrophic respiration, gross primary production)? Let us begin by considering a microbial cell. Microbial growth (i.e. cell division) requires the coordinated kinetics of thousands of enzymes including DNA/RNA polymerases, ribosomes, biosynthetic enzymes - all under a regime of highly complex regulatory effects. There is no a priori reason to expect that Michaelis-Menten kinetics and TST will adequately describe this vastly complex process. Indeed, Lloyd and Taylor showed 23 years ago that soil respiration is not well described by the Arrhenius function. More recently, Heskel and colleagues showed that leaf respiration is also not well described by the Arrhenius function. It is the same case for rates of photosynthesis. Despite this failure of the basic equations of biochemistry to map to biological rates at greater scales, what insights can biochemistry provide to ecosystem science? As nearly all of biological metabolism is mediated through enzyme kinetics, I will begin with the Michaelis-Menten equation under regimes of low and high substrate concentrations. This simplified view can provide surprising insights into processes at larger scales. I will also consider the relationship between the activation energy and the reaction rate. Many, many ecosystem-rate papers focus on the activation energy and thus, it is important to understand this relationship. Finally, I will consider the Arrhenius and TST equations and their failure for ecosystem processes and the reasons for this failure. Understanding the failure is a first step towards a resolution to this long-standing problem in ecosystem science.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Applications of the Peng-Robinson Equation of State Using Mathematica

ERIC Educational Resources Information Center

Binous, Housam

2008-01-01

A single equation of state (EOS) such as the Peng-Robinson EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state including adiabatic flash calculation, determination of the solubility of methanol in natural gas, and the calculation of high-pressure chemical equilibrium. The problems…

Chronic Kidney Disease Epidemiology Collaboration versus Modification of Diet in Renal Disease equations for renal function evaluation in patients undergoing partial nephrectomy.

PubMed

Shikanov, Sergey; Clark, Melanie A; Raman, Jay D; Smith, Benjamin; Kaag, Matthew; Russo, Paul; Wheat, Jeffrey C; Wolf, J Stuart; Huang, William C; Shalhav, Arieh L; Eggener, Scott E

2010-11-01

A novel equation, the Chronic Kidney Disease Epidemiology Collaboration, has been proposed to replace the Modification of Diet in Renal Disease for estimated glomerular filtration rate due to higher accuracy, particularly in the setting of normal renal function. We compared these equations in patients with 2 functioning kidneys undergoing partial nephrectomy. We assembled a cohort of 1,158 patients from 5 institutions who underwent partial nephrectomy between 1991 and 2009. Only subjects with 2 functioning kidneys were included in the study. The end points were baseline estimated glomerular filtration rate, last followup estimated glomerular filtration rate (3 to 18 months), absolute and percent change estimated glomerular filtration rate ([absolute change/baseline] × 100%), and proportion of newly developed chronic kidney disease stage III. The agreement between the equations was evaluated using Bland-Altman plots and the McNemar test for paired observations. Mean baseline estimated glomerular filtration rate derived from the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration equations were 73 and 77 ml/minute/1.73 m(2), respectively, and following surgery were 63 and 67 ml/minute/1.73 m(2), respectively. Mean percent change estimated glomerular filtration rate was -12% for both equations (p = 0.2). The proportion of patients with newly developed chronic kidney disease stage III following surgery was 32% and 25%, according to the Modification of Diet in Renal Disease and Chronic Kidney Disease Epidemiology Collaboration equations, respectively (p = 0.001). For patients with 2 functioning kidneys undergoing partial nephrectomy the Chronic Kidney Disease Epidemiology Collaboration equation provides slightly higher glomerular filtration rate estimates compared to the Modification of Diet in Renal Disease equation, with 7% fewer patients categorized as having chronic kidney disease stage III or worse. Copyright © 2010 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.

Spiral microstrip hyperthermia applicators: technical design and clinical performance.

PubMed

Samulski, T V; Fessenden, P; Lee, E R; Kapp, D S; Tanabe, E; McEuen, A

1990-01-01

Spiral microstrip microwave (MW) antennas have been developed and adapted for use as clinical hyperthermia applicators. The design has been configured in a variety of forms including single fixed antenna applicators, multi-element arrays, and mechanically scanned single or paired antennas. The latter three configurations have been used to allow an expansion of the effective heating area. Specific absorption rate (SAR) distributions measured in phantom have been used to estimate the depth and volume of effective heating. The estimates are made using the bioheat equation assuming uniformly perfused tissue. In excess of 500 treatments of patients with advanced or recurrent localized superficial tumors have been performed using this applicator technology. Data from clinical treatments have been analyzed to quantify the heating performance and verify the suitability of these applicators for clinical use. Good microwave coupling efficiency together with the compact applicator size have proved to be valuable clinical assets.

Generalized Master Equation with Non-Markovian Multichromophoric Förster Resonance Energy Transfer for Modular Exciton Densities

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

Jang, Seogjoo; Hoyer, Stephan; Fleming, Graham

2014-10-31

A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations of small length scales into dynamics over large length scales, and also provides a non-Markovian generalization and rigorous derivation of the Pauli master equation employing multichromophoric Förster resonance energy transfer rates. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic populations over coupled chromophores can be accurately describedmore » by transitions between subgroups (modules) of delocalized excitons. Application of the GME-MED to the exciton dynamics between a pair of light harvesting complexes in purple bacteria demonstrates its promise as a computationally efficient tool to investigate large scale exciton dynamics in complex environments.« less

Fluid and mass transport modelling to drive the design of cell-packed hollow fibre bioreactors for tissue engineering applications.

PubMed

Shipley, Rebecca J; Waters, Sarah L

2012-12-01

A model for fluid and mass transport in a single module of a tissue engineering hollow fibre bioreactor (HFB) is developed. Cells are seeded in alginate throughout the extra-capillary space (ECS), and fluid is pumped through a central lumen to feed the cells and remove waste products. Fluid transport is described using Navier-Stokes or Darcy equations as appropriate; this is overlaid with models of mass transport in the form of advection-diffusion-reaction equations that describe the distribution and uptake/production of nutrients/waste products. The small aspect ratio of a module is exploited and the option of opening an ECS port is explored. By proceeding analytically, operating equations are determined that enable a tissue engineer to prescribe the geometry and operation of the HFB by ensuring the nutrient and waste product concentrations are consistent with a functional cell population. Finally, results for chondrocyte and cardiomyocyte cell populations are presented, typifying two extremes of oxygen uptake rates.

STRUCTURAL ESTIMATES OF TREATMENT EFFECTS ON OUTCOMES USING RETROSPECTIVE DATA: AN APPLICATION TO DUCTAL CARCINOMA IN SITU

PubMed Central

Gold, Heather Taffet; Sorbero, Melony E. S.; Griggs, Jennifer J.; Do, Huong T.; Dick, Andrew W.

2013-01-01

Analysis of observational cohort data is subject to bias from unobservable risk selection. We compared econometric models and treatment effectiveness estimates using the linked Surveillance, Epidemiology, and End Results (SEER)-Medicare claims data for women diagnosed with ductal carcinoma in situ. Treatment effectiveness estimates for mastectomy and breast conserving surgery (BCS) with or without radiotherapy were compared using three different models: simultaneous-equations model, discrete-time survival model with unobserved heterogeneity (frailty), and proportional hazards model. Overall trends in disease-free survival (DFS), or time to first subsequent breast event, by treatment are similar regardless of the model, with mastectomy yielding the highest DFS over 8 years of follow-up, followed by BCS with radiotherapy, and then BCS alone. Absolute rates and direction of bias varied substantially by treatment strategy. DFS was underestimated by single-equation and frailty models compared to the simultaneous-equations model and RCT results for BCS with RT and overestimated for BCS alone. PMID:21602195

Stagnation point flow on bioconvection nanofluid over a stretching/shrinking surface with velocity and thermal slip effects

NASA Astrophysics Data System (ADS)

Chan, Sze Qi; Aman, Fazlina; Mansur, Syahira

2017-09-01

Nanofluid containing nanometer sized particles has become an ideal thermal conductivity medium for the flow and heat transfer in many industrial and engineering applications due to their high rate of heat transfer. However, swimming microorganisms are imposed into the nanofluid to overcome the instability of nanoparticles due to a bioconvection phenomenon. This paper investigates the stagnation point flow on bioconvection heat transfer of a nanofluid over a stretching/shrinking surface containing gyrotactic microorganisms. Velocity and thermal slip effects are the two conditions incorporated into the model. Similarity transformation is applied to reduce the governing nonlinear partial differential equations into the nonlinear ordinary differential equations. The transformed equations are then solved numerically. The results are displayed in the form of graphs and tables. The effects of these governing parameters on the skin friction coefficient, local Nusselt number, local Sherwood number and the local density of the motile microorganisms are analysed and discussed in details.

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

Bi-orthogonality relations for fluid-filled elastic cylindrical shells: Theory, generalisations and application to construct tailored Green's matrices

NASA Astrophysics Data System (ADS)

Ledet, Lasse S.; Sorokin, Sergey V.

2018-03-01

The paper addresses the classical problem of time-harmonic forced vibrations of a fluid-filled cylindrical shell considered as a multi-modal waveguide carrying infinitely many waves. The forced vibration problem is solved using tailored Green's matrices formulated in terms of eigenfunction expansions. The formulation of Green's matrix is based on special (bi-)orthogonality relations between the eigenfunctions, which are derived here for the fluid-filled shell. Further, the relations are generalised to any multi-modal symmetric waveguide. Using the orthogonality relations the transcendental equation system is converted into algebraic modal equations that can be solved analytically. Upon formulation of Green's matrices the solution space is studied in terms of completeness and convergence (uniformity and rate). Special features and findings exposed only through this modal decomposition method are elaborated and the physical interpretation of the bi-orthogonality relation is discussed in relation to the total energy flow which leads to derivation of simplified equations for the energy flow components.

Incorporating delayed neutrons into the point-model equations routinely used for neutron coincidence counting in nuclear safeguards

DOE PAGES

Croft, Stephen; Favalli, Andrea

2016-09-21

Here, we extend the familiar Bӧhnel point-model equations, which are routinely used to interpret neutron coincidence counting rates, by including the contribution of delayed neutrons. After developing the necessary equations we use them to show, by providing some numerical results, what the quantitative impact of neglecting delayed neutrons is across the full range of practical nuclear safeguards applications. The influence of delayed neutrons is predicted to be small for the types of deeply sub-critical assay problems which concern the nuclear safeguards community, smaller than uncertainties arising from other factors. This is most clearly demonstrated by considering the change in themore » effective (α,n)-to-spontaneous fission prompt-neutron ratio that the inclusion of delayed neutrons gives rise to. That the influence of delayed neutrons is small is fortunate, and our results justify the long standing practice of simply neglecting them in the analysis of field measurements.« less

A study of the liquid-vapor phase change of mercury based on irreversible thermodynamics.

NASA Technical Reports Server (NTRS)

Adt, R. R., Jr.; Hatsopoulos, G. N.; Bornhorst, W. J.

1972-01-01

The object of this work is to determine the transport coefficients which appear in linear irreversible-thermodynamic rate equations of a phase change. An experiment which involves the steady-state evaporation of mercury was performed to measure the principal transport coefficient appearing in the mass-rate equation and the coupling transport coefficient appearing in both the mass-rate equation and the energy-rate equation. The principal transport coefficient sigma, usually termed the 'condensation' or 'evaporation' coefficient, is found to be approximately 0.9, which is higher than that measured previously in condensation-of-mercury experiments. The experimental value of the coupling coefficient K does not agree with the value predicted from Schrage's kinetic analysis of the phase change. A modified kinetic analysis in which the Onsager reciprocal law and the conservation laws are invoked is presented which removes this discrepancy but which shows that the use of Schrage's equation for predicting mass rates of phase change is a good approximation.

Application of the Finite Element Method in Atomic and Molecular Physics

NASA Technical Reports Server (NTRS)

Shertzer, Janine

2007-01-01

The finite element method (FEM) is a numerical algorithm for solving second order differential equations. It has been successfully used to solve many problems in atomic and molecular physics, including bound state and scattering calculations. To illustrate the diversity of the method, we present here details of two applications. First, we calculate the non-adiabatic dipole polarizability of Hi by directly solving the first and second order equations of perturbation theory with FEM. In the second application, we calculate the scattering amplitude for e-H scattering (without partial wave analysis) by reducing the Schrodinger equation to set of integro-differential equations, which are then solved with FEM.

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Application of stochastic differential geometry to the term structure of interst rates in developed markets

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

Taranenko, Y.; Barnes, C.

1996-12-31

This paper deals with further developments of the new theory that applies stochastic differential geometry (SDG) to dynamics of interest rates. We examine mathematical constraints on the evolution of interest rate volatilities that arise from stochastic differential calculus under assumptions of an arbitrage free evolution of zero coupon bonds and developed markets (i.e., none of the party/factor can drive the whole market). The resulting new theory incorporates the Heath-Jarrow-Morton (HJM) model of interest rates and provides new equations for volatilities which makes the system of equations for interest rates and volatilities complete and self consistent. It results in much smallermore » amount of volatility data that should be guessed for the SDG model as compared to the HJM model. Limited analysis of the market volatility data suggests that the assumption of the developed market is violated around maturity of two years. Such maturities where the assumptions of the SDG model are violated are suggested to serve as boundaries at which volatilities should be specified independently from the model. Our numerical example with two boundaries (two years and five years) qualitatively resembles the market behavior. Under some conditions solutions of the SDG model become singular that may indicate market crashes. More detail comparison with the data is needed before the theory can be established or refuted.« less

Effect of temperature on microbial growth rate-mathematical analysis: the Arrhenius and Eyring-Polanyi connections.

PubMed

Huang, Lihan; Hwang, Andy; Phillips, John

2011-10-01

The objective of this work is to develop a mathematical model for evaluating the effect of temperature on the rate of microbial growth. The new mathematical model is derived by combination and modification of the Arrhenius equation and the Eyring-Polanyi transition theory. The new model, suitable for both suboptimal and the entire growth temperature ranges, was validated using a collection of 23 selected temperature-growth rate curves belonging to 5 groups of microorganisms, including Pseudomonas spp., Listeria monocytogenes, Salmonella spp., Clostridium perfringens, and Escherichia coli, from the published literature. The curve fitting is accomplished by nonlinear regression using the Levenberg-Marquardt algorithm. The resulting estimated growth rate (μ) values are highly correlated to the data collected from the literature (R(2) = 0.985, slope = 1.0, intercept = 0.0). The bias factor (B(f) ) of the new model is very close to 1.0, while the accuracy factor (A(f) ) ranges from 1.0 to 1.22 for most data sets. The new model is compared favorably with the Ratkowsky square root model and the Eyring equation. Even with more parameters, the Akaike information criterion, Bayesian information criterion, and mean square errors of the new model are not statistically different from the square root model and the Eyring equation, suggesting that the model can be used to describe the inherent relationship between temperature and microbial growth rates. The results of this work show that the new growth rate model is suitable for describing the effect of temperature on microbial growth rate. Practical Application:  Temperature is one of the most significant factors affecting the growth of microorganisms in foods. This study attempts to develop and validate a mathematical model to describe the temperature dependence of microbial growth rate. The findings show that the new model is accurate and can be used to describe the effect of temperature on microbial growth rate in foods. Journal of Food Science © 2011 Institute of Food Technologists® No claim to original US government works.

High-Modulation-Speed LEDs Based on III-Nitride

NASA Astrophysics Data System (ADS)

Chen, Hong

III-nitride InGaN light-emitting diodes (LEDs) enable wide range of applications in solid-state lighting, full-color displays, and high-speed visible-light communication. Conventional InGaN quantum well LEDs grown on polar c-plane substrate suffer from quantum confined Stark effect due to the large internal polarization-related fields, leading to a reduced radiative recombination rate and device efficiency, which limits the performance of InGaN LEDs in high-speed communication applications. To circumvent these negative effects, non-trivial-cavity designs such as flip-chip LEDs, metallic grating coated LEDs are proposed. This oral defense will show the works on the high-modulation-speed LEDs from basic ideas to applications. Fundamental principles such as rate equations for LEDs/laser diodes (LDs), plasmonic effects, Purcell effects will be briefly introduced. For applications, the modal properties of flip-chip LEDs are solved by implementing finite difference method in order to study the modulation response. The emission properties of highly polarized InGaN LEDs coated by metallic gratings are also investigated by finite difference time domain method.

Evaluation of equations that estimate glomerular filtration rate in renal transplant recipients.

PubMed

De Alencastro, M G; Veronese, F V; Vicari, A R; Gonçalves, L F; Manfro, R C

2014-03-01

The accuracy of equations that estimate the glomerular filtration rate (GFR) in renal transplant patients has not been established; thus their performance was assessed in stable renal transplant patients. Renal transplant patients (N.=213) with stable graft function were enrolled. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation was used as the reference method and compared with the Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), Mayo Clinic (MC) and Nankivell equations. Bias, accuracy and concordance rates were determined for all equation relative to CKD-EPI. Mean estimated GFR values of the equations differed significantly from the CKD-EPI values, though the correlations with the reference method were significant. Values of MDRD differed from the CG, MC and Nankivell estimations. The best agreement to classify the chronic kidney disease (CKD) stages was for the MDRD (Kappa=0.649, P<0.001), and for the other equations the agreement was moderate. The MDRD had less bias and narrower agreement limits but underestimated the GFR at levels above 60 mL/min/1.73 m2. Conversely, the CG, MC and Nankivell equations overestimated the GFR, and the Nankivell equation had the worst performance. The MDRD equation P15 and P30 values were higher than those of the other equations (P<0.001). Despite their correlations, equations estimated the GFR and CKD stage differently. The MDRD equation was the most accurate, but the sub-optimal performance of all the equations precludes their accurate use in clinical practice.

A generic rate equation for catalysed, template-directed polymerisation.

PubMed

Hofmeyr, Jan-Hendrik S; Gqwaka, Olona P C; Rohwer, Johann M

2013-09-02

Biosynthetic networks link to growth and reproduction processes through template-directed synthesis of macromolecules such as polynucleotides and polypeptides. No rate equation exists that captures this link in a way that it can effectively be incorporated into a single computational model of the overall process. This paper describes the derivation of such a generic steady-state rate equation for catalysed, template-directed polymerisation reactions with varying monomer stoichiometry and varying chain length. The derivation is based on a classical Michaelis-Menten mechanism with template binding and an arbitrary number of chain elongation steps that produce a polymer composed of an arbitrary number of monomer types. The rate equation only requires the identity of the first dimer in the polymer sequence; for the remainder only the monomer composition needs be known. Further simplification of a term in the denominator yielded an equation requiring no positional information at all, only the monomer composition of the polymer; this equation still gave an excellent estimate of the reaction rate provided that either the monomer concentrations are at least half-saturating, or the polymer is very long. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Application of an Engineering Inviscid-Boundary Layer Method to Slender Three-Dimensional Vehicle Forebodies

NASA Technical Reports Server (NTRS)

Riley, Christopher J.

1993-01-01

An engineering inviscid-boundary layer method has been modified for application to slender three-dimensional (3-D) forebodies which are characteristic of transatmospheric vehicles. An improved shock description in the nose region has been added to the inviscid technique which allows the calculation of a wider range of body geometries. The modified engineering method is applied to the perfect gas solution over a slender 3-D configuration at angle of attack. The method predicts surface pressures and laminar heating rates on the windward side of the vehicle that compare favorably with numerical solutions of the thin-layer Navier-Stokes equations. These improvements extend the 3-D capabilities of the engineering method and significantly increase its design applications.

Applications of the Peng-Robinson Equation of State Using MATLAB[R

ERIC Educational Resources Information Center

Nasri, Zakia; Binous, Housam

2009-01-01

A single equation of state (EOS) such as the Peng-Robinson (PR) EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state, including estimation of pure component properties and computation of the vapor-liquid equilibrium (VLE) diagram for binary mixtures. We perform high-pressure…

Dynamic Disorder in Quasi-Equilibrium Enzymatic Systems

PubMed Central

Chaudhury, Srabanti; Igoshin, Oleg A.

2010-01-01

Conformations and catalytic rates of enzymes fluctuate over a wide range of timescales. Despite these fluctuations, there exist some limiting cases in which the enzymatic catalytic rate follows the macroscopic rate equation such as the Michaelis-Menten law. In this paper we investigate the applicability of macroscopic rate laws for fluctuating enzyme systems in which catalytic transitions are slower than ligand binding-dissociation reactions. In this quasi-equilibrium limit, for an arbitrary reaction scheme we show that the catalytic rate has the same dependence on ligand concentrations as obtained from mass-action kinetics even in the presence of slow conformational fluctuations. These results indicate that the timescale of conformational dynamics – no matter how slow – will not affect the enzymatic rate in quasi-equilibrium limit. Our numerical results for two enzyme-catalyzed reaction schemes involving multiple substrates and inhibitors further support our general theory. PMID:20808776

Application of MSSIP-2 nutrient in marine phytoplankton culture to support the production of biomass for biofuel industry

NASA Astrophysics Data System (ADS)

Taba, Paulina; Kasim, S.; Raya, I.

2018-03-01

A research on the application of MSSIP-2 nutrient in marine phytoplankton culture has been conducted to produce biomass to be used as raw material for biofuel. Marine phytoplankton was cultivated using the nutrient media and the growth rates were studied by measuring the cell solidity at various growth times. Seven phytoplanktons; Isochrysis aff galbana, Spirulina sp., Thalassiosira sp., and Nitzchia sp., Chlorella vulgaris, Chaetoceros calcitrans and Isochrysis tahiti were used in the research. The experimental temperature, salinity, and pH of the media were measured and the specific growth rates of phytoplanktons were determined using the first order rate equation. Results showed that the highest specific growth rate was given by Chlorella vulgaris (0.0322 cells/hour) and the lowest one was by Thalassiosira sp. (0.0277 cells/hour). The highest biomass weight was obtained from Isochrysis aff galbana (0.329 g), whereas the lowest one (0.27 g) was from Nitzchia sp. The carbohydrate content was various, the highest content was 34.07% found in Isochrysis aff galbana and the lowest was 28.16% in Thalassiosira sp.

Pore structures in an implantable sol gel titania ceramic device used in controlled drug release applications: A modeling study

NASA Astrophysics Data System (ADS)

Peterson, Aaron; Lopez, Tessy; Islas, Emma Ortiz; Gonzalez, Richard D.

2007-04-01

Several process variables, which may be helpful in optimizing the rate at which drugs are released from implantable, sol-gel titania devices have been identified in this study. The controlled rate of drug release is compared for two different anticonvulsant drugs, valproic acid and sodic phenytoin. Contrary to what one might expect, when the concentration is increased in the titania reservoir the rate of initial drug delivery decreases. This is a desirable result, because it may reduce the danger of a high initial discharge, which may harm the epileptic rat. The structure of the porous structure within the titania network has been studied using a generalized form of the BET equation which considers only n layers. In general, following an initial discharge, the rate at which the drug is released will increase with the increasing concentration. Pore mouth blocking can present a problem. However, this problem tends to disappear following the initial discharge. The extent of drug loading is a useful variable parameter, which can be adjusted in order to deliver the amount of drug required in a given application.

Determination of Peukert's Constant Using Impedance Spectroscopy: Application to Supercapacitors.

PubMed

Mills, Edmund Martin; Kim, Sangtae

2016-12-15

Peukert's equation is widely used to model the rate dependence of battery capacity, and has recently attracted attention for application to supercapacitors. Here we present a newly developed method to readily determine Peukert's constant using impedance spectroscopy. Impedance spectroscopy is ideal for this purpose as it has the capability of probing electrical performance of a device over a wide range of time-scales within a single measurement. We demonstrate that the new method yields consistent results with conventional galvanostatic measurements through applying it to commercially available supercapacitors. Additionally, the novel method is much simpler and more precise, making it an attractive alternative for the determination of Peukert's constant.

Are cystatin C-based equations superior to creatinine-based equations for estimating GFR in Chinese elderly population?

PubMed

Pei, Xiaohua; Liu, Qiao; He, Juan; Bao, Lihua; Yan, Chengjing; Wu, Jianqing; Zhao, Weihong

2012-12-01

Cystatin C has been proposed as a surrogate marker of kidney function. The elderly population accounts for the largest proportion of chronic kidney disease (CKD) patients. The aim of this study was to assess the diagnostic value of serum cystatin C and compare the applicability of cystatin C-based equations with serum creatinine (Scr)-based equations for estimating glomerular filtration rate (GFR). The estimated GFR (eGFR) values from six cystatin C-based equations (Tan, MacIsaac, Ma, Stevens1-3) and three Scr-based equations (CG, MDRD, CKD-EPI) were compared with the reference GFR (rGFR) values from 99mTc-DTPA renal dynamic imaging method. A total of 110 elderly Chinese (60-92 year, 71.05±7.62 year) were enrolled. Cystatin C had better diagnostic value than Scr (relationship coefficient with rGFR: cystatin C -0.847 vs. Scr -0.729, P<0.01; sensitivity: cystatin C 0.90 vs. Scr 0.55, P<0.01; AUCROC: cystatin C 0.857 vs. Scr 0.757, P<0.01). All the equations predicted GFR more accurately for rGFR≥60 ml/min/1.73 m2 than for rGFR<60 ml/min/1.73 m2. Most equations had acceptable accuracy. The cystatin C-based equations deviated from rGFR by -12.78 ml/min/1.73 m2 to -2.12 ml/min/1.73 m2, with accuracy varying from 64.6 to 82.7%. The Scr-based equations deviated from rGFR by -5.37 ml/min/1.73 m2 to -0.68 ml/min/1.73 m2, with accuracy varying from 77.3 to 79.1%. The CKD-EPI, MacIsaac and Ma equations predicted no bias with rGFR (P>0.05), with higher accuracy and lower deviation in the total group. The MacIsaac, CKD-EPI and Stevens3 equations could be optimal for those with normal and mildly impaired kidney function, whereas the Ma equation for those with CKD. Cystatin C is a promising kidney function marker. However, not all cystatin C-based equations could be superior to the Scr-equations.

Performance of the chronic kidney disease-epidemiology study equations for estimating glomerular filtration rate before and after nephrectomy.

PubMed

Lane, Brian R; Demirjian, Sevag; Weight, Christopher J; Larson, Benjamin T; Poggio, Emilio D; Campbell, Steven C

2010-03-01

Accurate renal function determination before and after nephrectomy is essential for proper prevention and management of chronic kidney disease due to nephron loss and ischemic injury. We compared the estimated glomerular filtration rate using several serum creatinine based formulas against the measured rate based on (125)I-iothalamate clearance to determine which most accurately reflects the rate in this setting. Of 7,611 patients treated at our institution since 1975 the measured glomerular filtration rate was selectively determined before and after nephrectomy in 268 and 157, respectively. Performance of the Cockcroft-Gault, Modification of Diet in Renal Disease Study, re-expressed Modification of Diet in Renal Disease Study and Chronic Kidney Disease-Epidemiology Study equations, each of which estimates the glomerular filtration rate, were determined using serum creatinine, age, gender, weight and body surface area. The performance of serum creatinine, reciprocal serum creatinine and the 4 formulas was compared with the measured rate using Pearson's correlation, Lin's concordance coefficient and residual plots. Median serum creatinine was 1.4 mg/dl and the median measured glomerular filtration rate was 50 ml per minute per 1.73 m(2). The correlation between serum creatinine and the measured rate was poor (-0.66) compared with that of reciprocal serum creatinine (0.78) and the 4 equations (0.82 to 0.86). The Chronic Kidney Disease-Epidemiology Study equation performed with greatest precision and accuracy, and least bias of all equations. Stage 3 or greater chronic kidney disease ((125)I-iothalamate glomerular filtration rate 60 ml per minute per 1.73 m(2) or less) was present in 44% of patients with normal serum creatinine (1.4 mg/dl or less) postoperatively. Such missed diagnoses of chronic kidney disease decreased 42% using the Chronic Kidney Disease-Epidemiology Study equation. Glomerular filtration rate estimation equations outperform serum creatinine and better identify patients with perinephrectomy compromised renal function. The newly developed, serum creatinine based, Chronic Kidney Disease-Epidemiology Study equation has sufficient accuracy to render direct glomerular filtration rate measurement unnecessary before and after nephrectomy for cause in most circumstances. 2010 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.

Rigorous derivation of porous-media phase-field equations

NASA Astrophysics Data System (ADS)

Schmuck, Markus; Kalliadasis, Serafim

2017-11-01

The evolution of interfaces in Complex heterogeneous Multiphase Systems (CheMSs) plays a fundamental role in a wide range of scientific fields such as thermodynamic modelling of phase transitions, materials science, or as a computational tool for interfacial flow studies or material design. Here, we focus on phase-field equations in CheMSs such as porous media. To the best of our knowledge, we present the first rigorous derivation of error estimates for fourth order, upscaled, and nonlinear evolution equations. For CheMs with heterogeneity ɛ, we obtain the convergence rate ɛ 1 / 4 , which governs the error between the solution of the new upscaled formulation and the solution of the microscopic phase-field problem. This error behaviour has recently been validated computationally in. Due to the wide range of application of phase-field equations, we expect this upscaled formulation to allow for new modelling, analytic, and computational perspectives for interfacial transport and phase transformations in CheMSs. This work was supported by EPSRC, UK, through Grant Nos. EP/H034587/1, EP/L027186/1, EP/L025159/1, EP/L020564/1, EP/K008595/1, and EP/P011713/1 and from ERC via Advanced Grant No. 247031.

Master equation for open two-band systems and its applications to Hall conductance

NASA Astrophysics Data System (ADS)

Shen, H. Z.; Zhang, S. S.; Dai, C. M.; Yi, X. X.

2018-02-01

Hall conductivity in the presence of a dephasing environment has recently been investigated with a dissipative term introduced phenomenologically. In this paper, we study the dissipative topological insulator (TI) and its topological transition in the presence of quantized electromagnetic environments. A Lindblad-type equation is derived to determine the dynamics of a two-band system. When the two-band model describes TIs, the environment may be the fluctuations of radiation that surround the TIs. We find the dependence of decay rates in the master equation on Bloch vectors in the two-band system, which leads to a mixing of the band occupations. Hence the environment-induced current is in general not perfectly topological in the presence of coupling to the environment, although deviations are small in the weak limit. As an illustration, we apply the Bloch-vector-dependent master equation to TIs and calculate the Hall conductance of tight-binding electrons in a two-dimensional lattice. The influence of environments on the Hall conductance is presented and discussed. The calculations show that the phase transition points of the TIs are robust against the quantized electromagnetic environment. The results might bridge the gap between quantum optics and topological photonic materials.

Space-Time Joint Interference Cancellation Using Fuzzy-Inference-Based Adaptive Filtering Techniques in Frequency-Selective Multipath Channels

NASA Astrophysics Data System (ADS)

Hu, Chia-Chang; Lin, Hsuan-Yu; Chen, Yu-Fan; Wen, Jyh-Horng

2006-12-01

An adaptive minimum mean-square error (MMSE) array receiver based on the fuzzy-logic recursive least-squares (RLS) algorithm is developed for asynchronous DS-CDMA interference suppression in the presence of frequency-selective multipath fading. This receiver employs a fuzzy-logic control mechanism to perform the nonlinear mapping of the squared error and squared error variation, denoted by ([InlineEquation not available: see fulltext.],[InlineEquation not available: see fulltext.]), into a forgetting factor[InlineEquation not available: see fulltext.]. For the real-time applicability, a computationally efficient version of the proposed receiver is derived based on the least-mean-square (LMS) algorithm using the fuzzy-inference-controlled step-size[InlineEquation not available: see fulltext.]. This receiver is capable of providing both fast convergence/tracking capability as well as small steady-state misadjustment as compared with conventional LMS- and RLS-based MMSE DS-CDMA receivers. Simulations show that the fuzzy-logic LMS and RLS algorithms outperform, respectively, other variable step-size LMS (VSS-LMS) and variable forgetting factor RLS (VFF-RLS) algorithms at least 3 dB and 1.5 dB in bit-error-rate (BER) for multipath fading channels.

The Master Equation for Two-Level Accelerated Systems at Finite Temperature

NASA Astrophysics Data System (ADS)

Tomazelli, J. L.; Cunha, R. O.

2016-10-01

In this work, we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a reservoir in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a reservoir, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.

Biological electric fields and rate equations for biophotons.

PubMed

Alvermann, M; Srivastava, Y N; Swain, J; Widom, A

2015-04-01

Biophoton intensities depend upon the squared modulus of the electric field. Hence, we first make some general estimates about the inherent electric fields within various biosystems. Generally, these intensities do not follow a simple exponential decay law. After a brief discussion on the inapplicability of a linear rate equation that leads to strict exponential decay, we study other, nonlinear rate equations that have been successfully used for biosystems along with their physical origins when available.

SIERRA - A 3-D device simulator for reliability modeling

NASA Astrophysics Data System (ADS)

Chern, Jue-Hsien; Arledge, Lawrence A., Jr.; Yang, Ping; Maeda, John T.

1989-05-01

SIERRA is a three-dimensional general-purpose semiconductor-device simulation program which serves as a foundation for investigating integrated-circuit (IC) device and reliability issues. This program solves the Poisson and continuity equations in silicon under dc, transient, and small-signal conditions. Executing on a vector/parallel minisupercomputer, SIERRA utilizes a matrix solver which uses an incomplete LU (ILU) preconditioned conjugate gradient square (CGS, BCG) method. The ILU-CGS method provides a good compromise between memory size and convergence rate. The authors have observed a 5x to 7x speedup over standard direct methods in simulations of transient problems containing highly coupled Poisson and continuity equations such as those found in reliability-oriented simulations. The application of SIERRA to parasitic CMOS latchup and dynamic random-access memory single-event-upset studies is described.

Comparison of Slab and Cylinder Expansion Test Geometries for PBX 9501

NASA Astrophysics Data System (ADS)

Jackson, Scott; Anderson, Eric; Aslam, Tariq; Whitley, Von

2017-06-01

The slab expansion test or ``sandwich test'' is the two-dimensional analog of the axisymmetric cylinder expansion test. The test consists of a high-aspect-ratio rectangular cuboid of high explosive with the two large sides confined by a thin metal confiner. Analysis of the confiner motion after the passage of the detonation yields the detonation product isentrope, which is a specialized form of the product equation of state. The slab expansion geometry inherently exhibits a lower product expansion rate and lower plastic work on the confiner than the cylinder expansion geometry. The slab geometry does, however, have a shorter test time. We review recent slab and cylinder expansion data with PBX 9501, the associated equation of state analysis, and the advantages of each geometry for different applications.

Ion Streaming Instabilities in Pair Ion Plasma and Localized Structure with Non-Thermal Electrons

NASA Astrophysics Data System (ADS)

Nasir Khattak, M.; Mushtaq, A.; Qamar, A.

2015-12-01

Pair ion plasma with a fraction of non-thermal electrons is considered. We investigate the effects of the streaming motion of ions on linear and nonlinear properties of unmagnetized, collisionless plasma by using the fluid model. A dispersion relation is derived, and the growth rate of streaming instabilities with effect of streaming motion of ions and non-thermal electrons is calculated. A qausi-potential approach is adopted to study the characteristics of ion acoustic solitons. An energy integral equation involving Sagdeev potential is derived during this process. The presence of the streaming term in the energy integral equation affects the structure of the solitary waves significantly along with non-thermal electrons. Possible application of the work to the space and laboratory plasmas are highlighted.

Material characterization of structural adhesives in the lap shear mode

NASA Technical Reports Server (NTRS)

Sancaktar, E.; Schenck, S. C.

1983-01-01

A general method for characterizing structual adhesives in the bonded lap shear mode is proposed. Two approaches in the form of semiempirical and theoretical approaches are used. The semiempirical approach includes Ludwik's and Zhurkov's equations to describe respectively, the failure stresses in the constant strain rate and constant stress loading modes with the inclusion of the temperature effects. The theoretical approach is used to describe adhesive shear stress-strain behavior with the use of viscoelastic or nonlinear elastic constitutive equations. Two different model adhesives are used in the single lap shear mode with titanium adherends. These adhesives (one of which was developed at NASA Langley Research Center) are currently considered by NASA for possible aerospace applications. Use of different model adhesives helps in assessment of the generality of the method.

Modeling flow stress constitutive behavior of SA508-3 steel for nuclear reactor pressure vessels

NASA Astrophysics Data System (ADS)

Sun, Mingyue; Hao, Luhan; Li, Shijian; Li, Dianzhong; Li, Yiyi

2011-11-01

Based on the measured stress-strain curves under different temperatures and strain rates, a series of flow stress constitutive equations for SA508-3 steel were firstly established through the classical theories on work hardening and softening. The comparison between the experimental and modeling results has confirmed that the established constitutive equations can correctly describe the mechanical responses and microstructural evolutions of the steel under various hot deformation conditions. We further represented a successful industrial application of this model to simulate a forging process for a large conical shell used in a nuclear steam generator, which evidences its practical and promising perspective of our model with an aim of widely promoting the hot plasticity processing for heavy nuclear components of fission reactors.

Effect of misalignment on mechanical behavior of metals in creep. [computer programs

NASA Technical Reports Server (NTRS)

Wu, H. C.

1979-01-01

Application of the endochronic theory of viscoplasticity to creep, creep recovery, and stress relaxation at the small strain and short time range produced the following results: (1) The governing constitutive equations for constant-strain-rate stress-strain behavior, creep, creep recovery, and stress relaxation were derived by imposing appropriate constraints on the general constitutive equation of the endochronic theory. (2) A set of material constants was found which correlate strain-hardening, creep, creep recovery, and stress relaxation. (3) The theory predicts with reasonable accuracy the creep and creep recovery behaviors at short time. (4) The initial strain history prior to the creep stage affects the subsequent creep significantly. (5) A critical stress was established for creep recovery. A computer program, written for the misalignment problem is reported.

The application of dimensional analysis to the problem of solar wind-magnetosphere energy coupling

NASA Technical Reports Server (NTRS)

Bargatze, L. F.; Mcpherron, R. L.; Baker, D. N.; Hones, E. W., Jr.

1984-01-01

The constraints imposed by dimensional analysis are used to find how the solar wind-magnetosphere energy transfer rate depends upon interplanetary parameters. The analyses assume that only magnetohydrodynamic processes are important in controlling the rate of energy transfer. The study utilizes ISEE-3 solar wind observations, the AE index, and UT from three 10-day intervals during the International Magnetospheric Study. Simple linear regression and histogram techniques are used to find the value of the magnetohydrodynamic coupling exponent, alpha, which is consistent with observations of magnetospheric response. Once alpha is estimated, the form of the solar wind energy transfer rate is obtained by substitution into an equation of the interplanetary variables whose exponents depend upon alpha.

The Use of DNS in Turbulence Modeling

NASA Technical Reports Server (NTRS)

Mansour, Nagi N.; Merriam, Marshal (Technical Monitor)

1997-01-01

The use of Direct numerical simulations (DNS) data in developing and testing turbulence models is reviewed. The data is used to test turbulence models at all levels: algebraic, one-equation, two-equation and full Reynolds stress models were tested. Particular examples on the development of models for the dissipation rate equation are presented. Homogeneous flows are used to test new scaling arguments for the various terms in the dissipation rate equation. The channel flow data is used to develop modifications to the equation model that take into account near-wall effects. DNS of compressible flows under mean compression are used in testing new compressible modifications to the two-equation models.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Singh, Manjit; Gupta, R. K.

2017-11-01

In this paper, truncated Laurent expansion is used to obtain the bilinear equation of a nonlinear evolution equation. As an application of Hirota's method, multisoliton solutions are constructed from the bilinear equation. Extending the application of Hirota's method and employing multidimensional Riemann theta function, one and two-periodic wave solutions are also obtained in a straightforward manner. The asymptotic behavior of one and two-periodic wave solutions under small amplitude limits is presented, and their relations with soliton solutions are also demonstrated.

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

Schedule-induced drinking: rate of food delivery and Herrnstein's equation.

PubMed Central

Wetherington, C L

1979-01-01

Schedule-induced drinking was measured in four rats exposed to fixed-time schedules of food ranging from 30 to 480 seconds. Herrnstein's (1970, 1974) equation relating rate of a single response as a hyperbolic function of reinforcement rate provided a good fit to three measures of drinking: lick rate, ingestion rate, and relative time spent drinking. The functions relating the three measures of drinking to reinforcement rate were of similar form. Herrnstein's equation also provided a good description of some already published data on schedule-induced drinking. The fit both to the present data and to the already published data was improved somewhat by computing the measures by subtracting from the time base a latency constant representing the minimal time required to consume the food pellet and travel to the water source. The data from this study provide two correspondences between operant behavior and schedule-induced behavior: (a) conformity to Herrnstein's equation and (b) equivalence of rate and relative time measures. PMID:512568

Chlorite, Biotite, Illite, Muscovite, and Feldspar Dissolution Kinetics at Variable pH and Temperatures up to 280 C

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

Carroll, S.; Smith, M.; Lammers, K.

2016-10-05

Summary Sheet silicates and clays are ubiquitous in geothermal environments. Their dissolution is of interest because this process contributes to scaling reactions along fluid pathways and alteration of fracture surfaces, which could affect reservoir permeability. In order to better predict the geochemical impacts on long-term performance of engineered geothermal systems, we have measured chlorite, biotite, illite, and muscovite dissolution and developed generalized kinetic rate laws that are applicable over an expanded range of solution pH and temperature for each mineral. This report summarizes the rate equations for layered silicates where data were lacking for geothermal systems.

Tailoring drug release rates in hydrogel-based therapeutic delivery applications using graphene oxide

PubMed Central

Zhi, Z. L.; Craster, R. V.

2018-01-01

Graphene oxide (GO) is increasingly used for controlling mass diffusion in hydrogel-based drug delivery applications. On the macro-scale, the density of GO in the hydrogel is a critical parameter for modulating drug release. Here, we investigate the diffusion of a peptide drug through a network of GO membranes and GO-embedded hydrogels, modelled as porous matrices resembling both laminated and ‘house of cards’ structures. Our experiments use a therapeutic peptide and show a tunable nonlinear dependence of the peptide concentration upon time. We establish models using numerical simulations with a diffusion equation accounting for the photo-thermal degradation of fluorophores and an effective percolation model to simulate the experimental data. The modelling yields an interpretation of the control of drug diffusion through GO membranes, which is extended to the diffusion of the peptide in GO-embedded agarose hydrogels. Varying the density of micron-sized GO flakes allows for fine control of the drug diffusion. We further show that both GO density and size influence the drug release rate. The ability to tune the density of hydrogel-like GO membranes to control drug release rates has exciting implications to offer guidelines for tailoring drug release rates in hydrogel-based therapeutic delivery applications. PMID:29445040

Multiphysics Object Oriented Simulation Environment

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

The Multiphysics Object Oriented Simulation Environment (MOOSE) software library developed at Idaho National Laboratory is a tool. MOOSE, like other tools, doesn't actually complete a task. Instead, MOOSE seeks to reduce the effort required to create engineering simulation applications. MOOSE itself is a software library: a blank canvas upon which you write equations and then MOOSE can help you solve them. MOOSE is comparable to a spreadsheet application. A spreadsheet, by itself, doesn't do anything. Only once equations are entered into it will a spreadsheet application compute anything. Such is the same for MOOSE. An engineer or scientist can utilizemore » the equation solvers within MOOSE to solve equations related to their area of study. For instance, a geomechanical scientist can input equations related to water flow in underground reservoirs and MOOSE can solve those equations to give the scientist an idea of how water could move over time. An engineer might input equations related to the forces in steel beams in order to understand the load bearing capacity of a bridge. Because MOOSE is a blank canvas it can be useful in many scientific and engineering pursuits.« less

A Higher Order Iterative Method for Computing the Drazin Inverse

PubMed Central

Soleymani, F.; Stanimirović, Predrag S.

2013-01-01

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747

Reforming the Military Health Care System

DTIC Science & Technology

1988-01-01

Population Model and its Application ," International Journal of Health Services, vol. 10, no. 4 (1980). 7. "Understanding Variations in the Use of... Financial Management (November 1986), pp. 26- 34. 21. Based on the following multiple regression equation: OP/NOR= 0.51 + 0.35x(POP/NOR)-6.84x(CIV/NORxPOP) (t...Military Beneficiary Health Care Survey 95 B Actual and Expected Admission Rates 99 C The Statistical Model of Family Use 103 D The Capitation Budgeting

Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1986-01-01

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

The Arrhenius equation revisited.

PubMed

Peleg, Micha; Normand, Mark D; Corradini, Maria G

2012-01-01

The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T(reference), the plot of Ln k(T) vs. 1/(T+b) will always appear almost perfectly linear. Both the modified Arrhenius model version having the arbitrary constant b, Ln[k(T)/k(T(reference)) = a[1/ (T(reference)+b)-1/ (T+b)], and the exponential model can faithfully describe temperature dependencies traditionally described by the Arrhenius equation without the assumption of a temperature independent "energy of activation." This is demonstrated mathematically and with computer simulations, and with reprocessed classical kinetic data and published food results.

Multivariant function model generation

NASA Technical Reports Server (NTRS)

1974-01-01

The development of computer programs applicable to space vehicle guidance was conducted. The subjects discussed are as follows: (1) determination of optimum reentry trajectories, (2) development of equations for performance of trajectory computation, (3) vehicle control for fuel optimization, (4) development of equations for performance trajectory computations, (5) applications and solution of Hamilton-Jacobi equation, and (6) stresses in dome shaped shells with discontinuities at the apex.

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Infiltration on sloping terrain and its role on runoff generation and slope stability

NASA Astrophysics Data System (ADS)

Loáiciga, Hugo A.; Johnson, J. Michael

2018-06-01

A modified Green-and-Ampt model is formulated to quantify infiltration on sloping terrain underlain by homogeneous soil wetted by surficial water application. This paper's theory for quantifying infiltration relies on the mathematical statement of the coupled partial differential equations (pdes) governing infiltration and runoff. These pdes are solved by employing an explicit finite-difference numerical method that yields the infiltration, the infiltration rate, the depth to the wetting front, the rate of runoff, and the depth of runoff everywhere on the slope during external wetting. Data inputs consist of a water application rate or the rainfall hyetograph of a storm of arbitrary duration, soil hydraulic characteristics and antecedent moisture, and the slope's hydraulic and geometric characteristics. The presented theory predicts the effect an advancing wetting front has on slope stability with respect to translational sliding. This paper's theory also develops the 1D pde governing suspended sediment transport and slope degradation caused by runoff influenced by infiltration. Three examples illustrate the application of the developed theory to calculate infiltration and runoff on a slope and their role on the stability of cohesive and cohesionless soils forming sloping terrain.

SC-GRAPPA: Self-constraint noniterative GRAPPA reconstruction with closed-form solution.

PubMed

Ding, Yu; Xue, Hui; Ahmad, Rizwan; Ting, Samuel T; Simonetti, Orlando P

2012-12-01

Parallel MRI (pMRI) reconstruction techniques are commonly used to reduce scan time by undersampling the k-space data. GRAPPA, a k-space based pMRI technique, is widely used clinically because of its robustness. In GRAPPA, the missing k-space data are estimated by solving a set of linear equations; however, this set of equations does not take advantage of the correlations within the missing k-space data. All k-space data in a neighborhood acquired from a phased-array coil are correlated. The correlation can be estimated easily as a self-constraint condition, and formulated as an extra set of linear equations to improve the performance of GRAPPA. The authors propose a modified k-space based pMRI technique called self-constraint GRAPPA (SC-GRAPPA) which combines the linear equations of GRAPPA with these extra equations to solve for the missing k-space data. Since SC-GRAPPA utilizes a least-squares solution of the linear equations, it has a closed-form solution that does not require an iterative solver. The SC-GRAPPA equation was derived by incorporating GRAPPA as a prior estimate. SC-GRAPPA was tested in a uniform phantom and two normal volunteers. MR real-time cardiac cine images with acceleration rate 5 and 6 were reconstructed using GRAPPA and SC-GRAPPA. SC-GRAPPA showed a significantly lower artifact level, and a greater than 10% overall signal-to-noise ratio (SNR) gain over GRAPPA, with more significant SNR gain observed in low-SNR regions of the images. SC-GRAPPA offers improved pMRI reconstruction, and is expected to benefit clinical imaging applications in the future.

Ground-Water Contributions to Reservoir Storage and the Effect on Estimates of Firm Yield for Reservoirs in Massachusetts

USGS Publications Warehouse

Archfield, Stacey A.; Carlson, Carl S.

2006-01-01

Potential ground-water contributions to reservoir storage were determined for nine reservoirs in Massachusetts that had shorelines in contact with sand and gravel aquifers. The effect of ground water on firm yield was not only substantial, but furthermore, the firm yield of a reservoir in contact with a sand and gravel aquifer was always greater when the ground-water contribution was included in the water balance. Increases in firm yield ranged from 2 to 113 percent, with a median increase in firm yield of 10 percent. Additionally, the increase in firm yield in two reservoirs was greater than 85 percent. This study identified a set of equations that are based on an analytical solution to the ground-water-flow equation for the case of one-dimensional flow in a finite-width aquifer bounded by a linear surface-water feature such as a stream. These equations, which require only five input variables, were incorporated into an existing firm-yield-estimator (FYE) model, and the potential effect of ground water on firm yield was evaluated. To apply the FYE model to a reservoir in Massachusetts, the model requires that the drainage area to the reservoir be clearly defined and that some surface water flows into the reservoir. For surface-water-body shapes having a more realistic representation of a reservoir shoreline than a stream, a comparison of ground-water-flow rates simulated by the ground-water equations with flow rates simulated by a two-dimensional, finite-difference ground-water-flow model indicate that the agreement between the simulated flow rates is within ?10 percent when the ratio of the distance from the reservoir shoreline to the aquifer boundary to the length of shoreline in contact with the aquifer is between values of 0.5 and 3.5. Idealized reservoir-aquifer systems were assumed to verify that the ground-water-flow equations were implemented correctly into the existing FYE model; however, the modified FYE model has not been validated through a comparison of simulated and observed data. A comparison of simulated and observed reservoir water levels would further define limitations to the applicability of the ground-water-flow equations to reservoirs in Massachusetts whose shorelines are in contact with a sand and gravel aquifer.

Regression method for estimating long-term mean annual ground-water recharge rates from base flow in Pennsylvania

USGS Publications Warehouse

Risser, Dennis W.; Thompson, Ronald E.; Stuckey, Marla H.

2008-01-01

A method was developed for making estimates of long-term, mean annual ground-water recharge from streamflow data at 80 streamflow-gaging stations in Pennsylvania. The method relates mean annual base-flow yield derived from the streamflow data (as a proxy for recharge) to the climatic, geologic, hydrologic, and physiographic characteristics of the basins (basin characteristics) by use of a regression equation. Base-flow yield is the base flow of a stream divided by the drainage area of the basin, expressed in inches of water basinwide. Mean annual base-flow yield was computed for the period of available streamflow record at continuous streamflow-gaging stations by use of the computer program PART, which separates base flow from direct runoff on the streamflow hydrograph. Base flow provides a reasonable estimate of recharge for basins where streamflow is mostly unaffected by upstream regulation, diversion, or mining. Twenty-eight basin characteristics were included in the exploratory regression analysis as possible predictors of base-flow yield. Basin characteristics found to be statistically significant predictors of mean annual base-flow yield during 1971-2000 at the 95-percent confidence level were (1) mean annual precipitation, (2) average maximum daily temperature, (3) percentage of sand in the soil, (4) percentage of carbonate bedrock in the basin, and (5) stream channel slope. The equation for predicting recharge was developed using ordinary least-squares regression. The standard error of prediction for the equation on log-transformed data was 9.7 percent, and the coefficient of determination was 0.80. The equation can be used to predict long-term, mean annual recharge rates for ungaged basins, providing that the explanatory basin characteristics can be determined and that the underlying assumption is accepted that base-flow yield derived from PART is a reasonable estimate of ground-water recharge rates. For example, application of the equation for 370 hydrologic units in Pennsylvania predicted a range of ground-water recharge from about 6.0 to 22 inches per year. A map of the predicted recharge illustrates the general magnitude and variability of recharge throughout Pennsylvania.

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.

A Graphical Approach to Evaluating Equating Using Test Characteristic Curves

ERIC Educational Resources Information Center

Wyse, Adam E.; Reckase, Mark D.

2011-01-01

An essential concern in the application of any equating procedure is determining whether tests can be considered equated after the tests have been placed onto a common scale. This article clarifies one equating criterion, the first-order equity property of equating, and develops a new method for evaluating equating that is linked to this…

A novel approach to gravitation from fluid theory: Titius-Bode structures, flat rotation rate of galaxies, and other predictions

NASA Astrophysics Data System (ADS)

Munera, Hector A.

Following the discovery of quantum phenomena at laboratory scale (Couder & Fort 2006), de Broglie pilot wave theory (De Broglie 1962) has been revived under a hydrodynamic guise (Bush 2015). Theoretically, it boils down to solving the transport equations for the energy and linear momentum densities of a postulated fundamental fluid in terms of classical wave equations, which inherently are Lorentz-invariant and scale-invariant. Instead of the conventional harmonic solutions, for astronomical and gravitational problems the novel solutions for the homogeneous wave equation in spherical coordinates are more suitable (Munera et al. 1995, Munera & Guzman 1997, and Munera 2000). Two groups of solutions are particularly relevant: (a) The inherently-quantized helicoidal solutions that may be applicable to describe spiral galaxies, and (b) The non-harmonic solutions with time (t) and distance (r) entangled in the single variable q = Ct/r (C is the two-way local electromagnetic speed). When these functions are plotted against 1/q they manifestly depict quantum effects in the near field, and Newtonian-like gravity in the far-field. The near-field predicts quantized effects similar to ring structures and to Titius-Bode structures, both in our own solar system and in exoplanets, the correlation between predicted and observed structures being typically larger than 99 per cent. In the far-field, some non-harmonic functions have a rate of decrement with distance slower than inverse-square thus explaining the flat rotation rate of galaxies. Additional implications for Trojan orbits, and quantized effects in photon deflection were also noted.

Preconditioned conjugate residual methods for the solution of spectral equations

NASA Technical Reports Server (NTRS)

Wong, Y. S.; Zang, T. A.; Hussaini, M. Y.

1986-01-01

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

An Argument Against Augmenting the Lagrangean for Nonholonomic Systems

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Hodges, Dewey H.

2009-01-01

Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. An example has been proposed in support of augmentation and purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations; this paper shows that in fact the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton-Euler method, are verified by using Kane's method and a new approach to determining the directions of constraint forces. A correct application of the Newton-Euler method reproduces valid equations.

A Langevin equation for the rates of currency exchange based on the Markov analysis

NASA Astrophysics Data System (ADS)

Farahpour, F.; Eskandari, Z.; Bahraminasab, A.; Jafari, G. R.; Ghasemi, F.; Sahimi, Muhammad; Reza Rahimi Tabar, M.

2007-11-01

We propose a method for analyzing the data for the rates of exchange of various currencies versus the U.S. dollar. The method analyzes the return time series of the data as a Markov process, and develops an effective equation which reconstructs it. We find that the Markov time scale, i.e., the time scale over which the data are Markov-correlated, is one day for the majority of the daily exchange rates that we analyze. We derive an effective Langevin equation to describe the fluctuations in the rates. The equation contains two quantities, D and D, representing the drift and diffusion coefficients, respectively. We demonstrate how the two coefficients are estimated directly from the data, without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the U.S. dollar.

Theoretical study of low-frequency noise and amplitude – frequency characteristics of a semiconductor laser with a fiber Bragg grating

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

Kurnosov, V D; Kurnosov, K V

2013-09-30

Using the rate equations for the density of photons and charge carriers, we have studied the amplitude low-frequency noise of a fibre Bragg grating semiconductor laser. The calculations rely on two versions of the rate equation for the carriers, characterised by the presence of the optical confinement coefficient for the term, which takes into account the rate of stimulated recombination. It is shown that the relative noise intensity, which is calculated by using the rate equation for the carriers without optical confinement, agrees better with the experimental results. The calculation of the amplitude – frequency characteristics (AFCs) has shown thatmore » it is impossible to give preference to any one of these systems, since the AFCs for the two versions of the rate equations for the carriers coincide. (lasers)« less

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…

On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

ERIC Educational Resources Information Center

Savoye, Philippe

2009-01-01

In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

PubMed

Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications

PubMed Central

W. Hasan, W. Z.

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554

Vacuum-bag-only processing of composites

NASA Astrophysics Data System (ADS)

Thomas, Shad

Ultrasonic imaging in the C-scan mode in conjunction with the amplitude of the reflected signal was used to measure flow rates of an epoxy resin film penetrating through the thickness of single layers of woven carbon fabric. Assemblies, comprised of a single layer of fabric and film, were vacuum-bagged and ultrasonically scanned in a water tank during impregnation at 50°C, 60°C, 70°C, and 80°C. Measured flow rates were plotted versus inverse viscosity to determine the permeability in the thin film, non-saturated system. The results demonstrated that ultrasonic imaging in the C-scan mode is an effective method of measuring z-direction resin flow through a single layer of fabric. The permeability values determined in this work were consistent with permeability values reported in the literature. Capillary flow was not observed at the temperatures and times required for pressurized flow to occur. The flow rate at 65°C was predicted from the linear plot of flow rate versus inverse viscosity. The effects of fabric architecture on through-thickness flow rates during impregnation of an epoxy resin film were measured by ultrasonic imaging. Multilayered laminates comprised of woven carbon fabrics and epoxy films (prepregs) were fabricated by vacuum-bagging. Ultrasonic imaging was performed in a heated water tank (65°C) during impregnation. Impregnation rates showed a strong dependence on fabric architecture, despite similar areal densities. Impregnation rates are directly affected by inter-tow spacing and tow nesting, which depend on fabric architecture, and are indirectly affected by areal densities. A new method of predicting resin infusion rates in prepreg and resin film infusion processes was proposed. The Stokes equation was used to derive an equation to predict the impregnation rate of laminates as a function of fabric architecture. Flow rate data previously measured by ultrasound was analyzed with the new equation and the Kozeny-Carman equation. A fiber interaction parameter was determined as a function of fabric architecture. The derived equation is straight-forward to use, unlike the Kozeny-Carman equation. The results demonstrated that the newly derived equation can be used to predict the resin infusion rate of multilayer laminates.

Normative equations for central augmentation index: assessment of inter-population applicability and how it could be improved

PubMed Central

Jeroncic, Ana; Gunjaca, Grgo; Mrsic, Danijela Budimir; Mudnic, Ivana; Brizic, Ivica; Polasek, Ozren; Boban, Mladen

2016-01-01

Common reference values of arterial stiffness indices could be effective screening tool in detecting vascular phenotypes at risk. However, populations of the same ethnicity may differ in vascular phenotype due to different environmental pressure. We examined applicability of normative equations for central augmentation index (cAIx) derived from Danish population with low cardiovascular risk on the corresponding Croatian population from the Mediterranean area. Disagreement between measured and predicted cAIx was assessed by Bland-Altman analysis. Both, cAIx-age distribution and normative equation fitted on Croatian data were highly comparable to Danish low-risk sample. Contrarily, Bland-Altman analysis of cAIx disagreement revealed a curvilinear deviation from the line of full agreement indicating that the equations were not equally applicable across age ranges. Stratification of individual data into age decades eliminated curvilinearity in all but the 30–39 (men) and 40–49 (women) decades. In other decades, linear disagreement independent of age persisted indicating that cAIx determinants other than age were not envisaged/compensated for by proposed equations. Therefore, established normative equations are equally applicable to both Nordic and Mediterranean populations but are of limited use. If designed for narrower age ranges, the equations’ sensitivity in detecting vascular phenotypes at risk and applicability to different populations could be improved. PMID:27230110

[Effect of temperature on the aerobic degradation of vitamin C in citric fruit juices].

PubMed

Alvarado, J D; Palacios Viteri, N

1989-12-01

By means of the method of the 2,4-dinitrophenylhydrazine the total ascorbic acid content in lima, lemon, tangerine and grapefruit juices, fresh and kept at four temperatures and different times, was determined. It was confirmed that in all the cases, the aerobic degradation of ascorbic acid follows a kinetic first order and that the values of the reaction rate are different between species and even between varieties of lemon and tangerine. The values of the equation terms are reported, and examples of application given. Within a range from 20 degrees to 92 degrees C, the effect of temperature on the velocity of the ascorbic acid degradation is described satisfactorily following the Arrhenius equation, in accordance with which, the corresponding values of activation energy are calculated to compare them with other published values. With the simple application of the method, in two steps, and considering that the L-ascorbic acid and the L-dehydroascorbic acid are predominant, the results can be used to calculate the vitamin C losses in citric fruit juices, indicated when they are processed by traditional thermal treatments.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Investigating inhomogeneous Szekeres models and their applications to precision cosmology

NASA Astrophysics Data System (ADS)

Peel, Austin Chandler

Exact solutions of Einstein's field equations that can describe the evolution of complex structures in the universe provide complementary frameworks to standard perturbation theory in which to analyze cosmological and astrophysical phenomena. The flexibility and generality of the inhomogeneous and anisotropic Szekeres metric make it the best known exact solution to explore nonlinearities in the universe. We study applications of Szekeres models to precision cosmology, focusing on the influence of inhomogeneities in two primary contexts---the growth rate of cosmic structures and biases in distance determinations to remote sources. We first define and derive evolution equations for a Szekeres density contrast, which quantifies exact deviations from a smooth background cosmology. Solving these equations and comparing to the usual perturbative approach, we find that for models with the same matter content, the Szekeres growth rate is larger through the matter-dominated cosmic era. Including a cosmological constant, we consider exact global perturbations, as well as the evolution of a single extended structure surrounded by an almost homogeneous background. For the former, we use growth data to obtain a best fit Szekeres model and find that it can fit the data as well as the standard Lambda-Cold Dark Matter (LCDM) cosmological model but with different cosmological parameters. Next, to study effects of inhomogeneities on distance measures, we build an exact relativistic Swiss-cheese model of the universe, where a large number of non-symmetric and randomly placed Szekeres structures are embedded within a LCDM background. Solving the full relativistic propagation equations, light beams are traced through the model, where they traverse the inhomogeneous structures in a way that mimics the paths of real light beams in the universe. For beams crossing a single structure, their magnification or demagnification reflects primarily the net density encountered along the path. Despite nontrivial evolution and density distributions of the structures, the effect of tidal shearing on the beams remains small. Finally, we study source magnification probability distributions for various redshifts, finding a limitation of the models in that the distributions do not consistently resemble those of gravitational lensing analyses in cosmological simulations.

General existence principles for Stieltjes differential equations with applications to mathematical biology

NASA Astrophysics Data System (ADS)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

A gradual update method for simulating the steady-state solution of stiff differential equations in metabolic circuits.

PubMed

Shiraishi, Emi; Maeda, Kazuhiro; Kurata, Hiroyuki

2009-02-01

Numerical simulation of differential equation systems plays a major role in the understanding of how metabolic network models generate particular cellular functions. On the other hand, the classical and technical problems for stiff differential equations still remain to be solved, while many elegant algorithms have been presented. To relax the stiffness problem, we propose new practical methods: the gradual update of differential-algebraic equations based on gradual application of the steady-state approximation to stiff differential equations, and the gradual update of the initial values in differential-algebraic equations. These empirical methods show a high efficiency for simulating the steady-state solutions for the stiff differential equations that existing solvers alone cannot solve. They are effective in extending the applicability of dynamic simulation to biochemical network models.

Kinetic Glomerular Filtration Rate Equation Can Accommodate a Changing Body Volume: Derivation and Usage of the Formula.

PubMed

Chen, Sheldon

2018-05-22

Ascertaining a patient's kidney function is more difficult to do when the serum creatinine is changing than when it is stable. To accomplish the task, various kinetic clearance equations have been developed. To date, however, none of them have allowed for ongoing changes to the creatinine's volume of distribution. These diluting or concentrating effects on the [creatinine] can greatly impact the accuracy of kidney function assessment. Described herein is a model of creatinine kinetics that also accommodates volume changes. The differential equation is solved for the kinetic glomerular filtration rate (GFR), which is helpful information to the physician. Some of the equation's discontinuities, such as from dividing by a volume rate of zero, can be resolved by using limits. Being "volume-capable," the new kinetic equation reveals how a changing volume influences the maximum rate of rise in [creatinine], a parameter that heretofore was chosen empirically. To show the advantages of incorporating volume, the new and old kinetic equations are applied to a clinical case of overzealous fluid resuscitation. Appropriately, when the volume gain's dilution of [creatinine] is taken into account, the creatinine clearance is calculated to be substantially lower. In conclusion, the kinetic GFR equation has been upgraded to handle volume changes simultaneously with [creatinine] changes. Copyright © 2018. Published by Elsevier Inc.

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.

High Strain Rate Deformation Modeling of a Polymer Matrix Composite. Part 2; Composite Micromechanical Model

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Stouffer, Donald C.

1998-01-01

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this second paper of a two part report, a three-dimensional composite micromechanical model is described which allows for the analysis of the rate dependent, nonlinear deformation response of a polymer matrix composite. Strain rate dependent inelastic constitutive equations utilized to model the deformation response of a polymer are implemented within the micromechanics method. The deformation response of two representative laminated carbon fiber reinforced composite materials with varying fiber orientation has been predicted using the described technique. The predicted results compare favorably to both experimental values and the response predicted by the Generalized Method of Cells, a well-established micromechanics analysis method.

The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?

PubMed

Goličnik, Marko

2013-08-01

A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.

On the MAF solution of the uniformly lengthening pendulum via change of independent variable in the Bessel's equation

NASA Astrophysics Data System (ADS)

Deniz, Coşkun

Common recipe for the Lengthening Pendulum (LP) involves some change of variables to give a relationship with the Bessel's equation. In this work, semiclassical MAF (Modified Airy Function) solution of the LP is being obtained by first transforming the related Bessel's equation into the normal form via the suggested change of independent variable just as one of our recent work regarding the JWKB solution of the LP in (Deniz, 2017). MAF approximation of the first order Bessel Functions (ν = 1) of both type along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (ν = 0 and 2) by the recursion relations. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is small, MAF solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined via the use of MAF applicability criterion given in the literature. As a result, the semiclassical MAF method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully just as our previous work regarding the JWKB solution of the LP. Interestingly, we have very accurate results in the entire domain except for x ≈ 0 .

Two-dimensional extended fluid model for a dc glow discharge with nonlocal ionization source term

NASA Astrophysics Data System (ADS)

Rafatov, Ismail; Bogdanov, Eugeny; Kudryavtsev, Anatoliy

2013-09-01

Numerical techniques applied to the gas discharge plasma modelling are generally grouped into fluid and kinetic (particle) methods, and their combinations which lead to the hybrid models. Hybrid models usually employ Monte Carlo method to simulate fast electron dynamics, while slow plasma species are described as fluids. However, since fast electrons contribution to these models is limited to deriving the ionization rate distribution, their effect can be expressed by the analytical approximation of the ionization source function, and then integrating it into the fluid model. In the context of this approach, we incorporated effect of fast electrons into the ``extended fluid model'' of glow discharge, using two spatial dimensions. Slow electrons, ions and excited neutral species are described by the fluid plasma equations. Slow electron transport (diffusion and mobility) coefficients as well as electron induced reaction rates are determined from the solutions of the electron Boltzmann equation. The self-consistent electric field is calculated using the Poisson equation. We carried out test calculations for the discharge in argon gas. Comparison with the experimental data as well as with the hybrid model results exhibits good applicability of the proposed model. The work was supported by the joint research grant from the Scientific and Technical Research Council of Turkey (TUBITAK) 212T164 and Russian Foundation for Basic Research (RFBR).

Alternatives for the Bedside Schwartz Equation to Estimate Glomerular Filtration Rate in Children.

PubMed

Pottel, Hans; Dubourg, Laurence; Goffin, Karolien; Delanaye, Pierre

2018-01-01

The bedside Schwartz equation has long been and still is the recommended equation to estimate glomerular filtration rate (GFR) in children. However, this equation is probably best suited to estimate GFR in children with chronic kidney disease (reduced GFR) but is not optimal for children with GFR >75 mL/min/1.73 m 2 . Moreover, the Schwartz equation requires the height of the child, information that is usually not available in the clinical laboratory. This makes automatic reporting of estimated glomerular filtration rate (eGFR) along with serum creatinine impossible. As the majority of children (even children referred to nephrology clinics) have GFR >75 mL/min/1.73 m 2 , it might be interesting to evaluate possible alternatives to the bedside Schwartz equation. The pediatric form of the Full Age Spectrum (FAS) equation offers an alternative to Schwartz, allowing automatic reporting of eGFR since height is not necessary. However, when height is involved in the FAS equation, the equation is essentially equal to the Schwartz equation for children, but there are large differences for adolescents. Combining standardized biomarkers increases the prediction performance of eGFR equations for children, reaching P10 ≈ 45% and P30 ≈ 90%. There are currently good and simple alternatives to the bedside Schwartz equation, but the more complex equations combining serum creatinine, serum cystatin C, and height show the highest accuracy and precision. Copyright © 2017 National Kidney Foundation, Inc. Published by Elsevier Inc. All rights reserved.

Optically Pumped Coherent Mechanical Oscillators: The Laser Rate Equation Theory and Experimental Verification

DTIC Science & Technology

2012-10-23

Naeini A H, Hill J T, Krause A, Groblacher S, Aspelmeyer M and Painter O 2011 Nature 478 89 [14] Siegman A E 1986 Lasers (Sausalito, CA: University... laser rate equation theory and experimental verification 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT...coherent mechanical oscillators: the laser rate equation theory and experimental verification J B Khurgin1, M W Pruessner2,3, T H Stievater2 and W S

FDTD Simulation on Terahertz Waves Propagation Through a Dusty Plasma

NASA Astrophysics Data System (ADS)

Wang, Maoyan; Zhang, Meng; Li, Guiping; Jiang, Baojun; Zhang, Xiaochuan; Xu, Jun

2016-08-01

The frequency dependent permittivity for dusty plasmas is provided by introducing the charging response factor and charge relaxation rate of airborne particles. The field equations that describe the characteristics of Terahertz (THz) waves propagation in a dusty plasma sheath are derived and discretized on the basis of the auxiliary differential equation (ADE) in the finite difference time domain (FDTD) method. Compared with numerical solutions in reference, the accuracy for the ADE FDTD method is validated. The reflection property of the metal Aluminum interlayer of the sheath at THz frequencies is discussed. The effects of the thickness, effective collision frequency, airborne particle density, and charge relaxation rate of airborne particles on the electromagnetic properties of Terahertz waves through a dusty plasma slab are investigated. Finally, some potential applications for Terahertz waves in information and communication are analyzed. supported by National Natural Science Foundation of China (Nos. 41104097, 11504252, 61201007, 41304119), the Fundamental Research Funds for the Central Universities (Nos. ZYGX2015J039, ZYGX2015J041), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20120185120012)

Approximate solutions to Mathieu's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

Sympathetic influence on the pupillary light response in three red-eared slider turtles (Trachemys scripta elegans).

PubMed

Dearworth, James R; Cooper, Lori J

2008-01-01

We investigated the effects of phenylephrine and its combination with vecuronium bromide on the iris of turtles to determine if the pupillary light response is affected by sympathetic innervation. Three red-eared slider turtles, Trachemys scripta elegans. Diameters of light-adapted pupils were tracked before and after topical application of drugs to eyes. Phenylephrine was applied independently; in a second group of trials, vecuronium bromide was applied with phenylephrine. Rates of pupil dilation in response to drugs were quantified by fitting data with time constant (tau) equations. Phenylephrine dilated the pupil 24%, tau = 29 min. Combination of phenylephrine with vecuronium bromide increased the pupil size 35%, and dilation was more rapid, tau = 14 min. We also were able to predict these time constants by performing different mathematical operations with an equation developed from a prior study using only vecuronium bromide. When this equation was subtracted from the equation for eyes treated with both vecuronium bromide and phenylephrine, the difference gave the observed tau for phenylephrine; when added to phenylephrine, the sum closely matched the tau for eyes treated with vecuronium bromide and phenylephrine. Further, the tau for vecuronium bromide treated eyes was predicted by subtracting the equation for phenylephrine from that of eyes treated with both vecuronium bromide and phenylephrine. Our results suggest that sympathetic innervation interacts with the parasympathetic pathway to control the pupillary light response in turtles.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by Arrhenius equation.

PubMed

Nicoletti, Maria Aparecida; Siqueira, Evandro Luiz; Bombana, Antonio Carlos; Oliveira, Gabriella Guimarães de

2009-01-01

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 degrees C) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 degrees C (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 degrees C, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 degrees C. This model, however, makes it possible to calculate shelf-life at any other given temperature.

19 CFR Appendix B to Part 191 - Sample Formats for Applications for Specific Manufacturing Drawback Rulings

Code of Federal Regulations, 2011 CFR

2011-04-01

.... When applicable, give equations of the chemical reactions. The attachment of a flow chart in addition... measurement of the merchandise used. This loss or gain is caused by atmospheric conditions, chemical reactions... finished article is intended. When applicable, give equations of the chemical reactions. The attachment of...

19 CFR Appendix B to Part 191 - Sample Formats for Applications for Specific Manufacturing Drawback Rulings

Code of Federal Regulations, 2014 CFR

2014-04-01

.... When applicable, give equations of the chemical reactions. The attachment of a flow chart in addition... measurement of the merchandise used. This loss or gain is caused by atmospheric conditions, chemical reactions... finished article is intended. When applicable, give equations of the chemical reactions. The attachment of...

19 CFR Appendix B to Part 191 - Sample Formats for Applications for Specific Manufacturing Drawback Rulings

Code of Federal Regulations, 2013 CFR

2013-04-01

.... When applicable, give equations of the chemical reactions. The attachment of a flow chart in addition... measurement of the merchandise used. This loss or gain is caused by atmospheric conditions, chemical reactions... finished article is intended. When applicable, give equations of the chemical reactions. The attachment of...

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Modeling of adsorption dynamics at air-liquid interfaces using statistical rate theory (SRT).

PubMed

Biswas, M E; Chatzis, I; Ioannidis, M A; Chen, P

2005-06-01

A large number of natural and technological processes involve mass transfer at interfaces. Interfacial properties, e.g., adsorption, play a key role in such applications as wetting, foaming, coating, and stabilizing of liquid films. The mechanistic understanding of surface adsorption often assumes molecular diffusion in the bulk liquid and subsequent adsorption at the interface. Diffusion is well described by Fick's law, while adsorption kinetics is less understood and is commonly described using Langmuir-type empirical equations. In this study, a general theoretical model for adsorption kinetics/dynamics at the air-liquid interface is developed; in particular, a new kinetic equation based on the statistical rate theory (SRT) is derived. Similar to many reported kinetic equations, the new kinetic equation also involves a number of parameters, but all these parameters are theoretically obtainable. In the present model, the adsorption dynamics is governed by three dimensionless numbers: psi (ratio of adsorption thickness to diffusion length), lambda (ratio of square of the adsorption thickness to the ratio of adsorption to desorption rate constant), and Nk (ratio of the adsorption rate constant to the product of diffusion coefficient and bulk concentration). Numerical simulations for surface adsorption using the proposed model are carried out and verified. The difference in surface adsorption between the general and the diffusion controlled model is estimated and presented graphically as contours of deviation. Three different regions of adsorption dynamics are identified: diffusion controlled (deviation less than 10%), mixed diffusion and transfer controlled (deviation in the range of 10-90%), and transfer controlled (deviation more than 90%). These three different modes predominantly depend on the value of Nk. The corresponding ranges of Nk for the studied values of psi (10(-2)

Translational control of a graphically simulated robot arm by kinematic rate equations that overcome elbow joint singularity

NASA Technical Reports Server (NTRS)

Barker, L. K.; Houck, J. A.; Carzoo, S. W.

1984-01-01

An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.

Stochastic modeling of stock price process induced from the conjugate heat equation

NASA Astrophysics Data System (ADS)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Non-equilibrium reaction rates in chemical kinetic equations

NASA Astrophysics Data System (ADS)

Gorbachev, Yuriy

2018-05-01

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the chemical kinetic equations has been derived. Corresponding one-temperature non-equilibrium reaction rates are expressed in terms of specific heat capacities of the species participate in the chemical reactions, bracket integrals connected with the internal energy transfer in inelastic non-reactive collisions and energy transfer coefficients. Reactions of dissociation/recombination of homonuclear and heteronuclear diatomic molecules are considered. It is shown that all reaction rates are the complex functions of the species densities, similarly to the unimolecular reaction rates. For determining the rate coefficients it is recommended to tabulate corresponding bracket integrals, additionally to the equilibrium rate constants. Correlation of the obtained results with the irreversible thermodynamics is established.

Development of the Wake Behind a Circular Cylinder Impulsively Started into Rotatory and Rectilinear Motion: Intermediate Rotation Rates

DTIC Science & Technology

1991-01-01

cylindre fixe ou en rotation. Effet Magnus . J. Mec. 14, 109-134. Taneda, S. 1977 Visual study of unsteady separated flows around bodies. Prog. Aero...enhancement schemes employing the Magnus effect (Swanson 1961). Rotating all or part of a body may also have applications in active or feedback control of...and yt into the governing equations in the generalized coordinate system. In this study, the body-fitted grid is simply one of cylindrical polar

Theory of ion-matrix-sheath dynamics

NASA Astrophysics Data System (ADS)

Kos, L.; Tskhakaya, D. D.

2018-01-01

The time evolution of a one-dimensional, uni-polar ion sheath (an "ion matrix sheath") is investigated. The analytical solutions for the ion-fluid and Poisson's equations are found for an arbitrary time dependence of the wall-applied negative potential. In the case that the wall potential is large and remains constant after its ramp-up application, the explicit time dependencies of the sheath's parameters during the initial stage of the process are given. The characteristic rate of approaching the stationary state, satisfying the Child-Langmuir law, is determined.

Aspects and applications of patched grid calculations

NASA Technical Reports Server (NTRS)

Walters, R. W.; Switzer, G. F.; Thomas, J. L.

1986-01-01

Patched grid calculations within the framework of an implicit, flux-vector split upwind/relaxation algorithm for the Euler equations are presented. The effect of a metric-discontinuous interface on the convergence rate of the algorithm is discussed along with the spatial accuracy of the solution and the effect of curvature along an interface. Results are presented and discussed for the free-stream problem, shock reflection problem, supersonic inlet with a 5 degree ramp, aerodynamically choked inlet, and three-dimensional analytic forebody.

Application of the endochronic theory of viscoplasticity to solid propellants and sandasphalt concrete

NASA Technical Reports Server (NTRS)

Peng, S. T. J.; Valanis, K. C.

1977-01-01

Solid propellants, sand-asphalt concrete and hard plastics showed rate sensitive mechanical behavior which, in addition, indicated that these materials have a permanent memory of the strain (or loading) path by which their present state was attained. A constitutive equation was formulated in general three dimensional tensorial form by means of irreversible thermodynamics. By using a very simple analytical form, it was shown that the mechanical behavior of solid propellants and sand-asphalt concrete can be readily described.

Near contact phenomena and transient effects in far infrared photoconductors

NASA Technical Reports Server (NTRS)

Haegel, Nancy M.

1989-01-01

A combination of experimental and modeling work is summarized in two areas: first, the calculation of excess free carrier and space charge distributions near contacts and their effects on device resistivity, and second, the characterization of a slow transient response (tau approx. 1 sec) in Ge:Be detectors which is due to trapping associated with Be(+) formation. In both cases, analytical models, based on continuity and rate equations, have been developed to enable the application of these findings to a wide variety of photoconductor materials.

A Realizable Reynolds Stress Algebraic Equation Model

NASA Technical Reports Server (NTRS)

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

1993-01-01

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

The Aerodynamics of Axisymmetric Blunt Bodies Flying at Angle of Attack

NASA Technical Reports Server (NTRS)

Schoenenberger, Mark; Kutty, Prasad; Queen, Eric; Karlgaard, Chris

2014-01-01

The Mars Science Laboratory entry capsule is used as an example to demonstrate how a blunt body of revolution must be treated as asymmetric in some respects when flying at a non-zero trim angle of attack. A brief description of the axisymmetric moment equations are provided before solving a system of equations describing the lateral-directional moment equations for a blunt body trimming at an angle of attack. Simplifying assumptions are made which allow the solution to the equations to be rearranged to relate the roll and yaw stability with sideslip angle to the frequency of oscillation of the vehicle body rates. The equations show that for a blunt body the roll and yaw rates are in phase and proportional to each other. The ratio of the rates is determined by the static stability coefficients and mass properties about those axes. A trajectory simulation is used to validate the static yaw stability parameter identification equation and a simple method of identifying the oscillation frequency from the body rates. The approach is shown to successfully extract the modeled yaw stability coefficient along a simulated Mars entry in agreement with data earlier analysis of MSL flight data.

PC-CUBE: A Personal Computer Based Hypercube

NASA Technical Reports Server (NTRS)

Ho, Alex; Fox, Geoffrey; Walker, David; Snyder, Scott; Chang, Douglas; Chen, Stanley; Breaden, Matt; Cole, Terry

1988-01-01

PC-CUBE is an ensemble of IBM PCs or close compatibles connected in the hypercube topology with ordinary computer cables. Communication occurs at the rate of 115.2 K-band via the RS-232 serial links. Available for PC-CUBE is the Crystalline Operating System III (CrOS III), Mercury Operating System, CUBIX and PLOTIX which are parallel I/O and graphics libraries. A CrOS performance monitor was developed to facilitate the measurement of communication and computation time of a program and their effects on performance. Also available are CXLISP, a parallel version of the XLISP interpreter; GRAFIX, some graphics routines for the EGA and CGA; and a general execution profiler for determining execution time spent by program subroutines. PC-CUBE provides a programming environment similar to all hypercube systems running CrOS III, Mercury and CUBIX. In addition, every node (personal computer) has its own graphics display monitor and storage devices. These allow data to be displayed or stored at every processor, which has much instructional value and enables easier debugging of applications. Some application programs which are taken from the book Solving Problems on Concurrent Processors (Fox 88) were implemented with graphics enhancement on PC-CUBE. The applications range from solving the Mandelbrot set, Laplace equation, wave equation, long range force interaction, to WaTor, an ecological simulation.

Comparing National Water Model Inundation Predictions with Hydrodynamic Modeling

NASA Astrophysics Data System (ADS)

Egbert, R. J.; Shastry, A.; Aristizabal, F.; Luo, C.

2017-12-01

The National Water Model (NWM) simulates the hydrologic cycle and produces streamflow forecasts, runoff, and other variables for 2.7 million reaches along the National Hydrography Dataset for the continental United States. NWM applies Muskingum-Cunge channel routing which is based on the continuity equation. However, the momentum equation also needs to be considered to obtain better estimates of streamflow and stage in rivers especially for applications such as flood inundation mapping. Simulation Program for River NeTworks (SPRNT) is a fully dynamic model for large scale river networks that solves the full nonlinear Saint-Venant equations for 1D flow and stage height in river channel networks with non-uniform bathymetry. For the current work, the steady-state version of the SPRNT model was leveraged. An evaluation on SPRNT's and NWM's abilities to predict inundation was conducted for the record flood of Hurricane Matthew in October 2016 along the Neuse River in North Carolina. This event was known to have been influenced by backwater effects from the Hurricane's storm surge. Retrospective NWM discharge predictions were converted to stage using synthetic rating curves. The stages from both models were utilized to produce flood inundation maps using the Height Above Nearest Drainage (HAND) method which uses the local relative heights to provide a spatial representation of inundation depths. In order to validate the inundation produced by the models, Sentinel-1A synthetic aperture radar data in the VV and VH polarizations along with auxiliary data was used to produce a reference inundation map. A preliminary, binary comparison of the inundation maps to the reference, limited to the five HUC-12 areas of Goldsboro, NC, yielded that the flood inundation accuracies for NWM and SPRNT were 74.68% and 78.37%, respectively. The differences for all the relevant test statistics including accuracy, true positive rate, true negative rate, and positive predictive value were found to be statistically significant. Further research will include a larger segment of the Neuse River to make more confident conclusions on how SPRNT can improve on NWM predictions. An interactive Tethys web application was developed to display and compare the inundation maps.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

Newton's laws of motion in the form of a Riccati equation.

PubMed

Nowakowski, Marek; Rosu, Haret C

2002-04-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Existence and stability of periodic solutions of quasi-linear Korteweg — de Vries equation

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Kolesov, A. Yu; Preobrazhenskaia, M. M.

2017-01-01

We consider the scalar nonlinear differential-difference equation with two delays, which models electrical activity of a neuron. Under some additional suppositions for this equation well known method of quasi-normal forms can be applied. Its essence lies in the formal normalization of the Poincare - Dulac obtaining quasi-normal form and the subsequent application of the theorems of conformity. In this case, the result of the application of quasi-normal forms is a countable system of differential-difference equations, which can be turned into a boundary value problem of the Korteweg - de Vries equation. The investigation of this boundary value problem allows us to draw a conclusion about the behaviour of the original equation. Namely, for a suitable choice of parameters in the framework of this equation is implemented buffer phenomenon consisting in the presence of the bifurcation mechanism for the birth of an arbitrarily large number of stable cycles.

Detailed Analysis for the Solvolysis of Isopropenyl Chloroformate

PubMed Central

D’Souza, Malcolm John; Shuman, Kevin Edward; Omondi, Arnold Ochieng; Kevill, Dennis Neil

2011-01-01

The specific rates of solvolysis (including those obtained from the literature) of isopropenyl chloroformate (1) are analyzed using the extended Grunwald-Winstein equation, involving the NT scale of solvent nucleophilicity (S-methyldibenzothiophenium ion) combined with a YCl scale based on 1-adamantyl chloride solvolysis. A similarity model approach, using phenyl chloroformate solvolyses for comparison, indicated a dominant bimolecular carbonyl-addition mechanism for the solvolyses of 1 in all solvents except 97% 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP). An extensive evaluation of the outcomes acquired through the application of the extended Grunwald-Winstein equation resulted in the proposal of an addition-elimination mechanism dominating in most of the solvents, but in 97-70% HFIP, and 97% 2,2,2-trifluoroethanol (TFE), it is proposed that a superimposed unimolecular (SN1) type ionization is making a significant contribution. PMID:21881623

Dynamics and thermodynamics of open chemical networks

NASA Astrophysics Data System (ADS)

Esposito, Massimiliano

Open chemical networks (OCN) are large sets of coupled chemical reactions where some of the species are chemostated (i.e. continuously restored from the environment). Cell metabolism is a notable example of OCN. Two results will be presented. First, dissipation in OCN operating in nonequilibrium steady-states strongly depends on the network topology (algebraic properties of the stoichiometric matrix). An application to oligosaccharides exchange dynamics performed by so-called D-enzymes will be provided. Second, at low concentration the dissipation of OCN is in general inaccurately predicted by deterministic dynamics (i.e. nonlinear rate equations for the species concentrations). In this case a description in terms of the chemical master equation is necessary. A notable exception is provided by so-called deficiency zero networks, i.e. chemical networks with no hidden cycles present in the graph of reactant complexes.

Larvicidal activity of synthetic disinfectants and antibacterial soaps against mosquito, Culex quinquefasciatus (Diptera: Culicidae).

PubMed

Xue, Rui-De; Qualls, Whitney A

2013-01-01

Seven commercial synthetic disinfectant and antibacterial soap products were evaluated as mosquito larvicides against Culex quinquefasciatus Say in the laboratory. Three aerosol disinfectant products, at 0.01% concentration resulted in 58-76% mortality of laboratory-reared fourth instar mosquito larvae at 24 h posttreatment. Four antibacterial soap products at 0.0001% concentration resulted in 88-100% larval mortality at 24 h posttreatment. The active ingredient of the antibacterial soap products, triclosan (0.1%) resulted in 74% larval mortality. One of the antibacterial soap products, Equate caused the highest mosquito larval mortality in the laboratory. Equate antibacterial soap at the application rate of 0.000053 ppm resulted in 90% mortality of the introduced fourth instar larvae of Cx. quinquesfasicatus in the outdoor pools. In laboratory and field bioassays, the antibacterial soap resulted in significant larval mosquito mortality.

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

NASA Technical Reports Server (NTRS)

Thomas, P. D.

1980-01-01

A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Warming, R. F.; Harten, A.

1983-01-01

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Application of mixing-controlled combustion models to gas turbine combustors

NASA Technical Reports Server (NTRS)

Nguyen, Hung Lee

1990-01-01

Gas emissions were studied from a staged Rich Burn/Quick-Quench Mix/Lean Burn combustor were studied under test conditions encountered in High Speed Research engines. The combustor was modeled at conditions corresponding to different engine power settings, and the effect of primary dilution airflow split on emissions, flow field, flame size and shape, and combustion intensity, as well as mixing, was investigated. A mathematical model was developed from a two-equation model of turbulence, a quasi-global kinetics mechanism for the oxidation of propane, and the Zeldovich mechanism for nitric oxide formation. A mixing-controlled combustion model was used to account for turbulent mixing effects on the chemical reaction rate. This model assumes that the chemical reaction rate is much faster than the turbulent mixing rate.

Time dependent reliability model incorporating continuum damage mechanics for high-temperature ceramics

NASA Technical Reports Server (NTRS)

Duffy, Stephen F.; Gyekenyesi, John P.

1989-01-01

Presently there are many opportunities for the application of ceramic materials at elevated temperatures. In the near future ceramic materials are expected to supplant high temperature metal alloys in a number of applications. It thus becomes essential to develop a capability to predict the time-dependent response of these materials. The creep rupture phenomenon is discussed, and a time-dependent reliability model is outlined that integrates continuum damage mechanics principles and Weibull analysis. Several features of the model are presented in a qualitative fashion, including predictions of both reliability and hazard rate. In addition, a comparison of the continuum and the microstructural kinetic equations highlights a strong resemblance in the two approaches.

Domain decomposition methods for nonconforming finite element spaces of Lagrange-type

NASA Technical Reports Server (NTRS)

Cowsar, Lawrence C.

1993-01-01

In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming finite element discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming elements are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming elements is inherited from the existing theory for the conforming elements with only modest modification by constructing an isomorphism between the nonconforming finite element space and a space of continuous piecewise linear functions.

Generalized Boussinesq-Scriven surface fluid model with curvature dissipation for liquid surfaces and membranes.

PubMed

Aguilar Gutierrez, Oscar F; Herrera Valencia, Edtson E; Rey, Alejandro D

2017-10-01

Curvature dissipation is relevant in synthetic and biological processes, from fluctuations in semi-flexible polymer solutions, to buckling of liquid columns, tomembrane cell wall functioning. We present a micromechanical model of curvature dissipation relevant to fluid membranes and liquid surfaces based on a parallel surface parameterization and a stress constitutive equation appropriate for anisotropic fluids and fluid membranes.The derived model, aimed at high curvature and high rate of change of curvature in liquid surfaces and membranes, introduces additional viscous modes not included in the widely used 2D Boussinesq-Scriven rheological constitutive equation for surface fluids.The kinematic tensors that emerge from theparallel surface parameterization are the interfacial rate of deformation and the surface co-rotational Zaremba-Jaumann derivative of the curvature, which are used to classify all possibledissipative planar and non-planar modes. The curvature dissipation function that accounts for bending, torsion and twist rates is derived and analyzed under several constraints, including the important inextensional bending mode.A representative application of the curvature dissipation model to the periodic oscillation in nano-wrinkled outer hair cells show how and why curvature dissipation decreases with frequency, and why the 100kHz frequency range is selected. These results contribute to characterize curvature dissipation in membranes and liquid surfaces. Copyright © 2017 Elsevier Inc. All rights reserved.

A Canopy Density Model for Planar Orchard Target Detection Based on Ultrasonic Sensors

PubMed Central

Li, Hanzhe; Zhai, Changyuan; Weckler, Paul; Wang, Ning; Yang, Shuo; Zhang, Bo

2016-01-01

Orchard target-oriented variable rate spraying is an effective method to reduce pesticide drift and excessive residues. To accomplish this task, the orchard targets’ characteristic information is needed to control liquid flow rate and airflow rate. One of the most important characteristics is the canopy density. In order to establish the canopy density model for a planar orchard target which is indispensable for canopy density calculation, a target density detection testing system was developed based on an ultrasonic sensor. A time-domain energy analysis method was employed to analyze the ultrasonic signal. Orthogonal regression central composite experiments were designed and conducted using man-made canopies of known density with three or four layers of leaves. Two model equations were obtained, of which the model for the canopies with four layers was found to be the most reliable. A verification test was conducted with different layers at the same density values and detecting distances. The test results showed that the relative errors of model density values and actual values of five, four, three and two layers of leaves were acceptable, while the maximum relative errors were 17.68%, 25.64%, 21.33% and 29.92%, respectively. It also suggested the model equation with four layers had a good applicability with different layers which increased with adjacent layers. PMID:28029132

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

NASA Technical Reports Server (NTRS)

Thobe, Glenn E.; Bose, Sam C.

1987-01-01

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.

Effect of soil parameters on the kinetics of the displacement of Fe from FeEDDHA chelates by Cu.

PubMed

Schenkeveld, Walter D C; Reichwein, Arjen M; Temminghoff, Erwin J M; van Riemsdijk, Willem H

2012-06-28

In soil application, o,o-FeEDDHA (iron (3+) ethylene diamine-N,N'-bis(2-hydroxy phenyl acetic acid) complex) is the active ingredient of FeEDDHA chelate-based Fe fertilizers. The effectiveness of o,o-FeEDDHA is potentially compromised by the displacement of Fe from FeEDDHA by Cu. The actual impact of Cu competition is codetermined by the kinetics of the displacement reaction. In this study, the influence of soil parameters on the displacement kinetics has been examined in goethite suspensions. The displacement reaction predominantly takes place on the reactive surface rather than in solution. The rate at which the o,o-FeEDDHA concentration declined depended on the available reactive surface area, the Cu loading, and the FeEDDHA loading. Soil factors reducing FeEDDHA adsorption (high ionic strength, humic acid adsorption onto the goethite surface, and monovalent instead of divalent cations in the electrolyte) decreased the displacement rate. For meso o,o-FeEDDHA, the displacement rate equation was derived, which is first order in FeEDDHA loading and half order in Cu loading. For soil conditions, the equation can be simplified to an exponential decay function in meso o,o-FeEDDHA solution concentration.

Effects of Recovery Behavior and Strain-Rate Dependence of Stress-Strain Curve on Prediction Accuracy of Thermal Stress Analysis During Casting

NASA Astrophysics Data System (ADS)

Motoyama, Yuichi; Shiga, Hidetoshi; Sato, Takeshi; Kambe, Hiroshi; Yoshida, Makoto

2017-06-01

Recovery behavior (recovery) and strain-rate dependence of the stress-strain curve (strain-rate dependence) are incorporated into constitutive equations of alloys to predict residual stress and thermal stress during casting. Nevertheless, few studies have systematically investigated the effects of these metallurgical phenomena on the prediction accuracy of thermal stress in a casting. This study compares the thermal stress analysis results with in situ thermal stress measurement results of an Al-Si-Cu specimen during casting. The results underscore the importance for the alloy constitutive equation of incorporating strain-rate dependence to predict thermal stress that develops at high temperatures where the alloy shows strong strain-rate dependence of the stress-strain curve. However, the prediction accuracy of the thermal stress developed at low temperatures did not improve by considering the strain-rate dependence. Incorporating recovery into the constitutive equation improved the accuracy of the simulated thermal stress at low temperatures. Results of comparison implied that the constitutive equation should include strain-rate dependence to simulate defects that develop from thermal stress at high temperatures, such as hot tearing and hot cracking. Recovery should be incorporated into the alloy constitutive equation to predict the casting residual stress and deformation caused by the thermal stress developed mainly in the low temperature range.

A Few New 2+1-Dimensional Nonlinear Dynamics and the Representation of Riemann Curvature Tensors

NASA Astrophysics Data System (ADS)

Wang, Yan; Zhang, Yufeng; Zhang, Xiangzhi

2016-09-01

We first introduced a linear stationary equation with a quadratic operator in ∂x and ∂y, then a linear evolution equation is given by N-order polynomials of eigenfunctions. As applications, by taking N=2, we derived a (2+1)-dimensional generalized linear heat equation with two constant parameters associative with a symmetric space. When taking N=3, a pair of generalized Kadomtsev-Petviashvili equations with the same eigenvalues with the case of N=2 are generated. Similarly, a second-order flow associative with a homogeneous space is derived from the integrability condition of the two linear equations, which is a (2+1)-dimensional hyperbolic equation. When N=3, the third second flow associative with the homogeneous space is generated, which is a pair of new generalized Kadomtsev-Petviashvili equations. Finally, as an application of a Hermitian symmetric space, we established a pair of spectral problems to obtain a new (2+1)-dimensional generalized Schrödinger equation, which is expressed by the Riemann curvature tensors.

An efficient, explicit finite-rate algorithm to compute flows in chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

An explicit finite-rate code was developed to compute hypersonic viscous chemically reacting flows about three-dimensional bodies. Equations describing the finite-rate chemical reactions were fully coupled to the gas dynamic equations using a new coupling technique. The new technique maintains stability in the explicit finite-rate formulation while permitting relatively large global time steps.

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.

Mathematical model of salt cavern leaching for gas storage in high-insoluble salt formations.

PubMed

Li, Jinlong; Shi, Xilin; Yang, Chunhe; Li, Yinping; Wang, Tongtao; Ma, Hongling

2018-01-10

A mathematical model is established to predict the salt cavern development during leaching in high-insoluble salt formations. The salt-brine mass transfer rate is introduced, and the effects of the insoluble sediments on the development of the cavern are included. Considering the salt mass conservation in the cavern, the couple equations of the cavern shape, brine concentration and brine velocity are derived. According to the falling and accumulating rules of the insoluble particles, the governing equations of the insoluble sediments are deduced. A computer program using VC++ language is developed to obtain the numerical solution of these equations. To verify the proposed model, the leaching processes of two salt caverns of Jintan underground gas storage are simulated by the program, using the actual geological and technological parameters. The same simulation is performed by the current mainstream leaching software in China. The simulation results of the two programs are compared with the available field data. It shows that the proposed software is more accurate on the shape prediction of the cavern bottom and roof, which demonstrates the reliability and applicability of the model.

Exponential growth and Gaussian—like fluctuations of solutions of stochastic differential equations with maximum functionals

NASA Astrophysics Data System (ADS)

Appleby, J. A. D.; Wu, H.

2008-11-01

In this paper we consider functional differential equations subjected to either instantaneous state-dependent noise, or to a white noise perturbation. The drift of the equations depend linearly on the current value and on the maximum of the solution. The functional term always provides positive feedback, while the instantaneous term can be mean-reverting or can exhibit positive feedback. We show in the white noise case that if the instantaneous term is mean reverting and dominates the history term, then solutions are recurrent, and upper bounds on the a.s. growth rate of the partial maxima of the solution can be found. When the instantaneous term is weaker, or is of positive feedback type, we determine necessary and sufficient conditions on the diffusion coefficient which ensure the exact exponential growth of solutions. An application of these results to an inefficient financial market populated by reference traders and speculators is given, in which the difference between the current instantaneous returns and maximum of the returns over the last few time units is used to determine trading strategies.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

On Structural Equation Model Equivalence.

ERIC Educational Resources Information Center

Raykov, Tenko; Penev, Spiridon

1999-01-01

Presents a necessary and sufficient condition for the equivalence of structural-equation models that is applicable to models with parameter restrictions and models that may or may not fulfill assumptions of the rules. Illustrates the application of the approach for studying model equivalence. (SLD)

Coarsening strategies for unstructured multigrid techniques with application to anisotropic problems

NASA Technical Reports Server (NTRS)

Morano, E.; Mavriplis, D. J.; Venkatakrishnan, V.

1995-01-01

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect-ratio AR = delta y/delta x is much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotopic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Coarsening Strategies for Unstructured Multigrid Techniques with Application to Anisotropic Problems

NASA Technical Reports Server (NTRS)

Morano, E.; Mavriplis, D. J.; Venkatakrishnan, V.

1996-01-01

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e. the aspect-ratio AR = (delta)y/(delta)x much less than 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce proper convergence rates on isotropic meshes are not adequate for stretched meshes. This work focuses on the solution of Laplace's equation, discretized through a Galerkin finite-element formulation on unstructured stretched triangular meshes. A coarsening strategy is proposed and results are discussed.

Modeling the effect of topical oxygen therapy on wound healing

NASA Astrophysics Data System (ADS)

Agyingi, Ephraim; Ross, David; Maggelakis, Sophia

2011-11-01

Oxygen supply is a critical element for the healing of wounds. Clinical investigations have shown that topical oxygen therapy (TOT) increases the healing rate of wounds. The reason behind TOT increasing the healing rate of a wound remains unclear and hence current protocols are empirical. In this paper we present a mathematical model of wound healing that we use to simulate the application of TOT in the treatment of cutaneous wounds. At the core of our model is an account of the initiation of angiogenesis by macrophage-derived growth factors. The model is expressed as a system of reaction-diffusion equations. We present results of simulations for a version of the model with one spatial dimension.

Determination of Material Constitutive Laws for Inconel 718 Superalloy Under Different Strain Rates and Working Temperatures

NASA Astrophysics Data System (ADS)

Grzesik, W.; Niesłony, P.; Laskowski, P.

2017-12-01

In this paper, a special procedure for the prediction of parameters of the Johnson-Cook constitutive material models is proposed based on the experimental data and specially developed MATLAB scripts which allow advanced modeling of complex 3D response surfaces. Experimental investigations concern two various strain rates of 10-3 and 101 1/s and the testing temperature ranging from the ambient up to 700 °C. As a result, a set of mathematical equations which fit the experimental data is determined. The applicability of the experimentally derived constitutive models to the FEM modeling of real machining processes of Inconel 718 alloy is verified.

Kinetics studies of rapid strain-promoted [3 + 2]-cycloadditions of nitrones with biaryl-aza-cyclooctynone.

PubMed

McKay, Craig S; Chigrinova, Mariya; Blake, Jessie A; Pezacki, John Paul

2012-04-21

Strain-promoted cycloadditions of cyclic nitrones with biaryl-aza-cyclooctynone (BARAC) proceed with rate constants up to 47.3 M(-1) s(-1), this corresponds to a 47-fold rate enhancement relative to reaction of BARAC with benzyl azide and a 14-fold enhancement over previously reported strain promoted alkyne-nitrone cycloadditions (SPANC). Studies of the SPANC reaction using the linear free energy relationship defined by the Hammett equation demonstrated that the cycloaddition reaction has a rho value of 0.25 ± 0.04, indicating that reaction is not sensitive to substituents and thus should have broad applicability. This journal is © The Royal Society of Chemistry 2012

Evolution of complex dynamics

NASA Astrophysics Data System (ADS)

Wilds, Roy; Kauffman, Stuart A.; Glass, Leon

2008-09-01

We study the evolution of complex dynamics in a model of a genetic regulatory network. The fitness is associated with the topological entropy in a class of piecewise linear equations, and the mutations are associated with changes in the logical structure of the network. We compare hill climbing evolution, in which only mutations that increase the fitness are allowed, with neutral evolution, in which mutations that leave the fitness unchanged are allowed. The simple structure of the fitness landscape enables us to estimate analytically the rates of hill climbing and neutral evolution. In this model, allowing neutral mutations accelerates the rate of evolutionary advancement for low mutation frequencies. These results are applicable to evolution in natural and technological systems.

Kinetic theory of oxygen isotopic exchange between minerals and water

USGS Publications Warehouse

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

1987-01-01

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

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

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

Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

2014-08-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

Glomerular filtration rate is associated with free triiodothyronine in euthyroid subjects: Comparison between various equations to estimate renal function and creatinine clearance.

PubMed

Anderson, Josephine L C; Gruppen, Eke G; van Tienhoven-Wind, Lynnda; Eisenga, Michele F; de Vries, Hanne; Gansevoort, Ron T; Bakker, Stephan J L; Dullaart, Robin P F

2018-02-01

Effects of variations in thyroid function within the euthyroid range on renal function are unclear. Cystatin C-based equations to estimate glomerular filtration rate (GFR) are currently advocated for mortality and renal risk prediction. However, the applicability of cystatin C-based equations is discouraged in patients with overt thyroid dysfunction, since serum cystatin C and creatinine levels are oppositely affected by thyroid dysfunction. Here, we compared relationships of thyroid stimulating hormone (TSH), free thyroxine (FT4) and free triiodothyronine (FT3) with various measures of kidney function in euthyroid subjects. Relationships of eGFR, based on creatinine (eGFRcrea), cystatin C (eGFRcysC), creatinine+cystatin C combined (eGFRcrea-cysC) and creatinine clearance (CrCl) with TSH, FT4 and FT3 were determined in 2180 euthyroid subjects (TSH, FT4 and FT3 all within the reference range; anti-thyroid peroxidase autoantibodies negative) who did not use thyroid hormones, anti-thyroid drugs, amiodarone or lithium carbonate. In multivariable models including TSH, FT3 and FT4 together, eGFRcrea, eGFRcysC and eGFRcrea-cysC and CrCl were all positively related to FT3 (P≤0.001), translating into a 2.61 to 2.83mL/min/1.73m 2 increase in eGFR measures and a 3.92mL/min increase in CrCl per 1pmol/L increment in FT3. These relationships with FT3 remained taking account of relevant covariates. In euthyroid subjects renal function is associated with thyroid function status, especially by serum FT3, irrespective of the eGFR equation applied. In the euthyroid state, cystatin C-based eGFR equations are appropriate to assess the relationship of renal function with variation in thyroid function status. Copyright © 2017 European Federation of Internal Medicine. Published by Elsevier B.V. All rights reserved.

Explanation of climate and human impacts on sediment discharge change in Darwinian hydrology: Derivation of a differential equation

NASA Astrophysics Data System (ADS)

Zhang, Jianjun; Gao, Guangyao; Fu, Bojie; Zhang, Lu

2018-04-01

The assessment for impacts of climate variability and human activities on suspended sediment yield (SSY) change has long been a question of great interest. However, the sediment generation processes are sophisticated with high nonlinearity and great uncertainty, which give rise to extreme complexity for SSY change assessment in Newtonian approach. Consequently, few approaches can be simply but widely applied to decompose impacts of climatic variability and human activities on SSY change. Thus, it is an urgent need to develop advanced methods that are simple and robust. Since that the Newtonian approach is hardly achievable due to limitation of either observations or knowledge of mechanisms, there have been repeated calls to capture the hydrologic system in Darwinian approach for hydrological change prediction or explanation. As streamflow is the carrier of suspended sediment, SSY change are thus documented in changes of sediment concentrated flow and suspended sediment concentration - water discharge (C-Q) relationships. By deduced corollaries, a differential equation of sediment discharge change was derived to explicitly decompose impacts of climate variability and human activities in Darwinian hydrology. Besides, a new form of sediment rating curves was proposed and curved as C-Q relationships and probability distribution of sediment concentrated flow. River sediment flux can be revealed by this representation, which simply elucidates mechanism of SSY generation covering a range of time scales from finer than rainfall-event to long term. By the new sediment rating curves, the differential equation was partly solved using a segmentation algorithm proposed and validated in this paper, and then was submitted to water balance framework expressed by Budyko-type equation. Thus, for catchment management, hydrologists can obtain explicit explanation of how climate variation and human activities propagate through landscape and result in sediment discharge change. The differential equation is simple and robust for widely application in sediment discharge change assessment, as only discrete data of precipitation, potential evaporation and C-Q observed at gauging stations are required.

Leak rates in sealed cells.

NASA Technical Reports Server (NTRS)

Frank, H. A.; Uchiyama, A. A.

1973-01-01

Water vapor loss rates were determined from simulated and imperfectly sealed alkaline cells in the vacuum environment. The observed rates were found to be in agreement with a semi-empirical equation employed in vacuum technology. Results thereby give support for using this equation for the prediction of loss rates of battery gases and vapors to the aerospace environment. On this basis it was shown how the equation can be applied to the solution of many heretofore unresolved questions regarding leaks in batteries. Among these are the maximum permissible leak size consistent with a given cell life or conversely the maximum life consistent with a given leak size. It was also shown that loss rates of these cells in the terrestrial environment are several orders of magnitude less than the corresponding loss rates in the aerospace environment.

Interpretation of Bernoulli's Equation.

ERIC Educational Resources Information Center

Bauman, Robert P.; Schwaneberg, Rolf

1994-01-01

Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)

Analysis, Verification, and Application of Equations and Procedures for Design of Exhaust-pipe Shrouds

NASA Technical Reports Server (NTRS)

Ellerbrock, Herman H.; Wcislo, Chester R.; Dexter, Howard E.

1947-01-01

Investigations were made to develop a simplified method for designing exhaust-pipe shrouds to provide desired or maximum cooling of exhaust installations. Analysis of heat exchange and pressure drop of an adequate exhaust-pipe shroud system requires equations for predicting design temperatures and pressure drop on cooling air side of system. Present experiments derive such equations for usual straight annular exhaust-pipe shroud systems for both parallel flow and counter flow. Equations and methods presented are believed to be applicable under certain conditions to the design of shrouds for tail pipes of jet engines.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Nonlinear storage models of unconfined flow through a shallow aquifer on an inclined base and their quasi-steady flow application

NASA Astrophysics Data System (ADS)

Varvaris, Ioannis; Gravanis, Elias; Koussis, Antonis; Akylas, Evangelos

2013-04-01

Hillslope processes involving flow through an inclined shallow aquifer range from subsurface stormflow to stream base flow (drought flow, or groundwater recession flow). In the case of recharge, the infiltrating water moves vertically as unsaturated flow until it reaches the saturated groundwater, where the flow is approximately parallel to the base of the aquifer. Boussinesq used the Dupuit-Forchheimer (D-F) hydraulic theory to formulate unconfined groundwater flow through a soil layer resting on an impervious inclined bed, deriving a nonlinear equation for the flow rate that consists of a linear gravity-driven component and a quadratic pressure-gradient component. Inserting that flow rate equation into the differential storage balance equation (volume conservation) Boussinesq obtained a nonlinear second-order partial differential equation for the depth. So far however, only few special solutions have been advanced for that governing equation. The nonlinearity of the equation of Boussinesq is the major obstacle to deriving a general analytical solution for the depth profile of unconfined flow on a sloping base with recharge (from which the discharges could be then determined). Henderson and Wooding (1964) were able to obtain an exact analytical solution for steady unconfined flow on a sloping base, with recharge, and their work deserves special note in the realm of solutions of the nonlinear equation of Boussinesq. However, the absence of a general solution for the transient case, which is of practical interest to hydrologists, has been the motivation for developing approximate solutions of the non-linear equation of Boussinesq. In this work, we derive the aquifer storage function by integrating analytically over the aquifer base the depth profiles resulting from the complete nonlinear Boussinesq equation for steady flow. This storage function consists of a linear and a nonlinear outflow-dependent term. Then, we use this physics-based storage function in the transient storage balance over the hillslope, obtaining analytical solutions of the outflow and the storage, for recharge and drainage, via a quasi-steady flow calculation. The hydraulically derived storage model is thus embedded in a quasi-steady approximation of transient unconfined flow in sloping aquifers. We generalise this hydrologic model of groundwater flow by modifying the storage function to be the weighted sum of the linear and the nonlinear storage terms, determining the weighting factor objectively from a known integral quantity of the flow (either an initial volume of water stored in the aquifer or a drained water volume). We demonstrate the validity of this model through comparisons with experimental data and simulation results.

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures.

PubMed

Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel

2015-04-07

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy relaxation model, which can only be applied to molecules, the new model is applicable to atoms, molecules, ions, and their mixtures. Numerical examples and model validations are carried out with two gas mixtures using the maximum entropy linear model: one mixture consists of nitrogen molecules undergoing internal excitation and dissociation and the other consists of nitrogen atoms undergoing internal excitation and ionization. Results show that the original hundreds to thousands of microscopic equations can be reduced to two macroscopic equations with almost perfect agreement for the total number density and total internal energy using only one or two groups. We also obtain good prediction of the microscopic state populations using 5-10 groups in the macroscopic equations.

Smoothed Particle Hydrodynamics and its applications for multiphase flow and reactive transport in porous media

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

Tartakovsky, Alexandre M.; Trask, Nathaniel; Pan, K.

2016-03-11

Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and Advection-Diffusion-Reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

Numerical Modeling of a Vortex Stabilized Arcjet. Ph.D. Thesis, 1991 Final Report

NASA Technical Reports Server (NTRS)

Pawlas, Gary E.

1992-01-01

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.

Numerical modeling of a vortex stabilized arcjet

NASA Astrophysics Data System (ADS)

Pawlas, Gary E.

1992-11-01

Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased.

Rate equation analysis and non-Hermiticity in coupled semiconductor laser arrays

NASA Astrophysics Data System (ADS)

Gao, Zihe; Johnson, Matthew T.; Choquette, Kent D.

2018-05-01

Optically coupled semiconductor laser arrays are described by coupled rate equations. The coupled mode equations and carrier densities are included in the analysis, which inherently incorporate the carrier-induced nonlinearities including gain saturation and amplitude-phase coupling. We solve the steady-state coupled rate equations and consider the cavity frequency detuning and the individual laser pump rates as the experimentally controlled variables. We show that the carrier-induced nonlinearities play a critical role in the mode control, and we identify gain contrast induced by cavity frequency detuning as a unique mechanism for mode control. Photon-mediated energy transfer between cavities is also discussed. Parity-time symmetry and exceptional points in this system are studied. Unbroken parity-time symmetry can be achieved by judiciously combining cavity detuning and unequal pump rates, while broken symmetry lies on the boundary of the optical locking region. Exceptional points are identified at the intersection between broken symmetry and unbroken parity-time symmetry.

Emergent properties of interacting populations of spiking neurons.

PubMed

Cardanobile, Stefano; Rotter, Stefan

2011-01-01

Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system. Here, we present and discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks is faithfully reflected by a set of non-linear rate equations, describing all interactions on the population level. These equations are similar in structure to Lotka-Volterra equations, well known by their use in modeling predator-prey relations in population biology, but abundant applications to economic theory have also been described. We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of interacting neuronal populations.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

PubMed

Winkelmann, Stefanie; Schütte, Christof

2017-09-21

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

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.

Emergent Properties of Interacting Populations of Spiking Neurons

PubMed Central

Cardanobile, Stefano; Rotter, Stefan

2011-01-01

Dynamic neuronal networks are a key paradigm of increasing importance in brain research, concerned with the functional analysis of biological neuronal networks and, at the same time, with the synthesis of artificial brain-like systems. In this context, neuronal network models serve as mathematical tools to understand the function of brains, but they might as well develop into future tools for enhancing certain functions of our nervous system. Here, we present and discuss our recent achievements in developing multiplicative point processes into a viable mathematical framework for spiking network modeling. The perspective is that the dynamic behavior of these neuronal networks is faithfully reflected by a set of non-linear rate equations, describing all interactions on the population level. These equations are similar in structure to Lotka-Volterra equations, well known by their use in modeling predator-prey relations in population biology, but abundant applications to economic theory have also been described. We present a number of biologically relevant examples for spiking network function, which can be studied with the help of the aforementioned correspondence between spike trains and specific systems of non-linear coupled ordinary differential equations. We claim that, enabled by the use of multiplicative point processes, we can make essential contributions to a more thorough understanding of the dynamical properties of interacting neuronal populations. PMID:22207844

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

NASA Astrophysics Data System (ADS)

Winkelmann, Stefanie; Schütte, Christof

2017-09-01

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Near-wall modelling of compressible turbulent flows

NASA Technical Reports Server (NTRS)

So, Ronald M. C.

1990-01-01

Work was carried out to formulate near-wall models for the equations governing the transport of the temperature-variance and its dissipation rate. With these equations properly modeled, a foundation is laid for their extension together with the heat-flux equations to compressible flows. This extension is carried out in a manner similar to that used to extend the incompressible near-wall Reynolds-stress models to compressible flows. The methodology used to accomplish the extension of the near-wall Reynolds-stress models is examined and the actual extension of the models for the Reynolds-stress equations and the near-wall dissipation-rate equation to compressible flows is given. Then the formulation of the near-wall models for the equations governing the transport of the temperature variance and its dissipation rate is discussed. Finally, a sample calculation of a flat plate compressible turbulent boundary-layer flow with adiabatic wall boundary condition and a free-stream Mach number of 2.5 using a two-equation near-wall closure is presented. The results show that the near-wall two-equation closure formulated for compressible flows is quite valid and the calculated properties are in good agreement with measurements. Furthermore, the near-wall behavior of the turbulence statistics and structure parameters is consistent with that found in incompressible flows.

Simulation of finite-strain inelastic phenomena governed by creep and plasticity

NASA Astrophysics Data System (ADS)

Li, Zhen; Bloomfield, Max O.; Oberai, Assad A.

2017-11-01

Inelastic mechanical behavior plays an important role in many applications in science and engineering. Phenomenologically, this behavior is often modeled as plasticity or creep. Plasticity is used to represent the rate-independent component of inelastic deformation and creep is used to represent the rate-dependent component. In several applications, especially those at elevated temperatures and stresses, these processes occur simultaneously. In order to model these process, we develop a rate-objective, finite-deformation constitutive model for plasticity and creep. The plastic component of this model is based on rate-independent J_2 plasticity, and the creep component is based on a thermally activated Norton model. We describe the implementation of this model within a finite element formulation, and present a radial return mapping algorithm for it. This approach reduces the additional complexity of modeling plasticity and creep, over thermoelasticity, to just solving one nonlinear scalar equation at each quadrature point. We implement this algorithm within a multiphysics finite element code and evaluate the consistent tangent through automatic differentiation. We verify and validate the implementation, apply it to modeling the evolution of stresses in the flip chip manufacturing process, and test its parallel strong-scaling performance.

Phi-value analysis of a linear, sequential reaction mechanism: theory and application to ion channel gating.

PubMed

Zhou, Yu; Pearson, John E; Auerbach, Anthony

2005-12-01

We derive the analytical form of a rate-equilibrium free-energy relationship (with slope Phi) for a bounded, linear chain of coupled reactions having arbitrary connecting rate constants. The results confirm previous simulation studies showing that Phi-values reflect the position of the perturbed reaction within the chain, with reactions occurring earlier in the sequence producing higher Phi-values than those occurring later in the sequence. The derivation includes an expression for the transmission coefficients of the overall reaction based on the rate constants of an arbitrary, discrete, finite Markov chain. The results indicate that experimental Phi-values can be used to calculate the relative heights of the energy barriers between intermediate states of the chain but provide no information about the energies of the wells along the reaction path. Application of the equations to the case of diliganded acetylcholine receptor channel gating suggests that the transition-state ensemble for this reaction is nearly flat. Although this mechanism accounts for many of the basic features of diliganded and unliganded acetylcholine receptor channel gating, the experimental rate-equilibrium free-energy relationships appear to be more linear than those predicted by the theory.

2D and 3D impellers of centrifugal compressors - advantages, shortcomings and fields of application

NASA Astrophysics Data System (ADS)

Galerkin, Y.; Reksrin, A.; Drozdov, A.

2017-08-01

The simplified equations are presented for calculation of inlet dimensions and velocity values for impellers with three-dimensional blades located in axial and radial part of an impeller (3D impeller) and with two-dimensional blades in radial part (2D). Considerations concerning loss coefficients of 3D and 2D impellers at different design flow rate coefficients are given. The tendency of reduction of potential advantages of 3D impellers at medium and small design flow rate coefficients is shown. The data on high-efficiency compressors and stages with 2D impellers coefficients designed by the authors are presented. The reached efficiency level of 88 - 90% makes further increase of efficiency by the application of 3D impellers doubtful. CFD-analysis of stage candidates with medium flow rate coefficient with 3D and 2D impellers revealed specific problems. In some cases the constructive advantage of a 2D impeller is smaller hub ratio. It makes possible the reaching of higher efficiency. From other side, there is a positive tendency of gas turbine drive RPM increase. 3D impellers have no alternative for stages with high flow rate coefficients matching high-speed drive.

MULTISCALE MODELS OF TAXIS-DRIVEN PATTERNING IN BACTERIAL POPULATIONS

PubMed Central

XUE, CHUAN; OTHMER, HANS G.

2009-01-01

Spatially-distributed populations of various types of bacteria often display intricate spatial patterns that are thought to result from the cellular response to gradients of nutrients or other attractants. In the past decade a great deal has been learned about signal transduction, metabolism and movement in E. coli and other bacteria, but translating the individual-level behavior into population-level dynamics is still a challenging problem. However, this is a necessary step because it is computationally impractical to use a strictly cell-based model to understand patterning in growing populations, since the total number of cells may reach 1012 - 1014 in some experiments. In the past phenomenological equations such as the Patlak-Keller-Segel equations have been used in modeling the cell movement that is involved in the formation of such patterns, but the question remains as to how the microscopic behavior can be correctly described by a macroscopic equation. Significant progress has been made for bacterial species that employ a “run-and-tumble” strategy of movement, in that macroscopic equations based on simplified schemes for signal transduction and turning behavior have been derived [14, 15]. Here we extend previous work in a number of directions: (i) we allow for time-dependent signals, which extends the applicability of the equations to natural environments, (ii) we use a more general turning rate function that better describes the biological behavior, and (iii) we incorporate the effect of hydrodynamic forces that arise when cells swim in close proximity to a surface. We also develop a new approach to solving the moment equations derived from the transport equation that does not involve closure assumptions. Numerical examples show that the solution of the lowest-order macroscopic equation agrees well with the solution obtained from a Monte Carlo simulation of cell movement under a variety of temporal protocols for the signal. We also apply the method to derive equations of chemotactic movement that are governed by multiple chemotactic signals. PMID:19784399

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

The Identities Hidden in the Matching Laws, and Their Uses

ERIC Educational Resources Information Center

Thorne, David R.

2010-01-01

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…

Connecting Related Rates and Differential Equations

ERIC Educational Resources Information Center

Brandt, Keith

2012-01-01

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

Exact PDF equations and closure approximations for advective-reactive transport

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

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

Virus Sensitivity Index of UV disinfection.

PubMed

Tang, Walter Z; Sillanpää, Mika

2015-01-01

A new concept of Virus Sensitivity Index (VSI) is defined as the ratio between the first-order inactivation rate constant of a virus, ki, and that of MS2-phage during UV disinfection, kr. MS2-phage is chosen as the reference virus because it is recommended as a virus indicator during UV reactor design and validation by the US Environmental Protection Agency. VSI has wide applications in research, design, and validation of UV disinfection systems. For example, it can be used to rank the UV disinfection sensitivity of viruses in reference to MS2-phage. There are four major steps in deriving the equation between Hi/Hr and 1/VSI. First, the first-order inactivation rate constants are determined by regression analysis between Log I and fluence required. Second, the inactivation rate constants of MS2-phage are statistically analysed at 3, 4, 5, and 6 Log I levels. Third, different VSI values are obtained from the ki of different viruses dividing by the kr of MS2-phage. Fourth, correlation between Hi/Hr and 1/VSI is analysed by using linear, quadratic, and cubic models. As expected from the theoretical analysis, a linear relationship adequately correlates Hi/Hr and 1/VSI without an intercept. VSI is used to quantitatively predict the UV fluence required for any virus at any log inactivation (Log I). Four equations were developed at 3, 4, 5, and 6 Log I. These equations have been validated using external data which are not used for the virus development. At Log I less than 3, the equation tends to under-predict the required fluence at both low Log I such as 1 and 2 Log I. At Log I greater than 3 Log I, the equation tends to over-predict the fluence required. The reasons for these may very likely be due to the shoulder at the beginning and the tailing at the end of the collimated beam test experiments. At 3 Log I, the error percentage is less than 6%. The VSI is also used to predict inactivation rate constants under two different UV disinfection scenarios such as under sunlight and different virus aggregates. The correlation analysis shows that viruses will be about 40% more sensitive to sunlight than to UV254. On the other hand, virus size of 500 nm will reduce their VSI by 10%. This is the first attempt to use VSI to predict the required fluence at any given Log I. The equation can be used to quantitatively evaluate other parameters influencing UV disinfection. These factors include environmental species, antibiotic-resistant bacteria or genes, photo and dark repair, water quality such as suspended solids, and UV transmittance.

Efficient reporting of the estimated glomerular filtration rate without height in pediatric patients with cancer.

PubMed

Jeong, Tae-Dong; Cho, Eun-Jung; Lee, Woochang; Chun, Sail; Hong, Ki-Sook; Min, Won-Ki

2017-10-26

The updated bedside Schwartz equation requires constant, serum creatinine concentration and height measurements to calculate the estimated glomerular filtration rate (eGFR) in pediatric patients. Unlike the serum creatinine levels, obtaining height information from the laboratory information system (LIS) is not always possible in a clinical laboratory. Recently, the height-independent eGFR equation, the full age spectrum (FAS) equation, has been introduced. We evaluated the performance of height-independent eGFR equation in Korean children with cancer. A total of 250 children who underwent chromium-51-ethylenediamine tetra acetic-acid (51Cr-EDTA)-based glomerular filtration rate (GFR) measurements were enrolled. The 51Cr-EDTA GFR was used as the reference GFR. The bias (eGFR - measured GFR), precision (root mean square error [RMSE]) and accuracy (P30) of the FAS equations were compared to those of the updated Schwartz equation. P30 was defined as the percentage of patients whose eGFR was within ±30% of the measured GFR. The FAS equation showed significantly lower bias (mL/min/1.73 m2) than the updated Schwartz equation (4.2 vs. 8.7, p<0.001). The RMSE and P30 were: updated Schwartz of 43.8 and 64.4%, respectively, and FAS of 42.7 and 66.8%, respectively. The height-independent eGFR-FAS equation was less biased and as accurate as the updated Schwartz equation in Korean children. The use of the height-independent eGFR equation will allow for efficient reporting of eGFR through the LIS in clinical laboratories.

A Variable Turbulent Schmidt Number Formulation for Scramjet Application

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.; Cutler, A. D.

2004-01-01

In high speed engines, thorough turbulent mixing of fuel and air is required to obtain high performance and high efficiency. Thus, the ability to predict turbulent mixing is crucial in obtaining accurate numerical simulation of an engine and its performance. Current state of the art in CFD simulation is to assume both turbulent Prandtl number and Schmidt numbers to be constants. However, since the mixing of fuel and air is inversely proportional to the Schmidt number, a value of 0.45 for the Schmidt number will produce twice as much diffusion as that with a value of 0.9. Because of this, current CFD tools and models have not been able to provide the needed guidance required for the efficient design of a scramjet engine. The goal of this investigation is to develop the framework needed to calculate turbulent Prandtl and Schmidt numbers as part of the solution. This requires four additional equations: two for the temperature variance and its dissipation rate and two for the concentration variance and its dissipation rate. In the current investigation emphasis will be placed on studying mixing without reactions. For such flows, variable Prandtl number does not play a major role in determining the flow. This, however, will have to be addressed when combustion is present. The approach to be used is similar to that used to develop the k-zeta model. In this approach, relevant equations are derived from the exact Navier-Stokes equations and each individual correlation is modeled. This ensures that relevant physics is incorporated into the model equations. This task has been accomplished. The final set of equations have no wall or damping functions. Moreover, they are tensorially consistent and Galilean invariant. The derivation of the model equations is rather lengthy and thus will not be incorporated into this abstract, but will be included in the final paper. As a preliminary to formulating the proposed model, the original k-zeta model with constant turbulent Prandtl and Schmidt numbers is used to model the supersonic coaxial jet mixing experiments involving He, O2 and air.

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

PubMed Central

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

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

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

PubMed

Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel

2016-01-01

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

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.

Improved thermodynamics of the dense solar plasma and molecular-dynamics simulations of the nuclear-reaction rates

NASA Astrophysics Data System (ADS)

Mao, Dan

The conditions in the solar interior are so extreme that it has so far been impossible to match them in a laboratory. However, for nearly 50 years solar oscillations have been precisely observed, and the wealth of their data has enabled us to study the interior of the Sun as if it were a laboratory. Helioseismology is the name of this branch of astrophysics. It allows a high- precision diagnostic of the thermodynamic quantities in the solar interior. High-quality thermodynamic quantities are crucial for successful solar modeling. If good solar models are desired, considerable theoretical effort is required. Good solar models, in turn, are fundamental tools for solar physics. The most prominent example of this link between solar physics and basic physics was the resolution of the solar neutrino problem in 2002. The equation of state is a key material property that describes the relation between pressure, density and temperature. If the equation of state is derived from a thermodynamic potential it will also determine all associated thermodynamic quantities. A second key material property is the nuclear-energy production rate, which plays a crucial role in the solar core. Both are important physical properties describing the structure of the Sun. Both derive from microphysical models. In the equation-of-state part, we have studied two models of the equation of state (EOS). One is the MHD EOS, which is widely used in solar models. In our research, we have incorporated new terms into the MHD EOS. These terms have been borrowed from the major competing formalism, the OPAL EOS. They were missing in the original MHD EOS. Not only do the upgrades bring MHD closer to the OPAL equation of state, which is well known for its better match with observations. Most importantly it will allow solar modelers to use the OPAL equation of state directly, without recourse to the OPAL tables distributed by the Lawrence Livermore National Laboratory. Since the OPAL code is not publicly available, there is no alternative source. The official OPAL tables, however, have disadvantages. First, they are inflexible regarding the chemical mix, which is set once and for all by the producers of the tables. Our equation of state will allow the user to choose, in principle, an arbitrary mix. Second, the OPAL tables by their very nature are limited by the errors of interpolation within tables. The second equation of state model is a density expansion based on the Feynman-Kac path-integral formalism. By making use of the equivalence of quantum Hamiltonian matrix and the classical action of closed and open filaments (paths), an analytic formalism of equation of state. Although the character of density expansion limits its application, the formalism can still be valid in most region in the Sun. Our work provides the link between the abstract theoretical formalism that was developed in the 1990s and a numerically smooth realization that can be used in solar and stellar models. Since it is so far the most exact and systematic approach for an EOS, it provides another way to study the influence of different very fine physical effects, despite considerable limitations in its domain of applicability. In the nuclear-reaction part of the thesis, we have used a molecular-dynamics method to simulate the motion of protons in a hydrogen plasma (which is a good approximation for this purpose). Quantum tunneling explains why nuclear fusion can occur in the first place, considering the "low" temperature in the solar core. It is well known that this tunneling is enhanced (which leads to higher nuclear reaction rates) in the presence of Coulomb screening. In the 1950, Salpeter formulated a theory based on the static-screened Coulomb potential, as derived by Debye and H=FCckel in the 1920s. As expected, Salpeter obtained enhanced reaction rates. But from our simulation, we confirmed the results of a recent controversy about the existence of a dynamic effect. Since the bulk of fusion reactions happens at the high end of the Maxwell distribution, this is an relevant issue. Our work is the first independent confirmation of such a dynamic effect.

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Coupled radial Schrödinger equations written as Dirac-type equations: application to an amplitude-phase approach

NASA Astrophysics Data System (ADS)

Thylwe, Karl-Erik; McCabe, Patrick

2012-04-01

The classical amplitude-phase method due to Milne, Wilson, Young and Wheeler in the 1930s is known to be a powerful computational tool for determining phase shifts and energy eigenvalues in cases where a sufficiently slowly varying amplitude function can be found. The key for the efficient computations is that the original single-state radial Schrödinger equation is transformed to a nonlinear equation, the Milne equation. Such an equation has solutions that may or may not oscillate, depending on boundary conditions, which then requires a robust recipe for locating the (optimal) ‘almost constant’ solutions for its use in the method. For scattering problems the solutions of the amplitude equations always approach constants as the radial distance r tends to infinity, and there is no problem locating the ‘optimal’ amplitude functions from a low-order semiclassical approximation. In the present work, the amplitude-phase approach is generalized to two coupled Schrödinger equations similar to an earlier generalization to radial Dirac equations. The original scalar amplitude then becomes a vector quantity, and the original Milne equation is generalized accordingly. Numerical applications to resonant electron-atom scattering are illustrated.

Extension of Miles Equation for Ring Baffle Damping Predictions to Small Slosh Amplitudes and Large Baffle Widths

NASA Technical Reports Server (NTRS)

West, Jeff; Yang, H. Q.; Brodnick, Jacob; Sansone, Marco; Westra, Douglas

2016-01-01

The Miles equation has long been used to predict slosh damping in liquid propellant tanks due to ring baffles. The original work by Miles identifies defined limits to its range of application. Recent evaluations of the Space Launch System identified that the Core Stage baffle designs resulted in violating the limits of the application of the Miles equation. This paper describes the work conducted by NASA/MSFC to develop methods to predict slosh damping from ring baffles for conditions for which Miles equation is not applicable. For asymptotically small slosh amplitudes or conversely large baffle widths, an asymptotic expression for slosh damping was developed and calibrated using historical experimental sub-scale slosh damping data. For the parameter space that lies between region of applicability of the asymptotic expression and the Miles equation, Computational Fluid Dynamics simulations of slosh damping were used to develop an expression for slosh damping. The combined multi-regime slosh prediction methodology is shown to be smooth at regime boundaries and consistent with both sub-scale experimental slosh damping data and the results of validated Computational Fluid Dynamics predictions of slosh damping due to ring baffles.