Ghanaian Teacher Trainees' Conceptual Understanding of Stoichiometry

ERIC Educational Resources Information Center

Hanson, Ruby

2015-01-01

Chemical stoichiometry is a conceptual framework that encompasses other concepts such as the mole, writing of chemical equations in word and representative form, balancing of equations and the equilibrium concept. The underlying concepts enable students to understand relationships among entities of matter and required amounts for use when…

Ghanaian Teacher Trainees' Conceptual Understanding of Stoichiometry

ERIC Educational Resources Information Center

Hanson, Ruby

2016-01-01

Chemical stoichiometry is a conceptual framework that encompasses other concepts such as the mole, writing of chemical equations in word and representative form, balancing of equations and the equilibrium concept. The underlying concepts enable students to understand relationships among entities of matter and required amounts for use when…

Teaching Population Balances for Chemical Engineering Students: Application to Granulation Processes

ERIC Educational Resources Information Center

Bucala, Veronica; Pina, Juliana

2007-01-01

The population balance equation (PBE) is a useful tool to predict particle size distributions in granulation processes. When PBE is taught to advanced chemical engineering students, the internal coordinates (particle properties) are particularly hard to understand. In this paper, the flow of particles along different coordinates is carefully…

The Use of Computers to Aid Instruction in Beginning Chemistry

ERIC Educational Resources Information Center

Grandey, Robert C.

1971-01-01

Describes computer-aided lessons for determining chemical formulas from composition by weight, quantities from chemical equations, and balancing equations for oxidation-reduction reactions. Lessons were developed and used on the PLATO system at the University of Illinois. A brief analysis of student attitudes and of effectiveness of the programs…

40 CFR 1065.140 - Dilution for gaseous and PM constituents.

Code of Federal Regulations, 2013 CFR

2013-07-01

... nitrogen. For gaseous emission measurement the diluent must be at least 15 °C. Note that the composition of... chemical balance equations in § 1065.655 to calculate the mole fraction of water in the dilute exhaust... condensation (either measured or from the chemical balance), and set any negative values to zero. This...

40 CFR 1065.140 - Dilution for gaseous and PM constituents.

Code of Federal Regulations, 2011 CFR

2011-07-01

... nitrogen. For gaseous emission measurement the diluent must be at least 15 °C. Note that the composition of... chemical balance equations in § 1065.655 to calculate the mole fraction of water in the dilute exhaust... condensation (either measured or from the chemical balance), and set any negative values to zero. This...

40 CFR 1065.140 - Dilution for gaseous and PM constituents.

Code of Federal Regulations, 2010 CFR

2010-07-01

... nitrogen. For gaseous emission measurement the diluent must be at least 15 °C. Note that the composition of... chemical balance equations in § 1065.655 to calculate the mole fraction of water in the dilute exhaust... condensation (either measured or from the chemical balance), and set any negative values to zero. This...

40 CFR 1065.140 - Dilution for gaseous and PM constituents.

Code of Federal Regulations, 2012 CFR

2012-07-01

... nitrogen. For gaseous emission measurement the diluent must be at least 15 °C. Note that the composition of... chemical balance equations in § 1065.655 to calculate the mole fraction of water in the dilute exhaust... condensation (either measured or from the chemical balance), and set any negative values to zero. This...

The Influence of Cognitive Reasoning Level, Cognitive Restructuring Ability, Disembedding Ability, Working Memory Capacity, and Prior Knowledge On Students' Performance On Balancing Equations by Inspection.

ERIC Educational Resources Information Center

Staver, John R.; Jacks, Tom

1988-01-01

Investigates the influence of five cognitive variables on high school students' performance on balancing chemical equations by inspection. Reports that reasoning, restructuring, and disembedding variables could be a single variable, and that working memory capacity does not influence overall performance. Results of hierarchical regression analysis…

A spectral multi-domain technique applied to high-speed chemically reacting flows

NASA Technical Reports Server (NTRS)

Macaraeg, Michele G.; Streett, Craig L.; Hussaini, M. Yousuff

1989-01-01

The first applications of a spectral multidomain method for viscous compressible flow is presented. The method imposes a global flux balance condition at the interface so that high-order continuity of the solution is preserved. The global flux balance is imposed in terms of a spectral integral of the discrete equations across adjoining domains. Since the discretized equations interior to each domain solved are uncoupled from each other, and since the interface relation has a block structure, the solution scheme can be adapted to the particular requirements of each subdomain. The spectral multidomain technique presented is well-suited for the multiple scales associated with the chemically reacting and transition flows in hypersonic research. A nonstaggered multidomain discretization is used for the chemically reacting flow calculation, and the first implementation of a staggered multidomain mesh is presented for accurately solving the stability equation for a viscous compressible fluid.

An Investigation of the Use of Computer-Aided-Instruction in Teaching Students How to Solve Selected Multistep General Chemistry Problems.

ERIC Educational Resources Information Center

Grandey, Robert C.

The development of computer-assisted instructional lessons on the following three topics is discussed: 1) the mole concept and chemical formulas, 2) concentration of solutions and quantities from chemical equations, and 3) balancing equations for oxidation-reduction reactions. Emphasis was placed on developing computer routines which interpret…

An Illuminating Reaction.

ERIC Educational Resources Information Center

Matthews, Catherine E.

1996-01-01

Describes the use of carbide lights as an excellent mechanism for introducing or reviewing many basic chemistry concepts including elements and compounds, endothermic and exothermic reactions, physical and chemical changes, and balancing chemical equations. (JRH)

Photochemistry and dynamics of the ozone layer

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

Reviews.

ERIC Educational Resources Information Center

Journal of Chemical Education, 1989

1989-01-01

Reviews three chemistry software programs at the high school and college general chemistry level for the Apple II family. Includes "Chemical Nomenclature and Balancing Equations,""Principles of Stoichiometry," and "Solubility." (MVL)

40 CFR 1065.140 - Dilution for gaseous and PM constituents.

Code of Federal Regulations, 2014 CFR

2014-07-01

... nitrogen. References in this part to “dilution air” may include any of these. For gaseous emission... test interval does not exceed the specified limits. (A) Use chemical balance equations in § 1065.655 to... balance), and set any negative values to zero. This difference is the potential mole fraction of the...

Pressure and Chemical Potential: Effects Hydrophilic Soils Have on Adsorption and Transport

NASA Astrophysics Data System (ADS)

Bennethum, L. S.; Weinstein, T.

2003-12-01

Using the assumption that thermodynamic properties of fluid is affected by its proximity to the solid phase, a theoretical model has been developed based on upscaling and fundamental thermodynamic principles (termed Hybrid Mixture Theory). The theory indicates that Darcy's law and the Darcy-scale chemical potential (which determines the rate of adsorption and diffusion) need to be modified in order to apply to soils containing hydrophilic soils. In this talk we examine the Darcy-scale definition of pressure and chemical potential, especially as it applies to hydrophilic soils. To arrive at our model, we used hybrid mixture theory - first pioneered by Hassanizadeh and Gray in 1979. The technique involves averaging the field equations (i.e. conservation of mass, momentum balance, energy balance, etc.) to obtain macroscopic field equations, where each field variable is defined precisely in terms of its microscale counterpart. To close the system consistently with classical thermodynamics, the entropy inequality is exploited in the sense of Coleman and Noll. With the exceptions that the macroscale field variables are defined precisely in terms of their microscale counterparts and that microscopic interfacial equations can also be treated in a similar manner, the resulting system of equations is consistent with those derived using classical mixture theory. Hence the terminology, Hybrid Mixture Theory.

How strained are carbomeric-cycloalkanes?

PubMed

Wodrich, Matthew D; Gonthier, Jérôme F; Steinmann, Stephan N; Corminboeuf, Clémence

2010-06-24

The ring strain energies of carbomeric-cycloalkanes (molecules with one or more acetylene spacer units placed into carbon single bonds) are assessed using a series of isodesmic, homodesmotic, and hyperhomodesmotic chemical equations. Isodesmic bond separation reactions and other equations derived from the explicitly defined hierarchy of homodesmotic equations are insufficient for accurately determining these values, since not all perturbing effects (i.e., conjugation and hyperconjugation) are fully balanced. A set of homodesmotic reactions is proposed, which succeeds in balancing all stereoelectronic effects present within the carbomeric rings, allowing for a direct assessment of the strain energies. Values calculated from chemical equations are validated using an increment/additivity approach. The ring strain energy decreases as acetylene units are added, manifesting from the net stabilization gained by opening the C-CH(2)-C angle around the methylene groups and the destabilization arising from bending the C-C identical withC angles of the spacer groups. This destabilization vanishes with increasing parent ring size (i.e., the angle distortion is less in the carbomeric-cyclobutanes than in the carbomeric-cyclopropanes), leading to strain energies near zero for carbo(n)-cyclopentanes and carbo(n)-cyclohexanes.

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.

A rapid method for the computation of equilibrium chemical composition of air to 15000 K

NASA Technical Reports Server (NTRS)

Prabhu, Ramadas K.; Erickson, Wayne D.

1988-01-01

A rapid computational method has been developed to determine the chemical composition of equilibrium air to 15000 K. Eleven chemically reacting species, i.e., O2, N2, O, NO, N, NO+, e-, N+, O+, Ar, and Ar+ are included. The method involves combining algebraically seven nonlinear equilibrium equations and four linear elemental mass balance and charge neutrality equations. Computational speeds for determining the equilibrium chemical composition are significantly faster than the often used free energy minimization procedure. Data are also included from which the thermodynamic properties of air can be computed. A listing of the computer program together with a set of sample results are included.

Analysis of bacterial migration; 1: Numerical solution of balance equation

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

Frymier, P.D.; Ford, R.M.; Cummings, P.T.

1994-04-01

Chemotaxis describes the ability of motile bacteria to bias their motion in the direction of increasing gradients of chemicals, usually energy sources, known as attractants. In experimental studies of the migration of chemotactic bacteria, 1-D phenomenological cell balance equations have been used to quantitatively analyze experimental observations. While attractive for their simplicity and the ease of solution, they are limited in the strict mathematical sense to the situation in which individual bacteria are confined to motion in one dimension and respond to attractant gradients in one dimension only. Recently, Ford and Cummings (1992) reduced the general 3-D cell balance equationmore » of Alt (1980) to obtain an equation describing the migration of a bacterial population in response to a 1-D attractant gradient. Solutions of this equation for single gradients of attractants are compared to those of 1-D balance equations, results from cellular dynamics simulations, and experimental data from the authors' laboratory for E. coli responding to [alpha]-methylaspartate. The authors also investigate two aspects of the experimentally derived expression for the tumbling probability: the effect of different models for the down-gradient swimming behavior of the bacteria and the validity of ignoring the temporal derivative of the attractant concentration.« less

Carbon Footprint Calculations: An Application of Chemical Principles

ERIC Educational Resources Information Center

Treptow, Richard S.

2010-01-01

Topics commonly taught in a general chemistry course can be used to calculate the quantity of carbon dioxide emitted into the atmosphere by various human activities. Each calculation begins with the balanced chemical equation for the reaction that produces the CO[subscript 2] gas. Stoichiometry, thermochemistry, the ideal gas law, and dimensional…

College Chemistry Students' Use of Memorized Algorithms in Chemical Reactions

ERIC Educational Resources Information Center

Nyachwaya, James M.; Warfa, Abdi-Rizak M; Roehrig, Gillian H.; Schneider, Jamie L.

2014-01-01

This study sought to uncover memorized algorithms and procedures that students relied on in responding to questions based on the particulate nature of matter (PNM). We describe various memorized algorithms or processes used by students. In the study, students were asked to balance three equations of chemical reaction and then draw particulate…

Numerical modelling of multiphase multicomponent reactive transport in the Earth's interior

NASA Astrophysics Data System (ADS)

Oliveira, Beñat; Afonso, Juan Carlos; Zlotnik, Sergio; Diez, Pedro

2018-01-01

We present a conceptual and numerical approach to model processes in the Earth's interior that involve multiple phases that simultaneously interact thermally, mechanically and chemically. The approach is truly multiphase in the sense that each dynamic phase is explicitly modelled with an individual set of mass, momentum, energy and chemical mass balance equations coupled via interfacial interaction terms. It is also truly multicomponent in the sense that the compositions of the system and its constituent phases are expressed by a full set of fundamental chemical components (e.g. SiO2, Al2O3, MgO, etc.) rather than proxies. These chemical components evolve, react with and partition into different phases according to an internally consistent thermodynamic model. We combine concepts from Ensemble Averaging and Classical Irreversible Thermodynamics to obtain sets of macroscopic balance equations that describe the evolution of systems governed by multiphase multicomponent reactive transport (MPMCRT). Equilibrium mineral assemblages, their compositions and physical properties, and closure relations for the balance equations are obtained via a `dynamic' Gibbs free-energy minimization procedure (i.e. minimizations are performed on-the-fly as needed by the simulation). Surface tension and surface energy contributions to the dynamics and energetics of the system are taken into account. We show how complex rheologies, that is, visco-elasto-plastic, and/or different interfacial models can be incorporated into our MPMCRT ensemble-averaged formulation. The resulting model provides a reliable platform to study the dynamics and nonlinear feedbacks of MPMCRT systems of different nature and scales, as well as to make realistic comparisons with both geophysical and geochemical data sets. Several numerical examples are presented to illustrate the benefits and limitations of the model.

Estimating ground-water exchange with lakes using water-budget and chemical mass-balance approaches for ten lakes in ridge areas of Polk and Highlands counties, Florida

USGS Publications Warehouse

Sacks, L.A.; Swancar, Amy; Lee, T.M.

1998-01-01

Water budget and chemical mass-balance approaches were used to estimate ground-water exchange with 10 lakes in ridge areas of Polk and Highlands Counties, Florida. At each lake, heads were monitored in the surficial aquifer system and deeper Upper Floridan aquifer, lake stage and rainfall were measured continuously, and lakes and wells were sampled three times between October 1995 and December 1996. The water-budget approach computes net ground-water flow (ground-water inflow minus outflow) as the residual of the monthly waterbudget equation. Net ground-water flow varied seasonally at each of the 10 lakes, and was notably different between lakes, illustrating short-term differences in ground-water fluxes. Monthly patterns in net ground-water flow were related to monthly patterns of other hydrologic variables such as rainfall, ground-water flow patterns, and head differences between the lake and the Upper Floridan aquifer. The chemical mass-balance approach combines the water budget and solute or isotope mass-balance equations, and assumes steady-state conditions. Naturally occurring tracers that were analyzed for include calcium, magnesium, sodium, potassium, chloride, and bromide, the isotopes deuterium and oxygen-18. Chloride and sodium were the most successful solute tracers; however, their concentrations in ground water typically varied spatially, and in places were similar to that in lake water, limiting their sensitivity as tracers. In contrast, the isotopes were more robust tracers because the isotopic composition of ground water was relatively uniform and was distinctly different from the lake water. Groundwater inflow computed using the chemical massbalance method varied significantly between lakes, and ranged from less than 10 to more than 150 inches per year. Both water-budget and chemical mass-balance approaches had limitations, but the multiple lines of evidence gained using both approaches improved the understanding of the role of ground water in the water budget of the lakes.

A coupled chemo-thermo-hygro-mechanical model of concrete at high temperature and failure analysis

NASA Astrophysics Data System (ADS)

Li, Xikui; Li, Rongtao; Schrefler, B. A.

2006-06-01

A hierarchical mathematical model for analyses of coupled chemo-thermo-hygro-mechanical behaviour in concretes at high temperature is presented. The concretes are modelled as unsaturated deforming reactive porous media filled with two immiscible pore fluids, i.e. the gas mixture and the liquid mixture, in immiscible-miscible levels. The thermo-induced desalination process is particularly integrated into the model. The chemical effects of both the desalination and the dehydration processes on the material damage and the degradation of the material strength are taken into account. The mathematical model consists of a set of coupled, partial differential equations governing the mass balance of the dry air, the mass balance of the water species, the mass balance of the matrix components dissolved in the liquid phases, the enthalpy (energy) balance and momentum balance of the whole medium mixture. The governing equations, the state equations for the model and the constitutive laws used in the model are given. A mixed weak form for the finite element solution procedure is formulated for the numerical simulation of chemo-thermo-hygro-mechanical behaviours. Special considerations are given to spatial discretization of hyperbolic equation with non-self-adjoint operator nature. Numerical results demonstrate the performance and the effectiveness of the proposed model and its numerical procedure in reproducing coupled chemo-thermo-hygro-mechanical behaviour in concretes subjected to fire and thermal radiation.

Nonlinear magnetoacoustic wave propagation with chemical reactions

NASA Astrophysics Data System (ADS)

Margulies, Timothy Scott

2002-11-01

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

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.

Participatory Lecture Demonstrations.

ERIC Educational Resources Information Center

Battino, Rubin

1979-01-01

The use of participatory lecture demonstrations in the classroom is described. Examples are given for the following topics: chromatography, chemical kinetics, balancing equations, the gas laws, kinetic molecular theory, Henry's law of gas solubility, electronic energy levels in atoms, and translational, vibrational, and rotational energies of…

Hydrologic Transport of Dissolved Inorganic Carbon and Its Control on Chemical Weathering

NASA Astrophysics Data System (ADS)

Calabrese, Salvatore; Parolari, Anthony J.; Porporato, Amilcare

2017-10-01

Chemical weathering is one of the major processes interacting with climate and tectonics to form clays, supply nutrients to soil microorganisms and plants, and sequester atmospheric CO2. Hydrology and dissolution kinetics have been emphasized as factors controlling chemical weathering rates. However, the interaction between hydrology and transport of dissolved inorganic carbon (DIC) in controlling weathering has received less attention. In this paper, we present an analytical model that couples subsurface water and chemical molar balance equations to analyze the roles of hydrology and DIC transport on chemical weathering. The balance equations form a dynamical system that fully determines the dynamics of the weathering zone chemistry as forced by the transport of DIC. The model is formulated specifically for the silicate mineral albite, but it can be extended to other minerals, and is studied as a function of percolation rate and water transit time. Three weathering regimes are elucidated. For very small or large values of transit time, the weathering is limited by reaction kinetics or transport, respectively. For intermediate values, the system is transport controlled and is sensitive to transit time. We apply the model to a series of watersheds for which we estimate transit times and identify the type of weathering regime. The results suggest that hydrologic transport of DIC may be as important as reaction kinetics and dilution in determining chemical weathering rates.

Beyond "Hitting the Books"

ERIC Educational Resources Information Center

Entress, Cole; Wagner, Aimee

2014-01-01

Scientists, science teachers, and serious students recognize that success in science classes requires consistent practice--including study at home. Whether balancing chemical equations, calculating angular momentum, or memorizing the steps of cell division, students must review material repeatedly to fully understand new ideas--and must practice…

Hybrid Rocket Performance Prediction with Coupling Method of CFD and Thermal Conduction Calculation

NASA Astrophysics Data System (ADS)

Funami, Yuki; Shimada, Toru

The final purpose of this study is to develop a design tool for hybrid rocket engines. This tool is a computer code which will be used in order to investigate rocket performance characteristics and unsteady phenomena lasting through the burning time, such as fuel regression or combustion oscillation. When phenomena inside a combustion chamber, namely boundary layer combustion, are described, it is difficult to use rigorous models for this target. It is because calculation cost may be too expensive. Therefore simple models are required for this calculation. In this study, quasi-one-dimensional compressible Euler equations for flowfields inside a chamber and the equation for thermal conduction inside a solid fuel are numerically solved. The energy balance equation at the solid fuel surface is solved to estimate fuel regression rate. Heat feedback model is Karabeyoglu's model dependent on total mass flux. Combustion model is global single step reaction model for 4 chemical species or chemical equilibrium model for 9 chemical species. As a first step, steady-state solutions are reported.

Assessment of Expert-Novice Chemistry Problem Solving Using HyperCard: Early Findings.

ERIC Educational Resources Information Center

Kumar, David D.

1993-01-01

Results of a HyperCard method for assessing the performance of expert and novice high school chemistry students solving stoichiometric chemistry problems (balancing chemical equations) is reported. MANOVA results indicate significant difference between expert and novice students solving the five stoichiometric chemistry problems using…

One Bottleneck at a Time

ERIC Educational Resources Information Center

Bonner, J. Jose; Lotter, Christine; Harwood, William

2004-01-01

Teachers can easily identify what subjects their students have trouble with, whether it is transcription and translation, glycolysis and fermentation, balancing chemical equations, or vector analysis of forces acting on an object. Yet, no matter how teachers try to make these complex issues more accessible to students, or how new editions of…

Dynamic Nature of Atoms and Molecules, Science (Experimental): 5316.06.

ERIC Educational Resources Information Center

Buffaloe, Jacquelin F.

This unit of instruction deals with the study of both physical and chemical systems in equilibrium. It provides the student with instruction that will enable him to predict products in solubility, acid-base, and oxidation-reduction reactions and to write and balance equations for these reactions and solve problems involving equilibria constants.…

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

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2013-01-01

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

Exergy Based Analysis for the Environmental Control and Life Support Systems of the International Space Station

NASA Technical Reports Server (NTRS)

Clem, Kirk A.; Nelson, George J.; Mesmer, Bryan L.; Watson, Michael D.; Perry, Jay L.

2016-01-01

When optimizing the performance of complex systems, a logical area for concern is improving the efficiency of useful energy. The energy available for a system to perform work is defined as a system's energy content. Interactions between a system's subsystems and the surrounding environment can be accounted for by understanding various subsystem energy efficiencies. Energy balance of reactants and products, and enthalpies and entropies, can be used to represent a chemical process. Heat transfer energy represents heat loads, and flow energy represents system flows and filters. These elements allow for a system level energy balance. The energy balance equations are developed for the subsystems of the Environmental Control and Life Support (ECLS) system aboard the International Space Station (ISS). The use of these equations with system information would allow for the calculation of the energy efficiency of the system, enabling comparisons of the ISS ECLS system to other systems as well as allows for an integrated systems analysis for system optimization.

Mapping the Limitations of Breakthrough Analysis in Fixed-Bed Adsorption

NASA Technical Reports Server (NTRS)

Knox, James Clinton

2017-01-01

The separation of gases through adsorption plays an important role in the chemical processing industry, where the separation step is often the costliest part of a chemical process and thus worthy of careful study and optimization. This work developed a number of new, archival aspects on the computer simulations used for the refinement and design of these gas adsorption processes: 1. Presented a new approach to fit the undetermined heat and mass transfer coefficients in the axially dispersed plug flow equation and associated balance equations 2. Examined and described the conditions where non-physical simulation results can arise 3. Presented an approach to determine the limits of the axial dispersion and LDF mass transfer terms above which non-physical simulation results occur.

Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions

USGS Publications Warehouse

Rubin, Jacob

1983-01-01

Examples involving six broad reaction classes show that the nature of transport-affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass-balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport-equation system (e.g., whether it involves algebraic, partial-differential, or integro-partial-differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical-relation (i.e., equilibrium or rate) equations.

Bistability in the chemical master equation for dual phosphorylation cycles.

PubMed

Bazzani, Armando; Castellani, Gastone C; Giampieri, Enrico; Remondini, Daniel; Cooper, Leon N

2012-06-21

Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory, and cellular fate determination. Despite the large body of deterministic studies and the increasing work aimed at elucidating the effect of noise in such systems, some aspects remain unclear. Here we study the stationary distribution provided by the two-dimensional chemical master equation for a well-known model of a two step phospho/dephosphorylation cycle using the quasi-steady state approximation of enzymatic kinetics. Our aim is to analyze the role of fluctuations and the molecules distribution properties in the transition to a bistable regime. When detailed balance conditions are satisfied it is possible to compute equilibrium distributions in a closed and explicit form. When detailed balance is not satisfied, the stationary non-equilibrium state is strongly influenced by the chemical fluxes. In the last case, we show how the external field derived from the generation and recombination transition rates, can be decomposed by the Helmholtz theorem, into a conservative and a rotational (irreversible) part. Moreover, this decomposition allows to compute the stationary distribution via a perturbative approach. For a finite number of molecules there exists diffusion dynamics in a macroscopic region of the state space where a relevant transition rate between the two critical points is observed. Further, the stationary distribution function can be approximated by the solution of a Fokker-Planck equation. We illustrate the theoretical results using several numerical simulations.

A Novel Code System for Revealing Sources of Students' Difficulties with Stoichiometry

ERIC Educational Resources Information Center

Gulacar, Ozcan; Overton, Tina L.; Bowman, Charles R.; Fynewever, Herb

2013-01-01

A coding scheme is presented and used to evaluate solutions of seventeen students working on twenty five stoichiometry problems in a think-aloud protocol. The stoichiometry problems are evaluated as a series of sub-problems (e.g., empirical formulas, mass percent, or balancing chemical equations), and the coding scheme was used to categorize each…

Identification of Unknown Chloride Salts Using a Combination of Qualitative Analysis and Titration with Silver Nitrate: A General Chemistry Laboratory

ERIC Educational Resources Information Center

Maines, Laina L.; Bruch, Martha D.

2012-01-01

General chemistry students often have difficulty writing balanced equations and performing stoichiometry calculations for precipitation reactions, in part because of difficulty understanding the symbolic notation used to represent chemical reactions. We have developed a problem-based experiment to improve student learning of these concepts, and…

Approaches to Determining the Oxidation State of Nitrogen and Carbon Atoms in Organic Compounds for High School Students

ERIC Educational Resources Information Center

Jurowski, Kamil; Krzeczkowska, Malgorzata Krystyna; Jurowska, Anna

2015-01-01

The concept of oxidation state (or oxidation number) and related issues have always been difficult for students. In addition, there are misunderstandings and obscurities, which can cause improper balancing of the chemical equations (mostly in organic reactions). In particular, these problems are related to determination of the oxidation state of…

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

General theory of the multistage geminate reactions of the isolated pairs of reactants. II. Detailed balance and universal asymptotes of kinetics.

PubMed

Kipriyanov, Alexey A; Doktorov, Alexander B

2014-10-14

The analysis of general (matrix) kinetic equations for the mean survival probabilities of any of the species in a sample (or mean concentrations) has been made for a wide class of the multistage geminate reactions of the isolated pairs. These kinetic equations (obtained in the frame of the kinetic approach based on the concept of "effective" particles in Paper I) take into account various possible elementary reactions (stages of a multistage reaction) excluding monomolecular, but including physical and chemical processes of the change in internal quantum states carried out with the isolated pairs of reactants (or isolated reactants). The general basic principles of total and detailed balance have been established. The behavior of the reacting system has been considered on macroscopic time scales, and the universal long-term kinetics has been determined.

A self-consistent model of halo/sprite influence on the chemical balance of the mesosphere

NASA Astrophysics Data System (ADS)

Mareev, E.; Kuterin, F.; Evtushenko, A.

2013-12-01

We develop one-dimensional plasma-chemical self-consistent model to describe influence of high altitude discharges - sprite and halo - on the chemical balance of the mesosphere. We take into account 25 neutrals including 9 excited chemical components, electrons, 24 positive ions, 11 negative ions, and use 267 chemical reactions [1,2] to describe chemical perturbation in the mesosphere. The electric field on the heights of mesosphere is determined as a solution of the differential equation depending on the conductivity of the mesosphere and the external electric field, which is created by uncompensated electric charge in the troposphere after the strong lightning discharge. Taking into account the high conductivity of the Earth's surface, we use the dipole approach for the external field. To get the electron temperature dependence on the reduced electric field, we use the freeware solver of Boltzmann equation BOLSIG+ [3]. Initial values of chemical components different from zero are obtained from the latest version (v5) of WACCM [4]. The results of modeling can be summarized as follows: Results for sprite. Maximum dipole moment of uncompensated charge 740 C×km was used. The discharge begins at the height 78 km several hundred microseconds after the beginning of electric current in a lightning channel in the troposphere and reaches a height of 70 km after one millisecond. The conductivity of mesosphere is reduced by practically 2 orders of magnitude at the beginning of the discharge (because of electron temperature and collision frequency increase), which may play a significant role for the discharge initiation. The perturbation of electron concentration reaches 500 cm-3, O2+ - 600 cm-3, H5O2+ - 500 cm-3, O2- - cm-3, and relaxation time is more than 100 s at the top of the sprite. Volume emission rate for first positive band of nitrogen reaches 2×108 cm-3s-1. Results for halo. There is no perturbation concentration of electrons and ions. The reduced elec-tric field is no more than 80-95 Td on the heights of mesosphere. Optical emissions of halo are be-tween 77 and 81 km, and volume emission rate for the first positive band of nitrogen reaches only 2.5×105 cm-3s-1, for second positive band 2.3×104 cm-3s-1. References: 1. Evtushenko A.A., Mareev E.A. Simulation of chemical perturbation in mesosphere caused by sprite // Radiophysics and Quantum Electronics. 2011. N 2. P. 123-140. 2. Evtushenko A.A., Kuterin F.A., Mareev E.A. A model of sprite influence on the chemical balance of mesosphere // J. Atmos. Sol. Terr. Phys. 2013. Vol. 102. P. 298-310. 3. Hagelaar G.J.M., Pitchford L.C. Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models // Plasma Sources Sci. Technol. 2005. Vol. 14. P. 722-733. 4. http://www.cesm.ucar.edu/models/cesm1.1/cam/ [Online].

A coupled model of transport-reaction-mechanics with trapping. Part I - Small strain analysis

NASA Astrophysics Data System (ADS)

Salvadori, A.; McMeeking, R.; Grazioli, D.; Magri, M.

2018-05-01

A fully coupled model for mass and heat transport, mechanics, and chemical reactions with trapping is proposed. It is rooted in non-equilibrium rational thermodynamics and assumes that displacements and strains are small. Balance laws for mass, linear and angular momentum, energy, and entropy are stated. Thermodynamic restrictions are identified, based on an additive strain decomposition and on the definition of the Helmholtz free energy. Constitutive theory and chemical kinetics are studied in order to finally write the governing equations for the multi-physics problem. The field equations are solved numerically with the finite element method, stemming from a three-fields variational formulation. Three case-studies on vacancies redistribution in metals, hydrogen embrittlement, and the charge-discharge of active particles in Li-ion batteries demonstrate the features and the potential of the proposed model.

Model of Anoxic-Aerobic Wastewater Treatment at Phoenix 91st Avenue Plant

DTIC Science & Technology

1993-01-01

46 6. Storage Model; PCOD Profile 47.................... Accesion For NTS CRAMl 7. Storage Model; Oxygen Consumption Rate...69 iv 27. Compare 4 November and 17 November 1992 Data Sets; PCOD Concentrations; Storage Model .... 70 28. 4 November 1992...demand (SCOD), particulate chemical oxygen demand ( PCOD ), and the oxygen consumption rate in each stage. Mass balance equations were written for ammonia

FastChem: A computer program for efficient complex chemical equilibrium calculations in the neutral/ionized gas phase with applications to stellar and planetary atmospheres

NASA Astrophysics Data System (ADS)

Stock, Joachim W.; Kitzmann, Daniel; Patzer, A. Beate C.; Sedlmayr, Erwin

2018-06-01

For the calculation of complex neutral/ionized gas phase chemical equilibria, we present a semi-analytical versatile and efficient computer program, called FastChem. The applied method is based on the solution of a system of coupled nonlinear (and linear) algebraic equations, namely the law of mass action and the element conservation equations including charge balance, in many variables. Specifically, the system of equations is decomposed into a set of coupled nonlinear equations in one variable each, which are solved analytically whenever feasible to reduce computation time. Notably, the electron density is determined by using the method of Nelder and Mead at low temperatures. The program is written in object-oriented C++ which makes it easy to couple the code with other programs, although a stand-alone version is provided. FastChem can be used in parallel or sequentially and is available under the GNU General Public License version 3 at https://github.com/exoclime/FastChem together with several sample applications. The code has been successfully validated against previous studies and its convergence behavior has been tested even for extreme physical parameter ranges down to 100 K and up to 1000 bar. FastChem converges stable and robust in even most demanding chemical situations, which posed sometimes extreme challenges for previous algorithms.

Reciprocity theory of homogeneous reactions

NASA Astrophysics Data System (ADS)

Agbormbai, Adolf A.

1990-03-01

The reciprocity formalism is applied to the homogeneous gaseous reactions in which the structure of the participating molecules changes upon collision with one another, resulting in a change in the composition of the gas. The approach is applied to various classes of dissociation, recombination, rearrangement, ionizing, and photochemical reactions. It is shown that for the principle of reciprocity to be satisfied it is necessary that all chemical reactions exist in complementary pairs which consist of the forward and backward reactions. The backward reaction may be described by either the reverse or inverse process. The forward and backward processes must satisfy the same reciprocity equation. Because the number of dynamical variables is usually unbalanced on both sides of a chemical equation, it is necessary that this balance be established by including as many of the dynamical variables as needed before the reciprocity equation can be formulated. Statistical transformation models of the reactions are formulated. The models are classified under the titles free exchange, restricted exchange and simplified restricted exchange. The special equations for the forward and backward processes are obtained. The models are consistent with the H theorem and Le Chatelier's principle. The models are also formulated in the context of the direct simulation Monte Carlo method.

Mass balance approaches for estimating the intestinal absorption and metabolism of peptides and analogues: theoretical development and applications

NASA Technical Reports Server (NTRS)

Sinko, P. J.; Leesman, G. D.; Amidon, G. L.

1993-01-01

A theoretical analysis for estimating the extent of intestinal peptide and peptide analogue absorption was developed on the basis of a mass balance approach that incorporates convection, permeability, and reaction. The macroscopic mass balance analysis (MMBA) was extended to include chemical and enzymatic degradation. A microscopic mass balance analysis, a numerical approach, was also developed and the results compared to the MMBA. The mass balance equations for the fraction of a drug absorbed and reacted in the tube were derived from the general steady state mass balance in a tube: [formula: see text] where M is mass, z is the length of the tube, R is the tube radius, Pw is the intestinal wall permeability, kr is the reaction rate constant, C is the concentration of drug in the volume element over which the mass balance is taken, VL is the volume of the tube, and vz is the axial velocity of drug. The theory was first applied to the oral absorption of two tripeptide analogues, cefaclor (CCL) and cefatrizine (CZN), which degrade and dimerize in the intestine. Simulations using the mass balance equations, the experimental absorption parameters, and the literature stability rate constants yielded a mean estimated extent of CCL (250-mg dose) and CZN (1000-mg dose) absorption of 89 and 51%, respectively, which was similar to the mean extent of absorption reported in humans (90 and 50%). It was proposed previously that 15% of the CCL dose spontaneously degraded systematically; however, our simulations suggest that significant CCL degradation occurs (8 to 17%) presystemically in the intestinal lumen.(ABSTRACT TRUNCATED AT 250 WORDS).

How Should Equation Balancing Be Taught?

ERIC Educational Resources Information Center

Porter, Spencer K.

1985-01-01

Matrix methods and oxidation-number methods are currently advocated and used for balancing equations. This article shows how balancing equations can be introduced by a third method which is related to a fundamental principle, is easy to learn, and is powerful in its application. (JN)

User`s guide for UTCHEM-5.32m a three dimensional chemical flood simulator. Final report, September 30, 1992--December 31, 1995

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

NONE

1996-07-01

UTCHEM is a three-dimensional chemical flooding simulator. The solution scheme is analogous to IMPES, where pressure is solved for implicitly, but concentrations rather than saturations are then solved for explicitly. Phase saturations and concentrations are then solved in a flash routine. An energy balance equation is solved explicitly for reservoir temperature. The energy balance equation includes heat flow between the reservoir and the over-and under-burden rocks. The major physical phenomena modeled in the simulator are: dispersion; dilution effects; adsorption; interfacial tension; relative permeability; capillary trapping; cation exchange; phase density; compositional phase viscosity; phase behavior (pseudoquaternary); aqueous reactions; partitioning of chemicalmore » species between oil and water; dissolution/precipitation; cation exchange reactions involving more than two cations; in-situ generation of surfactant from acidic crude oil; pH dependent adsorption; polymer properties: shear thinning viscosity; inaccessible pore volume; permeability reduction; adsorption; gel properties: viscosity; permeability reduction; adsorption; tracer properties: partitioning; adsorption; radioactive decay; reaction (ester hydrolization); temperature dependent properties: viscosity; tracer reaction; gel reactions The following options are available with UTCHEM: isothermal or non-isothermal conditions, a constant or variable time-step, constant pressure or constant rate well conditions, horizontal and vertical wells, and a radial or Cartesian geometry. Please refer to the dissertation {open_quotes}Field Scale Simulation of Chemical Flooding{close_quotes} by Naji Saad, August, 1989, for a more detailed discussion of the UTCHEM simulator and its formulation.« less

A combustion model of vegetation burning in "Tiger" fire propagation tool

NASA Astrophysics Data System (ADS)

Giannino, F.; Ascoli, D.; Sirignano, M.; Mazzoleni, S.; Russo, L.; Rego, F.

2017-11-01

In this paper, we propose a semi-physical model for the burning of vegetation in a wildland fire. The main physical-chemical processes involved in fire spreading are modelled through a set of ordinary differential equations, which describe the combustion process as linearly related to the consumption of fuel. The water evaporation process from leaves and wood is also considered. Mass and energy balance equations are written for fuel (leaves and wood) assuming that combustion process is homogeneous in space. The model is developed with the final aim of simulating large-scale wildland fires which spread on heterogeneous landscape while keeping the computation cost very low.

A new interpretation of the Keller-Segel model based on multiphase modelling.

PubMed

Byrne, Helen M; Owen, Markus R

2004-12-01

In this paper an alternative derivation and interpretation are presented of the classical Keller-Segel model of cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a population of cells moves through a fluid containing a diffusible chemical to which the cells are attracted. The cells and fluid are viewed as distinct components of a two-phase mixture. The principles of mass and momentum balance are applied to each phase, and appropriate constitutive laws imposed to close the resulting equations. A key assumption here is that the stress in the cell phase is influenced by the concentration of the diffusible chemical. By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. These equations may be written in the form of the Patlak-Keller-Segel model, naturally including density-dependent nonlinearities in the cell motility coefficients. There is a direct relationship between the random motility and chemotaxis coefficients, both depending in an inter-related manner on the chemical concentration. We suggest that this may explain why many chemicals appear to stimulate both chemotactic and chemokinetic responses in cell populations. After specialising our model to describe slime mold we then show how the functional form of the chemical potential that drives cell locomotion influences the ability of the system to generate spatial patterns. The paper concludes with a summary of the key results and a discussion of avenues for future research.

Automatic computation and solution of generalized harmonic balance equations

NASA Astrophysics Data System (ADS)

Peyton Jones, J. C.; Yaser, K. S. A.; Stevenson, J.

2018-02-01

Generalized methods are presented for generating and solving the harmonic balance equations for a broad class of nonlinear differential or difference equations and for a general set of harmonics chosen by the user. In particular, a new algorithm for automatically generating the Jacobian of the balance equations enables efficient solution of these equations using continuation methods. Efficient numeric validation techniques are also presented, and the combined algorithm is applied to the analysis of dc, fundamental, second and third harmonic response of a nonlinear automotive damper.

2D Lattice Boltzmann Simulation Of Chemical Reactions Within Rayleigh-Bénard And Poiseuille-Bénard Convection Systems

NASA Astrophysics Data System (ADS)

Amaya-Ventura, Gilberto; Rodríguez-Romo, Suemi

2011-09-01

This paper deals with the computational simulation of the reaction-diffusion-advection phenomena emerging in Rayleigh-Bénard (RB) and Poiseuille-Bénard reactive convection systems. We use the Boussinesq's approximation for buoyancy forces and the Lattice Boltzmann method (LBM). The first kinetic mesoscopic model proposed here is based on the discrete Boltzmann equation needed to solve the momentum balance coupled with buoyancy forces. Then, a second lattice Boltzmann algorithm is applied to solve the reaction-diffusion-advection equation to calculate the evolution of the chemical species concentration. We use a reactive system composed by nitrous oxide (so call laughing gas) in air as an example; its spatio-temporal decomposition is calculated. Two cases are considered, a rectangular enclosed cavity and an open channel. The simulations are performed at low Reynolds numbers and in a steady state between the first and second thermo-hydrodynamic instabilities. The results presented here, for the thermo-hydrodynamic behavior, are in good agreement with experimental data; while our| chemical kinetics simulation yields expected results. Some applications of our approach are related to chemical reactors and atmospheric phenomena, among others.

Student Misconceptions in Writing Balanced Equations for Dissolving Ionic Compounds in Water

ERIC Educational Resources Information Center

Naah, Basil M.; Sanger, Michael J.

2012-01-01

The goal of this study was to identify student misconceptions and difficulties in writing symbolic-level balanced equations for dissolving ionic compounds in water. A sample of 105 college students were asked to provide balanced equations for dissolving four ionic compounds in water. Another 37 college students participated in semi-structured…

Influence of Primary Gage Sensitivities on the Convergence of Balance Load Iterations

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred

2012-01-01

The connection between the convergence of wind tunnel balance load iterations and the existence of the primary gage sensitivities of a balance is discussed. First, basic elements of two load iteration equations that the iterative method uses in combination with results of a calibration data analysis for the prediction of balance loads are reviewed. Then, the connection between the primary gage sensitivities, the load format, the gage output format, and the convergence characteristics of the load iteration equation choices is investigated. A new criterion is also introduced that may be used to objectively determine if the primary gage sensitivity of a balance gage exists. Then, it is shown that both load iteration equations will converge as long as a suitable regression model is used for the analysis of the balance calibration data, the combined influence of non linear terms of the regression model is very small, and the primary gage sensitivities of all balance gages exist. The last requirement is fulfilled, e.g., if force balance calibration data is analyzed in force balance format. Finally, it is demonstrated that only one of the two load iteration equation choices, i.e., the iteration equation used by the primary load iteration method, converges if one or more primary gage sensitivities are missing. This situation may occur, e.g., if force balance calibration data is analyzed in direct read format using the original gage outputs. Data from the calibration of a six component force balance is used to illustrate the connection between the convergence of the load iteration equation choices and the existence of the primary gage sensitivities.

Modeling snail breeding in Bioregenerative Life Support System

NASA Astrophysics Data System (ADS)

Kovalev, Vladimir; Tikhomirov, Alexander A.; Nickolay Manukovsky, D..

It is known that snail meat is a high quality food that is rich in protein. Hence, heliciculture or land snail farming spreads worldwide because it is a profitable business. The possibility to use the snails of Helix pomatia in Biological Life Support System (BLSS) was studied by Japanese Researches. In that study land snails were considered to be producers of animal protein. Also, snail breeding was an important part of waste processing, because snails were capable to eat the inedible plant biomass. As opposed to the agricultural snail farming, heliciculture in BLSS should be more carefully planned. The purpose of our work was to develop a model for snail breeding in BLSS that can predict mass flow rates in and out of snail facility. There are three linked parts in the model called “Stoichiometry”, “Population” and “Mass balance”, which are used in turn. Snail population is divided into 12 age groups from oviposition to one year. In the submodel “Stoichiometry” the individual snail growth and metabolism in each of 12 age groups are described with stoichiometry equations. Reactants are written on the left side of the equations, while products are written on the right side. Stoichiometry formulas of reactants and products consist of four chemical elements: C, H, O, N. The reactants are feed and oxygen, products are carbon dioxide, metabolic water, snail meat, shell, feces, slime and eggs. If formulas of substances in the stoichiometry equations are substituted with their molar masses, then stoichiometry equations are transformed to the equations of molar mass balance. To get the real mass balance of individual snail growth and metabolism one should multiply the value of each molar mass in the equations on the scale parameter, which is the ratio between mass of monthly consumed feed and molar mass of feed. Mass of monthly consumed feed and stoichiometry coefficients of formulas of meat, shell, feces, slime and eggs should be determined experimentally. An age structure and size of snail population are optimized on the base of individual growth and metabolic characteristics with the help of the second submodel "Population". In this simulation a daily amount of snail meat consumed by crewmembers is a guideline which specifies population productivity. Also, the daily amount of snail meat may have an optional value. Prescribed population characteristics are used in the third submodel "Mass balance" to equalize input and output mass flow rates of snail facility. In this submodel we add a water and ash to the organic masses of feed, meat, feces, shell and eggs. Moreover, masses of calcium carbonate and potable water are added to the left side of mass balance equations. Mass of calcium carbonate is distributed among shell, feces and eggs. Summarizing the twelve equations for each snail age, we get the mass balance equation for the snail facility. All simulations are performed by using Solver Add-In for Excel 2007.

Speciation distribution and mass balance of copper and zinc in urban rain, sediments, and road runoff.

PubMed

Zuo, Xiaojun; Fu, Dafang; Li, He

2012-11-01

Heavy metal pollution in road runoff had caused widespread concern since the last century. However, there are little references on metal speciation in multiple environmental media (e.g., rain, road sediments, and road runoff). Our research targeted the investigation of metal speciation in rain, road sediments, and runoff; the analysis of speciation variation and mass balance of metals among rain, road sediments, and runoff; the selection of main factors by principal component analysis (PCA); and the establishment of equation to evaluate the impact of rain and road sediments to metals in road runoff. Sequential extraction procedure contains five steps for the chemical fractionation of metals. Flame atomic absorption spectrometry (Shimadzu, AA-6800) was used to determine metal speciation concentration, as well as the total and dissolved fractions. The dissolved fractions for both Cu and Zn were dominant in rain. The speciation distribution of Zn was different from that of Cu in road sediments, while speciation distribution of Zn is similar to that of Cu in runoff. The bound to carbonates for both Cu and Zn in road sediments were prone to be dissolved by rain. The levels of Cu and Zn in runoff were not obviously influenced by rain, but significantly influenced by road sediments. The masses for both Cu and Zn among rain, road sediments, and road runoff approximately meet the mass balance equation for all rainfall patterns. Five principal factors were selected for metal regression equation based on PCA, including rainfall, average rainfall intensity, antecedent dry periods, total suspended particles, and temperature. The established regression equations could be used to predict the effect of road runoff on receiving environments.

Measurement of Surface Interfacial Tension as a Function of Temperature Using Pendant Drop Images

NASA Astrophysics Data System (ADS)

Yakhshi-Tafti, Ehsan; Kumar, Ranganathan; Cho, Hyoung J.

2011-10-01

Accurate and reliable measurements of surface tension at the interface of immiscible phases are crucial to understanding various physico-chemical reactions taking place between those. Based on the pendant drop method, an optical (graphical)-numerical procedure was developed to determine surface tension and its dependency on the surrounding temperature. For modeling and experimental verification, chemically inert and thermally stable perfluorocarbon (PFC) oil and water was used. Starting with geometrical force balance, governing equations were derived to provide non-dimensional parameters which were later used to extract values for surface tension. Comparative study verified the accuracy and reliability of the proposed method.

Balanced and Unbalanced Aspects of Tropical Cyclone Intensification

DTIC Science & Technology

2009-10-06

axisymmetric balance theory. The secondary ( overturning ) circulation and balanced tendency for the primary circulation are obtained by solving a...balance theory. The secondary ( overturning ) circulation and balanced tendency for the primary circulation are obtained by solving a general form of the... meridional circulation . This equation is often referred to as the Sawyer–Eliassen (SE) equation (Willoughby, 1979; Shapiro and Willoughby, 1982). For

A January angular momentum balance in the OSU two-level atmospheric general circulation model

NASA Technical Reports Server (NTRS)

Kim, J.-W.; Grady, W.

1982-01-01

The present investigation is concerned with an analysis of the atmospheric angular momentum balance, based on the simulation data of the Oregon State University two-level atmospheric general circulation model (AGCM). An attempt is also made to gain an understanding of the involved processes. Preliminary results on the angular momentum and mass balance in the AGCM are shown. The basic equations are examined, and questions of turbulent momentum transfer are investigated. The methods of analysis are discussed, taking into account time-averaged balance equations, time and longitude-averaged balance equations, mean meridional circulation, the mean meridional balance of relative angular momentum, and standing and transient components of motion.

Comparing Balance and Inverse Methods on Learning Conceptual and Procedural Knowledge in Equation Solving: A Cognitive Load Perspective

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy Phuong

2016-01-01

We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs -2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for…

40 CFR 1065.655 - Chemical balances of fuel, intake air, and exhaust.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 40 Protection of Environment 33 2014-07-01 2014-07-01 false Chemical balances of fuel, intake air... Chemical balances of fuel, intake air, and exhaust. (a) General. Chemical balances of fuel, intake air, and... balances to determine the flows of the other two. For example, you may use chemical balances along with...

40 CFR 1065.655 - Chemical balances of fuel, intake air, and exhaust.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 40 Protection of Environment 34 2012-07-01 2012-07-01 false Chemical balances of fuel, intake air... Chemical balances of fuel, intake air, and exhaust. (a) General. Chemical balances of fuel, intake air, and... balances to determine the flows of the other two. For example, you may use chemical balances along with...

40 CFR 1065.655 - Chemical balances of fuel, intake air, and exhaust.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 40 Protection of Environment 34 2013-07-01 2013-07-01 false Chemical balances of fuel, intake air... Chemical balances of fuel, intake air, and exhaust. (a) General. Chemical balances of fuel, intake air, and... balances to determine the flows of the other two. For example, you may use chemical balances along with...

40 CFR 1065.655 - Chemical balances of fuel, intake air, and exhaust.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 33 2011-07-01 2011-07-01 false Chemical balances of fuel, intake air... Chemical balances of fuel, intake air, and exhaust. (a) General. Chemical balances of fuel, intake air, and... balances to determine the flows of the other two. For example, you may use chemical balances along with...

40 CFR 1065.655 - Chemical balances of fuel, intake air, and exhaust.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Chemical balances of fuel, intake air... Chemical balances of fuel, intake air, and exhaust. (a) General. Chemical balances of fuel, intake air, and... balances to determine the flows of the other two. For example, you may use chemical balances along with...

Photochemistry of Pluto's Atmosphere

NASA Technical Reports Server (NTRS)

Krasnopolsky, Vladimir A.

1999-01-01

This work include studies of two problems: (1) Modeling thermal balance, structure. and escape processes in Pluto's upper atmosphere. This study has been completed in full. A new method, of analytic solution for the equation of hydrodynamic flow from in atmosphere been developed. It was found that the ultraviolet absorption by methane which was previously ignored is even more important in Pluto's thermal balance than the extreme ultraviolet absorption by nitrogen. Two basic models of the lower atmosphere have been suggested, with a tropopause and a planetary surface at the bottom of the stellar occultation lightcurve, respectively, Vertical profiles, of temperature, density, gas velocity, and the CH4 mixing ratio have been calculated for these two models at low, mean, and high solar activity (six models). We prove that Pluto' " s atmosphere is restricted to 3060-4500 km, which makes possible a close flyby of future spacecraft. Implication for Pluto's evolution have also been discussed. and (2) Modeling of Pluto's photochemistry. Based on the results of (1), we have made some changes in the basic continuity equation and in the boundary conditions which reflect a unique can of hydrodynamic escape and therefore have not been used in modeling of other planetary atmospheres. We model photochemistry of 44 neutral and 23 ion species. This work required solution of a set of 67 second-order nonlinear ordinary differential equations. Two models have been developed. Each model consists of the vertical profiles for 67 species, their escape and precipitation rates. These models predict the chemical structure and basic chemical processes in the current atmosphere and possible implication of these processes for evolution. This study has also been completed in full.

Non-stationary filtration mode during chemical reactions with the gas phase

NASA Astrophysics Data System (ADS)

Zavialov, Ivan; Konyukhov, Andrey; Negodyaev, Sergey

2015-04-01

An experimental and numerical study of filtration accompanied by chemical reactions between displacing fluid and solid skeleton is considered. Glass balls (400-500 μm in diameter) were placed in 1 cm gap between two glass sheets and were used as model porous medium. The baking soda was added to the glass balls. The 70% solution of acetic acid was used as the displacer. The modeling porous medium was saturated with a mineral oil, and then 70% solution of colored acetic acid was pumped through the medium. The glass balls and a mineral oil have a similar refractive index, so the model porous medium was optically transparent. During the filtration, the gas phase was generated by the chemical reactions between the baking soda and acetic acid, and time-dependent displacement of the chemical reaction front was observed. The front of the chemical reaction was associated with the most intensive gas separation. The front moved, stopped, and then moved again to the area where it had been already. We called this process a secondary oxidation wave. To describe this effect, we added to the balance equations a term associated with the formation and disappearance of phases due to chemical reactions. The equations were supplemented by Darcy's law for multiphase filtration. Nonstationarity front propagation of the chemical reaction in the numerical experiment was observed at Damköhler numbers greater than 100. The mathematical modelling was agreed well with the experimental results.

A BGK model for reactive mixtures of polyatomic gases with continuous internal energy

NASA Astrophysics Data System (ADS)

Bisi, M.; Monaco, R.; Soares, A. J.

2018-03-01

In this paper we derive a BGK relaxation model for a mixture of polyatomic gases with a continuous structure of internal energies. The emphasis of the paper is on the case of a quaternary mixture undergoing a reversible chemical reaction of bimolecular type. For such a mixture we prove an H -theorem and characterize the equilibrium solutions with the related mass action law of chemical kinetics. Further, a Chapman-Enskog asymptotic analysis is performed in view of computing the first-order non-equilibrium corrections to the distribution functions and investigating the transport properties of the reactive mixture. The chemical reaction rate is explicitly derived at the first order and the balance equations for the constituent number densities are derived at the Euler level.

"Why not stoichiometry" versus "stoichiometry--why not?" Part I: General context.

PubMed

Michałowska-Kaczmarczyk, Anna Maria; Asuero, Agustin G; Michałowski, Tadeusz

2015-01-01

The elementary concepts involved with stoichiometry are considered from different viewpoints. Some examples of approximate calculations made according to the stoichiometric scheme are indicated, and correct resolution of the problems involved is presented. The principles of balancing chemical equations, based on their apparent similarities with algebraic equations, are criticized. The review concerns some peculiarities inherent in chemical reaction notation and its use (and abuse) in stoichiometric calculations that provide inconsistent results for various reasons. This "conventional" approach to stoichiometry is put in context with the generalized approach to electrolytic systems (GATES) established by Michałowski. The article contains a number of proposals that could potentially be taken into account and included in the next edition of the Orange Book. Notation of ions used in this article is not, deliberately, in accordance with actual IUPAC requirements in this respect. This article is intended to be provocative with the hope that some critical debate around the important topics treated should be generated and creatively expanded in the scientific community.

Chemical and Hydrodynamical Models of Cometary Comae

NASA Technical Reports Server (NTRS)

Charnley, Steven

2012-01-01

Multi-fluid modelling of the outflowing gases which sublimate from cometary nuclei as they approach the Sun is necessary for understanding the important physical and chemical processes occurring in this complex plasma. Coma chemistry models can be employed to interpret observational data and to ultimately determine chemical composition and structure of the nuclear ices and dust. We describe a combined chemical and hydrodynamical model [1] in which differential equations for the chemical abundances and the energy balance are solved as a function of distance from the cometary nucleus. The presence of negative ions (anions) in cometary comae is known from Giotto mass spectrometry of 1P/Halley. The anions O(-), OH(-), C(-), CH(-) and CN(-) have been detected, as well as unidentified anions with masses 22-65 and 85-110 amu [2]. Organic molecular anions such as C4H(-) and C6H(-) are known to have a significant impact on the charge balance of interstellar clouds and circumstellar envelopes and have been shown to act as catalysts for the gas-phase synthesis of larger hydrocarbon molecules in the ISM, but their importance in cometary comae has not yet been fully explored. We present details of new models for the chemistry of cometary comae that include atomic and molecular anions and calculate the impact of these anions on the coma physics and chemistry af the coma.

A well-balanced scheme for Ten-Moment Gaussian closure equations with source term

NASA Astrophysics Data System (ADS)

Meena, Asha Kumari; Kumar, Harish

2018-02-01

In this article, we consider the Ten-Moment equations with source term, which occurs in many applications related to plasma flows. We present a well-balanced second-order finite volume scheme. The scheme is well-balanced for general equation of state, provided we can write the hydrostatic solution as a function of the space variables. This is achieved by combining hydrostatic reconstruction with contact preserving, consistent numerical flux, and appropriate source discretization. Several numerical experiments are presented to demonstrate the well-balanced property and resulting accuracy of the proposed scheme.

A two-phase micromorphic model for compressible granular materials

NASA Astrophysics Data System (ADS)

Paolucci, Samuel; Li, Weiming; Powers, Joseph

2009-11-01

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

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

Modeling chemical vapor deposition of silicon dioxide in microreactors at atmospheric pressure

NASA Astrophysics Data System (ADS)

Konakov, S. A.; Krzhizhanovskaya, V. V.

2015-01-01

We developed a multiphysics mathematical model for simulation of silicon dioxide Chemical Vapor Deposition (CVD) from tetraethyl orthosilicate (TEOS) and oxygen mixture in a microreactor at atmospheric pressure. Microfluidics is a promising technology with numerous applications in chemical synthesis due to its high heat and mass transfer efficiency and well-controlled flow parameters. Experimental studies of CVD microreactor technology are slow and expensive. Analytical solution of the governing equations is impossible due to the complexity of intertwined non-linear physical and chemical processes. Computer simulation is the most effective tool for design and optimization of microreactors. Our computational fluid dynamics model employs mass, momentum and energy balance equations for a laminar transient flow of a chemically reacting gas mixture at low Reynolds number. Simulation results show the influence of microreactor configuration and process parameters on SiO2 deposition rate and uniformity. We simulated three microreactors with the central channel diameter of 5, 10, 20 micrometers, varying gas flow rate in the range of 5-100 microliters per hour and temperature in the range of 300-800 °C. For each microchannel diameter we found an optimal set of process parameters providing the best quality of deposited material. The model will be used for optimization of the microreactor configuration and technological parameters to facilitate the experimental stage of this research.

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

Ghosh, Debojyoti; Constantinescu, Emil M.

The numerical simulation of meso-, convective-, and microscale atmospheric flows requires the solution of the Euler or the Navier-Stokes equations. Nonhydrostatic weather prediction algorithms often solve the equations in terms of derived quantities such as Exner pressure and potential temperature (and are thus not conservative) and/or as perturbations to the hydrostatically balanced equilibrium state. This paper presents a well-balanced, conservative finite difference formulation for the Euler equations with a gravitational source term, where the governing equations are solved as conservation laws for mass, momentum, and energy. Preservation of the hydrostatic balance to machine precision by the discretized equations is essentialmore » because atmospheric phenomena are often small perturbations to this balance. The proposed algorithm uses the weighted essentially nonoscillatory and compact-reconstruction weighted essentially nonoscillatory schemes for spatial discretization that yields high-order accurate solutions for smooth flows and is essentially nonoscillatory across strong gradients; however, the well-balanced formulation may be used with other conservative finite difference methods. The performance of the algorithm is demonstrated on test problems as well as benchmark atmospheric flow problems, and the results are verified with those in the literature.« less

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

NASA Astrophysics Data System (ADS)

Wang, Yaping; Lin, Shunjiang; Yang, Zhibin

2017-05-01

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

A simulation study on the abatement of CO2 emissions by de-absorption with monoethanolamine.

PubMed

Greer, T; Bedelbayev, A; Igreja, J M; Gomes, J F; Lie, B

2010-01-01

Because of the adverse effect of CO2 from fossil fuel combustion on the earth's ecosystems, the most cost-effective method for CO2 capture is an important area of research. The predominant process for CO2 capture currently employed by industry is chemical absorption in amine solutions. A dynamic model for the de-absorption process was developed with monoethanolamine (MEA) solution. Henry's law was used for modelling the vapour phase equilibrium of the CO2, and fugacity ratios calculated by the Peng-Robinson equation of state (EOS) were used for H2O, MEA, N2 and O2. Chemical reactions between CO2 and MEA were included in the model along with the enhancement factor for chemical absorption. Liquid and vapour energy balances were developed to calculate the liquid and vapour temperature, respectively.

Research into the influence of spatial variability and scale on the parameterization of hydrological processes

NASA Technical Reports Server (NTRS)

Wood, Eric F.

1993-01-01

The objectives of the research were as follows: (1) Extend the Representative Elementary Area (RE) concept, first proposed and developed in Wood et al, (1988), to the water balance fluxes of the interstorm period (redistribution, evapotranspiration and baseflow) necessary for the analysis of long-term water balance processes. (2) Derive spatially averaged water balance model equations for spatially variable soil, topography and vegetation, over A RANGE OF CLIMATES. This is a necessary step in our goal to derive consistent hydrologic results up to GCM grid scales necessary for global climate modeling. (3) Apply the above macroscale water balance equations with remotely sensed data and begin to explore the feasibility of parameterizing the water balance constitutive equations at GCM grid scale.

A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction

NASA Astrophysics Data System (ADS)

Zhang, Xiaolong; Zhong, Zheng

2017-10-01

To analyse the frequently encountered thermo-chemo-mechanical problems in chemically active material applications, we develop a thermodynamically-consistent continuum theory of coupled deformation, mass diffusion, heat conduction and chemical reaction. Basic balance equations of force, mass and energy are presented at first, and then fully coupled constitutive laws interpreting multi-field interactions and evolving equations governing irreversible fluxes are constructed according to the energy dissipation inequality and the chemical kinetics. To consider the essential distinction between mass diffusion and chemical reactions in affecting free energy and dissipations of a highly coupled system, we regard both the concentrations of diffusive species and the extent of reaction as independent state variables. This new formulation then distinguishes between the energy contribution from the diffusive species entering the solid and that from the subsequent chemical reactions occurring among these species and the host solid, which not only interact with stresses or strains in different manners and on different time scales, but also induce different variations of solid microstructures and material properties. Taking advantage of this new description, we further establish a specialized isothermal model to predict precisely the transient chemo-mechanical response of a swelling solid with a proposed volumetric constraint that accounts for material incompressibility. Coupled kinetics is incorporated to capture the volumetric swelling of the solid caused by imbibition of external species and the simultaneous dilation arised from chemical reactions between the diffusing species and the solid. The model is then exemplified with two numerical examples of transient swelling accompanied by chemical reaction. Various ratios of characteristic times of diffusion and chemical reaction are taken into account to shed light on the dependency on kinetic time scales of evolution patterns for a diffusion-reaction controlled deformable solid.

Influence of reactions heats on variation of radius, temperature, pressure and chemical species amounts within a single acoustic cavitation bubble.

PubMed

Kerboua, Kaouther; Hamdaoui, Oualid

2018-03-01

The scientific interest toward the study of acoustic bubble is mainly explained by its practical benefit in providing a reactional media favorable to the rapid evolution of chemical mechanism. The evolution of this mechanism is related to the simultaneous and dependent variation of the volume, temperature and pressure within the bubble, retrieved by the resolution of a differential equations system, including among others the thermal balance. This last one is subject to different assumptions, some authors deem simply that the temperature varies adiabatically during the collapsing phase, without considering the reactions heat of the studied mechanism. This paper aims to evaluate the pertinence of neglecting reactions heats in the thermal balance, by analyzing their effect on the variation of radius, temperature, pressure and chemical species amounts. The results show that the introduction of reactions heats conducts to a decrease of the temperature, an increase of the pressure and a reduction of the bubble volume. As a consequence, this leads to a drop of the quantities of free radicals produced by the chemical mechanism evolving within the bubble. This paper also proved that the impact of the consideration of reactions heats is dependent of the frequency and the acoustic amplitude of the ultrasonic wave. Copyright © 2017 Elsevier B.V. All rights reserved.

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration.

PubMed

Sciumè, G; Boso, D P; Gray, W G; Cobelli, C; Schrefler, B A

2014-11-01

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot. Copyright © 2014 John Wiley & Sons, Ltd.

The Role of Deformation Energetics in Long-Term Tectonic Modeling

NASA Astrophysics Data System (ADS)

Ahamed, S.; Choi, E.

2017-12-01

The deformation-related energy budget is usually considered in the simplest form or even entirely omitted from the energy balance equation. We derive a full energy balance equation that accounts not only for heat energy but also for mechanical (elastic, plastic and viscous) work. The derived equation is implemented in DES3D, an unstructured finite element solver for long-term tectonic deformation. We verify the implementation by comparing numerical solutions to the corresponding semi-analytic solutions in three benchmarks extended from the classical oedometer test. We also investigate the long-term effects of deformation energetics on the evolution of large offset normal faults. We find that the models considering the full energy balance equation tend to produce more secondary faults and an elongated core complex. Our results for the normal fault system confirm that persistent inelastic deformation has a significant impact on the long-term evolution of faults, motivating further exploration of the role of the full energy balance equation in other geodynamic systems.

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.

Group Contribution Methods for Phase Equilibrium Calculations.

PubMed

Gmehling, Jürgen; Constantinescu, Dana; Schmid, Bastian

2015-01-01

The development and design of chemical processes are carried out by solving the balance equations of a mathematical model for sections of or the whole chemical plant with the help of process simulators. For process simulation, besides kinetic data for the chemical reaction, various pure component and mixture properties are required. Because of the great importance of separation processes for a chemical plant in particular, a reliable knowledge of the phase equilibrium behavior is required. The phase equilibrium behavior can be calculated with the help of modern equations of state or g(E)-models using only binary parameters. But unfortunately, only a very small part of the experimental data for fitting the required binary model parameters is available, so very often these models cannot be applied directly. To solve this problem, powerful predictive thermodynamic models have been developed. Group contribution methods allow the prediction of the required phase equilibrium data using only a limited number of group interaction parameters. A prerequisite for fitting the required group interaction parameters is a comprehensive database. That is why for the development of powerful group contribution methods almost all published pure component properties, phase equilibrium data, excess properties, etc., were stored in computerized form in the Dortmund Data Bank. In this review, the present status, weaknesses, advantages and disadvantages, possible applications, and typical results of the different group contribution methods for the calculation of phase equilibria are presented.

Effect of multiplicative noise on stationary stochastic process

NASA Astrophysics Data System (ADS)

Kargovsky, A. V.; Chikishev, A. Yu.; Chichigina, O. A.

2018-03-01

An open system that can be analyzed using the Langevin equation with multiplicative noise is considered. The stationary state of the system results from a balance of deterministic damping and random pumping simulated as noise with controlled periodicity. The dependence of statistical moments of the variable that characterizes the system on parameters of the problem is studied. A nontrivial decrease in the mean value of the main variable with an increase in noise stochasticity is revealed. Applications of the results in several physical, chemical, biological, and technical problems of natural and humanitarian sciences are discussed.

A Well-Balanced Central-Upwind Scheme for the 2D Shallow Water Equations on Triangular Meshes

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We are interested in approximating solutions of the two-dimensional shallow water equations with a bottom topography on triangular meshes. We show that there is a certain flexibility in choosing the numerical fluxes in the design of semi-discrete Godunov-type central schemes. We take advantage of this fact to generate a new second-order, central-upwind method for the two-dimensional shallow water equations that is well-balanced. We demonstrate the accuracy of our method as well as its balance properties in a variety of examples.

Catchment Water-Energy Balance Model: Development and Applications

NASA Astrophysics Data System (ADS)

Yang, D.; Yang, H.

2017-12-01

International Hydrological community has widely recognized that the catchment water-energy balance exists, which can be expressed as a general form of E/P = f(E0/P, c), where P is precipitation, E0 is potential evaporation, and c is a parameter. Many empirical/rational formulations of the catchment water-energy balance have been proposed. Several analytical solutions of the water-energy balance equation E/P = f(E0/P, c) have been derived by using dimensional analysis and mathematic reasoning and introducing additional boundary conditions. This paper will summarize the catchment water-energy balance equations and discuss their advantages and limitations. Catchment hydrology has been greatly influenced by the intensive variability in land use/cover, precipitation and air temperature due to climate change and local human activities. The water-energy balance equation, which are usually called the Budyko framework is widely used to analyze the impacts of climate and landscape changes on regional hydrology especially the annual runoff change. In order to quantify impacts of climate change and landscape change on the catchment runoff, the climate elasticity and landscape elasticity are estimated theoretically from the catchment water-energy balance equation. The elasticity of runoff has less of a dependency on the aridity index when the climate is drier (larger aridity index). The precipitation elasticity of runoff was close to 1.0 and that of potential evaporation close to 0.0 in the extreme humid climate with no relation to the landscape conditions, which implies that catchment water balance under extremely wet condition is controlled mainly by the climate condition. We establishes a relationship between the change in the landscape parameter in the catchment water-energy balance equation and vegetation change represented by fPAR, the fraction of Photosynthetically Active Radiation absorbed by vegetation. The fPAR elasticity of runoff is introduced and estimated over China, which indicate that runoff is more sensitive to the change in fPAR in relatively dry catchments. This paper will summarize applications of the water-energy balance equation and discuss on the future development.

The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation

NASA Astrophysics Data System (ADS)

de Oliveira, Luciana Renata; Bazzani, Armando; Giampieri, Enrico; Castellani, Gastone C.

2014-08-01

We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their "far from equilibrium behavior," hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative "external vector field" whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the "plasticity property" of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.

The role of non-equilibrium fluxes in the relaxation processes of the linear chemical master equation.

PubMed

de Oliveira, Luciana Renata; Bazzani, Armando; Giampieri, Enrico; Castellani, Gastone C

2014-08-14

We propose a non-equilibrium thermodynamical description in terms of the Chemical Master Equation (CME) to characterize the dynamics of a chemical cycle chain reaction among m different species. These systems can be closed or open for energy and molecules exchange with the environment, which determines how they relax to the stationary state. Closed systems reach an equilibrium state (characterized by the detailed balance condition (D.B.)), while open systems will reach a non-equilibrium steady state (NESS). The principal difference between D.B. and NESS is due to the presence of chemical fluxes. In the D.B. condition the fluxes are absent while for the NESS case, the chemical fluxes are necessary for the state maintaining. All the biological systems are characterized by their "far from equilibrium behavior," hence the NESS is a good candidate for a realistic description of the dynamical and thermodynamical properties of living organisms. In this work we consider a CME written in terms of a discrete Kolmogorov forward equation, which lead us to write explicitly the non-equilibrium chemical fluxes. For systems in NESS, we show that there is a non-conservative "external vector field" whose is linearly proportional to the chemical fluxes. We also demonstrate that the modulation of these external fields does not change their stationary distributions, which ensure us to study the same system and outline the differences in the system's behavior when it switches from the D.B. regime to NESS. We were interested to see how the non-equilibrium fluxes influence the relaxation process during the reaching of the stationary distribution. By performing analytical and numerical analysis, our central result is that the presence of the non-equilibrium chemical fluxes reduces the characteristic relaxation time with respect to the D.B. condition. Within a biochemical and biological perspective, this result can be related to the "plasticity property" of biological systems and to their capabilities to switch from one state to another as is observed during synaptic plasticity, cell fate determination, and differentiation.

Rates and time scales of clay-mineral formation by weathering in saprolitic regoliths of the southern Appalachians from geochemical mass balance

Treesearch

Jason R. Price; Michael A. Velbel; Lina C. Patino

2005-01-01

Rates of clay formation in three watersheds located at the Coweeta Hydrologic Laboratory, western North Carolina, have been determined from solute flux-based mass balance methods. A system of mass balance equations with enough equations and unknowns to allow calculation of secondary mineral formation rates as well as the more commonly determined primary-...

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

NASA Astrophysics Data System (ADS)

Chertock, Alina; Cui, Shumo; Kurganov, Alexander; Özcan, Şeyma Nur; Tadmor, Eitan

2018-04-01

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one- and two-dimensional examples.

Analysis of an algae-based CELSS. I - Model development

NASA Technical Reports Server (NTRS)

Holtzapple, Mark T.; Little, Frank E.; Makela, Merry E.; Patterson, C. O.

1989-01-01

A steady state chemical model and computer program have been developed for a life support system and applied to trade-off studies. The model is based on human demand for food and oxygen determined from crew metabolic needs. The model includes modules for water recycle, waste treatment, CO2 removal and treatment, and food production. The computer program calculates rates of use and material balance for food, O2, the recycle of human waste and trash, H2O, N2, and food production/supply. A simple noniterative solution for the model has been developed using the steady state rate equations for the chemical reactions. The model and program have been used in system sizing and subsystem trade-off studies of a partially closed life support system.

Analysis of an algae-based CELSS. Part 1: model development

NASA Technical Reports Server (NTRS)

Holtzapple, M. T.; Little, F. E.; Makela, M. E.; Patterson, C. O.

1989-01-01

A steady state chemical model and computer program have been developed for a life support system and applied to trade-off studies. The model is based on human demand for food and oxygen determined from crew metabolic needs. The model includes modules for water recycle, waste treatment, CO2 removal and treatment, and food production. The computer program calculates rates of use and material balance for food. O2, the recycle of human waste and trash, H2O, N2, and food production supply. A simple non-iterative solution for the model has been developed using the steady state rate equations for the chemical reactions. The model and program have been used in system sizing and subsystem trade-off studies of a partially closed life support system.

Simulation of the toxicokinetics of trichloroethylene, methylene chloride, styrene and n-hexane by a toxicokinetics/toxicodynamics model using experimental data.

PubMed

Nakayama, Yumiko; Kishida, Fumio; Nakatsuka, Iwao; Matsuo, Masatoshi

2005-01-01

The toxicokinetics/toxicodynamics (TKTD) model simulates the toxicokinetics of a chemical based on physiological data such as blood flow, tissue partition coefficients and metabolism. In this study, Andersen and Clewell's TKTD model was used with seven compartments and ten differential equations for calculating chemical balances in the compartments (Andersen and Clewell 1996, Workshop on physiologically-based pharmacokinetic/pharmacodynamic modeling and risk assessment, Aug. 5-16 at Colorado State University, U.S.A) . Using this model, the authors attempted to simulate the behavior of four chemicals: trichloroethylene, methylene chloride, styrene and n-hexane, and the results were evaluated. Simulations of the behavior of trichloroethylene taken in via inhalation and oral exposure routes were also done. The differences between simulations and measurements are due to the differences between the absorption rates of the exposure routes. By changing the absorption rates, the simulation showed agreement with the measured values. The simulations of the other three chemicals showed good results. Thus, this model is useful for simulating the behavior of chemicals for preliminary toxicity assessment.

Analysis of biochemical phase shift oscillators by a harmonic balancing technique.

PubMed

Rapp, P

1976-11-25

The use of harmonic balancing techniques for theoretically investigating a large class of biochemical phase shift oscillators is outlined and the accuracy of this approximate technique for large dimension nonlinear chemical systems is considered. It is concluded that for the equations under study these techniques can be successfully employed to both find periodic solutions and to indicate those cases which can not oscillate. The technique is a general one and it is possible to state a step by step procedure for its application. It has a substantial advantage in producing results which are immediately valid for arbitrary dimension. As the accuracy of the method increases with dimension, it complements classical small dimension methods. The results obtained by harmonic balancing analysis are compared with those obtained by studying the local stability properties of the singular points of the differential equation. A general theorem is derived which identifies those special cases where the results of first order harmonic balancing are identical to those of local stability analysis, and a necessary condition for this equivalence is derived. As a concrete example, the n-dimensional Goodwin oscillator is considered where p, the Hill coefficient of the feedback metabolite, is equal to three and four. It is shown that for p = 3 or 4 and n less than or equal to 4 the approximation indicates that it is impossible to construct a set of physically permissible reaction constants such that the system possesses a periodic solution. However for n greater than or equal to 5 it is always possible to find a large domain in the reaction constant space giving stable oscillations. A means of constructing such a parameter set is given. The results obtained here are compared with previously derived results for p = 1 and p = 2.

Greenland Ice Sheet Mass Balance

NASA Technical Reports Server (NTRS)

Reeh, N.

1984-01-01

Mass balance equation for glaciers; areal distribution and ice volumes; estimates of actual mass balance; loss by calving of icebergs; hydrological budget for Greenland; and temporal variations of Greenland mass balance are examined.

Dynamic crack propagation in a 2D elastic body: The out-of-plane case

NASA Astrophysics Data System (ADS)

Nicaise, Serge; Sandig, Anna-Margarete

2007-05-01

Already in 1920 Griffith has formulated an energy balance criterion for quasistatic crack propagation in brittle elastic materials. Nowadays, a generalized energy balance law is used in mechanics [F. Erdogan, Crack propagation theories, in: H. Liebowitz (Ed.), Fracture, vol. 2, Academic Press, New York, 1968, pp. 498-586; L.B. Freund, Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990; D. Gross, Bruchmechanik, Springer-Verlag, Berlin, 1996] in order to predict how a running crack will grow. We discuss this situation in a rigorous mathematical way for the out-of-plane state. This model is described by two coupled equations in the reference configuration: a two-dimensional scalar wave equation for the displacement fields in a cracked bounded domain and an ordinary differential equation for the crack position derived from the energy balance law. We handle both equations separately, assuming at first that the crack position is known. Then the weak and strong solvability of the wave equation will be studied and the crack tip singularities will be derived under the assumption that the crack is straight and moves tangentially. Using the energy balance law and the crack tip behavior of the displacement fields we finally arrive at an ordinary differential equation for the motion of the crack tip.

Reference values and equations reference of balance for children of 8 to 12 years.

PubMed

Libardoni, Thiele de Cássia; Silveira, Carolina Buzzi da; Sinhorim, Larissa Milani Brognoli; Oliveira, Anamaria Siriani de; Santos, Márcio José Dos; Santos, Gilmar Moraes

2018-02-01

There are still no normative data in balance sway for school-age children in Brazil. We aimed to establish the reference ranges for balance scores and to develop prediction equations for estimation of balance scores in children aged 8 to 12 years old. The study included 165 healthy children (83 boys and 82 girls; age, 8-12 years) recruited from a public school in the city of Florianópolis, Santa Catarina, Brazil. We used the Sensory Organization Test to assess the balance scores and both a digital scale and a stadiometer to measure the anthropometric variables. We tested a stepwise multiple-regression model with sex, height, weight, and mid-thigh circumference of the dominant leg as predictors of the balance score. For all experimental conditions, girls' age accounted for over 85% of the variability in balance scores; while, boys' age accounted only 55% of the variability in balance scores. Therefore, balance scores increase with age for boys and girls. This study described the ranges of age- and sex-specific normative values for balance scores in children during 6 different testing conditions established by the sensory organization test. We confirmed that age was the predictor that best explained the variability in balance scores in children between 8 and 12 years old. This study stimulates a new and more comprehensive study to estimate balance scores from prediction equations for overall Brazilian pediatric population. Copyright © 2017 Elsevier B.V. All rights reserved.

A fugacity-based indoor residential pesticide fate model

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

Bennett, Deborah H.; Furtaw, Edward J.; McKone, Thomas E.

Dermal and non-dietary pathways are potentially significant exposure pathways to pesticides used in residences. Exposure pathways include dermal contact with residues on surfaces, ingestion from hand- and object-to-mouth activities, and absorption of pesticides into food. A limited amount of data has been collected on pesticide concentrations in various residential compartments following an application. But models are needed to interpret this data and make predictions about other pesticides based on chemical properties. In this paper, we propose a mass-balance compartment model based on fugacity principles. We include air (both gas phase and aerosols), carpet, smooth flooring, and walls as model compartments.more » Pesticide concentrations on furniture and toys, and in food, are being added to the model as data becomes available. We determine the compartmental fugacity capacity and mass transfer-rate coefficient for wallboard as an example. We also present the framework and equations needed for a dynamic mass-balance model.« less

Improving traditional balancing methods for high-speed rotors

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

Ling, J.; Cao, Y.

1996-01-01

This paper introduces frequency response functions, analyzes the relationships between the frequency response functions and influence coefficients theoretically, and derives corresponding mathematical equations for high-speed rotor balancing. The relationships between the imbalance masses on the rotor and frequency response functions are also analyzed based upon the modal balancing method, and the equations related to the static and dynamic imbalance masses and the frequency response function are obtained. Experiments on a high-speed rotor balancing rig were performed to verify the theory, and the experimental data agree satisfactorily with the analytical solutions. The improvement on the traditional balancing method proposed in thismore » paper will substantially reduce the number of rotor startups required during the balancing process of rotating machinery.« less

A well-balanced finite volume scheme for the Euler equations with gravitation. The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification

NASA Astrophysics Data System (ADS)

Käppeli, R.; Mishra, S.

2016-03-01

Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.

THOR: an open-source exo-GCM

NASA Astrophysics Data System (ADS)

Grosheintz, Luc; Mendonça, João; Käppeli, Roger; Lukas Grimm, Simon; Mishra, Siddhartha; Heng, Kevin

2015-12-01

In this talk, I will present THOR, the first fully conservative, GPU-accelerated exo-GCM (general circulation model) on a nearly uniform, global grid that treats shocks and is non-hydrostatic. THOR will be freely available to the community as a standard tool.Unlike most GCMs THOR solves the full, non-hydrostatic Euler equations instead of the primitive equations. The equations are solved on a global three-dimensional icosahedral grid by a second order Finite Volume Method (FVM). Icosahedral grids are nearly uniform refinements of an icosahedron. We've implemented three different versions of this grid. FVM conserves the prognostic variables (density, momentum and energy) exactly and doesn't require a diffusion term (artificial viscosity) in the Euler equations to stabilize our solver. Historically FVM was designed to treat discontinuities correctly. Hence it excels at resolving shocks, including those present in hot exoplanetary atmospheres.Atmospheres are generally in near hydrostatic equilibrium. We therefore implement a well-balancing technique recently developed at the ETH Zurich. This well-balancing ensures that our FVM maintains hydrostatic equilibrium to machine precision. Better yet, it is able to resolve pressure perturbations from this equilibrium as small as one part in 100'000. It is important to realize that these perturbations are significantly smaller than the truncation error of the same scheme without well-balancing. If during the course of the simulation (due to forcing) the atmosphere becomes non-hydrostatic, our solver continues to function correctly.THOR just passed an important mile stone. We've implemented the explicit part of the solver. The explicit solver is useful to study instabilities or local problems on relatively short time scales. I'll show some nice properties of the explicit THOR. An explicit solver is not appropriate for climate study because the time step is limited by the sound speed. Therefore, we are working on the first fully implicit GCM. By ESS3, I hope to present results for the advection equation.THOR is part of the Exoclimes Simulation Platform (ESP), a set of open-source community codes for simulating and understanding the atmospheres of exoplanets. The ESP also includes tools for radiative transfer and retrieval (HELIOS), an opacity calculator (HELIOS-K), and a chemical kinetics solver (VULCAN). We expect to publicly release an initial version of THOR in 2016 on www.exoclime.org.

Dissipation, generalized free energy, and a self-consistent nonequilibrium thermodynamics of chemically driven open subsystems.

PubMed

Ge, Hao; Qian, Hong

2013-06-01

Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed "universe." A question remains with regard to what the minimally required description for the surrounding of such an open driven system is so that its nonequilibrium thermodynamics can be established solely based on the internal stochastic kinetics. We provide a solution to this problem using insights from studies of molecular motors in a chemical nonequilibrium steady state (NESS) with sustained external drive through a regenerating system or in a quasisteady state (QSS) with an excess amount of adenosine triphosphate (ATP), adenosine diphosphate (ADP), and inorganic phosphate (Pi). We introduce the key notion of minimal work that is needed, W(min), for the external regenerating system to sustain a NESS (e.g., maintaining constant concentrations of ATP, ADP and Pi for a molecular motor). Using a Markov (master-equation) description of a motor protein, we illustrate that the NESS and QSS have identical kinetics as well as the second law in terms of the same positive entropy production rate. The heat dissipation of a NESS without mechanical output is exactly the W(min). This provides a justification for introducing an ideal external regenerating system and yields a free-energy balance equation between the net free-energy input F(in) and total dissipation F(dis) in an NESS: F(in) consists of chemical input minus mechanical output; F(dis) consists of dissipative heat, i.e. the amount of useful energy becoming heat, which also equals the NESS entropy production. Furthermore, we show that for nonstationary systems, the F(dis) and F(in) correspond to the entropy production rate and housekeeping heat in stochastic thermodynamics and identify a relative entropy H as a generalized free energy. We reach a new formulation of Markovian nonequilibrium thermodynamics based on only the internal kinetic equation without further reference to the intrinsic degree of freedom within each Markov state. It includes an extended free-energy balance and a second law which are valid for driven stochastic dynamics with an ideal external regenerating system. Our result suggests new ingredients for a generalized thermodynamics of self-organization in driven systems.

An efficient algorithm using matrix methods to solve wind tunnel force-balance equations

NASA Technical Reports Server (NTRS)

Smith, D. L.

1972-01-01

An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.

Rheodynamic model of cardiac pressure pulsations.

PubMed

Petrov, V G; Nikolov, S G

1999-03-15

To analyse parametrically (in terms of the qualitative theory of dynamical systems) the mechanical influence of inertia, resistance (positive and negative), elasticity and other global properties of the heart-muscle on the left ventricular pressure, an active rheodynamic model based on the Newtons's principles is proposed. The equation of motion of the heart mass centre is derived from an energy conservation law balancing the rate of mechanical (kinetic and potential) energy variation and the power of chemical energy influx and dissipative energy outflux. A corresponding dynamical system of two ordinary differential equations is obtained and parametrically analysed in physiological conditions. As a result, the following main conclusion is made: in physiological norm, because of the heart electrical activity, its equilibrium state is unstable and around it, mechanical self-oscillations emerge. In case the electrical activity ceases, an inverse phase reconstruction occurs during which the unstable equilibrium state of the system becomes stable and the self-oscillations disappear.

Mass-balance modeling of mineral weathering rates and CO2 consumption in the forested, metabasaltic Hauver Branch watershed, Catoctin Mountain, Maryland, USA

USGS Publications Warehouse

Rice, Karen; Price, Jason R.; Szymanski, David W.

2013-01-01

Mineral weathering rates and a forest macronutrient uptake stoichiometry were determined for the forested, metabasaltic Hauver Branch watershed in north-central Maryland, USA. Previous studies of Hauver Branch have had an insufficient number of analytes to permit determination of rates of all the minerals involved in chemical weathering, including biomass. More equations in the mass-balance matrix were added using existing mineralogic information. The stoichiometry of a deciduous biomass term was determined using multi-year weekly to biweekly stream-water chemistry for a nearby watershed, which drains relatively unreactive quartzite bedrock.At Hauver Branch, calcite hosts ~38 mol% of the calcium ion (Ca2+) contained in weathering minerals, but its weathering provides ~90% of the stream water Ca2+. This occurs in a landscape with a regolith residence time of more than several Ka (kiloannum). Previous studies indicate that such old regolith does not typically contain dissolving calcite that affects stream Ca2+/Na+ ratios. The relatively high calcite dissolution rate likely reflects dissolution of calcite in fractures of the deep critical zone.Of the carbon dioxide (CO2) consumed by mineral weathering, calcite is responsible for approximately 27%, with the silicate weathering consumption rate far exceeding that of the global average. The chemical weathering of mafic terrains in decaying orogens thus may be capable of influencing global geochemical cycles, and therefore, climate, on geological timescales. Based on carbon-balance calculations, atmospheric-derived sulfuric acid is responsible for approximately 22% of the mineral weathering occurring in the watershed. Our results suggest that rising air temperatures, driven by global warming and resulting in higher precipitation, will cause the rate of chemical weathering in the Hauver Branch watershed to increase until a threshold temperature is reached. Beyond the threshold temperature, increased recharge would produce a shallower groundwater table and reduced chemical weathering rates.

A theoretical analysis of fluid flow and energy transport in hydrothermal systems

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

A mathematical derivation for fluid flow and energy transport in hydrothermal systems is presented. Specifically, the mathematical model describes the three-dimensional flow of both single- and two-phase, single-component water and the transport of heat in porous media. The derivation begins with the point balance equations for mass, momentum, and energy. These equations are then averaged over a finite volume to obtain the macroscopic balance equations for a porous medium. The macroscopic equations are combined by appropriate constitutive relationships to form two similified partial differential equations posed in terms of fluid pressure and enthalpy. A two-dimensional formulation of the simplified equations is also derived by partial integration in the vertical dimension. (Woodard-USGS)

Students' Understanding of Conservation of Matter, Stoichiometry and Balancing Equations in Indonesia

ERIC Educational Resources Information Center

Agung, Salamah; Schwartz, Marc S.

2007-01-01

This study examines Indonesian students' understanding of conservation of matter, balancing of equations and stoichiometry. Eight hundred and sixty-seven Grade 12 students from 22 schools across four different cities in two developed provinces in Indonesia participated in the study. Nineteen teachers also participated in order to validate the…

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

NASA Astrophysics Data System (ADS)

Oliver, Marcel; Vasylkevych, Sergiy

2016-05-01

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

Modelling system dynamics and phytoplankton diversity at Ranchi lake using the carbon and nutrient mass balance equations.

PubMed

Mukherjee, B; Nivedita, M; Mukherjee, D

2014-05-01

Modelling system dynamics in a hyper-eutrophic lake is quite complex especially with a constant influx of detergents and sewage material which continually changes the state variables and interferes with the assessment of the chemical rhythm occurring in polluted conditions as compared to unpolluted systems. In this paper, a carbon and nutrient mass balance model for predicting system dynamics in a complex environment was studied. Studies were conducted at Ranchi lake to understand the altered environmental dynamics in hyper-eutrophic conditions, and its impact on the plankton community. The lake was monitored regularly for five years (2007 - 2011) and the data collected on the carbon flux, nitrates, phosphates and silicates was used to design a mass balance model for evaluating and predicting the system. The model was then used to correlate the chemical rhythm with that of the phytoplankton dynamics and diversity. Nitrates and phosphates were not limiting (mean nitrate and phosphate concentrations were 1.74 and 0.83 mgl⁻¹ respectively). Free carbon dioxide was found to control the system and, interacting with other parameters determined the diversity and dynamics of the plankton community. N/P ratio determined which group of phytoplankton dominated the community, above 5 it favoured the growth of chlorophyceae while below 5 cyanobacteria dominates. TOC/TIC ratio determined the abundance. The overall system was controlled by the availability of free carbon dioxide which served as a limiting factor.

The chemical formula of a magnetotactic bacterium.

PubMed

Naresh, Mohit; Das, Sayoni; Mishra, Prashant; Mittal, Aditya

2012-05-01

Elucidation of the chemical logic of life is one of the grand challenges in biology, and essential to the progress of the upcoming field of synthetic biology. Treatment of microbial cells explicitly as a "chemical" species in controlled reaction (growth) environments has allowed fascinating discoveries of elemental formulae of a few species that have guided the modern views on compositions of a living cell. Application of mass and energy balances on living cells has proved to be useful in modeling of bioengineering systems, particularly in deriving optimized media compositions for growing microorganisms to maximize yields of desired bio-derived products by regulating intra-cellular metabolic networks. In this work, application of elemental mass balance during growth of Magnetospirillum gryphiswaldense in bioreactors has resulted in the discovery of the chemical formula of the magnetotactic bacterium. By developing a stoichiometric equation characterizing the formation of a magnetotactic bacterial cell, coupled with rigorous experimental measurements and robust calculations, we report the elemental formula of M. gryphiswaldense cell as CH(2.06)O(0.13)N(0.28)Fe(1.74×10(-3)). Remarkably, we find that iron metabolism during growth of this magnetotactic bacterium is much more correlated individually with carbon and nitrogen, compared to carbon and nitrogen with each other, indicating that iron serves more as a nutrient during bacterial growth rather than just a mineral. Magnetotactic bacteria have not only invoked some interest in the field of astrobiology for the last two decades, but are also prokaryotes having the unique ability of synthesizing membrane bound intracellular organelles. Our findings on these unique prokaryotes are a strong addition to the limited repertoire, of elemental compositions of living cells, aimed at exploring the chemical logic of life. Copyright © 2011 Wiley Periodicals, Inc.

Theory and modeling of atmospheric turbulence, part 2

NASA Technical Reports Server (NTRS)

Chen, C. M.

1984-01-01

Two dimensional geostrophic turbulence driven by a random force is investigated. Based on the Liouville equation, which simulates the primitive hydrodynamical equations, a group-kinetic theory of turbulence is developed and the kinetic equation of the scaled singlet distribution is derived. The kinetic equation is transformed into an equation of spectral balance in the equilibrium and non-equilibrium states. Comparison is made between the propagators and the Green's functions in the case of the non-asymptotic quasi-linear equation to prove the equivalence of both kinds of approximations used to describe perturbed trajectories of plasma turbulence. The microdynamical state of fluid turbulence is described by a hydrodynamical system and transformed into a master equation analogous to the Vlasov equation for plasma turbulence. The spectral balance for the velocity fluctuations of individual components shows that the scaled pressure strain correlation and the cascade transfer are two transport functions that play the most important roles.

Recommendations for terminology and databases for biochemical thermodynamics.

PubMed

Alberty, Robert A; Cornish-Bowden, Athel; Goldberg, Robert N; Hammes, Gordon G; Tipton, Keith; Westerhoff, Hans V

2011-05-01

Chemical equations are normally written in terms of specific ionic and elemental species and balance atoms of elements and electric charge. However, in a biochemical context it is usually better to write them with ionic reactants expressed as totals of species in equilibrium with each other. This implies that atoms of elements assumed to be at fixed concentrations, such as hydrogen at a specified pH, should not be balanced in a biochemical equation used for thermodynamic analysis. However, both kinds of equations are needed in biochemistry. The apparent equilibrium constant K' for a biochemical reaction is written in terms of such sums of species and can be used to calculate standard transformed Gibbs energies of reaction Δ(r)G'°. This property for a biochemical reaction can be calculated from the standard transformed Gibbs energies of formation Δ(f)G(i)'° of reactants, which can be calculated from the standard Gibbs energies of formation of species Δ(f)G(j)° and measured apparent equilibrium constants of enzyme-catalyzed reactions. Tables of Δ(r)G'° of reactions and Δ(f)G(i)'° of reactants as functions of pH and temperature are available on the web, as are functions for calculating these properties. Biochemical thermodynamics is also important in enzyme kinetics because apparent equilibrium constant K' can be calculated from experimentally determined kinetic parameters when initial velocities have been determined for both forward and reverse reactions. Specific recommendations are made for reporting experimental results in the literature. Copyright © 2011 Elsevier B.V. All rights reserved.

The chemical (not mechanical) paradigm of thermodynamics of colloid and interface science.

PubMed

Kaptay, George

2018-06-01

In the most influential monograph on colloid and interfacial science by Adamson three fundamental equations of "physical chemistry of surfaces" are identified: the Laplace equation, the Kelvin equation and the Gibbs adsorption equation, with a mechanical definition of surface tension by Young as a starting point. Three of them (Young, Laplace and Kelvin) are called here the "mechanical paradigm". In contrary it is shown here that there is only one fundamental equation of the thermodynamics of colloid and interface science and all the above (and other) equations of this field follow as its derivatives. This equation is due to chemical thermodynamics of Gibbs, called here the "chemical paradigm", leading to the definition of surface tension and to 5 rows of equations (see Graphical abstract). The first row is the general equation for interfacial forces, leading to the Young equation, to the Bakker equation and to the Laplace equation, etc. Although the principally wrong extension of the Laplace equation formally leads to the Kelvin equation, using the chemical paradigm it becomes clear that the Kelvin equation is generally incorrect, although it provides right results in special cases. The second row of equations provides equilibrium shapes and positions of phases, including sessile drops of Young, crystals of Wulff, liquids in capillaries, etc. The third row of equations leads to the size-dependent equations of molar Gibbs energies of nano-phases and chemical potentials of their components; from here the corrected versions of the Kelvin equation and its derivatives (the Gibbs-Thomson equation and the Freundlich-Ostwald equation) are derived, including equations for more complex problems. The fourth row of equations is the nucleation theory of Gibbs, also contradicting the Kelvin equation. The fifth row of equations is the adsorption equation of Gibbs, and also the definition of the partial surface tension, leading to the Butler equation and to its derivatives, including the Langmuir equation and the Szyszkowski equation. Positioning the single fundamental equation of Gibbs into the thermodynamic origin of colloid and interface science leads to a coherent set of correct equations of this field. The same provides the chemical (not mechanical) foundation of the chemical (not mechanical) discipline of colloid and interface science. Copyright © 2018 Elsevier B.V. All rights reserved.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators.

PubMed

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H-S; Ahn, Jaewook

2018-05-04

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

Detailed Balance of Thermalization Dynamics in Rydberg-Atom Quantum Simulators

NASA Astrophysics Data System (ADS)

Kim, Hyosub; Park, YeJe; Kim, Kyungtae; Sim, H.-S.; Ahn, Jaewook

2018-05-01

Dynamics of large complex systems, such as relaxation towards equilibrium in classical statistical mechanics, often obeys a master equation that captures essential information from the complexities. Here, we find that thermalization of an isolated many-body quantum state can be described by a master equation. We observe sudden quench dynamics of quantum Ising-like models implemented in our quantum simulator, defect-free single-atom tweezers in conjunction with Rydberg-atom interaction. Saturation of their local observables, a thermalization signature, obeys a master equation experimentally constructed by monitoring the occupation probabilities of prequench states and imposing the principle of the detailed balance. Our experiment agrees with theories and demonstrates the detailed balance in a thermalization dynamics that does not require coupling to baths or postulated randomness.

Fish tissue lipid-C:N relationships for correcting δ(13) C values and estimating lipid content in aquatic food-web studies.

PubMed

Hoffman, Joel C; Sierszen, Michael E; Cotter, Anne M

2015-11-15

Normalizing δ(13) C values of animal tissue for lipid content is necessary to accurately interpret food-web relationships from stable isotope analysis. To reduce the effort and expense associated with chemical extraction of lipids, various studies have tested arithmetic mass balance to mathematically normalize δ(13) C values for lipid content; however, the approach assumes that lipid content is related to the tissue C:N ratio. We evaluated two commonly used models for estimating tissue lipid content based on C:N ratio (a mass balance model and a stoichiometric model) by comparing model predictions to measure the lipid content of white muscle tissue. We then determined the effect of lipid model choice on δ(13) C values normalized using arithmetic mass balance. To do so, we used a collection of fish from Lake Superior spanning a wide range in lipid content (5% to 73% lipid). We found that the lipid content was positively related to the bulk muscle tissue C:N ratio. The two different lipid models produced similar estimates of lipid content based on tissue C:N, within 6% for tissue C:N values <7. Normalizing δ(13) C values using an arithmetic mass-balance equation based on either model yielded similar results, with a small bias (<1‰) compared with results based on chemical extraction. Among-species consistency in the relationship between fish muscle tissue C:N ratio and lipid content supports the application of arithmetic mass balance to normalize δ(13) C values for lipid content. The uncertainty associated with both lipid extraction quality and choice of model parameters constrains the achievable precision of normalized δ(13) C values to about ±1.0‰. Published in 2015. This article is a U.S. Government work and is in the public domain in the U.S.A.

Direct Determination of the Dependence of the Surface Shear and Dilatational Viscosities on the Thermodynamic State of the Interface: Theoretical Foundations.

PubMed

Lopez; Hirsa

1998-10-01

Recent developments in nonlinear optical techniques for noninvasive probing of a surfactant influenced gas/liquid interface allow for the measurement of the surfactant surface concentration, c, and thus provide new opportunities for the direct determination of its intrinsic viscosities. Here, we present the theoretical foundations, based on the Boussinesq-Scriven surface model without the usual simplification of constant viscosities, for an experimental technique to directly measure the surface shear (µs) and dilatational (kappas) viscosities of a Newtonian interface as functions of the surfactant surface concentration. This ability to directly measure the surfactant concentration permits the use of a simple surface flow for the measurement of the surface viscosities. The requirements are that the interface must be nearly flat, and the flow steady, axisymmetric, and swirling; these flow conditions can be achieved in the deep-channel viscometer driven at relatively fast rates. The tangential stress balance on such an interface leads to two equations; the balance in the azimuthal direction involves only µs and its gradients, and the balance in the radial direction involves both µs and kappas and their gradients. By further exploiting recent developments in laser-based flow measuring techniques, the surface velocities and their gradients which appear in the two equations can be measured directly. The surface tension gradient, which appears in the radial balance equation, is incorporated from the equation of state for the surfactant system and direct measurements of the surfactant surface concentration distribution. The stress balance equations are then ordinary differential equations in the surface viscosities as functions of radial position, which can be readily integrated. Since c is measured as a function of radial position, we then have a direct measurement of µs and kappas as functions of c. Numerical computations of the Navier-Stokes equations are performed to determine the appropriate conditions to achieve the requisite secondary flow. Copyright 1998 Academic Press.

Myths and methodologies: Making sense of exercise mass and water balance.

PubMed

Cheuvront, Samuel N; Montain, Scott J

2017-09-01

What is the topic of this review? There is a need to revisit the basic principles of exercise mass and water balance, the use of common equations and the practice of interpreting outcomes. What advances does it highlight? We propose use of the following equation as a way of simplifying exercise mass and water balance calculations in conditions where food is not consumed and waste is not excreted: ∆body mass - 0.20 g/kcal -1  = ∆body water. The relative efficacy of exercise drinking behaviours can be judged using the following equation: percentage dehydration = [(∆body mass - 0.20 g kcal -1 )/starting body mass] × 100. Changes in body mass occur because of flux in liquids, solids and gases. This knowledge is crucial for understanding metabolism, health and human water needs. In exercise science, corrections to observed changes in body mass to estimate water balance are inconsistently applied and often misinterpreted, particularly after prolonged exercise. Although acute body mass losses in response to exercise can represent a close surrogate for body water losses, the discordance between mass and water balance equivalence becomes increasingly inaccurate as more and more energy is expended. The purpose of this paper is briefly to clarify the roles that respiratory water loss, gas exchange and metabolic water production play in the correction of body mass changes for fluid balance determinations during prolonged exercise. Computations do not include waters of association with glycogen because any movement of water among body water compartments contributes nothing to water or mass flux from the body. Estimates of sweat loss from changes in body mass should adjust for non-sweat losses when possible. We propose use of the following equation as a way of simplifying the study of exercise mass and water balance: ∆body mass - 0.20 g kcal -1  = ∆body water. This equation directly controls for the influence of energy expenditure on body mass balance and the approximate offsetting equivalence of respiratory water loss and metabolic water production on body water balance. The relative efficacy of exercise drinking behaviours can be judged using the following equation: percentage dehydration = [(∆body mass - 0.20 g kcal -1 )/starting body mass] × 100. Published 2017. This article is a U.S. Government work and is in the public domain in the USA.

A Variational Formalism for the Radiative Transfer Equation and a Geostrophic, Hydrostatic Atmosphere: Prelude to Model 3

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.

1991-01-01

The second step in development of MODEL III is summarized. It combines the four radiative transfer equations of the first step with the equations for a geostrophic and hydrostatic atmosphere. This step is intended to bring radiance into a three dimensional balance with wind, height, and temperature. The use of the geostrophic approximation in place of the full set of primitive equations allows for an easier evaluation of how the inclusion of the radiative transfer equation increases the complexity of the variational equations. Seven different variational formulations were developed for geostrophic, hydrostatic, and radiative transfer equations. The first derivation was too complex to yield solutions that were physically meaningful. For the remaining six derivations, the variational method gave the same physical interpretation (the observed brightness temperatures could provide no meaningful input to a geostrophic, hydrostatic balance) at least through the problem solving methodology used in these studies. The variational method is presented and the Euler-Lagrange equations rederived for the geostrophic, hydrostatic, and radiative transfer equations.

Principles of the radiosity method versus radiative transfer for canopy reflectance modeling

NASA Technical Reports Server (NTRS)

Gerstl, Siegfried A. W.; Borel, Christoph C.

1992-01-01

The radiosity method is introduced to plant canopy reflectance modeling. We review the physics principles of the radiosity method which originates in thermal radiative transfer analyses when hot and cold surfaces are considered within a given enclosure. The radiosity equation, which is an energy balance equation for discrete surfaces, is described and contrasted with the radiative transfer equation, which is a volumetric energy balance equation. Comparing the strengths and weaknesses of the radiosity method and the radiative transfer method, we conclude that both methods are complementary to each other. Results of sample calculations are given for canopy models with up to 20,000 discrete leaves.

Gain and loss of esteem, direct reciprocity and Heider balance

NASA Astrophysics Data System (ADS)

Hassanibesheli, Forough; Hedayatifar, Leila; Gawroński, Przemysław; Stojkow, Maria; Żuchowska-Skiba, Dorota; Kułakowski, Krzysztof

2017-02-01

The effect of gain and loss of esteem is introduced into the equations of time evolution of social relations, hostile or friendly, in a group of actors. The equations allow for asymmetric relations. We prove that in the presence of this asymmetry, the majority of stable solutions are jammed states, i.e. the Heider balance is not attained there. A phase diagram is constructed with three phases: the jammed phase, the balanced phase with two mutually hostile groups, and the phase of so-called paradise, where all relations are friendly.

Geostrophic balance with a full Coriolis Force: implications for low latitutde studies

NASA Technical Reports Server (NTRS)

Juarez, M. de la Torre

2002-01-01

In its standard form, geostrophic balance uses a partial representation of the Coriolis force. The resulting formation has a singularity at the equator, and violates mass and momentum conservation. When the horizontal projection of the planetary rotation vector is considered, the singularity at the equator disappears, continuity can be preserved, and quasigeostrophy can be formulated at planetary scale.

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

NASA Technical Reports Server (NTRS)

Hoffert, M. I.

1985-01-01

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

A complete multifluid model for bipolar semiconductors, with interacting carriers, phonons, and photons

NASA Astrophysics Data System (ADS)

Rossani, A.

2017-12-01

If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures T_e and T_h greater than the lattice temperature, the electron-phonon interaction causes energy relaxation. In the non-uniform case a momentum relaxation occurs as well. In view of such an application, a new model, based on an asymptotic procedure for solving the kinetic equations of carriers, phonons, and photons, is proposed, which gives naturally the displaced Maxwellian at the leading order. Several generation-recombination (GR) events occur in bipolar semiconductors. In the presence of photons the most important ones are the radiative GR events, direct, indirect, and exciton-catalyzed. Phonons and photons are treated here as a participating species, with their own equation. All the phonon-photon interactions are accounted for. Moreover, carrier-photon (Compton) interactions are introduced, which make complete the model. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of macroscopic equations for the chemical potentials (carriers), the temperatures (carriers and bosons), and the drift velocities (carriers and bosons). In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered, even in the presence of an external magnetic field.

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

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2011-01-01

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

Development of a multichemical food web model: application to PBDEs in Lake Ellasjoen, Bear Island, Norway.

PubMed

Gandhi, Nilima; Bhavsar, Satyendra P; Gewurtz, Sarah B; Diamond, Miriam L; Evenset, Anita; Christensen, Guttorm N; Gregor, Dennis

2006-08-01

A multichemical food web model has been developed to estimate the biomagnification of interconverting chemicals in aquatic food webs. We extended a fugacity-based food web model for single chemicals to account for reversible and irreversible biotransformation among a parent chemical and transformation products, by simultaneously solving mass balance equations of the chemicals using a matrix solution. The model can be applied to any number of chemicals and organisms or taxonomic groups in a food web. The model was illustratively applied to four PBDE congeners, BDE-47, -99, -100, and -153, in the food web of Lake Ellasjøen, Bear Island, Norway. In Ellasjøen arctic char (Salvelinus alpinus), the multichemical model estimated PBDE biotransformation from higher to lower brominated congeners and improved the correspondence between estimated and measured concentrations in comparison to estimates from the single-chemical food web model. The underestimation of BDE-47, even after considering bioformation due to biotransformation of the otherthree congeners, suggests its formation from additional biotransformation pathways not considered in this application. The model estimates approximate values for congener-specific biotransformation half-lives of 5.7,0.8,1.14, and 0.45 years for BDE-47, -99, -100, and -153, respectively, in large arctic char (S. alpinus) of Lake Ellasjøen.

Estimation of air-water gas exchange coefficient in a shallow lagoon based on 222Rn mass balance.

PubMed

Cockenpot, S; Claude, C; Radakovitch, O

2015-05-01

The radon-222 mass balance is now commonly used to quantify water fluxes due to Submarine Groundwater Discharge (SGD) in coastal areas. One of the main loss terms of this mass balance, the radon evasion to the atmosphere, is based on empirical equations. This term is generally estimated using one among the many empirical equations describing the gas transfer velocity as a function of wind speed that have been proposed in the literature. These equations were, however, mainly obtained from areas of deep water and may be less appropriate for shallow areas. Here, we calculate the radon mass balance for a windy shallow coastal lagoon (mean depth of 6m and surface area of 1.55*10(8) m(2)) and use these data to estimate the radon loss to the atmosphere and the corresponding gas transfer velocity. We present new equations, adapted to our shallow water body, to express the gas transfer velocity as a function of wind speed at 10 m height (wind range from 2 to 12.5 m/s). When compared with those from the literature, these equations fit particularly well with the one of Kremer et al. (2003). Finally, we emphasize that some gas transfer exchange may always occur, even for conditions without wind. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modeling of non-thermal plasma in flammable gas mixtures

NASA Astrophysics Data System (ADS)

Napartovich, A. P.; Kochetov, I. V.; Leonov, S. B.

2008-07-01

An idea of using plasma-assisted methods of fuel ignition is based on non-equilibrium generation of chemically active species that speed up the combustion process. It is believed that gain in energy consumed for combustion acceleration by plasmas is due to the non-equilibrium nature of discharge plasma, which allows radicals to be produced in an above-equilibrium amount. Evidently, the size of the effect is strongly dependent on the initial temperature, pressure, and composition of the mixture. Of particular interest is comparison between thermal ignition of a fuel-air mixture and non-thermal plasma initiation of the combustion. Mechanisms of thermal ignition in various fuel-air mixtures have been studied for years, and a number of different mechanisms are known providing an agreement with experiments at various conditions. The problem is -- how to conform thermal chemistry approach to essentially non-equilibrium plasma description. The electric discharge produces much above-equilibrium amounts of chemically active species: atoms, radicals and ions. The point is that despite excess concentrations of a number of species, total concentration of these species is far below concentrations of the initial gas mixture. Therefore, rate coefficients for reactions of these discharge produced species with other gas mixture components are well known quantities controlled by the translational temperature, which can be calculated from the energy balance equation taking into account numerous processes initiated by plasma. A numerical model was developed combining traditional approach of thermal combustion chemistry with advanced description of the plasma kinetics based on solution of electron Boltzmann equation. This approach allows us to describe self-consistently strongly non-equilibrium electric discharge in chemically unstable (ignited) gas. Equations of pseudo-one-dimensional gas dynamics were solved in parallel with a system of thermal chemistry equations, kinetic equations for charged particles (electrons, positive and negative ions), and with the electric circuit equation. The electric circuit comprises power supply, ballast resistor connected in series with the discharge and capacity. Rate coefficients for electron-assisted reactions were calculated from solving the two-term spherical harmonic expansion of the Boltzmann equation. Such an approach allows us to describe influence of thermal chemistry reactions (burning) on the discharge characteristics. Results of comparison between the discharge and thermal ignition effects for mixtures of hydrogen or ethylene with dry air will be reported. Effects of acceleration of ignition by discharge plasma will be analyzed. In particular, the role of singlet oxygen produced effectively in the discharge in ignition speeding up will be discussed.

Cognitive Load in Algebra: Element Interactivity in Solving Equations

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

2015-01-01

Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

Generalized Spencer-Lewis equation

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

Filippone, W.L.

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.

Phase field approaches of bone remodeling based on TIP

NASA Astrophysics Data System (ADS)

Ganghoffer, Jean-François; Rahouadj, Rachid; Boisse, Julien; Forest, Samuel

2016-01-01

The process of bone remodeling includes a cycle of repair, renewal, and optimization. This adaptation process, in response to variations in external loads and chemical driving factors, involves three main types of bone cells: osteoclasts, which remove the old pre-existing bone; osteoblasts, which form the new bone in a second phase; osteocytes, which are sensing cells embedded into the bone matrix, trigger the aforementioned sequence of events. The remodeling process involves mineralization of the bone in the diffuse interface separating the marrow, which contains all specialized cells, from the newly formed bone. The main objective advocated in this contribution is the setting up of a modeling and simulation framework relying on the phase field method to capture the evolution of the diffuse interface between the new bone and the marrow at the scale of individual trabeculae. The phase field describes the degree of mineralization of this diffuse interface; it varies continuously between the lower value (no mineral) and unity (fully mineralized phase, e.g. new bone), allowing the consideration of a diffuse moving interface. The modeling framework is the theory of continuous media, for which field equations for the mechanical, chemical, and interfacial phenomena are written, based on the thermodynamics of irreversible processes. Additional models for the cellular activity are formulated to describe the coupling of the cell activity responsible for bone production/resorption to the kinetics of the internal variables. Kinetic equations for the internal variables are obtained from a pseudo-potential of dissipation. The combination of the balance equations for the microforce associated to the phase field and the kinetic equations lead to the Ginzburg-Landau equation satisfied by the phase field with a source term accounting for the dissipative microforce. Simulations illustrating the proposed framework are performed in a one-dimensional situation showing the evolution of the diffuse interface separating new bone from marrow.

Estimation of Infiltration Parameters and the Irrigation Coefficients with the Surface Irrigation Advance Distance

PubMed Central

Beibei, Zhou; Quanjiu, Wang; Shuai, Tan

2014-01-01

A theory based on Manning roughness equation, Philip equation and water balance equation was developed which only employed the advance distance in the calculation of the infiltration parameters and irrigation coefficients in both the border irrigation and the surge irrigation. The improved procedure was validated with both the border irrigation and surge irrigation experiments. The main results are shown as follows. Infiltration parameters of the Philip equation could be calculated accurately only using water advance distance in the irrigation process comparing to the experimental data. With the calculated parameters and the water balance equation, the irrigation coefficients were also estimated. The water advance velocity should be measured at about 0.5 m to 1.0 m far from the water advance in the experimental corn fields. PMID:25061664

Mechanical Balance Laws for Boussinesq Models of Surface Water Waves

NASA Astrophysics Data System (ADS)

Ali, Alfatih; Kalisch, Henrik

2012-06-01

Depth-integrated long-wave models, such as the shallow-water and Boussinesq equations, are standard fare in the study of small amplitude surface waves in shallow water. While the shallow-water theory features conservation of mass, momentum and energy for smooth solutions, mechanical balance equations are not widely used in Boussinesq scaling, and it appears that the expressions for many of these quantities are not known. This work presents a systematic derivation of mass, momentum and energy densities and fluxes associated with a general family of Boussinesq systems. The derivation is based on a reconstruction of the velocity field and the pressure in the fluid column below the free surface, and the derivation of differential balance equations which are of the same asymptotic validity as the evolution equations. It is shown that all these mechanical quantities can be expressed in terms of the principal dependent variables of the Boussinesq system: the surface excursion η and the horizontal velocity w at a given level in the fluid.

High order finite volume WENO schemes for the Euler equations under gravitational fields

NASA Astrophysics Data System (ADS)

Li, Gang; Xing, Yulong

2016-07-01

Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

Simulation of 0.3 MWt AFBC test rig burning Turkish lignites

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

Selcuk, N.; Degirmenci, E.; Oymak, O.

1997-12-31

A system model coupling bed and freeboard models for continuous combustion of lignite particles of wide size distribution burning in their own ash in a fluidized bed combustor was modified to incorporate: (1) a procedure for faster computation of particle size distributions (PSDs) without any sacrifice in accuracy; (2) energy balance on char particles for the determination of variation of temperature with particle size, (3) plug flow assumption for the interstitial gas. An efficient and accurate computer code developed for the solution of the conservation equations for energy and chemical species was applied to the prediction of the behavior ofmore » a 0.3 MWt AFBC test rig burning low quality Turkish lignites. The construction and operation of the test rig was carried out within the scope of a cooperation agreement between Middle East Technical University (METU) and Babcock and Wilcox GAMA (BWG) under the auspices of Canadian International Development Agency (CIDA). Predicted concentration and temperature profiles and particle size distributions of solid streams were compared with measured data and found to be in reasonable agreement. The computer code replaces the conventional numerical integration of the analytical solution of population balance with direct integration in ODE form by using a powerful integrator LSODE (Livermore Solver for Ordinary Differential Equations) resulting in two orders of magnitude decrease in CPU (Central Processing Unit) time.« less

Systematic Approach to Calculate the Concentration of Chemical Species in Multi-Equilibrium Problems

ERIC Educational Resources Information Center

Baeza-Baeza, Juan Jose; Garcia-Alvarez-Coque, Maria Celia

2011-01-01

A general systematic approach is proposed for the numerical calculation of multi-equilibrium problems. The approach involves several steps: (i) the establishment of balances involving the chemical species in solution (e.g., mass balances, charge balance, and stoichiometric balance for the reaction products), (ii) the selection of the unknowns (the…

Identifying Students' Misconceptions in Writing Balanced Equations for Dissolving Ionic Compounds in Water and Using Multiple-Choice Questions at the Symbolic and Particulate Levels to Confront These Misconceptions

ERIC Educational Resources Information Center

Naah, Basil M.

2012-01-01

Students who harbor misconceptions often find chemistry difficult to understand. To improve teaching about the dissolving process, first semester introductory chemistry students were asked to complete a free-response questionnaire on writing balanced equations for dissolving ionic compounds in water. To corroborate errors and misconceptions…

Balance in non-hydrostatic rotating stratified turbulence

NASA Astrophysics Data System (ADS)

McKiver, William J.; Dritschel, David G.

It is now well established that two distinct types of motion occur in geophysical turbulence: slow motions associated with potential vorticity advection and fast oscillations due to inertiamaster variable this is known as balance. In real geophysical flows, deviations from balance in the form of inertiaimbalance|N/f) where optimal potential vorticity balancenonlinear quasi-geostrophic balance’ procedure expands the equations of motion to second order in Rossby number but retains the exact (unexpanded) definition of potential vorticity. This proves crucial for obtaining an accurate estimate of balanced motions. In the analysis of rotating stratified turbulence at Ro1 and N/f1, this procedure captures a significantly greater fraction of the underlying balance than standard (linear) quasi-geostrophic balance (which is based on the linearized equations about a state of rest). Nonlinear quasi-geostrophic balance also compares well with optimal potential vorticity balance, which captures the greatest fraction of the underlying balance overall.More fundamentally, the results of these analyses indicate that balance dominates in carefully initialized simulations of freely decaying rotating stratified turbulence up to O(1) Rossby numbers when N/f1. The fluid motion exhibits important quasi-geostrophic features with, in particular, typical height-to-width scale ratios remaining comparable to f/N.

Solving Nonlinear Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Mitchell, L.; David, J.

1986-01-01

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

A Balance of Power?

ERIC Educational Resources Information Center

Mosey, Edward

1991-01-01

The booming economy of the Pacific Northwest region promotes the dilemma of balancing the need for increased electrical power with the desire to maintain that region's unspoiled natural environment. Pertinent factors discussed within the balance equation are population trends, economic considerations, industrial power requirements, and…

Multi-scale kinetic description of granular clusters: invariance, balance, and temperature

NASA Astrophysics Data System (ADS)

Capriz, Gianfranco; Mariano, Paolo Maria

2017-12-01

We discuss a multi-scale continuum representation of bodies made of several mass particles flowing independently each other. From an invariance procedure and a nonstandard balance of inertial actions, we derive the balance equations introduced in earlier work directly in pointwise form, essentially on the basis of physical plausibility. In this way, we analyze their foundations. Then, we propose a Boltzmann-type equation for the distribution of kinetic energies within control volumes in space and indicate how such a distribution allows us to propose a definition of (granular) temperature along processes far from equilibrium.

A self-consistent fluid model for radio-frequency discharges in SiH4-H2 compared to experiments

NASA Astrophysics Data System (ADS)

Nienhuis, G. J.; Goedheer, W. J.; Hamers, E. A. G.; van Sark, W. G. J. H. M.; Bezemer, J.

1997-09-01

A one-dimensional fluid model for radio-frequency glow discharges is presented which describes silane/hydrogen discharges that are used for the deposition of amorphous silicon (a-Si:H). The model is used to investigate the relation between the external settings (such as pressure, gas inlet, applied power, and frequency) and the resulting composition of the gas and the deposition rate. In the model, discharge quantities such as the electric field, densities, and fluxes of the particles are calculated self-consistently. Look-up tables of the rates of the electron impact collisions as a function of the average electron energy are obtained by solving the Boltzmann equation in a two term approximation for a sequence of values of the reduced electric field. These tables are updated as the composition of the background neutral gas evolves under the influence of chemical reactions and pumping. Pumping configuration and gas inlet are taken into account by adding source terms in the density balance equations. The effect of pumping is represented by an average residence time. The gas inlet is represented by uniformly distributed particle sources. Also the radial transport of neutrals from the discharge volume into the discharge-free volume is important. As the fluid model is one dimensional, this radial transport is taken into account by an additional source term in the density balance equations. Plasma-wall interaction of the radicals (i.e., the growth of a-Si:H) is included through the use of sticking coefficients. A sensitivity study has been used to find a minimum set of different particles and reactions needed to describe the discharge adequately and to reduce the computational effort. This study has also been used to identify the most important plasma-chemical processes and resulted in a minimum set of 24 species, 15 electron-neutral reactions, and 22 chemical reactions. In order to verify the model, including the chemistry used, the results are compared with data from experiments. The partial pressures of silane, hydrogen, disilane, and the growth rate of amorphous silicon are compared for various combinations of the operating pressure (10-50 Pa), the power (2.5-10 W), and the frequency (13.56-65 MHz). The model shows good agreement with the experimental data in the dust free α regime. Discharges in the γ' regime, where dust has a significant influence, could not be used to validate the model.

An electrical analogy relating the Atlantic multidecadal oscillation to the Atlantic meridional overturning circulation.

PubMed

Kurtz, Bruce E

2014-01-01

The Atlantic meridional overturning circulation (AMOC) is the northward flow of surface water to subpolar latitudes where deepwater is formed, balanced by southward abyssal flow and upwelling in the vicinity of the Southern Ocean. It is generally accepted that AMOC flow oscillates with a period of 60-80 years, creating a regular variation in North Atlantic sea surface temperature known as the Atlantic multidecadal oscillation (AMO). This article attempts to answer two questions: how is the AMOC driven and why does it oscillate? Using methods commonly employed by chemical engineers for analyzing processes involving flowing liquids, apparently not previously applied to trying to understand the AMOC, an equation is developed for AMOC flow as a function of the meridional density gradient or the corresponding temperature gradient. The equation is based on the similarity between the AMOC and an industrial thermosyphon loop cooler, which circulates a heat transfer liquid without using a mechanical pump. Extending this equation with an analogy between the flow of heat and electricity explains why the AMOC flow oscillates and what determines its period. Calculated values for AMOC flow and AMO oscillation period are in good agreement with measured values.

An Electrical Analogy Relating the Atlantic Multidecadal Oscillation to the Atlantic Meridional Overturning Circulation

PubMed Central

Kurtz, Bruce E.

2014-01-01

The Atlantic meridional overturning circulation (AMOC) is the northward flow of surface water to subpolar latitudes where deepwater is formed, balanced by southward abyssal flow and upwelling in the vicinity of the Southern Ocean. It is generally accepted that AMOC flow oscillates with a period of 60–80 years, creating a regular variation in North Atlantic sea surface temperature known as the Atlantic multidecadal oscillation (AMO). This article attempts to answer two questions: how is the AMOC driven and why does it oscillate? Using methods commonly employed by chemical engineers for analyzing processes involving flowing liquids, apparently not previously applied to trying to understand the AMOC, an equation is developed for AMOC flow as a function of the meridional density gradient or the corresponding temperature gradient. The equation is based on the similarity between the AMOC and an industrial thermosyphon loop cooler, which circulates a heat transfer liquid without using a mechanical pump. Extending this equation with an analogy between the flow of heat and electricity explains why the AMOC flow oscillates and what determines its period. Calculated values for AMOC flow and AMO oscillation period are in good agreement with measured values. PMID:24940739

Numerical approaches to model perturbation fire in turing pattern formations

NASA Astrophysics Data System (ADS)

Campagna, R.; Brancaccio, M.; Cuomo, S.; Mazzoleni, S.; Russo, L.; Siettos, K.; Giannino, F.

2017-11-01

Turing patterns were observed in chemical, physical and biological systems described by coupled reaction-diffusion equations. Several models have been formulated proposing the water as the causal mechanism of vegetation pattern formation, but this isn't an exhaustive hypothesis in some natural environments. An alternative explanation has been related to the plant-soil negative feedback. In Marasco et al. [1] the authors explored the hypothesis that both mechanisms contribute in the formation of regular and irregular vegetation patterns. The mathematical model consists in three partial differential equations (PDEs) that take into account for a dynamic balance between biomass, water and toxic compounds. A numerical approach is mandatory also to investigate on the predictions of this kind of models. In this paper we start from the mathematical model described in [1], set the model parameters such that the biomass reaches a stable spatial pattern (spots) and present preliminary studies about the occurrence of perturbing events, such as wildfire, that can affect the regularity of the biomass configuration.

Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio

NASA Astrophysics Data System (ADS)

Ramos-Méndez, J.; Perl, J.; Schuemann, J.; McNamara, A.; Paganetti, H.; Faddegon, B.

2018-05-01

Simulation of water radiolysis and the subsequent chemistry provides important information on the effect of ionizing radiation on biological material. The Geant4 Monte Carlo toolkit has added chemical processes via the Geant4-DNA project. The TOPAS tool simplifies the modeling of complex radiotherapy applications with Geant4 without requiring advanced computational skills, extending the pool of users. Thus, a new extension to TOPAS, TOPAS-nBio, is under development to facilitate the configuration of track-structure simulations as well as water radiolysis simulations with Geant4-DNA for radiobiological studies. In this work, radiolysis simulations were implemented in TOPAS-nBio. Users may now easily add chemical species and their reactions, and set parameters including branching ratios, dissociation schemes, diffusion coefficients, and reaction rates. In addition, parameters for the chemical stage were re-evaluated and updated from those used by default in Geant4-DNA to improve the accuracy of chemical yields. Simulation results of time-dependent and LET-dependent primary yields Gx (chemical species per 100 eV deposited) produced at neutral pH and 25 °C by short track-segments of charged particles were compared to published measurements. The LET range was 0.05–230 keV µm‑1. The calculated Gx values for electrons satisfied the material balance equation within 0.3%, similar for protons albeit with long calculation time. A smaller geometry was used to speed up proton and alpha simulations, with an acceptable difference in the balance equation of 1.3%. Available experimental data of time-dependent G-values for agreed with simulated results within 7%  ±  8% over the entire time range; for over the full time range within 3%  ±  4% for H2O2 from 49%  ±  7% at earliest stages and 3%  ±  12% at saturation. For the LET-dependent Gx, the mean ratios to the experimental data were 1.11  ±  0.98, 1.21  ±  1.11, 1.05  ±  0.52, 1.23  ±  0.59 and 1.49  ±  0.63 (1 standard deviation) for , , H2, H2O2 and , respectively. In conclusion, radiolysis and subsequent chemistry with Geant4-DNA has been successfully incorporated in TOPAS-nBio. Results are in reasonable agreement with published measured and simulated data.

Nutrition, Balance and Fear of Falling as Predictors of Risk for Falls among Filipino Elderly in Nursing Homes: A Structural Equation Model (SEM)

ERIC Educational Resources Information Center

de Guzman, Allan B.; Ines, Joanna Louise C.; Inofinada, Nina Josefa A.; Ituralde, Nielson Louie J.; Janolo, John Robert E.; Jerezo, Jnyv L.; Jhun, Hyae Suk J.

2013-01-01

While a number of empirical studies have been conducted regarding risk for falls among the elderly, there is still a paucity of similar studies in a developing country like the Philippines. This study purports to test through Structural Equation Modeling (SEM) a model that shows the interaction between and among nutrition, balance, fear of…

Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity

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

Lee, Kok Foong; Patterson, Robert I.A.; Wagner, Wolfgang

2015-12-15

Graphical abstract: -- Highlights: •Problems concerning multi-compartment population balance equations are studied. •A class of fragmentation weight transfer functions is presented. •Three stochastic weighted algorithms are compared against the direct simulation algorithm. •The numerical errors of the stochastic solutions are assessed as a function of fragmentation rate. •The algorithms are applied to a multi-dimensional granulation model. -- Abstract: This paper introduces stochastic weighted particle algorithms for the solution of multi-compartment population balance equations. In particular, it presents a class of fragmentation weight transfer functions which are constructed such that the number of computational particles stays constant during fragmentation events. Themore » weight transfer functions are constructed based on systems of weighted computational particles and each of it leads to a stochastic particle algorithm for the numerical treatment of population balance equations. Besides fragmentation, the algorithms also consider physical processes such as coagulation and the exchange of mass with the surroundings. The numerical properties of the algorithms are compared to the direct simulation algorithm and an existing method for the fragmentation of weighted particles. It is found that the new algorithms show better numerical performance over the two existing methods especially for systems with significant amount of large particles and high fragmentation rates.« less

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

NASA Astrophysics Data System (ADS)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

The mechanical and chemical equations of motion of muscle contraction

NASA Astrophysics Data System (ADS)

Shiner, J. S.; Sieniutycz, Stanislaw

1997-11-01

Up to now no formulation of muscle contraction has provided both the chemical kinetic equations for the reactions responsible for the contraction and the mechanical equation of motion for the muscle. This has most likely been due to the lack of general formalisms for nonlinear systems with chemical-nonchemical coupling valid under the far from equilibrium conditions under which muscle operates physiologically. We have recently developed such formalisms and apply them here to the formulation of muscle contraction to obtain both the chemical and the mechanical equations. The standard formulation up to now has yielded only the dynamic equations for the chemical variables and has considered these to be functions of both time and an appropriate mechanical variable. The macroscopically observable quantities were then obtained by averaging over the mechanical variable. When attempting to derive the dynamics equations for both the chemistry and mechanics this choice of variables leads to conflicting results for the mechanical equation of motion when two different general formalisms are applied. The conflict can be resolved by choosing the variables such that both the chemical variables and the mechanical variables are considered to be functions of time alone. This adds one equation to the set of differential equations to be solved but is actually a simplification of the problem, since these equations are ordinary differential equations, not the partial differential equations of the now standard formulation, and since in this choice of variables the variables themselves are the macroscopic observables the procedure of averaging over the mechanical variable is eliminated. Furthermore, the parameters occurring in the equations at this level of description should be accessible to direct experimental determination.

Numerical simulation of the generation of reactive oxygen and nitrogen species (RONS) in water by atmospheric-pressure plasmas and their effects on Escherichia coli (E. coli)

NASA Astrophysics Data System (ADS)

Ikuse, Kazumasa; Hamaguchi, Satoshi

2016-09-01

We have used two types of numerical simulations to examine biological effects of reactive oxygen and nitrogen species (RONS) generated in water by an atmospheric-pressure plasma (APP) that irradiates the water surface. One is numerical simulation for the generation and transport of RONS in water based on the reaction-diffusion-advection equations coupled with Poisson equation. The rate constants, mobilities, and diffusion coefficients used in the equations are obtained from the literature. The gaseous species are given as boundary conditions and time evolution of the concentrations of chemical species in pure water is solved numerically as functions of the depth in one dimension. Although it is not clear how living organisms respond to such exogenous RONS, we also use numerical simulation for metabolic reactions of Escherichia coli (E. coli) and examine possible effects of such RONS on an in-silico model organism. The computation model is based on the flux balance analysis (FBA), where the fluxes of the metabolites in a biological system are evaluated in steady state, i.e., under the assumption that the fluxes do not change in time. The fluxes are determined with liner programming to maximize the growth rate of the bacteria under the given conditions. Although FBA cannot be directly applied to dynamical responses of metabolic reactions, the simulation still gives insight into the biological reactions to exogenous chemical species generated by an APP. Partially supported by JSPS Grants-in-Aid for Scientific Research.

On Thermodiffusion and Gauge Transformations for Thermodynamic Fluxes and Driving Forces

NASA Astrophysics Data System (ADS)

Goldobin, D. S.

2017-12-01

We discuss the molecular diffusion transport in infinitely dilute liquid solutions under nonisothermal conditions. This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of chemical potential in the presence of temperature gradient. The transport equations contain the contributions owned by a gauge transformation related to the fact that chemical potential is determined up to the summand of form ( AT + B) with arbitrary constants A and B, where constant A is owned by the entropy invariance with respect to shifts by a constant value and B is owned by the potential energy invariance with respect to shifts by a constant value. The coefficients of the cross-effect terms in thermodynamic fluxes are contributed by this gauge transformation and, generally, are not the actual cross-effect physical transport coefficients. Our treatment is based on consideration of the entropy balance and suggests a promising hint for attempts of evaluation of the thermal diffusion constant from the first principles. We also discuss the impossibility of the "barodiffusion" for dilute solutions, understood in a sense of diffusion flux driven by the pressure gradient itself. When one speaks of "barodiffusion" terms in literature, these terms typically represent the drift in external potential force field (e.g., electric or gravitational fields), where in the final equations the specific force on molecules is substituted with an expression with the hydrostatic pressure gradient this external force field produces. Obviously, the interpretation of the latter as barodiffusion is fragile and may hinder the accounting for the diffusion fluxes produced by the pressure gradient itself.

The role of boundary layer momentum advection in the mean location of the ITCZ

NASA Astrophysics Data System (ADS)

Dixit, Vishal; Srinivasan, J.

2017-08-01

The inter-tropical convergence zones (ITCZ) form closer to the equator during equinoxes while they form well away from the equator during the boreal summer. A simple three-way balance between the pressure gradients, Coriolis force and effective Rayleigh friction has been classically used to diagnose the location of maximum boundary layer convergence in the near equatorial ITCZ. If such a balance can capture the dynamics of off-equatorial convergence was not known. We used idealized aqua planet simulations with fixed, zonally symmetric sea surface temperature boundary conditions to simulate the near equatorial and off-equatorial ITCZ. As opposed to the convergence of inter-hemispheric flows in the near equatorial convergence, the off-equatorial convergence forms due to the deceleration of cross-equatorial meridional flow. The detailed momentum budget of the off-equatorial convergence zone reveals that the simple balance is not sufficient to capture the relevant dynamics. The deceleration of the meridional flow is strongly modulated by the inertial effects due to the meridional advection of zonal momentum in addition to the terms in the simple balance. The simple balance predicts a spurious near equatorial convergence and a consistent off-equatorial convergence of the meridional flow. The spurious convergence disappears when inertial effects are included in the balance. As cross equatorial meridional flow decelerates to form convergence, the inertial effects cancel the pressure gradient effects near the equator while they add away from the equator. The contribution to the off-equatorial convergence induced by the pressure gradients is significantly larger than the contribution due to the inertial effects and hence pressure gradients appear to be the primary factor in anchoring the strength and location of the off-equatorial convergence.

Model reduction for stochastic chemical systems with abundant species.

PubMed

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2015-12-07

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.

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

PubMed

Grima, R

2010-07-21

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.

Comparison of SOC estimates and uncertainties from aerosol chemical composition and gas phase data in Atlanta

NASA Astrophysics Data System (ADS)

Pachon, Jorge E.; Balachandran, Sivaraman; Hu, Yongtao; Weber, Rodney J.; Mulholland, James A.; Russell, Armistead G.

2010-10-01

In the Southeastern US, organic carbon (OC) comprises about 30% of the PM 2.5 mass. A large fraction of OC is estimated to be of secondary origin. Long-term estimates of SOC and uncertainties are necessary in the evaluation of air quality policy effectiveness and epidemiologic studies. Four methods to estimate secondary organic carbon (SOC) and respective uncertainties are compared utilizing PM 2.5 chemical composition and gas phase data available in Atlanta from 1999 to 2007. The elemental carbon (EC) tracer and the regression methods, which rely on the use of tracer species of primary and secondary OC formation, provided intermediate estimates of SOC as 30% of OC. The other two methods, chemical mass balance (CMB) and positive matrix factorization (PMF) solve mass balance equations to estimate primary and secondary fractions based on source profiles and statistically-derived common factors, respectively. CMB had the highest estimate of SOC (46% of OC) while PMF led to the lowest (26% of OC). The comparison of SOC uncertainties, estimated based on propagation of errors, led to the regression method having the lowest uncertainty among the four methods. We compared the estimates with the water soluble fraction of the OC, which has been suggested as a surrogate of SOC when biomass burning is negligible, and found a similar trend with SOC estimates from the regression method. The regression method also showed the strongest correlation with daily SOC estimates from CMB using molecular markers. The regression method shows advantages over the other methods in the calculation of a long-term series of SOC estimates.

Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Bryson, Steve; Levy, Doron

2004-01-01

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.

A Four-parameter Budyko Equation for Mean Annual Water Balance

NASA Astrophysics Data System (ADS)

Tang, Y.; Wang, D.

2016-12-01

In this study, a four-parameter Budyko equation for long-term water balance at watershed scale is derived based on the proportionality relationships of the two-stage partitioning of precipitation. The four-parameter Budyko equation provides a practical solution to balance model simplicity and representation of dominated hydrologic processes. Under the four-parameter Budyko framework, the key hydrologic processes related to the lower bound of Budyko curve are determined, that is, the lower bound is corresponding to the situation when surface runoff and initial evaporation not competing with base flow generation are zero. The derived model is applied to 166 MOPEX watersheds in United States, and the dominant controlling factors on each parameter are determined. Then, four statistical models are proposed to predict the four model parameters based on the dominant controlling factors, e.g., saturated hydraulic conductivity, fraction of sand, time period between two storms, watershed slope, and Normalized Difference Vegetation Index. This study shows a potential application of the four-parameter Budyko equation to constrain land-surface parameterizations in ungauged watersheds or general circulation models.

Work-life balance culture, work-home interaction, and emotional exhaustion: a structural equation modeling approach.

PubMed

Nitzsche, Anika; Pfaff, Holger; Jung, Julia; Driller, Elke

2013-01-01

To examine the relationships among employees' emotional exhaustion, positive and negative work-home interaction, and perceived work-life balance culture in companies. Data for this study were collected through online surveys of employees from companies in the micro- and nanotechnology sectors (N = 509). A structural equation modeling analysis was performed. A company culture perceived by employees as supportive of their work-life balance was found to have both a direct negative effect on emotional exhaustion and an indirect negative effect meditated by negative work-home interaction. In addition, whereas negative work-home interaction associated positively with emotional exhaustion, positive work-home interaction had no significant effect. The direct and indirect relationship between work-life balance culture and emotional exhaustion has practical implications for health promotion in companies.

DNS, Enstrophy Balance, and the Dissipation Equation in a Separated Turbulent Channel Flow

NASA Technical Reports Server (NTRS)

Balakumar, Ponnampalam; Rubinstein, Robert; Rumsey, Christopher L.

2013-01-01

The turbulent flows through a plane channel and a channel with a constriction (2-D hill) are numerically simulated using DNS and RANS calculations. The Navier-Stokes equations in the DNS are solved using a higher order kinetic energy preserving central schemes and a fifth order accurate upwind biased WENO scheme for the space discretization. RANS calculations are performed using the NASA code CFL3D with the komega SST two-equation model and a full Reynolds stress model. Using DNS, the magnitudes of different terms that appear in the enstrophy equation are evaluated. The results show that the dissipation and the diffusion terms reach large values at the wall. All the vortex stretching terms have similar magnitudes within the buffer region. Beyond that the triple correlation among the vorticity and strain rate fluctuations becomes the important kinematic term in the enstrophy equation. This term is balanced by the viscous dissipation. In the separated flow, the triple correlation term and the viscous dissipation term peak locally and balance each other near the separated shear layer region. These findings concur with the analysis of Tennekes and Lumley, confirming that the energy transfer terms associated with the small-scale dissipation and the fluctuations of the vortex stretching essentially cancel each other, leaving an equation for the dissipation that is governed by the large-scale motion.

The roles of time and displacement in velocity-dependent volumetric strain of fault zones

USGS Publications Warehouse

Beeler, N.M.; Tullis, T.E.

1997-01-01

The relationship between measured friction??A and volumetric strain during frictional sliding was determined using a rate and state variable dependent friction constitutive equation, a common work balance relating friction and volume change, and two types of experimental faults: initially bare surfaces of Westerly granite and rock surfaces separated by a 1 mm layer of < 90 ??m Westerly granite gouge. The constitutive equation is the sum of a constant term representing the nominal resistance to sliding and two smaller terms: a rate dependent term representing the shear viscosity of the fault surface (direct effect), and a term which represents variations in the area of contact (evolution effect). The work balance relationship requires that ??A differs from the frictional resistance that leads to shear heating by the derivative of fault normal displacement with respect shear displacement, d??n ld??s. An implication of this relationship is that the rate dependence of d??n ld??s contributes to the rate dependence of ??A. Experiments show changes in sliding velocity lead to changes in both fault strength and volume. Analysis of data with the rate and state equations combined with the work balance relationship preclude the conventional interpretation of the direct effect in the rate and state variable constitutive equations. Consideration of a model bare surface fault consisting of an undeformable indentor sliding on a deformable surface reveals a serious flaw in the work balance relationship if volume change is time-dependent. For the model, at zero slip rate indentation creep under the normal load leads to time-dependent strengthening of the fault surface but, according to the work balance relationship, no work is done because compaction or dilatancy can only be induced by shearing. Additional tests on initially bare surfaces and gouges show that fault normal strain in experiments is time-dependent, consistent with the model. This time-dependent fault normal strain, which is not accounted for in the work balance relationship, explains the inconsistency between the constitutive equations and the work balance. For initially bare surface faults, all rate dependence of volume change is due to time dependence. Similar results are found for gouge. We conclude that ??A reflects the frictional resistance that results in shear heating, and no correction needs to be made for the volume changes. The result that time-dependent volume changes do not contribute to ??A is a general result and extends beyond these experiments, the simple indentor model and particular constitutive equations used to illustrate the principle.

An Analysis of the Algebraic Method for Balancing Chemical Reactions.

ERIC Educational Resources Information Center

Olson, John A.

1997-01-01

Analyzes the algebraic method for balancing chemical reactions. Introduces a third general condition that involves a balance between the total amount of oxidation and reduction. Requires the specification of oxidation states for all elements throughout the reaction. Describes the general conditions, the mathematical treatment, redox reactions, and…

Determination of dryout localization using a five-equation model of annular flow for boiling in minichannels

NASA Astrophysics Data System (ADS)

Wajs, Jan; Mikielewicz, Dariusz

2017-03-01

Detailed studies have suggested that the critical heat flux in the form of dryout in minichannels occurs when the combined effects of entrainment, deposition, and evaporation of the film make the film flow rate go gradually and smoothly to zero. Most approaches so far used the mass balance equation for the liquid film with appropriate formulations for the rate of deposition and entrainment respectively. It must be acknowledged that any discrepancy in determination of deposition and entrainment rates, together with cross-correlations between them, leads to the loss of accuracy of model predictions. Conservation equations relating the primary parameters are established for the liquid film and vapor core. The model consists of three mass balance equations, for liquid in the film as well as two-phase core and the gas phase itself. These equations are supplemented by the corresponding momentum equations for liquid in the film and the two-phase core. Applicability of the model has been tested on some experimental data.

Managing Element Interactivity in Equation Solving

ERIC Educational Resources Information Center

Ngu, Bing Hiong; Phan, Huy P.; Yeung, Alexander Seeshing; Chung, Siu Fung

2018-01-01

Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…

``Lock and key mechanism'' for ligand binding with adrenergic receptors and the arising mechanical effects on the cell membrane

NASA Astrophysics Data System (ADS)

Lunghi, Laura; Deseri, Luca

2013-03-01

Chemicals hitting the surface of cell aggregates are known to give arise to cyclic Adenosine Mono Phosphate (cAMP), a second messenger that transduces inside the cell the effects of species that cannot get through the cell membrane. Ligands bind to a specific receptor following the so called ``lock and key mechanism'' (beta)-adrenergic receptors are proteins embedded in the lipid bilayer characterized by seven transmembrane helices. Thinning and thickening in cell membranes may be initiated by conformational changes of some of three of the seven domains above. The cell response is linked to the coupling of chemical, conformational and mechanical effects. Part of the cAMP remains intracellular, whereas the remaining fractions migrates outside the cell due to membrane transporters. A new Helmholtz free energy, accounting for receptor and transporter densities, receptor conformation field and membrane elasticity is investigated. It is shown how the density of active receptors is directly related to the conformation field and it enters the resulting balance equation for the membrane stress. Balance laws for fluxes of transporters and receptors, coupled with the former because of the outgoing cAMP flux caused by the transporters, as well as for the diffusive powers must be supplied. The Center for Nonlinear Analysis through the NSF Grant No. DMS-0635983 is gratefully acknowledged.

Exact solutions of the population balance equation including particle transport, using group analysis

NASA Astrophysics Data System (ADS)

Lin, Fubiao; Meleshko, Sergey V.; Flood, Adrian E.

2018-06-01

The population balance equation (PBE) has received an unprecedented amount of attention in recent years from both academics and industrial practitioners because of its long history, widespread use in engineering, and applicability to a wide variety of particulate and discrete-phase processes. However it is typically impossible to obtain analytical solutions, although in almost every case a numerical solution of the PBEs can be obtained. In this article, the symmetries of PBEs with homogeneous coagulation kernels involving aggregation, breakage and growth processes and particle transport in one dimension are found by direct solving the determining equations. Using the optimal system of one and two-dimensional subalgebras, all invariant solutions and reduced equations are obtained. In particular, an explicit analytical physical solution is also presented.

40 CFR 98.123 - Calculating GHG emissions.

Code of Federal Regulations, 2012 CFR

2012-07-01

... mass balance approach to estimate your fluorinated GHG emissions from a process, you must ensure that... relative errors associated with using the mass balance approach on that process using Equations L-1 through... mass-balance approach to estimate emissions from the process if this calculation results in an absolute...

40 CFR 98.123 - Calculating GHG emissions.

Code of Federal Regulations, 2014 CFR

2014-07-01

... mass balance approach to estimate your fluorinated GHG emissions from a process, you must ensure that... relative errors associated with using the mass balance approach on that process using Equations L-1 through... mass-balance approach to estimate emissions from the process if this calculation results in an absolute...

40 CFR 98.123 - Calculating GHG emissions.

Code of Federal Regulations, 2013 CFR

2013-07-01

... mass balance approach to estimate your fluorinated GHG emissions from a process, you must ensure that... relative errors associated with using the mass balance approach on that process using Equations L-1 through... mass-balance approach to estimate emissions from the process if this calculation results in an absolute...

40 CFR 98.123 - Calculating GHG emissions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... mass balance approach to estimate your fluorinated GHG emissions from a process, you must ensure that... relative errors associated with using the mass balance approach on that process using Equations L-1 through... mass-balance approach to estimate emissions from the process if this calculation results in an absolute...

Chemical Equilibrium in Supramolecular Systems as Studied by NMR Spectrometry

ERIC Educational Resources Information Center

Gonzalez-Gaitano, Gustavo; Tardajos, Gloria

2004-01-01

Undergraduate students are required to study the chemical balance in supramolecular assemblies constituting two or more interacting species, by using proton NMR spectrometry. A good knowledge of physical chemistry, fundamentals of chemical balance, and NMR are pre-requisites for conducting this study.

How many stakes are required to measure the mass balance of a glacier?

USGS Publications Warehouse

Fountain, A.G.; Vecchia, A.

1999-01-01

Glacier mass balance is estimated for South Cascade Glacier and Maclure Glacier using a one-dimensional regression of mass balance with altitude as an alternative to the traditional approach of contouring mass balance values. One attractive feature of regression is that it can be applied to sparse data sets where contouring is not possible and can provide an objective error of the resulting estimate. Regression methods yielded mass balance values equivalent to contouring methods. The effect of the number of mass balance measurements on the final value for the glacier showed that sample sizes as small as five stakes provided reasonable estimates, although the error estimates were greater than for larger sample sizes. Different spatial patterns of measurement locations showed no appreciable influence on the final value as long as different surface altitudes were intermittently sampled over the altitude range of the glacier. Two different regression equations were examined, a quadratic, and a piecewise linear spline, and comparison of results showed little sensitivity to the type of equation. These results point to the dominant effect of the gradient of mass balance with altitude of alpine glaciers compared to transverse variations. The number of mass balance measurements required to determine the glacier balance appears to be scale invariant for small glaciers and five to ten stakes are sufficient.

Compression of turbulent magnetized gas in giant molecular clouds

NASA Astrophysics Data System (ADS)

Birnboim, Yuval; Federrath, Christoph; Krumholz, Mark

2018-01-01

Interstellar gas clouds are often both highly magnetized and supersonically turbulent, with velocity dispersions set by a competition between driving and dissipation. This balance has been studied extensively in the context of gases with constant mean density. However, many astrophysical systems are contracting under the influence of external pressure or gravity, and the balance between driving and dissipation in a contracting, magnetized medium has yet to be studied. In this paper, we present three-dimensional magnetohydrodynamic simulations of compression in a turbulent, magnetized medium that resembles the physical conditions inside molecular clouds. We find that in some circumstances the combination of compression and magnetic fields leads to a rate of turbulent dissipation far less than that observed in non-magnetized gas, or in non-compressing magnetized gas. As a result, a compressing, magnetized gas reaches an equilibrium velocity dispersion much greater than would be expected for either the hydrodynamic or the non-compressing case. We use the simulation results to construct an analytic model that gives an effective equation of state for a coarse-grained parcel of the gas, in the form of an ideal equation of state with a polytropic index that depends on the dissipation and energy transfer rates between the magnetic and turbulent components. We argue that the reduced dissipation rate and larger equilibrium velocity dispersion has important implications for the driving and maintenance of turbulence in molecular clouds and for the rates of chemical and radiative processes that are sensitive to shocks and dissipation.

REVIEW OF VOLATILE ORGANIC COMPOUND SOURCE APPORTIONMENT BY CHEMICAL MASS BALANCE. (R826237)

EPA Science Inventory

The chemical mass balance (CMB) receptor model has apportioned volatile organic compounds (VOCs) in more than 20 urban areas, mostly in the United States. These applications differ in terms of the total fraction apportioned, the calculation method, the chemical compounds used ...

Model reduction for stochastic chemical systems with abundant species

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

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2015-12-07

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equationmore » which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.« less

Reactive Radial Diffusion Model for the Aging/Sequestration Process

NASA Astrophysics Data System (ADS)

Ginn, T. R.; Basagaoglu, H.; McCoy, B. J.; Scow, K. M.

2001-12-01

A radial diffusion model has been formulated to simulate age-dependent bioavailability of chemical compounds to micro-organisms residing outside (and/or inside) the porous soil particles. Experimental findings in the literature indicate that the sequestration and reduction in bioavailability of contaminants are controlled presumably by the diffusion-limited sorption kinetics and the time-variant desorption process. Here we combine radial-diffusion mass transfer modeling with the exposure-time concept to generate mass-balance equations for the intra- and extra-particle concentrations. The model accomodates reversible sorption kinetics involving sorption time-dependence of the rate coefficients, distinct intra- and extra-particle biodegradation rates; and a dynamic mass interaction between the intra- and extra-particle concentrations arising from the radial diffusion concept. The model explicitly treats multiple particle classes distributed in size and chemical properties in a bulk aquifer or soil volume, which allows the simulation of the sequestration and bioavailability of contaminants in different particle size classes that have distinct diffusion, reaction, and aging properties.

Differential Geometry Based Multiscale Models

PubMed Central

Wei, Guo-Wei

2010-01-01

Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that are coupled to generalized Navier–Stokes equations for fluid dynamics, Newton's equation for molecular dynamics, and potential and surface driving geometric flows for the micro-macro interface. For excessively large aqueous macromolecular complexes in chemistry and biology, we further develop differential geometry based multiscale fluid-electro-elastic models to replace the expensive molecular dynamics description with an alternative elasticity formulation. PMID:20169418

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1990-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that were reduced to a relatively compact set of equations of a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-averaged behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equation a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. For hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates, chemical nonequilibrium is considered and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Hypervelocity atmospheric flight: Real gas flow fields

NASA Technical Reports Server (NTRS)

Howe, John T.

1989-01-01

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

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

USGS Publications Warehouse

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

1996-01-01

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

Balancing Safety and Free Speech

ERIC Educational Resources Information Center

Hudson, David L., Jr.

2004-01-01

According to Jay Worona, general counsel for the New York State School Board Association, "Balancing safety and student constitutional rights is not easy. It has to be a careful balance. School officials must be prudent and not overreact. But one part of the equation has to be paramount. And safety should be the primary concern"…

Thermodynamic energy balance equations for Space Shuttle Orbiter gas compartment during ascent and re-entry

NASA Technical Reports Server (NTRS)

Ting, P. C.

1982-01-01

Thermodynamic energy balance equations are derived and applied to midsection Orbiter-payload atmospheric thermal math models (TMMs) to predict Orbiter component, element, compartment, internal insolation and structure temperatures in support of NASA/JSC mission planning, postflight thermal analysis and payload thermal integration planning. The equations are extended and applied to the forward section, midsection, and aft section of the TMMs for five Orbiter mission phases: prelaunch on pad with purge, lift-off to ascent, re-entry to touchdown, post landing without purge, and post-landing with purge. Predicted results from the 390 node/DFI atmospheric TMM are in good agreement with STS-1 flight measurement data.

Understanding the interrelationship between the synthesis of urea and gluconeogenesis by formulating an overall balanced equation.

PubMed

Ipata, Piero L; Pesi, Rossana

2017-06-01

It is well known that a strong metabolic interrelationship exists between ureagenesis and gluconeogenesis. In this paper, we present a detailed, overall equation, describing a possible metabolic link between ureagenesis and gluconeogenesis. We adopted a guided approach in which we strongly suggest that students, when faced with the problem of obtaining the overall equation of a metabolic pathway, carefully account for all atoms and charges of the single reactions, as well as the cellular localizations of the substrates, and the related transport systems. If this suggestion is always taken into account, a balanced, overall equation of a metabolic pathway will be obtained, which strongly facilitates the discussion of its physiological role. Unfortunately, textbooks often report unbalanced overall equations of metabolic pathways, including ureagenesis and gluconeogenesis. Most likely the reason is that metabolism and enzymology have been neglected for about three decades, owing to the remarkable advances of molecular biology and molecular genetics. In this paper, we strongly suggest that students, when faced with the problem of obtaining the overall reaction of a metabolic pathway, carefully control if the single reactions are properly balanced for atoms and charges. Following this suggestion, we were able to obtain an overall equation describing the metabolic interrelationship between ureagenesis and gluconeogenesis, in which urea and glucose are the final products. The aim is to better rationalize this topic and to convince students and teachers that metabolism is an important and rewarding chapter of human physiology. Copyright © 2017 the American Physiological Society.

Water balance at a low-level radioactive-waste disposal site

USGS Publications Warehouse

Healy, R.W.; Gray, J.R.; De Vries, G. M.; Mills, P.C.

1989-01-01

The water balance at a low-level radioactive-waste disposal site in northwestern Illinois was studied from July 1982 through June 1984. Continuous data collection allowed estimates to be made for each component of the water-balance equation independent of other components. The average annual precipitation was 948 millimeters. Average annual evapotranspiration was estimated at 637 millimeters, runoff was 160 millimeters, change in water storage in a waste-trench cover was 24 millimeters, and deep percolation was 208 millimeters. The magnitude of the difference between precipitation and all other components (81 millimeters per year) indicates that, in a similar environment, the water-budget method would be useful in estimating evapotranspiration, but questionable for estimation of other components. Precipitation depth and temporal distribution had a very strong effect on all other components of the water-balance equation. Due to the variability of precipitation from year to year, it appears that two years of data are inadequate for characterization of the long-term average water balance at the site.

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

NASA Astrophysics Data System (ADS)

Rahman, Md. Saifur; Lee, Yiu-Yin

2017-10-01

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

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.

Computational Cellular Dynamics Based on the Chemical Master Equation: A Challenge for Understanding Complexity

PubMed Central

Liang, Jie; Qian, Hong

2010-01-01

Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand “complex behavior” and complexity theory, and from which important biological insight can be gained. PMID:24999297

Computational Cellular Dynamics Based on the Chemical Master Equation: A Challenge for Understanding Complexity.

PubMed

Liang, Jie; Qian, Hong

2010-01-01

Modern molecular biology has always been a great source of inspiration for computational science. Half a century ago, the challenge from understanding macromolecular dynamics has led the way for computations to be part of the tool set to study molecular biology. Twenty-five years ago, the demand from genome science has inspired an entire generation of computer scientists with an interest in discrete mathematics to join the field that is now called bioinformatics. In this paper, we shall lay out a new mathematical theory for dynamics of biochemical reaction systems in a small volume (i.e., mesoscopic) in terms of a stochastic, discrete-state continuous-time formulation, called the chemical master equation (CME). Similar to the wavefunction in quantum mechanics, the dynamically changing probability landscape associated with the state space provides a fundamental characterization of the biochemical reaction system. The stochastic trajectories of the dynamics are best known through the simulations using the Gillespie algorithm. In contrast to the Metropolis algorithm, this Monte Carlo sampling technique does not follow a process with detailed balance. We shall show several examples how CMEs are used to model cellular biochemical systems. We shall also illustrate the computational challenges involved: multiscale phenomena, the interplay between stochasticity and nonlinearity, and how macroscopic determinism arises from mesoscopic dynamics. We point out recent advances in computing solutions to the CME, including exact solution of the steady state landscape and stochastic differential equations that offer alternatives to the Gilespie algorithm. We argue that the CME is an ideal system from which one can learn to understand "complex behavior" and complexity theory, and from which important biological insight can be gained.

Semiconductor spintronics: The full matrix approach

NASA Astrophysics Data System (ADS)

Rossani, A.

2015-12-01

A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi-Dirac distribution function at the leading order. The balance equations for the electron number, energy density and momentum, plus the Poisson’s equation, constitute now a system of six equations. Moreover, two equations for the evolution of the spin densities are added, which account for a general dispersion relation.

Self-regulation of charged defect compensation and formation energy pinning in semiconductors

PubMed Central

Yang, Ji-Hui; Yin, Wan-Jian; Park, Ji-Sang; Wei, Su-Huai

2015-01-01

Current theoretical analyses of defect properties without solving the detailed balance equations often estimate Fermi-level pinning position by omitting free carriers and assume defect concentrations can be always tuned by atomic chemical potentials. This could be misleading in some circumstance. Here we clarify that: (1) Because the Fermi-level pinning is determined not only by defect states but also by free carriers from band-edge states, band-edge states should be treated explicitly in the same footing as the defect states in practice; (2) defect formation energy, thus defect density, could be pinned and independent on atomic chemical potentials due to the entanglement of atomic chemical potentials and Fermi energy, in contrast to the usual expectation that defect formation energy can always be tuned by varying the atomic chemical potentials; and (3) the charged defect compensation behavior, i.e., most of donors are compensated by acceptors or vice versa, is self-regulated when defect formation energies are pinned. The last two phenomena are more dominant in wide-gap semiconductors or when the defect formation energies are small. Using NaCl and CH3NH3PbI3 as examples, we illustrate these unexpected behaviors. Our analysis thus provides new insights that enrich the understanding of the defect physics in semiconductors and insulators. PMID:26584670

Growth and Interaction of Colloid Nuclei

NASA Astrophysics Data System (ADS)

Lam, Michael-Angelo; Khusid, Boris; Meyer, William; Kondic, Lou

2017-11-01

We study evolution of colloid systems under zero-gravity conditions. In particular, we focus on the regime where there is a coexistence between a liquid and a solid state. Under zero gravity, the dominating process in the bulk of the fluid phase and the solid phase is diffusion. At the moving solid/liquid interface, osmotic pressure is balanced by surface tension, as well as balancing fluxes (conservation of mass) with the kinematics of nuclei growth (Wilson-Frenkel law). Due to the highly nonlinear boundary condition at the moving boundary, care has to be taken when performing numerical simulations. In this work, we present a nonlinear model for colloid nuclei growth. Numerical simulations using a finite volume method are compared with asymptotic analysis of the governing equation and experimental results for nuclei growth. Novel component in our numerical simulations is the inclusion of nonlinear (collective) diffusion terms that depend on the chemical potentials of the colloid in the solid and fluid phase. The results include growth and dissolution of a single colloidal nucleus, as well as evolution of multiple interacting nuclei. Supported by NASA Grant No. NNX16AQ79G.

40 CFR 1065.220 - Fuel flow meter.

Code of Federal Regulations, 2010 CFR

2010-07-01

.... (a) Application. You may use fuel flow in combination with a chemical balance of carbon (or oxygen... concentrations, if the same signal is used in a chemical-balance calculation to determine work from brake...

40 CFR 1065.220 - Fuel flow meter.

Code of Federal Regulations, 2011 CFR

2011-07-01

.... (a) Application. You may use fuel flow in combination with a chemical balance of carbon (or oxygen... concentrations, if the same signal is used in a chemical-balance calculation to determine work from brake...

Evaluation de l'impact du vent et des manoeuvres hydrauliques sur le calcul des apports naturels par bilan hydrique pour un reservoir hydroelectrique

NASA Astrophysics Data System (ADS)

Roy, Mathieu

Natural inflow is an important data for a water resource manager. In fact, Hydro-Quebec uses historical natural inflow data to perform a daily prediction of the amount of water that will be received in each of its hydroelectric reservoirs. This prediction allows the establishment of reservoir operating rules in order to optimize hydropower without compromising the safety of hydraulic structures. To obtain an accurate prediction, it follows that the system's input needs to be very well known. However, it can be very difficult to accurately measure the natural supply of a set of regulated reservoirs. Therefore, Hydro-Quebec uses an indirect method of calculation. This method consists of evaluating the reservoir's inflow using the water balance equation. Yet, this equation is not immune to errors and uncertainties. Water level measurement is an important input in order to compute the water balance equation. However, several sources of uncertainty including the effect of wind and hydraulic maneuvers can affect the readings of limnimetric gages. Fluctuations in water level caused by these effects carry over in the water balance equation. Consequently, natural inflow's signal may become noisy and affected by external errors. The main objective of this report is to evaluate the uncertainty caused by the effects of wind and hydraulic maneuvers on water balance equation. To this end, hydrodynamic models of reservoirs Outardes 4 and Gouin were prepared. According to the literature review, wind effects can be studied either by an unsteady state approach or by assuming steady state approach. Unsteady state simulation of wind effects on reservoir Gouin and Outardes 4 were performed by hydrodynamic modelling. Consideration of an unsteady state implies that the wind conditions vary throughout the simulation. This feature allows taking into account temporal effect of wind duration. In addition, it also allows the consideration of inertial forces such as seiches which are caused by wind conditions that can vary abruptly. Once the models were calibrated, unsteady state simulations were conducted in closed system where unsteady observed winds were the only forces included. From the simulated water levels obtained at each gage, water balance equation was calculated to determine the daily uncertainty of natural inflow in unsteady conditions. At Outardes 4, a maximum uncertainty of 20 m3/s was estimated during the month of October 2010. On the other hand, at the Gouin reservoir, a maximum uncertainty of 340m3/s was estimated during the month of July 2012. Steady state modelling is another approach to evaluate wind effect uncertainty in the water balance equation. This type of approach consists of assuming that the water level is instantly tilted under the influence of wind. Hence, temporal effect of wind duration and seiches cannot be taken into account. However, the advantage of steady state modelling is that it's better suited than unsteady state modelling to evaluate wind uncertainty in real time. Two steady state modelling methods were experimented to estimate water level difference between gages in function of wind characteristics: hydrodynamic modelling and non-parametric regression. It has been found that non-parametric models are more efficient when it comes to estimate water level differences between gages. However, the use of hydrodynamic model demonstrated that to study wind uncertainty in the water balance equation, it is preferable to assess wind responses individually at each gage instead of using water level differences. Finally, a combination method of water level gages observations has been developed. It allows reducing wind/hydraulic maneuvers impacts on the water balance equation. This method, which is applicable in real time, consists of assigning a variable weight at each limnimetric gages. In other words, the weights automatically adjust in order to minimize steady state modeled wind responses. The estimation of hydraulic maneuvers has also been included in the gage weight adjustment. It has been found that this new combination method allows the correction of noisy natural inflow signal under wind and hydraulic maneuvers effects. However, some fluctuations persist which reflects the complexity of correcting these effects on a real time based daily water balance equation. (Abstract shortened by UMI.).

Digital computer program for generating dynamic turbofan engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.; Krosel, S. M.; Szuch, J. R.; Westerkamp, E. J.

1983-01-01

This report describes DIGTEM, a digital computer program that simulates two spool, two-stream turbofan engines. The turbofan engine model in DIGTEM contains steady-state performance maps for all of the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. Altogether there are 16 state variables and state equations. DIGTEM features a backward-differnce integration scheme for integrating stiff systems. It trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off-design points and iterates to a balanced engine condition. Transients can also be run. They are generated by defining controls as a function of time (open-loop control) in a user-written subroutine (TMRSP). DIGTEM has run on the IBM 370/3033 computer using implicit integration with time steps ranging from 1.0 msec to 1.0 sec. DIGTEM is generalized in the aerothermodynamic treatment of components.

[Nutrition, acid-base metabolism, cation-anion difference and total base balance in humans].

PubMed

Mioni, R; Sala, P; Mioni, G

2008-01-01

The relationship between dietary intake and acid-base metabolism has been investigated in the past by means of the inorganic cation-anion difference (C(+)(nm)-A(-)(nm)) method based on dietary ash-acidity titration after the oxidative combustion of food samples. Besides the inorganic components of TA (A(-)(nm)-C(+)(nm)), which are under renal control, there are also metabolizable components (A(-)(nm)-C(+)(nm)) of TA, which are under the control of the intermediate metabolism. The whole body base balance, NBb(W), is obtained only by the application of C(+)(nm)-A(-)(nm) to food, feces and urine, while the metabolizable component (A(-)(nm)-C(+)(nm)) is disregarded. A novel method has been subsequently suggested to calculate the net balance of fixed acid, made up by the difference between the input of net endogenous acid production: NEAP = SO(4)(2-)+A(-)(m)-(C(+)(nm)-A(-)(nm)), and the output of net acid excretion: NAE = TA + NH(4)(+) - HCO(3)(-). This approach has been criticized because 1) it includes metabolizable acids, whose production cannot be measured independently; 2) the specific control of metabolizable acid and base has been incorrectly attributed to the kidney; 3) the inclusion of A-m in the balance input generates an acid overload; 4) the object of measurement in making up a balance has to be the same, a condition not fulfilled as NEAP is different from NAE. Lastly, by rearranging the net balance of the acid equation, the balance of nonmetabolizable acid equation is obtained. Therefore, any discrepancy between these two equations is due to the inaccuracy in the urine measurement of metabolizable cations and/or anions.

A theory of wheelchair wheelie performance.

PubMed

Kauzlarich, J J; Thacker, J G

1987-01-01

The results of this analytical study of wheelchair wheelie performance can be summarized into two wheelchair design equations, or rules of thumb, as developed in the paper. The equation containing the significant parameters involved in popping a wheelie for curb climbing is: fh = 0.8 mg theta c.g. [A] where fh is handrim force, m is the mass of the wheelchair + user less rear wheels, g is acceleration of gravity (9.807 m/s2), and theta c.g. is "c.g. angle," i.e., the angle between the vertical through the rear axle and a line connecting the rear axle and the system center-of-gravity. Equation [A] shows that reducing the mass and/or the c.g. angle will make it easier to pop a wheelie. The c.g. angle is reduced by moving the rear axle position forward on the wheelchair. Wheelie balance is the other aspect of performance considered; where the user balances the wheelchair on the rear wheels for going down curbs or just for fun. The ease with which a system can be controlled (balanced) is related to the static stability of the system. The static stability is defined as: omega 2 = mgl/J [B] where J is the mass moment of inertia at the center of gravity of the system about the direction perpendicular to the sideframe. For better wheelchair control during wheelchair balance the static stability should be reduced. Measurements of the value for the polar mass moment of inertia for a typical wheelchair + user of m = 90 kg was found to be J = 8.7 kg-m2. In order to decrease the value of the static stability, Equation [B], one can increase J or decrease m and/or l, where l is the distance from the rear axle to the c.g. of the system. It is also shown that balancing a rod in the palm of the hand (inverted pendulum) is a mathematical problem similar to the wheelie balance problem, and a rod of length 1.56 meters is similar to a wheelchair + user system mass of 90 kg. However, balancing a rod is done primarily by using visual perception, whereas wheelie balance involves human joint proprioceptors and visual plus vestibular (inner ear) perception. Thus, a simple test of determining the shortest length of rod one can balance in the palm of the hand (plus measuring handrim force capability and simple reaction time) may indicate if a wheelchair user will find it easy to do a wheelie balance.

The Approach to Equilibrium: Detailed Balance and the Master Equation

ERIC Educational Resources Information Center

Alexander, Millard H.; Hall, Gregory E.; Dagdigian, Paul J.

2011-01-01

The approach to the equilibrium (Boltzmann) distribution of populations of internal states of a molecule is governed by inelastic collisions in the gas phase and with surfaces. The set of differential equations governing the time evolution of the internal state populations is commonly called the master equation. An analytic solution to the master…

The Auto-Bäcklund transformations for the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet

2017-01-01

In this work, the homogeneous balance method is used to construct Auto-Bäcklund transformation of the Boiti-Leon-Manna-Pempinelli (BLMP) equation. With the aid of the transformations founded in this paper and Maple packet programme, abundant exact and explicit solutions to the BLMP equation are constructed.

A Predictive Model for Microbial Counts on Beaches where Intertidal Sand is the Primary Source

PubMed Central

Feng, Zhixuan; Reniers, Ad; Haus, Brian K.; Solo-Gabriele, Helena M.; Wang, John D.; Fleming, Lora E.

2015-01-01

Human health protection at recreational beaches requires accurate and timely information on microbiological conditions to issue advisories. The objective of this study was to develop a new numerical mass balance model for enterococci levels on nonpoint source beaches. The significant advantage of this model is its easy implementation, and it provides a detailed description of the cross-shore distribution of enterococci that is useful for beach management purposes. The performance of the balance model was evaluated by comparing predicted exceedances of a beach advisory threshold value to field data, and to a traditional regression model. Both the balance model and regression equation predicted approximately 70% the advisories correctly at the knee depth and over 90% at the waist depth. The balance model has the advantage over the regression equation in its ability to simulate spatiotemporal variations of microbial levels, and it is recommended for making more informed management decisions. PMID:25840869

Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species

NASA Astrophysics Data System (ADS)

Chen, Xiuqing; Daus, Esther S.; Jüngel, Ansgar

2018-02-01

The existence of global-in-time weak solutions to reaction-cross-diffusion systems for an arbitrary number of competing population species is proved. The equations can be derived from an on-lattice random-walk model with general transition rates. In the case of linear transition rates, it extends the two-species population model of Shigesada, Kawasaki, and Teramoto. The equations are considered in a bounded domain with homogeneous Neumann boundary conditions. The existence proof is based on a refined entropy method and a new approximation scheme. Global existence follows under a detailed balance or weak cross-diffusion condition. The detailed balance condition is related to the symmetry of the mobility matrix, which mirrors Onsager's principle in thermodynamics. Under detailed balance (and without reaction) the entropy is nonincreasing in time, but counter-examples show that the entropy may increase initially if detailed balance does not hold.

Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio.

PubMed

Ramos-Méndez, J; Perl, J; Schuemann, J; McNamara, A; Paganetti, H; Faddegon, B

2018-05-17

Simulation of water radiolysis and the subsequent chemistry provides important information on the effect of ionizing radiation on biological material. The Geant4 Monte Carlo toolkit has added chemical processes via the Geant4-DNA project. The TOPAS tool simplifies the modeling of complex radiotherapy applications with Geant4 without requiring advanced computational skills, extending the pool of users. Thus, a new extension to TOPAS, TOPAS-nBio, is under development to facilitate the configuration of track-structure simulations as well as water radiolysis simulations with Geant4-DNA for radiobiological studies. In this work, radiolysis simulations were implemented in TOPAS-nBio. Users may now easily add chemical species and their reactions, and set parameters including branching ratios, dissociation schemes, diffusion coefficients, and reaction rates. In addition, parameters for the chemical stage were re-evaluated and updated from those used by default in Geant4-DNA to improve the accuracy of chemical yields. Simulation results of time-dependent and LET-dependent primary yields G x (chemical species per 100 eV deposited) produced at neutral pH and 25 °C by short track-segments of charged particles were compared to published measurements. The LET range was 0.05-230 keV µm -1 . The calculated G x values for electrons satisfied the material balance equation within 0.3%, similar for protons albeit with long calculation time. A smaller geometry was used to speed up proton and alpha simulations, with an acceptable difference in the balance equation of 1.3%. Available experimental data of time-dependent G-values for [Formula: see text] agreed with simulated results within 7%  ±  8% over the entire time range; for [Formula: see text] over the full time range within 3%  ±  4%; for H 2 O 2 from 49%  ±  7% at earliest stages and 3%  ±  12% at saturation. For the LET-dependent G x , the mean ratios to the experimental data were 1.11  ±  0.98, 1.21  ±  1.11, 1.05  ±  0.52, 1.23  ±  0.59 and 1.49  ±  0.63 (1 standard deviation) for [Formula: see text], [Formula: see text], H 2 , H 2 O 2 and [Formula: see text], respectively. In conclusion, radiolysis and subsequent chemistry with Geant4-DNA has been successfully incorporated in TOPAS-nBio. Results are in reasonable agreement with published measured and simulated data.

Microscale Procedure for Inorganic Qualitative Analysis with Emphasis on Writing Equations: Chemical Fingerprinting Applied to the "n"-bottle Problem of Matching Samples with Their Formulas

ERIC Educational Resources Information Center

Sattsangi, Prem D.

2014-01-01

A laboratory method for teaching inorganic qualitative analysis and chemical equations is described. The experiment has been designed to focus attention on cations and anions that react to form products. This leads to a logical approach to understand and write chemical equations. The procedure uses 3 mL plastic micropipettes to store and deliver…

Convergence of the flow of a chemically reacting gaseous mixture to incompressible Euler equations in a unbounded domain

NASA Astrophysics Data System (ADS)

Kwon, Young-Sam

2017-12-01

The flow of chemically reacting gaseous mixture is associated with a variety of phenomena and processes. We study the combined quasineutral and inviscid limit from the flow of chemically reacting gaseous mixture governed by Poisson equation to incompressible Euler equations with the ill-prepared initial data in the unbounded domain R^2× T. Furthermore, the convergence rates are obtained.

Gas-particle partitioning of alcohol vapors on organic aerosols.

PubMed

Chan, Lap P; Lee, Alex K Y; Chan, Chak K

2010-01-01

Single particle levitation using an electrodynamic balance (EDB) has been found to give accurate and direct hygroscopic measurements (gas-particle partitioning of water) for a number of inorganic and organic aerosol systems. In this paper, we extend the use of an EDB to examine the gas-particle partitioning of volatile to semivolatile alcohols, including methanol, n-butanol, n-octanol, and n-decanol, on levitated oleic acid particles. The measured K(p) agreed with Pankow's absorptive partitioning model. At high n-butanol vapor concentrations (10(3) ppm), the uptake of n-butanol reduced the average molecular-weight of the oleic acid particle appreciably and hence increased the K(p) according to Pankow's equation. Moreover, the hygroscopicity of mixed oleic acid/n-butanol particles was higher than the predictions given by the UNIFAC model (molecular group contribution method) and the ZSR equation (additive rule), presumably due to molecular interactions between the chemical species in the mixed particles. Despite the high vapor concentrations used, these findings warrant further research on the partitioning of atmospheric organic vapors (K(p)) near sources and how collectively they affect the hygroscopic properties of organic aerosols.

A multichannel model for the self-consistent analysis of coherent transport in graphene nanoribbons.

PubMed

Mencarelli, Davide; Pierantoni, Luca; Farina, Marco; Di Donato, Andrea; Rozzi, Tullio

2011-08-23

In this contribution, we analyze the multichannel coherent transport in graphene nanoribbons (GNRs) by a scattering matrix approach. We consider the transport properties of GNR devices of a very general form, involving multiple bands and multiple leads. The 2D quantum transport over the whole GNR surface, described by the Schrödinger equation, is strongly nonlinear as it implies calculation of self-generated and externally applied electrostatic potentials, solutions of the 3D Poisson equation. The surface charge density is computed as a balance of carriers traveling through the channel at all of the allowed energies. Moreover, formation of bound charges corresponding to a discrete modal spectrum is observed and included in the model. We provide simulation examples by considering GNR configurations typical for transistor devices and GNR protrusions that find an interesting application as cold cathodes for X-ray generation. With reference to the latter case, a unified model is required in order to couple charge transport and charge emission. However, to a first approximation, these could be considered as independent problems, as in the example. © 2011 American Chemical Society

A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms

PubMed Central

2014-01-01

Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be “well balanced” and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments. PMID:24563581

A reaction-based paradigm to model reactive chemical transport in groundwater with general kinetic and equilibrium reactions.

PubMed

Zhang, Fan; Yeh, Gour-Tsyh; Parker, Jack C; Brooks, Scott C; Pace, Molly N; Kim, Young-Jin; Jardine, Philip M; Watson, David B

2007-06-16

This paper presents a reaction-based water quality transport model in subsurface flow systems. Transport of chemical species with a variety of chemical and physical processes is mathematically described by M partial differential equations (PDEs). Decomposition via Gauss-Jordan column reduction of the reaction network transforms M species reactive transport equations into two sets of equations: a set of thermodynamic equilibrium equations representing N(E) equilibrium reactions and a set of reactive transport equations of M-N(E) kinetic-variables involving no equilibrium reactions (a kinetic-variable is a linear combination of species). The elimination of equilibrium reactions from reactive transport equations allows robust and efficient numerical integration. The model solves the PDEs of kinetic-variables rather than individual chemical species, which reduces the number of reactive transport equations and simplifies the reaction terms in the equations. A variety of numerical methods are investigated for solving the coupled transport and reaction equations. Simulation comparisons with exact solutions were performed to verify numerical accuracy and assess the effectiveness of various numerical strategies to deal with different application circumstances. Two validation examples involving simulations of uranium transport in soil columns are presented to evaluate the ability of the model to simulate reactive transport with complex reaction networks involving both kinetic and equilibrium reactions.

40 CFR 1065.15 - Overview of procedures for laboratory and field testing.

Code of Federal Regulations, 2011 CFR

2011-07-01

... nitrogen, NOX. (2) Hydrocarbons (HC), which may be expressed in the following ways: (i) Total hydrocarbons... chemical balances of the fuel, intake air, and exhaust. To calculate fuel consumed by a chemical balance...

40 CFR 1065.15 - Overview of procedures for laboratory and field testing.

Code of Federal Regulations, 2012 CFR

2012-07-01

... nitrogen, NOX. (2) Hydrocarbons (HC), which may be expressed in the following ways: (i) Total hydrocarbons... chemical balances of the fuel, intake air, and exhaust. To calculate fuel consumed by a chemical balance...

40 CFR 1065.15 - Overview of procedures for laboratory and field testing.

Code of Federal Regulations, 2013 CFR

2013-07-01

... nitrogen, NOX. (2) Hydrocarbons (HC), which may be expressed in the following ways: (i) Total hydrocarbons... chemical balances of the fuel, intake air, and exhaust. To calculate fuel consumed by a chemical balance...

40 CFR 1065.15 - Overview of procedures for laboratory and field testing.

Code of Federal Regulations, 2010 CFR

2010-07-01

... nitrogen, NOX. (2) Hydrocarbons (HC), which may be expressed in the following ways: (i) Total hydrocarbons... chemical balances of the fuel, intake air, and exhaust. To calculate fuel consumed by a chemical balance...

SOURCE APPORTIONMENT OF PM 2.5 AND CARBON IN SEATTLE USING CHEMICAL MASS BALANCE AND POSITIVE MATRIX FACTORIZATION

EPA Science Inventory

Three years of PM2.5 speciated data were collected and chemically analyzed using the IMPROVE protocol at the Beacon Hill site in Seattle. The data were analyzed by the Chemical Mass Balance Version 8 (CMB8) and Positive Matrix Factorization (PMF) source apportionment models. T...

75 FR 81365 - Call for Information: Information on Inputs to Emission Equations Under the Mandatory Reporting...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-12-27

... consider a long-term approach that will balance data quality and transparency with the reporting businesses... balances data quality and transparency with the need to protect sensitive business information. When EPA...

Local 4/5-law and energy dissipation anomaly in turbulence of incompressible MHD Equations

NASA Astrophysics Data System (ADS)

Guo, Shanshan; Tan, Zhong

2016-12-01

In this paper, we establish the longitudinal and transverse local energy balance equation of distributional solutions of the incompressible three-dimensional MHD equations. In particular, we find that the functions D_L^ɛ (u,B) and D_T^ɛ (u,B) appeared in the energy balance, all converging to the defect distribution (in the sense of distributions) D(u,B) which has been defined in Gao et al. (Acta Math Sci 33:865-871, 2013). Furthermore, we give a simpler form of defect distribution term, which is similar to the relation in turbulence theory, called the "4 / 3-law." As a corollary, we give the analogous "4 / 5-law" holds in the local sense.

A complete analytical solution of the Fokker-Planck and balance equations for nucleation and growth of crystals

NASA Astrophysics Data System (ADS)

Makoveeva, Eugenya V.; Alexandrov, Dmitri V.

2018-01-01

This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Supporting Students' Understanding of Linear Equations with One Variable Using Algebra Tiles

ERIC Educational Resources Information Center

Saraswati, Sari; Putri, Ratu Ilma Indra; Somakim

2016-01-01

This research aimed to describe how algebra tiles can support students' understanding of linear equations with one variable. This article is a part of a larger research on learning design of linear equations with one variable using algebra tiles combined with balancing method. Therefore, it will merely discuss one activity focused on how students…

The measurement of energy exchange in man: an analysis.

PubMed

Webb, P

1980-06-01

This report analyzes two kinds of studies of human energy balance; direct and indirect calorimetry for 24-hr periods, and complete measurements of food intake, waste, and tissue storage for 3 weeks and longer. Equations of energy balance are written to show that the daily quantity of metabolic energy, QM, is coupled with an unidentified quantity of unmeasured energy, QX, in order to make the equation balance. The equations challenge the assumed equivalence of direct and indirect calorimetry. The analysis takes the form of employing experimental data to calculate values for the arguable quantity, QX. Studies employing 24-hr direct calorimetry, 202 complete days, show that when food intake nearly matches QM, values for QX are small and probably insignificant, but when there is a large food deficit, large positive values for QX appear. Calculations are also made from studies of nutrient balance during prolonged overeating and undereating, and in nearly all cases there were large negative values for QX. In 52 sets of data from studies lasting 3 weeks or longer, where all the terms in the balance equation except QX were either directly measured or could be readily estimated, the average value for QX amounts to 705 kcal/day, or 27% of QM. A discussion of the nature of QX considers error and the noninclusion of small quantities like the energy of combustible gases, which are not thought to be sufficient to explain QX. It might represent the cost of mobilizing stored fuel, or of storing excess fuel, or it might represent a change in internal energy other than fuel stores, but none of these is thought to be likely. Finally, it is emphasized that entropy exchange in man as an open thermodynamic system is not presently included in the equations of energy balance, and perhaps it must be, even though it is not directly measurable. The significance of unmeasured energy is considered in light of the poor control of obesity, of the inability to predict weight change during prolonged diet restriction or intentional overeating, and of the energetics of tissue gain in growth and loss in cachexia. It is not even well established how much food man requires to maintain constant weight. New studies as they are undertaken should try to account completely for all the possible terms of energy exchange.

Statistical foundations of liquid-crystal theory: II: Macroscopic balance laws.

PubMed

Seguin, Brian; Fried, Eliot

2013-01-01

Working on a state space determined by considering a discrete system of rigid rods, we use nonequilibrium statistical mechanics to derive macroscopic balance laws for liquid crystals. A probability function that satisfies the Liouville equation serves as the starting point for deriving each macroscopic balance. The terms appearing in the derived balances are interpreted as expected values and explicit formulas for these terms are obtained. Among the list of derived balances appear two, the tensor moment of inertia balance and the mesofluctuation balance, that are not standard in previously proposed macroscopic theories for liquid crystals but which have precedents in other theories for structured media.

Simulating Chemical Kinetics Without Differential Equations: A Quantitative Theory Based on Chemical Pathways.

PubMed

Bai, Shirong; Skodje, Rex T

2017-08-17

A new approach is presented for simulating the time-evolution of chemically reactive systems. This method provides an alternative to conventional modeling of mass-action kinetics that involves solving differential equations for the species concentrations. The method presented here avoids the need to solve the rate equations by switching to a representation based on chemical pathways. In the Sum Over Histories Representation (or SOHR) method, any time-dependent kinetic observable, such as concentration, is written as a linear combination of probabilities for chemical pathways leading to a desired outcome. In this work, an iterative method is introduced that allows the time-dependent pathway probabilities to be generated from a knowledge of the elementary rate coefficients, thus avoiding the pitfalls involved in solving the differential equations of kinetics. The method is successfully applied to the model Lotka-Volterra system and to a realistic H 2 combustion model.

A comparative study of energy balance among housewives of Ludhiana city.

PubMed

Kaur, N; Mann, S K; Sidhu, P; Sangha, J K

1997-01-01

Energy gap is the main nutritional factor which affects work efficiency in all age groups. The low intake of food results in impaired working efficiency and a low level of vitality. Energy balance was evaluated among 30 healthy, nonpregnant, nonlactating housewives aged 29-40 years drawn from the campus of Punjab Agricultural University and its surrounding areas. The women's mean overall energy intake was 1777 +or- 31 kcal/day, 87% of the ICMR (1990) recommended allowances. Total energy expenditure was measured using a computer-based Nutriguide program of Song et al., Caltrac, FAO/WHO/UNU (1985) equations based upon body weight, and an ICMR (1990) prediction equation also based upon body weight. Statistical analysis identified a significant difference in the energy expenditure measured by all 4 methods except between the FAO/WHO/UNU and ICMR prediction equations. The overall energy balance was maximum and positive according to Caltrac at 4.5 kcal/day. The energy expenditure measured by the Nutriguide, FAO/WHO/UNU, and ICMR methods was significantly correlated to weight. Energy intake was significantly and highly correlated to energy balance in all of the 4 methods. While the subjects were overweight when compared with Life Insurance Corporation of India (1965) Standards, the women's body mass index of 23.11 kg/sq.m was within the normal range.

An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations

PubMed Central

Nakagawa, Masaki; Togashi, Yuichi

2016-01-01

Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed. PMID:27047384

Using chemical benchmarking to determine the persistence of chemicals in a Swedish lake.

PubMed

Zou, Hongyan; Radke, Michael; Kierkegaard, Amelie; MacLeod, Matthew; McLachlan, Michael S

2015-02-03

It is challenging to measure the persistence of chemicals under field conditions. In this work, two approaches for measuring persistence in the field were compared: the chemical mass balance approach, and a novel chemical benchmarking approach. Ten pharmaceuticals, an X-ray contrast agent, and an artificial sweetener were studied in a Swedish lake. Acesulfame K was selected as a benchmark to quantify persistence using the chemical benchmarking approach. The 95% confidence intervals of the half-life for transformation in the lake system ranged from 780-5700 days for carbamazepine to <1-2 days for ketoprofen. The persistence estimates obtained using the benchmarking approach agreed well with those from the mass balance approach (1-21% difference), indicating that chemical benchmarking can be a valid and useful method to measure the persistence of chemicals under field conditions. Compared to the mass balance approach, the benchmarking approach partially or completely eliminates the need to quantify mass flow of chemicals, so it is particularly advantageous when the quantification of mass flow of chemicals is difficult. Furthermore, the benchmarking approach allows for ready comparison and ranking of the persistence of different chemicals.

Nonequilibrium radiative hypersonic flow simulation

NASA Astrophysics Data System (ADS)

Shang, J. S.; Surzhikov, S. T.

2012-08-01

Nearly all the required scientific disciplines for computational hypersonic flow simulation have been developed on the framework of gas kinetic theory. However when high-temperature physical phenomena occur beneath the molecular and atomic scales, the knowledge of quantum physics and quantum chemical-physics becomes essential. Therefore the most challenging topics in computational simulation probably can be identified as the chemical-physical models for a high-temperature gaseous medium. The thermal radiation is also associated with quantum transitions of molecular and electronic states. The radiative energy exchange is characterized by the mechanisms of emission, absorption, and scattering. In developing a simulation capability for nonequilibrium radiation, an efficient numerical procedure is equally important both for solving the radiative transfer equation and for generating the required optical data via the ab-initio approach. In computational simulation, the initial values and boundary conditions are paramount for physical fidelity. Precise information at the material interface of ablating environment requires more than just a balance of the fluxes across the interface but must also consider the boundary deformation. The foundation of this theoretic development shall be built on the eigenvalue structure of the governing equations which can be described by Reynolds' transport theorem. Recent innovations for possible aerospace vehicle performance enhancement via an electromagnetic effect appear to be very attractive. The effectiveness of this mechanism is dependent strongly on the degree of ionization of the flow medium, the consecutive interactions of fluid dynamics and electrodynamics, as well as an externally applied magnetic field. Some verified research results in this area will be highlighted. An assessment of all these most recent advancements in nonequilibrium modeling of chemical kinetics, chemical-physics kinetics, ablation, radiative exchange, computational algorithms, and the aerodynamic-electromagnetic interaction are summarized and delineated. The critical basic research areas for physic-based hypersonic flow simulation should become self-evident through the present discussion. Nevertheless intensive basic research efforts must be sustained in these areas for fundamental knowledge and future technology advancement.

Quantifying evapotranspiration from urban green roofs: a comparison of chamber measurements with commonly used predictive methods.

PubMed

Marasco, Daniel E; Hunter, Betsy N; Culligan, Patricia J; Gaffin, Stuart R; McGillis, Wade R

2014-09-02

Quantifying green roof evapotranspiration (ET) in urban climates is important for assessing environmental benefits, including stormwater runoff attenuation and urban heat island mitigation. In this study, a dynamic chamber method was developed to quantify ET on two extensive green roofs located in New York City, NY. Hourly chamber measurements taken from July 2009 to December 2009 and April 2012 to October 2013 illustrate both diurnal and seasonal variations in ET. Observed monthly total ET depth ranged from 0.22 cm in winter to 15.36 cm in summer. Chamber results were compared to two predictive methods for estimating ET; namely the Penman-based ASCE Standardized Reference Evapotranspiration (ASCE RET) equation, and an energy balance model, both parametrized using on-site environmental conditions. Dynamic chamber ET results were similar to ASCE RET estimates; however, the ASCE RET equation overestimated bottommost ET values during the winter months, and underestimated peak ET values during the summer months. The energy balance method was shown to underestimate ET compared the ASCE RET equation. The work highlights the utility of the chamber method for quantifying green roof evapotranspiration and indicates green roof ET might be better estimated by Penman-based evapotranspiration equations than energy balance methods.

Path length differencing and energy conservation of the S[sub N] Boltzmann/Spencer-Lewis equation

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

Filippone, W.L.; Monahan, S.P.

It is shown that the S[sub N] Boltzmann/Spencer-Lewis equations conserve energy locally if and only if they satisfy particle balance and diamond differencing is used in path length. In contrast, the spatial differencing schemes have no bearing on the energy balance. Energy is conserved globally if it is conserved locally and the multigroup cross sections are energy conserving. Although the coupled electron-photon cross sections generated by CEPXS conserve particles and charge, they do not precisely conserve energy. It is demonstrated that these cross sections can be adjusted such that particles, charge, and energy are conserved. Finally, since a conventional negativemore » flux fixup destroys energy balance when applied to path legend, a modified fixup scheme that does not is presented.« less

Skylab water balance analysis

NASA Technical Reports Server (NTRS)

Leonard, J. I.

1977-01-01

The water balance of the Skylab crew was analyzed. Evaporative water loss using a whole body input/output balance equation, water, body tissue, and energy balance was analyzed. The approach utilizes the results of several major Skylab medical experiments. Subsystems were designed for the use of the software necessary for the analysis. A partitional water balance that graphically depicts the changes due to water intake is presented. The energy balance analysis determines the net available energy to the individual crewman during any period. The balances produce a visual description of the total change of a particular body component during the course of the mission. The information is salvaged from metabolic balance data if certain techniques are used to reduce errors inherent in the balance method.

Introducing DAE Systems in Undergraduate and Graduate Chemical Engineering Curriculum

ERIC Educational Resources Information Center

Mandela, Ravi Kumar; Sridhar, L. N.; Rengaswamy, Raghunathan

2010-01-01

Models play an important role in understanding chemical engineering systems. While differential equation models are taught in standard modeling and control courses, Differential Algebraic Equation (DAE) system models are not usually introduced. These models appear naturally in several chemical engineering problems. In this paper, the introduction…

Analysis of a resistance-energy balance method for estimating daily evaporation from wheat plots using one-time-of-day infrared temperature observations

NASA Technical Reports Server (NTRS)

Choudhury, B. J.; Idso, S. B.; Reginato, R. J.

1986-01-01

Accurate estimates of evaporation over field-scale or larger areas are needed in hydrologic studies, irrigation scheduling, and meteorology. Remotely sensed surface temperature might be used in a model to calculate evaporation. A resistance-energy balance model, which combines an energy balance equation, the Penman-Monteith (1981) evaporation equation, and van den Honert's (1948) equation for water extraction by plant roots, is analyzed for estimating daily evaporation from wheat using postnoon canopy temperature measurements. Additional data requirements are half-hourly averages of solar radiation, air and dew point temperatures, and wind speed, along with reasonable estimates of canopy emissivity, albedo, height, and leaf area index. Evaporation fluxes were measured in the field by precision weighing lysimeters for well-watered and water-stressed wheat. Errors in computed daily evaporation were generally less than 10 percent, while errors in cumulative evaporation for 10 clear sky days were less than 5 percent for both well-watered and water-stressed wheat. Some results from sensitivity analysis of the model are also given.

Measuring the effects of heat wave episodes on the human body's thermal balance

NASA Astrophysics Data System (ADS)

Katavoutas, George; Theoharatos, George; Flocas, Helena A.; Asimakopoulos, Dimosthenis N.

2009-03-01

During the peak of an extensive heat wave episode on 23-25 July 2007, simultaneous thermophysiological measurements were made in two non-acclimated healthy adults of different sex in a suburban area of Greater Athens, Greece. Based on experimental measurements of mean skin temperature and metabolic heat production, heat fluxes to and from the human body were calculated, and the biometeorological index heat load (HL) produced was determined according to the heat balance equation. Comparing experimental values with those derived from theoretical estimates revealed a great heat stress for both individuals, especially the male, while theoretical values underestimated heat stress. The study also revealed that thermophysiological factors, such as mean skin temperature and metabolic heat production, play an important role in determining heat fluxes patterns in the heat balance equation. The theoretical values of mean skin temperature as derived from an empirical equation may not be appropriate to describe the changes that take place in a non-acclimated individual. Furthermore, the changes in metabolic heat production were significant even for standard activity.

Nested variant of the method of moments of coupled cluster equations for vertical excitation energies and excited-state potential energy surfaces.

PubMed

Kowalski, Karol

2009-05-21

In this article we discuss the problem of proper balancing of the noniterative corrections to the ground- and excited-state energies obtained with approximate coupled cluster (CC) and equation-of-motion CC (EOMCC) approaches. It is demonstrated that for a class of excited states dominated by single excitations and for states with medium doubly excited component, the newly introduced nested variant of the method of moments of CC equations provides mathematically rigorous way of balancing the ground- and excited-state correlation effects. The resulting noniterative methodology accounting for the effect of triples is tested using its parallel implementation on the systems, for which iterative CC/EOMCC calculations with full inclusion of triply excited configurations or their most important subset are numerically feasible.

Modern gyrokinetic formulation of collisional and turbulent transport in toroidally rotating plasmas

NASA Astrophysics Data System (ADS)

Sugama, H.

2017-12-01

Collisional and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity are formulated based on the modern gyrokinetic theory. Governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions are derived from the Lagrangian variational principle with effects of collisions and external sources taken into account. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms which are desirable properties for long-time global transport simulation. The resultant balance equations are shown to include the classical, neoclassical, and turbulent transport fluxes which agree with those obtained from the conventional recursive formulations.

A mass-balanced definition of corrected retention volume in gas chromatography.

PubMed

Kurganov, A

2007-05-25

The mass balance equation of a chromatographic system using a compressible moving phase has been compiled for mass flow of the mobile phase instead of traditional volumetric flow allowing solution of the equation in an analytical form. The relation obtained correlates retention volume measured under ambient conditions with the partition coefficient of the solute. Compared to the relation in the ideal chromatographic system the equation derived contains an additional correction term accounting for the compressibility of the moving phase. When the retention volume is measured under the mean column pressure and column temperature the correction term is reduced to unit and the relation is simplified to those known for the ideal system. This volume according to International Union of Pure and Applied Chemistry (IUPAC) is called the corrected retention volume.

Matrix approaches to assess terrestrial nitrogen scheme in CLM4.5

NASA Astrophysics Data System (ADS)

Du, Z.

2017-12-01

Terrestrial carbon (C) and nitrogen (N) cycles have been commonly represented by a series of balance equations to track their influxes into and effluxes out of individual pools in earth system models (ESMs). This representation matches our understanding of C and N cycle processes well but makes it difficult to track model behaviors. To overcome these challenges, we developed a matrix approach, which reorganizes the series of terrestrial C and N balance equations in the CLM4.5 into two matrix equations based on original representation of C and N cycle processes and mechanisms. The matrix approach would consequently help improve the comparability of models and data, evaluate impacts of additional model components, facilitate benchmark analyses, model intercomparisons, and data-model fusion, and improve model predictive power.

Cellulose-reinforced composites and SRIM and RTM modeling

NASA Astrophysics Data System (ADS)

Fahrurrozi, Mohammad

Structural reaction injection molding (SRIM) cellulosic/polyurethane composites were prepared from various forms of cellulosic mats, and elastomeric polyurea-urethane (PUU) and rigid polyurethane (PU) formulations. Mats (woven and non-woven) prepared from different sources of fibers with lignin content ranging from zero (cotton) to at least 10% (sugar cane and kenaf fibers) performed comparably in PUU/cellulosic composites. Young's modulus and tensile strength of PUU/cellulosic composites were doubled with 5% and 7% fiber loading respectively. Young's modulus and tensile strength of PU/cellulosic composites were improved by 300% and 30%, respectively, with 7% fiber loading, whereas their bending moduli and strengths were improved up to 100% and 50%, respectively, with 18% fiber loading. However, the mechanical properties of PU composites were more sensitive to the fiber properties and fiber macroscopic arrangements. The study with chemical ratio variations indicates that as the fiber loading increases, the cellulose hydroxyl presence starts shifting the chemical balance and thus should be accounted for. Mats prepared from sugar cane fibers extracted from rind with low alkali concentration (0.2 N) followed by steam explosion require lower injection pressures compared to the ones prepared from fiber obtained from higher alkali treatment (above 0.5 N) without steam explosion. Hence, the steam exploded mats are more suitable for SRIM purposes. The PU kinetics was studied using an adiabatic temperature rise method. An Arrhenius type empirical equation was used to fit the data. The fitted equation was second order to the partial conversion, and the gelling time at adiabatic condition is less than 5 seconds (much quicker than the 10 to 12 seconds in mold gel time quoted by the manufacturer). FORTRAN programs were written to solve the SRIM model based on Darcy's equation. The model incorporated heat transfer and chemical reaction. The modeling was intended to aid in interpreting in-mold pressure data obtained from mat permeability characterization. The model also has other wider applications such as mold design and SRIM and resin transfer molding (RTM) simulation. The model predicts some experimental data from this work and the literature satisfactorily.

A classical but new kinetic equation for hydride transfer reactions.

PubMed

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

2013-09-28

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

CHEMICAL MASS BALANCE MODEL: EPA-CMB8.2

EPA Science Inventory

The Chemical Mass Balance (CMB) method has been a popular approach for receptor modeling of ambient air pollutants for over two decades. For the past few years the U.S. Environmental Protection Agency's Office of Research and Development (ORD) and Office of Air Quality Plannin...

Redox Redone.

ERIC Educational Resources Information Center

Petty, John T.

1996-01-01

Presents an extension of the change in oxidation number method that is used for balancing skeletal redox reactions in aqueous solutions. Retains most of the simplicity of the change in oxidation number method but provides the additional step-by-step process necessary for the beginner to balance an equation. (JRH)

Self-regulation of charged defect compensation and formation energy pinning in semiconductors

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

Yang, Ji -Hui; Yin, Wan -Jian; Park, Ji -Sang

2015-11-20

Current theoretical analyses of defect properties without solving the detailed balance equations often estimate Fermi-level pinning position by omitting free carriers and assume defect concentrations can be always tuned by atomic chemical potentials. This could be misleading in some circumstance. Here we clarify that: (1) Because the Fermi-level pinning is determined not only by defect states but also by free carriers from band-edge states, band-edge states should be treated explicitly in the same footing as the defect states in practice; (2) defect formation energy, thus defect density, could be pinned and independent on atomic chemical potentials due to the entanglementmore » of atomic chemical potentials and Fermi energy, in contrast to the usual expectation that defect formation energy can always be tuned by varying the atomic chemical potentials; and (3) the charged defect compensation behavior, i.e., most of donors are compensated by acceptors or vice versa, is self-regulated when defect formation energies are pinned. The last two phenomena are more dominant in wide-gap semiconductors or when the defect formation energies are small. Using NaCl and CH 3NH 3PbI 3 as examples, we illustrate these unexpected behaviors. Furthermore, our analysis thus provides new insights that enrich the understanding of the defect physics in semiconductors and insulators.« less

Analysis of bacterial migration. 2: Studies with multiple attractant gradients

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

Strauss, I.; Frymier, P.D.; Hahn, C.M.

1995-02-01

Many motile bacteria exhibit chemotaxis, the ability to bias their random motion toward or away from increasing concentrations of chemical substances which benefit or inhibit their survival, respectively. Since bacteria encounter numerous chemical concentration gradients simultaneously in natural surroundings, it is necessary to know quantitatively how a bacterial population responds in the presence of more than one chemical stimulus to develop predictive mathematical models describing bacterial migration in natural systems. This work evaluates three hypothetical models describing the integration of chemical signals from multiple stimuli: high sensitivity, maximum signal, and simple additivity. An expression for the tumbling probability for individualmore » stimuli is modified according to the proposed models and incorporated into the cell balance equation for a 1-D attractant gradient. Random motility and chemotactic sensitivity coefficients, required input parameters for the model, are measured for single stimulus responses. Theoretical predictions with the three signal integration models are compared to the net chemotactic response of Escherichia coli to co- and antidirectional gradients of D-fucose and [alpha]-methylaspartate in the stopped-flow diffusion chamber assay. Results eliminate the high-sensitivity model and favor the simple additivity over the maximum signal. None of the simple models, however, accurately predict the observed behavior, suggesting a more complex model with more steps in the signal processing mechanism is required to predict responses to multiple stimuli.« less

Groundwater geochemistry in the Seminole Well Field, Cedar Rapids, Iowa

USGS Publications Warehouse

Boyd, Robert A.

1999-01-01

The City of Cedar Rapids obtains its municipal water supply from four well fields in an alluvial aquifer along the Cedar River in east-central Iowa. Since 1992, the City and the U.S. Geological Survey have cooperatively studied the groundwater-flow system and water chemistry near the well fields. The geochemistry in the alluvial aquifer near the Seminole Well Field was assessed to identify potentially reactive minerals and possible chemical reactions that produce observed changes in water chemistry. Calcite, dolomite, ferrihydrite, quartz, rhodochrosite, and siderite were identified as potentially reactive minerals by calculating saturation indexes. Aluminosiicate minerals including albite, Ca-montmorillonite, gibbsite, illite, K-feldspar, and kaolinite were identified as potentially reactive minerals using hypothetical saturation indexes calculated with an assumed dissolved aluminum concentration of 1 microgram per liter. Balanced chemical equations derived from inverse-modeling techniques were used to assess chemical reactions as precipitation percolates to the water table. Calcite dissolution was predominate, but aluminosilicate weathering, cation exchange, and redox reactions also likely occurred. Microbial-catalyzed redox reactions altered the chemical composition of water infiltrating from the Cedar River into the alluvial aquifer by consuming dissolved oxygen, reducing nitrate, and increasing dissolved iron and manganese concentrations. Nitrate reduction only occurred in relatively shallow (3 to 7 meters below land surface) groundwater near the Cedar River and did not occur in water infiltrating to deeper zones of the alluvial aquifer.

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited.

PubMed

Vellela, Melissa; Qian, Hong

2009-10-06

Schlögl's model is the canonical example of a chemical reaction system that exhibits bistability. Because the biological examples of bistability and switching behaviour are increasingly numerous, this paper presents an integrated deterministic, stochastic and thermodynamic analysis of the model. After a brief review of the deterministic and stochastic modelling frameworks, the concepts of chemical and mathematical detailed balances are discussed and non-equilibrium conditions are shown to be necessary for bistability. Thermodynamic quantities such as the flux, chemical potential and entropy production rate are defined and compared across the two models. In the bistable region, the stochastic model exhibits an exchange of the global stability between the two stable states under changes in the pump parameters and volume size. The stochastic entropy production rate shows a sharp transition that mirrors this exchange. A new hybrid model that includes continuous diffusion and discrete jumps is suggested to deal with the multiscale dynamics of the bistable system. Accurate approximations of the exponentially small eigenvalue associated with the time scale of this switching and the full time-dependent solution are calculated using Matlab. A breakdown of previously known asymptotic approximations on small volume scales is observed through comparison with these and Monte Carlo results. Finally, in the appendix section is an illustration of how the diffusion approximation of the chemical master equation can fail to represent correctly the mesoscopically interesting steady-state behaviour of the system.

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

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

Fillion-Gourdeau, F., E-mail: filliong@CRM.UMontreal.ca; Centre de Recherches Mathématiques, Université de Montréal, Montréal, H3T 1J4; Lorin, E., E-mail: elorin@math.carleton.ca

2016-02-15

A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron–molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic balanced basis, which allows for an efficient and accurate determination of the Dirac spectrum and eigenfunctions. B-spline basis functions are used to obtain high accuracy. This numerical method is used to compute the energy spectrum of the two-center problem and then the evolution of eigenstate wavefunctions in an external electromagnetic field.

A coupled problem of finite deformation and flow in porous media

NASA Astrophysics Data System (ADS)

Moussa, A. B.

1980-06-01

A theory for deformation and two phase flow in porous media was developed. Equations of balance of mass, momentum, moment of momentum and energy for each constituent were postulated. These led to equivalent balance equations for the mixture as a whole to which an entropy production inequality was also postulated. The formulation was then applied to the silage material. A constitutive theory was developed for the mixture. General appropriate constitutive assumptions were suggested and made to satisfy the axiom of material objectivity and entropy production inequality. Material incompressibility was defined and introduced into the general form of constitutive relations.

Statistical foundations of liquid-crystal theory

PubMed Central

Seguin, Brian; Fried, Eliot

2013-01-01

Working on a state space determined by considering a discrete system of rigid rods, we use nonequilibrium statistical mechanics to derive macroscopic balance laws for liquid crystals. A probability function that satisfies the Liouville equation serves as the starting point for deriving each macroscopic balance. The terms appearing in the derived balances are interpreted as expected values and explicit formulas for these terms are obtained. Among the list of derived balances appear two, the tensor moment of inertia balance and the mesofluctuation balance, that are not standard in previously proposed macroscopic theories for liquid crystals but which have precedents in other theories for structured media. PMID:23554513

Parameter Estimates in Differential Equation Models for Chemical Kinetics

ERIC Educational Resources Information Center

Winkel, Brian

2011-01-01

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

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

Mondy, Lisa Ann; Rao, Rekha Ranjana; Shelden, Bion

We are developing computational models to elucidate the expansion and dynamic filling process of a polyurethane foam, PMDI. The polyurethane of interest is chemically blown, where carbon dioxide is produced via the reaction of water, the blowing agent, and isocyanate. The isocyanate also reacts with polyol in a competing reaction, which produces the polymer. Here we detail the experiments needed to populate a processing model and provide parameters for the model based on these experiments. The model entails solving the conservation equations, including the equations of motion, an energy balance, and two rate equations for the polymerization and foaming reactions,more » following a simplified mathematical formalism that decouples these two reactions. Parameters for the polymerization kinetics model are reported based on infrared spectrophotometry. Parameters describing the gas generating reaction are reported based on measurements of volume, temperature and pressure evolution with time. A foam rheology model is proposed and parameters determined through steady-shear and oscillatory tests. Heat of reaction and heat capacity are determined through differential scanning calorimetry. Thermal conductivity of the foam as a function of density is measured using a transient method based on the theory of the transient plane source technique. Finally, density variations of the resulting solid foam in several simple geometries are directly measured by sectioning and sampling mass, as well as through x-ray computed tomography. These density measurements will be useful for model validation once the complete model is implemented in an engineering code.« less

A POLLUTION REDUCTION METHODOLOGY FOR CHEMICAL PROCESS SIMULATORS

EPA Science Inventory

A pollution minimization methodology was developed for chemical process design using computer simulation. It is based on a pollution balance that at steady state is used to define a pollution index with units of mass of pollution per mass of products. The pollution balance has be...

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...

Non-Linear Steady State Vibrations of Beams Excited by Vortex Shedding

NASA Astrophysics Data System (ADS)

LEWANDOWSKI, R.

2002-05-01

In this paper the non-linear vibrations of beams excited by vortex-shedding are considered. In particular, the steady state responses of beams near the synchronization region are taken into account. The main aerodynamic properties of wind are described by using the semi-empirical model proposed by Hartlen and Currie. The finite element method and the strip method are used to formulate the equation of motion of the system treated. The harmonic balance method is adopted to derive the amplitude equations. These equations are solved with the help of the continuation method which is very convenient to perform the parametric studies of the problem and to determine the response curve in the synchronization region. Moreover, the equations of motion are also integrated using the Newmark method. The results of calculations of several example problems are also shown to confirm the efficiency and accuracy of the presented method. The results obtained by the harmonic balance method and by the Newmark methods are in good agreement with each other.

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

PubMed

Grima, Ramon

2011-11-01

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

Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Moon, H. T.; Goldman, M. V.

1984-01-01

The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.

Comparison of prognostic and diagnostic surface flux modeling approaches over the Nile River Basin

USDA-ARS?s Scientific Manuscript database

Regional evapotranspiration (ET) can be estimated using diagnostic remote sensing models, generally based on principles of energy balance, or with spatially distributed prognostic models that simultaneously balance both the energy and water budgets over landscapes using predictive equations for land...

Work-Family Balance and Psychosocial Adjustment of Married International Students

ERIC Educational Resources Information Center

Bulgan, Gökçe; Çiftçi, Ayse

2018-01-01

The authors investigated how work-family balance mediated the relationship between personality traits, gender roles, social support, and psychosocial adjustment. Data were collected from 243 married international graduate students (MIGSs) studying in the United States. Results of structural equation modeling indicated that personality traits…

Evapotranspiration from areas of native vegetation in west-central Florida

USGS Publications Warehouse

Bidlake, W.R.; Woodham, W.M.; Lopez, M.A.

1993-01-01

A study was made to examine the suitability of three different micrometeorological methods for estimating evapotranspiration from selected areas of native vegetation in west-central Florida and to estimate annual evapotranspiration from those areas. Evapotranspiration was estimated using the energy- balance Bowen ratio and eddy correlation methods. Potential evapotranspiration was computed using the Penman equation. The energy-balance Bowen ratio method was used to estimate diurnal evapotrans- piration at unforested sites and yielded reasonable results; however, measurements indicated that the magnitudes of air temperature and vapor-pressure gradients above the forested sites were too small to obtain reliable evapotranspiration measurements with the energy balance Bowen ratio system. Analysis of the surface energy-balance indicated that sensible and latent heat fluxes computed using standard eddy correlation computation methods did not adequately account for available energy. Eddy correlation data were combined with the equation for the surface energy balance to yield two additional estimates of evapotranspiration. Daily potential evapotranspiration and evapotranspira- tion estimated using the energy-balance Bowen ratio method were not correlated at a unforested, dry prairie site, but they were correlated at a marsh site. Estimates of annual evapotranspiration for sites within the four vegetation types, which were based on energy-balance Bowen ratio and eddy correlation measurements, were 1,010 millimeters for dry prairie sites, 990 millimeters for marsh sites, 1,060 millimeters for pine flatwood sites, and 970 millimeters for a cypress swamp site.

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

Xing, Yulong; Shu, Chi-wang; Noelle, Sebastian

This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium. For such examples, still-water well-balanced methods are not capable of capturing the small perturbations of the moving-water equilibrium and may generate significant spurious oscillations, unless an extremely refined mesh is used. On the other hand, moving-water well-balanced methods perform well in these tests. The numerical examples in this note clearly demonstrate the importance of utilizing moving-water well-balanced methods for solutions near a moving-water equilibrium.

Considerations affecting the additional weight required in mass balance of ailerons

NASA Technical Reports Server (NTRS)

Diehl, W S

1937-01-01

This paper is essentially a consideration of mass balance of ailerons from a preliminary design standpoint, in which the extra weight of the mass counterbalance is the most important phase of the problem. Equations are developed for the required balance weight for a simple aileron and this weight is correlated with the mass-balance coefficient. It is concluded the location of the c.g. of the basic aileron is of paramount importance and that complete mass balance imposes no great weight penalty if the aileron is designed to have its c.g. inherently near to the hinge axis.

Pdf - Transport equations for chemically reacting flows

NASA Technical Reports Server (NTRS)

Kollmann, W.

1989-01-01

The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

Expanding a dynamic flux balance model of yeast fermentation to genome-scale

PubMed Central

2011-01-01

Background Yeast is considered to be a workhorse of the biotechnology industry for the production of many value-added chemicals, alcoholic beverages and biofuels. Optimization of the fermentation is a challenging task that greatly benefits from dynamic models able to accurately describe and predict the fermentation profile and resulting products under different genetic and environmental conditions. In this article, we developed and validated a genome-scale dynamic flux balance model, using experimentally determined kinetic constraints. Results Appropriate equations for maintenance, biomass composition, anaerobic metabolism and nutrient uptake are key to improve model performance, especially for predicting glycerol and ethanol synthesis. Prediction profiles of synthesis and consumption of the main metabolites involved in alcoholic fermentation closely agreed with experimental data obtained from numerous lab and industrial fermentations under different environmental conditions. Finally, fermentation simulations of genetically engineered yeasts closely reproduced previously reported experimental results regarding final concentrations of the main fermentation products such as ethanol and glycerol. Conclusion A useful tool to describe, understand and predict metabolite production in batch yeast cultures was developed. The resulting model, if used wisely, could help to search for new metabolic engineering strategies to manage ethanol content in batch fermentations. PMID:21595919

On the thermodynamics of smooth muscle contraction

NASA Astrophysics Data System (ADS)

Stålhand, Jonas; McMeeking, Robert M.; Holzapfel, Gerhard A.

2016-09-01

Cell function is based on many dynamically complex networks of interacting biochemical reactions. Enzymes may increase the rate of only those reactions that are thermodynamically consistent. In this paper we specifically treat the contraction of smooth muscle cells from the continuum thermodynamics point of view by considering them as an open system where matter passes through the cell membrane. We systematically set up a well-known four-state kinetic model for the cross-bridge interaction of actin and myosin in smooth muscle, where the transition between each state is driven by forward and reverse reactions. Chemical, mechanical and energy balance laws are provided in local forms, while energy balance is also formulated in the more convenient temperature form. We derive the local (non-negative) production of entropy from which we deduce the reduced entropy inequality and the constitutive equations for the first Piola-Kirchhoff stress tensor, the heat flux, the ion and molecular flux and the entropy. One example for smooth muscle contraction is analyzed in more detail in order to provide orientation within the established general thermodynamic framework. In particular the stress evolution, heat generation, muscle shorting rate and a condition for muscle cooling are derived.

Edemagenic gain and interstitial fluid volume regulation.

PubMed

Dongaonkar, R M; Quick, C M; Stewart, R H; Drake, R E; Cox, C S; Laine, G A

2008-02-01

Under physiological conditions, interstitial fluid volume is tightly regulated by balancing microvascular filtration and lymphatic return to the central venous circulation. Even though microvascular filtration and lymphatic return are governed by conservation of mass, their interaction can result in exceedingly complex behavior. Without making simplifying assumptions, investigators must solve the fluid balance equations numerically, which limits the generality of the results. We thus made critical simplifying assumptions to develop a simple solution to the standard fluid balance equations that is expressed as an algebraic formula. Using a classical approach to describe systems with negative feedback, we formulated our solution as a "gain" relating the change in interstitial fluid volume to a change in effective microvascular driving pressure. The resulting "edemagenic gain" is a function of microvascular filtration coefficient (K(f)), effective lymphatic resistance (R(L)), and interstitial compliance (C). This formulation suggests two types of gain: "multivariate" dependent on C, R(L), and K(f), and "compliance-dominated" approximately equal to C. The latter forms a basis of a novel method to estimate C without measuring interstitial fluid pressure. Data from ovine experiments illustrate how edemagenic gain is altered with pulmonary edema induced by venous hypertension, histamine, and endotoxin. Reformulation of the classical equations governing fluid balance in terms of edemagenic gain thus yields new insight into the factors affecting an organ's susceptibility to edema.

MICHTOX: A MASS BALANCE AND BIOACCUMULATION MODEL FOR TOXIC CHEMICALS IN LAKE MICHIGAN

EPA Science Inventory

MICHTOX is a toxic chemical mass balance and bioaccumulation model for Lake Michigan. It was developed for USEPA's Region V in support of the Lake Michigan Lake-wide Management Plan (LaMP) to provide guidance on expected water quality improvements in response to critical pollutan...

In vivo ultrasound and biometric measurements predict the empty body chemical composition in Nellore cattle.

PubMed

Castilhos, A M; Francisco, C L; Branco, R H; Bonilha, S F M; Mercadante, M E Z; Meirelles, P R L; Pariz, C M; Jorge, A M

2018-05-04

Evaluation of the body chemical composition of beef cattle can only be measured postmortem and those data cannot be used in real production scenarios to adjust nutritional plans. The objective of this study was to develop multiple linear regression equations from in vivo measurements, such as ultrasound parameters [backfat thickness (uBFT, mm), rump fat thickness (uRF, mm), and ribeye area (uLMA, cm2)], shrunk body weight (SBW, kg), age (AG, d), hip height (HH, m), as well as from postmortem measurements (composition of the 9th to 11th rib section) to predict the empty body and carcass chemical composition for Nellore cattle. Thirty-three young bulls were used (339 ± 36.15 kg and 448 ± 17.78 d for initial weight and age, respectively). Empty body chemical composition (protein, fat, water, and ash in kg) was obtained by combining noncarcass and carcass components. Data were analyzed using the PROC REG procedure of SAS software. Mallows' Cp values were close to the ideal value of number of independent variables in the prediction equations plus one. Equations to predict chemical components of both empty body and carcass using in vivo measurements presented higher R2 values than those determined by postmortem measurements. Chemical composition of the empty body using in vivo measurements was predicted with R2 > 0.73. Equations to predict chemical composition of the carcass from in vivo measurements showed R2 lower (R2< 0.68) than observed for empty body, except for the water (R2 = 0.84). The independent variables SBW, uRF, and AG were sufficient to predict the fat, water, energy components of the empty body, whereas for estimation of protein content the uRF, HH, and SBW were satisfactory. For the calculation of the ash, the SBW variable in the equation was sufficient. Chemical compounds from components of the empty body of Nellore cattle can be calculated by the following equations: protein (kg) = 47.92 + 0.18 × SBW - 1.46 × uRF - 30.72 × HH (R2 = 0.94, RMSPE = 1.79); fat (kg) = 11.33 + 0.16 × SBW + 2.09 × uRF - 0.06 × AG (R2 = 0.74, RMSPE = 4.18); water (kg) = - 34.00 + 0.55 × SBW + 0.10 × AG - 2.34 × uRF (R2 = 0.96, RMSPE = 5.47). In conclusion, the coefficients of determination (for determining the chemical composition of the empty body) of the equations derived from in vivo measures were higher than those of the equations obtained from rib section measurements taken postmortem, and better than coefficients of determination of the equations to predict the chemical composition of the carcass.

Parametric Identification of Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Water and energy balances in the soil-plant atmosphere continuum

USDA-ARS?s Scientific Manuscript database

Energy fluxes at soil-atmosphere and plant-atmosphere interfaces can be summed to zero because the surfaces have no capacity for energy storage. The resulting energy balance equations may be written in terms of physical descriptions of these fluxes; and have been the basis for problem casting and so...

POLLUTION BALANCE: A NEW METHODOLOGY FOR MINIMIZING WASTE PRODUCTION IN MANUFACTURING PROCESSES.

EPA Science Inventory

A new methodolgy based on a generic pollution balance equation, has been developed for minimizing waste production in manufacturing processes. A "pollution index," defined as the mass of waste produced per unit mass of a product, has been introduced to provide a quantitative meas...

Spousal Support and Work--Family Balance in Launching a Family Business

ERIC Educational Resources Information Center

Gudmunson, Clinton G.; Danes, Sharon M.; Werbel, James D.; Loy, Johnben Teik-Cheok

2009-01-01

This study examines whether emotional spousal support contributes to business owners' perceived work-family balance while launching a family business. Hobfoll's Conservation of Resources theory of stress is applied to 109 family business owners and their spouses. Results from structural equation models support several hypotheses. First, reports of…

Metabolite-balancing techniques vs. 13C tracer experiments to determine metabolic fluxes in hybridoma cells.

PubMed

Bonarius, H P; Timmerarends, B; de Gooijer, C D; Tramper, J

The estimation of intracellular fluxes of mammalian cells using only mass balances of the relevant metabolites is not possible because the set of linear equations defined by these mass balances is underdetermined. In order to quantify fluxes in cyclic pathways the mass balance equations can be complemented with several constraints: (1) the mass balances of co-metabolites, such as ATP or NAD(P)H, (2) linear objective functions, (3) flux data obtained by isotopic-tracer experiments. Here, these three methods are compared for the analysis of fluxes in the primary metabolism of continuously cultured hybridoma cells. The significance of different theoretical constraints and different objective functions is discussed after comparing their resulting flux distributions to the fluxes determined using 13CO2 and 13C-lactate measurements of 1 - 13C-glucose-fed hybridoma cells. Metabolic fluxes estimated using the objective functions "maximize ATP" and "maximize NADH" are relatively similar to the experimentally determined fluxes. This is consistent with the observation that cancer cells, such as hybridomas, are metabolically hyperactive, and produce ATP and NADH regardless of the need for these cofactors. Copyright 1998 John Wiley & Sons, Inc.

The energy balance within a bubble column evaporator

NASA Astrophysics Data System (ADS)

Fan, Chao; Shahid, Muhammad; Pashley, Richard M.

2018-05-01

Bubble column evaporator (BCE) systems have been studied and developed for many applications, such as thermal desalination, sterilization, evaporative cooling and controlled precipitation. The heat supplied from warm/hot dry bubbles is to vaporize the water in various salt solutions until the solution temperature reaches steady state, which was derived into the energy balance of the BCE. The energy balance and utilization involved in each BCE process form the fundamental theory of these applications. More importantly, it opened a new field for the thermodynamics study in the form of heat and vapor transfer in the bubbles. In this paper, the originally derived energy balance was reviewed on the basis of its physics in the BCE process and compared with new proposed energy balance equations in terms of obtained the enthalpy of vaporization (Δ H vap) values of salt solutions from BCE experiments. Based on the analysis of derivation and Δ H vap values comparison, it is demonstrated that the original balance equation has high accuracy and precision, within 2% over 19-55 °C using improved systems. Also, the experimental and theoretical techniques used for determining Δ H vap values of salt solutions were reviewed for the operation conditions and their accuracies compared to the literature data. The BCE method, as one of the most simple and accurate techniques, offers a novel way to determine Δ H vap values of salt solutions based on its energy balance equation, which had error less than 3%. The thermal energy required to heat the inlet gas, the energy used for water evaporation in the BCE and the energy conserved from water vapor condensation were estimated in an overall energy balance analysis. The good agreement observed between input and potential vapor condensation energy illustrates the efficiency of the BCE system. Typical energy consumption levels for thermal desalination for producing pure water using the BCE process was also analyzed for different inlet air temperatures, and indicated the better energy efficiency, of 7.55 kW·h per m3 of pure water, compared to traditional thermal desalination techniques.

Analytical method for optimal source reduction with monitored natural attenuation in contaminated aquifers

USGS Publications Warehouse

Widdowson, M.A.; Chapelle, F.H.; Brauner, J.S.; ,

2003-01-01

A method is developed for optimizing monitored natural attenuation (MNA) and the reduction in the aqueous source zone concentration (??C) required to meet a site-specific regulatory target concentration. The mathematical model consists of two one-dimensional equations of mass balance for the aqueous phase contaminant, to coincide with up to two distinct zones of transformation, and appropriate boundary and intermediate conditions. The solution is written in terms of zone-dependent Peclet and Damko??hler numbers. The model is illustrated at a chlorinated solvent site where MNA was implemented following source treatment using in-situ chemical oxidation. The results demonstrate that by not taking into account a variable natural attenuation capacity (NAC), a lower target ??C is predicted, resulting in unnecessary source concentration reduction and cost with little benefit to achieving site-specific remediation goals.

Temporal cross-correlation asymmetry and departure from equilibrium in a bistable chemical system.

PubMed

Bianca, C; Lemarchand, A

2014-06-14

This paper aims at determining sustained reaction fluxes in a nonlinear chemical system driven in a nonequilibrium steady state. The method relies on the computation of cross-correlation functions for the internal fluctuations of chemical species concentrations. By employing Langevin-type equations, we derive approximate analytical formulas for the cross-correlation functions associated with nonlinear dynamics. Kinetic Monte Carlo simulations of the chemical master equation are performed in order to check the validity of the Langevin equations for a bistable chemical system. The two approaches are found in excellent agreement, except for critical parameter values where the bifurcation between monostability and bistability occurs. From the theoretical point of view, the results imply that the behavior of cross-correlation functions cannot be exploited to measure sustained reaction fluxes in a specific nonlinear system without the prior knowledge of the associated chemical mechanism and the rate constants.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

NASA Astrophysics Data System (ADS)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

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

NASA Technical Reports Server (NTRS)

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

2001-01-01

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

Incorporation of a Chemical Equilibrium Equation of State into LOCI-Chem

NASA Technical Reports Server (NTRS)

Cox, Carey F.

2005-01-01

Renewed interest in development of advanced high-speed transport, reentry vehicles and propulsion systems has led to a resurgence of research into high speed aerodynamics. As this flow regime is typically dominated by hot reacting gaseous flow, efficient models for the characteristic chemical activity are necessary for accurate and cost effective analysis and design of aerodynamic vehicles that transit this regime. The LOCI-Chem code recently developed by Ed Luke at Mississippi State University for NASA/MSFC and used by NASA/MSFC and SSC represents an important step in providing an accurate, efficient computational tool for the simulation of reacting flows through the use of finite-rate kinetics [3]. Finite rate chemistry however, requires the solution of an additional N-1 species mass conservation equations with source terms involving reaction kinetics that are not fully understood. In the equilibrium limit, where the reaction rates approach infinity, these equations become very stiff. Through the use of the assumption of local chemical equilibrium the set of governing equations is reduced back to the usual gas dynamic equations, and thus requires less computation, while still allowing for the inclusion of reacting flow phenomenology. The incorporation of a chemical equilibrium equation of state module into the LOCI-Chem code was the primary objective of the current research. The major goals of the project were: (1) the development of a chemical equilibrium composition solver, and (2) the incorporation of chemical equilibrium solver into LOCI-Chem. Due to time and resource constraints, code optimization was not considered unless it was important to the proper functioning of the code.

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Smeltzer, Stanley S., III

2000-01-01

A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.

Population balance modeling: current status and future prospects.

PubMed

Ramkrishna, Doraiswami; Singh, Meenesh R

2014-01-01

Population balance modeling is undergoing phenomenal growth in its applications, and this growth is accompanied by multifarious reviews. This review aims to fortify the model's fundamental base, as well as point to a variety of new applications, including modeling of crystal morphology, cell growth and differentiation, gene regulatory processes, and transfer of drug resistance. This is accomplished by presenting the many faces of population balance equations that arise in the foregoing applications.

Modeling of Two-Wheeled Self-Balancing Robot Driven by DC Gearmotors

NASA Astrophysics Data System (ADS)

Frankovský, P.; Dominik, L.; Gmiterko, A.; Virgala, I.; Kurylo, P.; Perminova, O.

2017-08-01

This paper is aimed at modelling a two-wheeled self-balancing robot driven by the geared DC motors. A mathematical model consists of two main parts, the model of robot's mechanical structure and the model of the actuator. Linearized equations of motion are derived and the overall model of the two-wheeled self-balancing robot is represented in state-space realization for the purpose of state feedback controller design.

Choosing the Best Method to Introduce Accounting.

ERIC Educational Resources Information Center

Guerrieri, Donald J.

1988-01-01

Of the traditional approaches to teaching accounting--single entry, journal, "T" account, balance sheet, and accounting equation--the author recommends the accounting equation approach. It is the foundation of the double entry system, new material is easy to introduce, and it provides students with a rationale for understanding basic concepts.…

Coordinating Procedural and Conceptual Knowledge to Make Sense of Word Equations: Understanding the Complexity of a "Simple" Completion Task at the Learner's Resolution

ERIC Educational Resources Information Center

Taber, Keith S.; Bricheno, Pat

2009-01-01

The present paper discusses the conceptual demands of an apparently straightforward task set to secondary-level students--completing chemical word equations with a single omitted term. Chemical equations are of considerable importance in chemistry, and school students are expected to learn to be able to write and interpret them. However, it is…

40 CFR 1065.15 - Overview of procedures for laboratory and field testing.

Code of Federal Regulations, 2014 CFR

2014-07-01

... nitrogen, NOX. (2) Hydrocarbons, HC, which may be expressed in the following ways: (i) Total hydrocarbons... fuel consumed or calculate it with chemical balances of the fuel, intake air, and exhaust. To calculate fuel consumed by a chemical balance, you must also measure either intake-air flow rate or exhaust flow...

Interior. Looking from balance room to the front entrance. Chemicals ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Interior. Looking from balance room to the front entrance. Chemicals related to Edison's experiments on the extraction of latex for rubber from the goldenrod plant. Room is set up based on reconstruction research done in 1972. - Thomas A. Edison Laboratories, Building No. 2, Main Street & Lakeside Avenue, West Orange, Essex County, NJ

Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

NASA Technical Reports Server (NTRS)

Egolfopoulos, Fokion N.; Campbell, Charles S.

1999-01-01

A detailed numerical study was conducted on the dynamics and thermal response of inert, spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport, For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.

Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

NASA Technical Reports Server (NTRS)

Egolfopoulos, Fokion N.; Campbell, Charles S.; Wu, Ming-Shin (Technical Monitor)

1999-01-01

A detailed numerical study was conducted on the dynamics and thermal response of inert spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport. For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.

Prediction of light aircraft interior sound pressure level using the room equation

NASA Technical Reports Server (NTRS)

Atwal, M.; Bernhard, R.

1984-01-01

The room equation is investigated for predicting interior sound level. The method makes use of an acoustic power balance, by equating net power flow into the cabin volume to power dissipated within the cabin using the room equation. The sound power level transmitted through the panels was calculated by multiplying the measured space averaged transmitted intensity for each panel by its surface area. The sound pressure level was obtained by summing the mean square sound pressures radiated from each panel. The data obtained supported the room equation model in predicting the cabin interior sound pressure level.

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

NASA Technical Reports Server (NTRS)

Peters, D. A.; Ormiston, R. A.

1975-01-01

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

Theoretical study of the ionospheric G factor

NASA Technical Reports Server (NTRS)

Hagenbuch, K. M.

1972-01-01

A derivation from kinetic theory of the energy balance equation used in wave interaction work is reviewed. Then G is defined and two models for G are presented: one, a model based on Gerjuoy-Stein cross sections for both O2 and N2; the other based on a more recent model for O2 cross sections. The two models differ considerably in their temperature dependence. The limits of applicability of the useful energy balance equation (hence of the concept of G) are discussed and it is found that no difficulty arises unless the transmitter power is more than 1000 times that now employed at the present operating frequency.

First principles pulse pile-up balance equation and fast deterministic solution

NASA Astrophysics Data System (ADS)

Sabbatucci, Lorenzo; Fernández, Jorge E.

2017-08-01

Pulse pile-up (PPU) is an always present effect which introduces a distortion into the spectrum measured with radiation detectors and that worsen with the increasing emission rate of the radiation source. It is fully ascribable to the pulse handling circuitry of the detector and it is not comprised in the detector response function which is well explained by a physical model. The PPU changes both the number and the height of the recorded pulses, which are related, respectively, with the number of detected particles and their energy. In the present work, it is derived a first principles balance equation for second order PPU to obtain a post-processing correction to apply to X-ray measurements. The balance equation is solved for the particular case of rectangular pulse shape using a deterministic iterative procedure for which it will be shown the convergence. The proposed method, deterministic rectangular PPU (DRPPU), requires minimum amount of information and, as example, it is applied to a solid state Si detector with active or off-line PPU suppression circuitry. A comparison shows that the results obtained with this fast and simple approach are comparable to those from the more sophisticated procedure using precise detector pulse shapes.

Schrödinger and Dirac solutions to few-body problems

NASA Astrophysics Data System (ADS)

Muolo, Andrea; Reiher, Markus

We elaborate on the variational solution of the Schrödinger and Dirac equations for small atomic and molecular systems without relying on the Born-Oppenheimer approximation. The all-particle equations of motion are solved in a numerical procedure that relies on the variational principle, Cartesian coordinates and parametrized explicitly correlated Gaussians functions. A stochastic optimization of the variational parameters allows the calculation of accurate wave functions for ground and excited states. Expectation values such as the radial and angular distribution functions or the dipole moment can be calculated. We developed a simple strategy for the elimination of the global translation that allows to generally adopt laboratory-fixed cartesian coordinates. Simple expressions for the coordinates and operators are then preserved throughout the formalism. For relativistic calculations we devised a kinetic-balance condition for explicitly correlated basis functions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation between all components of the spinor of an N-fermion system. ETH Zürich, Laboratorium für Physikalische Chemie, CH-8093 Zürich, Switzerland.

Meta-Analysis of Mass Balances Examining Chemical Fate during Wastewater Treatment

PubMed Central

2008-01-01

Mass balances are an instructive means for investigating the fate of chemicals during wastewater treatment. In addition to the aqueous-phase removal efficiency (Φ), they can inform on chemical partitioning, transformation, and persistence, as well as on the chemical loading to streams and soils receiving, respectively, treated effluent and digested sewage sludge (biosolids). Release rates computed on a per-capita basis can serve to extrapolate findings to a larger scale. This review examines over a dozen mass balances conducted for various organic wastewater contaminants, including prescription drugs, estrogens, fragrances, antimicrobials, and surfactants of differing sorption potential (hydrophobicity), here expressed as the 1-octanol−water partition coefficient (KOW) and the organic carbon normalized sorption coefficient (KOC). Major challenges to mass balances are the collection of representative samples and accurate quantification of chemicals in sludge. A meta-analysis of peer-reviewed data identified sorption potential as the principal determinant governing chemical persistence in biosolids. Occurrence data for organic wastewater compounds detected in digested sludge followed a simple nonlinear model that required only KOW or KOC as the input and yielded a correlation coefficient of 0.9 in both instances. The model predicted persistence in biosolids for the majority (>50%) of the input load of organic wastewater compounds featuring a log10KOW value of greater than 5.2 (log10KOC > 4.4). In contrast, hydrophobicity had no or only limited value for estimating, respectively, Φ and the overall persistence of a chemical during conventional wastewater treatment. PMID:18800497

Lévy targeting and the principle of detailed balance.

PubMed

Garbaczewski, Piotr; Stephanovich, Vladimir

2011-07-01

We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) solution of the master equation. Here, an asymptotic behavior of different μ-motion scenarios ceases to depend on μ. That is exemplified by considering Gaussian and Cauchy family target PDFs. A complementary problem of the reverse engineering is analyzed: given a priori a semigroup potential, quantify how sensitive upon the choice of the μ driver is an asymptotic behavior of solutions of the associated master equation and thus an invariant PDF itself. This task is accomplished for so-called μ family of Lévy oscillators.

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.

Acid-Base Chemistry According to Robert Boyle: Chemical Reactions in Words as well as Symbols

ERIC Educational Resources Information Center

Goodney, David E.

2006-01-01

Examples of acid-base reactions from Robert Boyle's "The Sceptical Chemist" are used to illustrate the rich information content of chemical equations. Boyle required lengthy passages of florid language to describe the same reaction that can be done quite simply with a chemical equation. Reading or hearing the words, however, enriches the student's…

An LES-PBE-PDF approach for modeling particle formation in turbulent reacting flows

NASA Astrophysics Data System (ADS)

Sewerin, Fabian; Rigopoulos, Stelios

2017-10-01

Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size, and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact. In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported probability density function (PDF) approach for fluid phase scalars by the particle number density and obtain a modeled evolution equation for the filtered PDF associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost. As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model but also indicates the computational efficiency of the numerical solution scheme.

Unpacking students' atomistic uderstanding of stoichiometry

NASA Astrophysics Data System (ADS)

Baluyut, John Ysrael

Despite the use by instructors of particulate nature of matter (PNOM) diagrams in the general chemistry classroom, misconceptions on stoichiometry continue to prevail among students tasked with conceptual problems on concepts of limiting and excess reagents, and reaction yields. This dissertation set out to explore students' understanding of stoichiometry at the microscopic level as they solved problems that using PNOM diagrams. In particular, the study investigated how students coordinated symbolic and microscopic representations to demonstrate their knowledge of stoichiometric concepts, quantified the prevalence and explained the nature of stoichiometric misconceptions in terms of dual processing and dual coding theories, and used eye tracking to identify visual behaviors that accompanied cognitive processes students used to solve conceptual stoichiometry problems with PNOM diagrams. Interviews with students asked to draw diagrams for specific stoichiometric situations showed dual processing systems were in play. Many students were found to have used these processing systems in a heuristic-analytic sequence. Heuristics, such as the factor-label method and the least amount misconception, were often used by students to select information for further processing in an attempt to reduce the cognitive load of the subsequent analytic stage of the solution process. Diagrams drawn by students were used then to develop an instrument administered over a much larger sample of the general chemistry student population. The robustness of the dual processing theory was manifested by response patterns observed with large proportions of the student samples. These response patterns suggest that many students seemed to rely on heuristics to respond to a specific item for one of two diagrams given for the same chemical context, and then used a more analytic approach in dealing with the same item for the other diagram. It was also found that many students incorrectly treated items dealing with the same chemical context independently of each other instead of using a more integrative approach. A comparison of the visual behaviors of high-performing subjects with those of low-performers revealed that high performers relied heavily on the given diagrams to obtain information. They were found to have spent more time fixating on diagrams, looked between the chemical equation and the diagram for each problem more often, and used their episodic memory more heavily to collect information early on than low performers did. Retrospective think-alouds used with eye tracking also revealed specific strategies, such as counting and balancing of atoms and molecules across both sides of a diagram, as well as comparing ratios between atoms and molecules in a diagram with those given in a balanced equation, used by students to analyze PNOM diagrams.

Computer program determines chemical equilibria in complex systems

NASA Technical Reports Server (NTRS)

Gordon, S.; Zeleznik, F. J.

1966-01-01

Computer program numerically solves nonlinear algebraic equations for chemical equilibrium based on iteration equations independent of choice of components. This program calculates theoretical performance for frozen and equilibrium composition during expansion and Chapman-Jouguet flame properties, studies combustion, and designs hardware.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

The effect of the electric wind on the spatial distribution of chemical species in the positive corona discharge

NASA Astrophysics Data System (ADS)

Yanallah, K.; Pontiga, F.; Bouazza, M. R.; Chen, J. H.

2017-08-01

The electrohydrodynamic air flow generated by a positive corona discharge, and its effect on the spatial distribution of chemical species within a wire-plate corona reactor, have been numerically simulated. The computational model is based on the solutions of the Navier-Stokes equation and the continuity equation of each chemical species generated by the electrical discharge. A simplified analytical expression of the electric force density, which only requires the current density as the input parameter, has been used in the Navier-Stokes equation to obtain the velocity field. For the solution of the continuity equations, a plasma chemistry model that includes the most important reactions between electrons, atoms and molecules in air has been used. Similar to the electric force, the electron density distribution has been approximated by using a semi-analytical expression appropriate for the electrode geometry. The results of the study show that the spatial distribution of chemical species can be very different, and depends on the interplay between the electrohydrodynamic flow, the chemical kinetics of the species and its characteristic lifetime.

Energetics of muscle contraction: further trials.

PubMed

Yamada, Kazuhiro

2017-01-01

Knowledge accumulated in the field of energetics of muscle contraction has been reviewed in this article. Active muscle converts chemical energy into heat and work. Therefore, measurements of heat production and mechanical work provide the framework for understanding the process of energy conversion in contraction. In the 1970s, precise comparison between energy output and the associated chemical reactions was performed. It has been found that the two do not match in several situations, resulting in an energy balance discrepancy. More recently, efforts in resolving these discrepancies in the energy balance have been made involving chemical analysis, phosphorus nuclear magnetic resonance spectroscopy, and microcalorimetry. Through reviewing the evidence from these studies, the energy balance discrepancy developed early during isometric contraction has become well understood on a quantitative basis. In this situation energy balance is established when we take into account the binding of Ca to sarcoplasmic proteins such as troponin and parvalbumin, and also the shift of cross-bridge states. On the other hand, the energy balance discrepancy observed during rapid shortening still remains to be clarified. The problem may be related to the essential mechanism of cross-bridge action.

On the transmit field inhomogeneity correction of relaxation‐compensated amide and NOE CEST effects at 7 T

PubMed Central

Windschuh, Johannes; Siero, Jeroen C.W.; Zaiss, Moritz; Luijten, Peter R.; Klomp, Dennis W.J.; Hoogduin, Hans

2017-01-01

High field MRI is beneficial for chemical exchange saturation transfer (CEST) in terms of high SNR, CNR, and chemical shift dispersion. These advantages may, however, be counter‐balanced by the increased transmit field inhomogeneity normally associated with high field MRI. The relatively high sensitivity of the CEST contrast to B 1 inhomogeneity necessitates the development of correction methods, which is essential for the clinical translation of CEST. In this work, two B 1 correction algorithms for the most studied CEST effects, amide‐CEST and nuclear Overhauser enhancement (NOE), were analyzed. Both methods rely on fitting the multi‐pool Bloch‐McConnell equations to the densely sampled CEST spectra. In the first method, the correction is achieved by using a linear B 1 correction of the calculated amide and NOE CEST effects. The second method uses the Bloch‐McConnell fit parameters and the desired B 1 amplitude to recalculate the CEST spectra, followed by the calculation of B 1‐corrected amide and NOE CEST effects. Both algorithms were systematically studied in Bloch‐McConnell equations and in human data, and compared with the earlier proposed ideal interpolation‐based B 1 correction method. In the low B 1 regime of 0.15–0.50 μT (average power), a simple linear model was sufficient to mitigate B 1 inhomogeneity effects on a par with the interpolation B 1 correction, as demonstrated by a reduced correlation of the CEST contrast with B 1 in both the simulations and the experiments. PMID:28111824

Modeling and Analysis of the Reverse Water Gas Shift Process for In-Situ Propellant Production

NASA Technical Reports Server (NTRS)

Whitlow, Jonathan E.

2000-01-01

This report focuses on the development of mathematical models and simulation tools developed for the Reverse Water Gas Shift (RWGS) process. This process is a candidate technology for oxygen production on Mars under the In-Situ Propellant Production (ISPP) project. An analysis of the RWGS process was performed using a material balance for the system. The material balance is very complex due to the downstream separations and subsequent recycle inherent with the process. A numerical simulation was developed for the RWGS process to provide a tool for analysis and optimization of experimental hardware, which will be constructed later this year at Kennedy Space Center (KSC). Attempts to solve the material balance for the system, which can be defined by 27 nonlinear equations, initially failed. A convergence scheme was developed which led to successful solution of the material balance, however the simplified equations used for the gas separation membrane were found insufficient. Additional more rigorous models were successfully developed and solved for the membrane separation. Sample results from these models are included in this report, with recommendations for experimental work needed for model validation.

Modeling thermionic emission from laser-heated nanoparticles

DOE PAGES

Mitrani, J. M.; Shneider, M. N.; Stratton, B. C.; ...

2016-02-01

An adjusted form of thermionic emission is applied to calculate emitted current from laser-heated nanoparticles and to interpret time-resolved laser-induced incandescence (TR-LII) signals. This adjusted form of thermionic emission predicts significantly lower values of emitted current compared to the commonly used Richardson-Dushman equation, since the buildup of positive charge in a laser-heated nanoparticle increases the energy barrier for further emission of electrons. Thermionic emission influences the particle's energy balance equation, which can influence TR-LII signals. Additionally, reports suggest that thermionic emission can induce disintegration of nanoparticle aggregates when the electrostatic Coulomb repulsion energy between two positively charged primary particles ismore » greater than the van der Waals bond energy. Furthermore, since the presence and size of aggregates strongly influences the particle's energy balance equation, using an appropriate form of thermionic emission to calculate emitted current may improve interpretation of TR-LII signals.« less

Consistent transport coefficients in astrophysics

NASA Technical Reports Server (NTRS)

Fontenla, Juan M.; Rovira, M.; Ferrofontan, C.

1986-01-01

A consistent theory for dealing with transport phenomena in stellar atmospheres starting with the kinetic equations and introducing three cases (LTE, partial LTE, and non-LTE) was developed. The consistent hydrodynamical equations were presented for partial-LTE, the transport coefficients defined, and a method shown to calculate them. The method is based on the numerical solution of kinetic equations considering Landau, Boltzmann, and Focker-Planck collision terms. Finally a set of results for the transport coefficients derived for a partially ionized hydrogen gas with radiation was shown, considering ionization and recombination as well as elastic collisions. The results obtained imply major changes is some types of theoretical model calculations and can resolve some important current problems concerning energy and mass balance in the solar atmosphere. It is shown that energy balance in the lower solar transition region can be fully explained by means of radiation losses and conductive flux.

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.

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

Energy balance in TM-1-MH Tokamak (ohmical heating)

NASA Astrophysics Data System (ADS)

Stoeckel, J.; Koerbel, S.; Kryska, L.; Kopecky, V.; Dadalec, V.; Datlov, J.; Jakubka, K.; Magula, P.; Zacek, F.; Pereverzev, G. V.

1981-10-01

Plasma in the TM-1-MH Tokamak was experimentally studied in the parameter range: tor. mg. field B = 1,3 T, plasma current I sub p = 14 kA, electron density N sub E 3.10 to the 19th power cubic meters. The two numerical codes are available for the comparison with experimental data. TOKATA-code solves simplified energy balance equations for electron and ion components. TOKSAS-code solves the detailed energy balance of the ion component.

OBERON: OBliquity and Energy balance Run on N-body systems

NASA Astrophysics Data System (ADS)

Forgan, Duncan H.

2016-08-01

OBERON (OBliquity and Energy balance Run on N-body systems) models the climate of Earthlike planets under the effects of an arbitrary number and arrangement of other bodies, such as stars, planets and moons. The code, written in C++, simultaneously computes N body motions using a 4th order Hermite integrator, simulates climates using a 1D latitudinal energy balance model, and evolves the orbital spin of bodies using the equations of Laskar (1986a,b).

Thermal Characterization of the Air Force Institute of Technology Solar Simulation Thermal Vacuum Chamber

DTIC Science & Technology

2014-03-27

mass and surface area, Equation 12 demonstrates an energy balance for the material, assuming the rest of the surfaces of the material are isothermal...radiation in order to dissipate heat from 18 the spacecraft [8]. As discussed in the system thermal energy balance defined previously, emission of IR... energy balance calculations will be utilized. The Monte Carlo/Ray Trace Radiation Method The Monte Carlo/Ray Trace method is utilized in order to

Mass balance computation in SAGUARO

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

Baker, B.L.; Eaton, R.R.

1986-12-01

This report describes the development of the mass balance subroutines used with the finite-element code, SAGUARO, which models fluid flow in partially saturated porous media. Derivation of the basic mass storage and mass flux equations is included. The results of the SAGUARO mass-balance subroutine, MASS, are shown to compare favorably with the linked results of FEMTRAN. Implementation of the MASS option in SAGUARO is described. Instructions for use of the MASS option are demonstrated with the three sample cases.

40 CFR 1065.546 - Validation of minimum dilution ratio for PM batch sampling.

Code of Federal Regulations, 2012 CFR

2012-07-01

... chemical balance terms as given in § 1065.655(e). You may determine the raw exhaust flow rate based on the measured intake air and dilute exhaust molar flow rates and the dilute exhaust chemical balance terms as... air, fuel rate measurements, and fuel properties, consistent with good engineering judgment. (b...

40 CFR 1065.546 - Validation of minimum dilution ratio for PM batch sampling.

Code of Federal Regulations, 2013 CFR

2013-07-01

... chemical balance terms as given in § 1065.655(e). You may determine the raw exhaust flow rate based on the measured intake air and dilute exhaust molar flow rates and the dilute exhaust chemical balance terms as... air, fuel rate measurements, and fuel properties, consistent with good engineering judgment. (b...

40 CFR 1065.546 - Verification of minimum dilution ratio for PM batch sampling.

Code of Federal Regulations, 2014 CFR

2014-07-01

... chemical balance terms as given in § 1065.655(e). You may determine the raw exhaust flow rate based on the measured intake air and dilute exhaust molar flow rates and the dilute exhaust chemical balance terms as... air, fuel rate measurements, and fuel properties, consistent with good engineering judgment. (b...

Rapid computation of chemical equilibrium composition - An application to hydrocarbon combustion

NASA Technical Reports Server (NTRS)

Erickson, W. D.; Prabhu, R. K.

1986-01-01

A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free-energy minimization method. The general approach also has application to many other chemical systems.

Balancing the Readiness Equation in Early Childhood Education Reform

ERIC Educational Resources Information Center

Brown, Christopher P.

2010-01-01

As policy-makers continue to implement early childhood education reforms that frame the field as a mechanism that is to ready children for elementary school success, questions arise as to how the multiple variables in the readiness equation, such as the child, family, and program, are affected by these policies. The instrumental case study…

Waste disposal technologies for polychlorinated biphenyls.

PubMed Central

Piver, W T; Lindstrom, F T

1985-01-01

Improper practices in the disposal of polychlorinated biphenyl (PCB) wastes by land burial, chemical means and incineration distribute these chemicals and related compounds such as polychlorinated dibenzofurans (PCDFs) and polychlorinated dibenzodioxins (PCDDs) throughout the environment. The complete range of methods for disposal that have been proposed and are in use are examined and analyzed, with emphasis given to the two most commonly used methods: land burial and incineration. The understanding of aquifer contamination caused by migration of PCBs from subsurface burial sites requires a description of the physical, chemical and biological processes governing transport in unsaturated and saturated soils. For this purpose, a model is developed and solved for different soil conditions and external driving functions. The model couples together the fundamental transport phenomena for heat, mass, and moisture flow within the soil. To rehabilitate a contaminated aquifer, contaminated groundwaters are withdrawn through drainage wells, PCBs are extracted with solvents or activated carbon and treated by chemical, photochemical or thermal methods. The chemical and photochemical methods are reviewed, but primary emphasis is devoted to the use of incineration as the preferred method of disposal. After discussing the formation of PCDFs and PCDDs during combustion from chloroaromatic, chloroaliphatic, as well as organic and inorganic chloride precursors, performance characteristics of different thermal destructors are presented and analyzed. To understand how this information can be used, basic design equations are developed from governing heat and mass balances that can be applied to the construction of incinerators capable of more than 99.99% destruction with minimal to nondetectable levels of PCDFs and PCDDs. PMID:3921358

The Enskog Equation for Confined Elastic Hard Spheres

NASA Astrophysics Data System (ADS)

Maynar, P.; García de Soria, M. I.; Brey, J. Javier

2018-03-01

A kinetic equation for a system of elastic hard spheres or disks confined by a hard wall of arbitrary shape is derived. It is a generalization of the modified Enskog equation in which the effects of the confinement are taken into account and it is supposed to be valid up to moderate densities. From the equation, balance equations for the hydrodynamic fields are derived, identifying the collisional transfer contributions to the pressure tensor and heat flux. A Lyapunov functional, H[f], is identified. For any solution of the kinetic equation, H decays monotonically in time until the system reaches the inhomogeneous equilibrium distribution, that is a Maxwellian distribution with a density field consistent with equilibrium statistical mechanics.

The momentum constraints on the shallow meridional circulation associated with the marine ITCZ

NASA Astrophysics Data System (ADS)

Dixit, Vishal; Srinivasan, J.

2017-12-01

Recent studies have shown that the shallow meridional circulation (SMC) coexists with the deep circulation in the marine ITCZ. The SMC has been assumed to be forced by strong meridional gradients of Sea Surface Temperature (SST) which affect the atmosphere under hydrostatic balance. In this paper, we present a new viewpoint that the shallow meridional circulation is a part of circulation that forms when the marine ITCZ is located away from the equator. To support this view, we have used reanalysis data over east Pacific ocean to show that the shallow meridional circulation is absent when the ITCZ is located near the equator while it is strong to the south of the ITCZ when the ITCZ is located away from the equator. To further support this view, we have conducted idealized aquaplanet experiments by shifting SST maximum polewards to simulate the observed contrast in the meridional circulation associated with near equatorial and off-equatorial ITCZ. The detailed momentum budget of the flow above the boundary layer shows that, to the south of an off-equatorial ITCZ, the dominant balance between the Coriolis force and the advection of relative vorticity by the mean flow leads to cancellation of the planetary rotational effects. As a result, the net rotational effects experienced by the diverging flow above the boundary layer are negligible and a shallow meridional flow along the pressure gradients is generated. This dominant balance does not occur in the aquaplanet GCM when the ITCZ forms near the equator.

DEVELOPMENT OF A CONTAMINANT TRANSPORT AND FATE MASS BALANCE CALIBRATION MODEL FOR LAKE MICHIGAN MASS BALANCE PROJECT (LMMBP)

EPA Science Inventory

Lake Michigan Mass Balance Project (LMMBP) was initiated to directly support the development of a lakewide management plan (LaMP) for Lake Michigan. A mass balance modeling approach is proposed for the project to addrss the realtionship between sources of toxic chemicals and thei...

Extension of Gibbs-Duhem equation including influences of external fields

NASA Astrophysics Data System (ADS)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

Model reduction of multiscale chemical langevin equations: a numerical case study.

PubMed

Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N

2009-01-01

Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

Well-Balanced Second-Order Approximation of the Shallow Water Equations With Friction via Continuous Galerkin Finite Elements

NASA Astrophysics Data System (ADS)

Quezada de Luna, M.; Farthing, M.; Guermond, J. L.; Kees, C. E.; Popov, B.

2017-12-01

The Shallow Water Equations (SWEs) are popular for modeling non-dispersive incompressible water waves where the horizontal wavelength is much larger than the vertical scales. They can be derived from the incompressible Navier-Stokes equations assuming a constant vertical velocity. The SWEs are important in Geophysical Fluid Dynamics for modeling surface gravity waves in shallow regimes; e.g., in the deep ocean. Some common geophysical applications are the evolution of tsunamis, river flooding and dam breaks, storm surge simulations, atmospheric flows and others. This work is concerned with the approximation of the time-dependent Shallow Water Equations with friction using explicit time stepping and continuous finite elements. The objective is to construct a method that is at least second-order accurate in space and third or higher-order accurate in time, positivity preserving, well-balanced with respect to rest states, well-balanced with respect to steady sliding solutions on inclined planes and robust with respect to dry states. Methods fulfilling the desired goals are common within the finite volume literature. However, to the best of our knowledge, schemes with the above properties are not well developed in the context of continuous finite elements. We start this work based on a finite element method that is second-order accurate in space, positivity preserving and well-balanced with respect to rest states. We extend it by: modifying the artificial viscosity (via the entropy viscosity method) to deal with issues of loss of accuracy around local extrema, considering a singular Manning friction term handled via an explicit discretization under the usual CFL condition, considering a water height regularization that depends on the mesh size and is consistent with the polynomial approximation, reducing dispersive errors introduced by lumping the mass matrix and others. After presenting the details of the method we show numerical tests that demonstrate the well-balanced nature of the scheme and its convergence properties. We conclude with well-known benchmark problems including the Malpasset dam break (see the attached figure). All numerical experiments are performed and available in the Proteus toolkit, which is an open source python package for modeling continuum mechanical processes and fluid flow.

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

NASA Astrophysics Data System (ADS)

Kari, Leif

2017-09-01

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

Heat Balance Limits in Football Uniforms: How Different Uniform Ensembles Alter the Equation.

ERIC Educational Resources Information Center

Kulka, Hasha J.; Kenney, W. Larry

2002-01-01

Because football season becomes dangerous when warm weather collides with the need for protective gear, researchers investigated critical heat balance limits in non-heat- acclimatized men who wore various football uniform ensembles and exercised at 35 percent VO2 max in a programmable environmental chamber. The air temperature and humidity limits…

On Pell, Pell-Lucas, and balancing numbers.

PubMed

Karadeniz Gözeri, Gül

2018-01-01

In this paper, we derive some identities on Pell, Pell-Lucas, and balancing numbers and the relationships between them. We also deduce some formulas on the sums, divisibility properties, perfect squares, Pythagorean triples involving these numbers. Moreover, we obtain the set of positive integer solutions of some specific Pell equations in terms of the integer sequences mentioned in the text.

Teaching Children To Love: 80 Games & Fun Activities for Raising Balanced Children in Unbalanced Times.

ERIC Educational Resources Information Center

Childre, Doc Lew; Paddison, Sara Hatch, Ed.

Raising children in today's fast-paced society requires love and technique. Ways that parents can teach children to love, teach them values, and help them balance their lives are discussed in this activity book. The text opens with a discussion of heart intelligence (what is sometimes equated with emotional intelligence). Heart intelligence…

Weak periodic solutions of xẍ + 1 = 0 and the Harmonic Balance Method

NASA Astrophysics Data System (ADS)

García-Saldaña, J. D.; Gasull, A.

2017-02-01

We prove that the differential equation xẍ + 1 = 0 has continuous weak periodic solutions and compute their periods. Then, we use the Harmonic Balance Method until order six to approximate these periods and to illustrate how the accuracy of the method increases with the order. Our computations rely on the Gröbner basis approach.

High Order Well-balanced WENO Scheme for the Gas Dynamics Equations under Gravitational Fields

DTIC Science & Technology

2011-11-12

there exists the hydrostatic balance where the flux produced by the pressure is canceled by the gravitational source term. Many astro - physical...approximation to W (x) to obtain an approximation to W ′(xi) = fx (U(xi, yj)). See again [7, 15] for more details of finite difference WENO schemes in

Ergodicity-breaking bifurcations and tunneling in hyperbolic transport models

NASA Astrophysics Data System (ADS)

Giona, M.; Brasiello, A.; Crescitelli, S.

2015-11-01

One of the main differences between parabolic transport, associated with Langevin equations driven by Wiener processes, and hyperbolic models related to generalized Kac equations driven by Poisson processes, is the occurrence in the latter of multiple stable invariant densities (Frobenius multiplicity) in certain regions of the parameter space. This phenomenon is associated with the occurrence in linear hyperbolic balance equations of a typical bifurcation, referred to as the ergodicity-breaking bifurcation, the properties of which are thoroughly analyzed.

Balancing novelty with confined chemical space in modern drug discovery.

PubMed

Medina-Franco, José L; Martinez-Mayorga, Karina; Meurice, Nathalie

2014-02-01

The concept of chemical space has broad applications in drug discovery. In response to the needs of drug discovery campaigns, different approaches are followed to efficiently populate, mine and select relevant chemical spaces that overlap with biologically relevant chemical spaces. This paper reviews major trends in current drug discovery and their impact on the mining and population of chemical space. We also survey different approaches to develop screening libraries with confined chemical spaces balancing physicochemical properties. In this context, the confinement is guided by criteria that can be divided in two broad categories: i) library design focused on a relevant therapeutic target or disease and ii) library design focused on the chemistry or a desired molecular function. The design and development of chemical libraries should be associated with the specific purpose of the library and the project goals. The high complexity of drug discovery and the inherent imperfection of individual experimental and computational technologies prompt the integration of complementary library design and screening approaches to expedite the identification of new and better drugs. Library design approaches including diversity-oriented synthesis, biological-oriented synthesis or combinatorial library design, to name a few, and the design of focused libraries driven by target/disease, chemical structure or molecular function are more efficient if they are guided by multi-parameter optimization. In this context, consideration of pharmaceutically relevant properties is essential for balancing novelty with chemical space in drug discovery.

Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Smeltzer, Stanley S., III

2000-01-01

An analytical, parametric study of the attenuation of bending boundary layers or edge effects in balanced and unbalanced, symmetrically and unsymmetrically laminated thin cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize and quantify the effects of laminate orthotropy and laminate anisotropy on the bending boundary-layer decay length in a very general and encompassing manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all the laminate constructions considered, the results show that the differences between results that were obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that in some cases neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and in other cases it results in an overestimation.

The influence of vertical sorbed phase transport on the fate of organic chemicals in surface soils.

PubMed

McLachlan, Michael S; Czub, Gertje; Wania, Frank

2002-11-15

Gaseous exchange between surface soil and the atmosphere is an important process in the environmental fate of many chemicals. It was hypothesized that this process is influenced by vertical transport of chemicals sorbed to soil particles. Vertical sorbed phase transport in surface soils occurs by many processes such as bioturbation, cryoturbation, and erosion into cracks formed by soil drying. The solution of the advection/diffusion equation proposed by Jury et al. to describe organic chemical fate in a uniformly contaminated surface soil was modified to include vertical sorbed phase transport This process was modeled using a sorbed phase diffusion coefficient, the value of which was derived from soil carbon mass balances in the literature. The effective diffusivity of the chemical in a typical soil was greater in the modified model than in the model without sorbed phase transport for compounds with log K(OW) > 2 and log K(OA) > 6. Within this chemical partitioning space, the rate of volatilization from the surface soil was larger in the modified model than in the original model by up to a factor of 65. The volatilization rate was insensitive to the value of the sorbed phase diffusion coefficient throughout much of this chemical partitioning space, indicating that the surface soil layer was essentially well-mixed and that the mass transfer coefficient was determined by diffusion through the atmospheric boundary layer only. When this process was included in a non-steady-state regional multimedia chemical fate model running with a generic emissions scenario to air, the predicted soil concentrations increased by upto a factor of 25,whilethe air concentrations decreased by as much as a factor of approximately 3. Vertical sorbed phase transport in the soil thus has a major impact on predicted air and soil concentrations, the state of equilibrium, and the direction and magnitude of the chemical flux between air and soil. It is a key process influencing the environmental fate of persistent organic pollutants (POPs).

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).

Chemical potential, Gibbs-Duhem equation and quantum gases

NASA Astrophysics Data System (ADS)

Lee, M. Howard

2017-05-01

Thermodynamic relations like the Gibbs-Duhem are valid from the lowest to the highest temperatures. But they cannot by themselves provide any specific temperature behavior of thermodynamic functions like the chemical potential. In this work, we show that if some general conditions are attached to the Gibbs-Duhem equation, it is possible to obtain the low temperature form of the chemical potential for the ideal Fermi and Bose gases very directly.

Chemical Equilibrium and Polynomial Equations: Beware of Roots.

ERIC Educational Resources Information Center

Smith, William R.; Missen, Ronald W.

1989-01-01

Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…

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.

Development and application of a unified balancing approach with multiple constraints

NASA Technical Reports Server (NTRS)

Zorzi, E. S.; Lee, C. C.; Giordano, J. C.

1985-01-01

The development of a general analytic approach to constrained balancing that is consistent with past influence coefficient methods is described. The approach uses Lagrange multipliers to impose orbit and/or weight constraints; these constraints are combined with the least squares minimization process to provide a set of coupled equations that result in a single solution form for determining correction weights. Proper selection of constraints results in the capability to: (1) balance higher speeds without disturbing previously balanced modes, thru the use of modal trial weight sets; (2) balance off-critical speeds; and (3) balance decoupled modes by use of a single balance plane. If no constraints are imposed, this solution form reduces to the general weighted least squares influence coefficient method. A test facility used to examine the use of the general constrained balancing procedure and application of modal trial weight ratios is also described.

Bidirectional reaction steps in metabolic networks: I. Modeling and simulation of carbon isotope labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1997-07-05

The extension of metabolite balancing with carbon labeling experiments, as described by Marx et al. (Biotechnol. Bioeng. 49: 11-29), results in a much more detailed stationary metabolic flux analysis. As opposed to basic metabolite flux balancing alone, this method enables both flux directions of bidirectional reaction steps to be quantitated. However, the mathematical treatment of carbon labeling systems is much more complicated, because it requires the solution of numerous balance equations that are bilinear with respect to fluxes and fractional labeling. In this study, a universal modeling framework is presented for describing the metabolite and carbon atom flux in a metabolic network. Bidirectional reaction steps are extensively treated and their impact on the system's labeling state is investigated. Various kinds of modeling assumptions, as usually made for metabolic fluxes, are expressed by linear constraint equations. A numerical algorithm for the solution of the resulting linear constrained set of nonlinear equations is developed. The numerical stability problems caused by large bidirectional fluxes are solved by a specially developed transformation method. Finally, the simulation of carbon labeling experiments is facilitated by a flexible software tool for network synthesis. An illustrative simulation study on flux identifiability from available flux and labeling measurements in the cyclic pentose phosphate pathway of a recombinant strain of Zymomonas mobilis concludes this contribution.

Dissolution Front Instabilities in Reacting Porous Media

NASA Astrophysics Data System (ADS)

Raoof, Amir; Spiers, Chris; Hassanizadeh, Majid

2013-04-01

The main objective of this research is to gain a better understanding of the relation between regime of reaction and dissolution front instability, leading to formation of channels or wormholes. Potential applications are geological sequestration of CO2 and acid-gas injection during enhanced oil recovery. The microscopic pore space is modeled using a multi-directional pore network, allowing for a distribution of pore coordination number, together with distribution of pore sizes. In order to simulate transport of multi-component chemical species, mass balance equations are solved within each element of the network (i.e., pore body and pore throat). We have considered advective and diffusive transport processes within the pore spaces together with multi-component chemical reactions, including both equilibrium and kinetic reactions. Using dimensionless scaling groups (such as Damköhler number and Péclet-Damköhler number) we characterized the dissolution front behavior, and by averaging over the network domain we calculated the evolution of porosity and permeability as well as flux-averaged concentration breakthrough curves. We obtain constitutive relations linking porosity and permeability, under conditions relevant to geological storage of CO2. Effect of distribution of reactive minerals is also evaluated and regime of reaction is shown to play a key role.

Criteria for selecting electrodes for electrical stimulation: theoretical and practical considerations.

PubMed

Brummer, S B; Robblee, L S; Hambrecht, F T

1983-01-01

Smaller, more charge-intensive electrodes are needed for "safe" stimulation of the nervous system. In this paper we review critical concepts and the state of the art in electrodes. Control of charge density and charge balance are essential to avoid tissue electrolysis. Chemical criteria for "safe" stimulation are reviewed ("safe" is equated with "chemically reversible"). An example of a safe, but generally impractical, charge-injection process is double-layer charging. The limit here is the onset of irreversible faradaic processes. More charge can be safely injected with so-called "capacitor" electrodes, such as porous intermixtures of Ta/Ta2O5. BaTiO3 has excellent dielectric properties and may provide a new generation of capacitor electrodes. Faradaic charge injection is usually partially irreversible since some of the products escape into the solution. With Pt, up to 400 muc/cm2 real area can be absorbed by faradaic reactions of surface-adsorbed species, but a small part is lost due to metal dissolution. The surface of "activated" Ir is covered with a multilayer hydrated oxide. Charge injection occurs via rapid valence change within this oxide. Little or no metal dissolution is observed, and gassing limits are not exceeded even under stringent conditions.

Climate Modeling in the Calculus and Differential Equations Classroom

ERIC Educational Resources Information Center

Kose, Emek; Kunze, Jennifer

2013-01-01

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

Visualization in Mechanics: The Dynamics of an Unbalanced Roller

ERIC Educational Resources Information Center

Cumber, Peter S.

2017-01-01

It is well known that mechanical engineering students often find mechanics a difficult area to grasp. This article describes a system of equations describing the motion of a balanced and an unbalanced roller constrained by a pivot arm. A wide range of dynamics can be simulated with the model. The equations of motion are embedded in a graphical…

On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

Biodegradation of organic chemicals in soil/water microcosms system: Model development

USGS Publications Warehouse

Liu, L.; Tindall, J.A.; Friedel, M.J.; Zhang, W.

2007-01-01

The chemical interactions of hydrophobic organic contaminants with soils and sediments may result in strong binding and slow subsequent release rates that significantly affect remediation rates and endpoints. In order to illustrate the recalcitrance of chemical to degradation on sites, a sorption mechanism of intraparticle sequestration was postulated to operate on chemical remediation sites. Pseudo-first order sequestration kinetics is used in the study with the hypothesis that sequestration is an irreversibly surface-mediated process. A mathematical model based on mass balance equations was developed to describe the fate of chemical degradation in soil/water microcosm systems. In the model, diffusion was represented by Fick's second law, local sorption-desorption by a linear isotherm, irreversible sequestration by a pseudo-first order kinetics and biodegradation by Monod kinetics. Solutions were obtained to provide estimates of chemical concentrations. The mathematical model was applied to a benzene biodegradation batch test and simulated model responses correlated well compared to measurements of biodegradation of benzene in the batch soil/water microcosm system. A sensitivity analysis was performed to assess the effects of several parameters on model behavior. Overall chemical removal rate decreased and sequestration increased quickly with an increase in the sorption partition coefficient. When soil particle radius, a, was greater than 1 mm, an increase in radius produced a significant decrease in overall chemical removal rate as well as an increase in sequestration. However, when soil particle radius was less than 0.1 mm, an increase in radius resulted in small changes in the removal rate and sequestration. As pseudo-first order sequestration rate increased, both chemical removal rate and sequestration increased slightly. Model simulation results showed that desorption resistance played an important role in the bioavailability of organic chemicals in porous media. Complete biostabilization of chemicals on remediation sites can be achieved when the concentration of the reversibly sorbed chemical reduces to zero (i.e., undetectable), with a certain amount of irreversibly sequestrated chemical left inside the soil particle solid phase. ?? 2006 Springer Science + Business Media B.V.

Liquefaction of Saturated Soil and the Diffusion Equation

NASA Astrophysics Data System (ADS)

Sawicki, Andrzej; Sławińska, Justyna

2015-06-01

The paper deals with the diffusion equation for pore water pressures with the source term, which is widely promoted in the marine engineering literature. It is shown that such an equation cannot be derived in a consistent way from the mass balance and the Darcy law. The shortcomings of the artificial source term are pointed out, including inconsistencies with experimental data. It is concluded that liquefaction and the preceding process of pore pressure generation and the weakening of the soil skeleton should be described by constitutive equations within the well-known framework of applied mechanics. Relevant references are provided

On the Mechanism for a Gravity Effect Using Type 2 Superconductors

NASA Technical Reports Server (NTRS)

Robertson, Glen A.

1999-01-01

In this paper, we formulate a percent mass change equation based on Woodward's transient mass shift and the Cavendish balance equations applied to superconductor Josephson junctions, A correction to the transient mass shift equation is presented due to the emission of the mass energy from the superconductor. The percentage of mass change predicted by the equation was estimated against the maximum percent mass change reported by Podkletnov in his gravity shielding experiments. An experiment is then discussed, which could shed light on the transient mass shift near superconductor and verify the corrected gravitational potential.

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

Dynamics of droplet motion under electrowetting actuation.

PubMed

Annapragada, S Ravi; Dash, Susmita; Garimella, Suresh V; Murthy, Jayathi Y

2011-07-05

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities. © 2011 American Chemical Society

Correlation of Experimental and Theoretical Steady-State Spinning Motion for a Current Fighter Airplane Using Rotation-Balance Aerodynamic Data

DTIC Science & Technology

1978-07-01

were input into the computer program. The program was numerically intergrated with time by using a fourth-order Runge-Kutta integration algorithm with...equations of motion are numerically intergrated to provide time histories of the aircraft spinning motion. A.2 EQUATIONS DEFINING THE FORCE AND MOMENT...by Cy or Cn. 50 AE DC-TR-77-126 A . 4 where EQUATIONS FOR TRANSFERRING AERODYNAMIC DATA INPUTS TO THE PROPER HORIZONTAL CENTER OF GRAVITY

KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

NASA Astrophysics Data System (ADS)

El-Shorbagy, Kh. H.; Mahassen, Hania; El-Bendary, Atef Ahmed

2017-12-01

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev-Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.

An auto-Bäcklund transformation and exact solutions for Wick-type stochastic generalized KdV equations

NASA Astrophysics Data System (ADS)

Xie, Yingchao

2004-05-01

Wick-type stochastic generalized KdV equations are researched. By using the homogeneous balance, an auto-Bäcklund transformation to the Wick-type stochastic generalized KdV equations is derived. And stochastic single soliton and stochastic multi-soliton solutions are shown by using the Hermite transform. Research supported by the National Natural Science Foundation of China (19971072) and the Natural Science Foundation of Education Committee of Jiangsu Province of China (03KJB110135).

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Greenhouse gases inventory and carbon balance of two dairy systems obtained from two methane-estimation methods.

PubMed

Cunha, C S; Lopes, N L; Veloso, C M; Jacovine, L A G; Tomich, T R; Pereira, L G R; Marcondes, M I

2016-11-15

The adoption of carbon inventories for dairy farms in tropical countries based on models developed from animals and diets of temperate climates is questionable. Thus, the objectives of this study were to estimate enteric methane (CH4) emissions through the SF6 tracer gas technique and through equations proposed by the Intergovernmental Panel on Climate Change (IPCC) Tier 2 and to calculate the inventory of greenhouse gas (GHG) emissions from two dairy systems. In addition, the carbon balance of these properties was estimated using enteric CH4 emissions obtained using both methodologies. In trial 1, the CH4 emissions were estimated from seven Holstein dairy cattle categories based on the SF6 tracer gas technique and on IPCC equations. The categories used in the study were prepubertal heifers (n=6); pubertal heifers (n=4); pregnant heifers (n=5); high-producing (n=6); medium-producing (n=5); low-producing (n=4) and dry cows (n=5). Enteric methane emission was higher for the category comprising prepubertal heifers when estimated by the equations proposed by the IPCC Tier 2. However, higher CH4 emissions were estimated by the SF6 technique in the categories including medium- and high-producing cows and dry cows. Pubertal heifers, pregnant heifers, and low-producing cows had equal CH4 emissions as estimated by both methods. In trial 2, two dairy farms were monitored for one year to identify all activities that contributed in any way to GHG emissions. The total emission from Farm 1 was 3.21t CO2e/animal/yr, of which 1.63t corresponded to enteric CH4. Farm 2 emitted 3.18t CO2e/animal/yr, with 1.70t of enteric CH4. IPCC estimations can underestimate CH4 emissions from some categories while overestimate others. However, considering the whole property, these discrepancies are offset and we would submit that the equations suggested by the IPCC properly estimate the total CH4 emission and carbon balance of the properties. Thus, the IPCC equations should be utilized with caution, and the herd composition should be analysed at the property level. When the carbon stock in pasture and other crops was considered, the carbon balance suggested that both farms are sustainable for GHG, by both methods. On the other hand, carbon balance without carbon stock, by both methods, suggests that farms emit more carbon than the system is capable of stock. Copyright © 2016 Elsevier B.V. All rights reserved.

Conceptual design of a bioregenerative life support system containing crops and silkworms

NASA Astrophysics Data System (ADS)

Hu, Enzhu; Bartsev, Sergey I.; Liu, Hong

2010-04-01

This article summarizes a conceptual design of a bioregenerative life support system for permanent lunar base or planetary exploration. The system consists of seven compartments - higher plants cultivation, animal rearing, human habitation, water recovery, waste treatment, atmosphere management, and storages. Fifteen kinds of crops, such as wheat, rice, soybean, lettuce, and mulberry, were selected as main life support contributors to provide the crew with air, water, and vegetable food. Silkworms fed by crop leaves were designated to produce partial animal nutrition for the crew. Various physical-chemical and biological methods were combined to reclaim wastewater and solid waste. Condensate collected from atmosphere was recycled into potable water through granular activated carbon adsorption, iodine sterilization, and trace element supplementation. All grey water was also purified though multifiltration and ultraviolet sterilization. Plant residue, human excrement, silkworm feces, etc. were decomposed into inorganic substances which were finally absorbed by higher plants. Some meat, ingredients, as well as nitrogen fertilizer were prestored and resupplied periodically. Meanwhile, the same amount and chemical composition of organic waste was dumped to maintain the steady state of the system. A nutritional balanced diet was developed by means of the linear programming method. It could provide 2721 kcal of energy, 375.5 g of carbohydrate, 99.47 g of protein, and 91.19 g of fat per capita per day. Silkworm powder covered 12.54% of total animal protein intakes. The balance of material flows between compartments was described by the system of stoichiometric equations. Basic life support requirements for crews including oxygen, food, potable and hygiene water summed up to 29.68 kg per capita per day. The coefficient of system material closure reached 99.40%.

Thermophysical Fluid Dynamics: the Key to the Structures of Fluid Objects

NASA Astrophysics Data System (ADS)

Houben, H.

2013-12-01

It has become customary to model the hydrodynamics of fluid planets like Jupiter and Saturn by spinning up general circulation models until they reach a statistical steady state. This approach is physically sound, based on the thermodynamic expectation that the system will eventually achieve a state of maximum entropy, but the models have not been specifically designed for this purpose. Over the course of long integrations, numerical artifacts can drive the system to a state that does not correspond to the physically realistic end state. A different formulation of the governing equations promises better results. The equations of motion are recast as scalar conservation laws in which the diabatic and irreversible terms (both entropy-changing) are clearly identified. The balance between these terms defines the steady state of the system analytically, without the need for any temporal integrations. The conservation of mass in this system is trivial. Conservation of angular momentum replaces the zonal momentum equation and determines the zonal wind from a balance between the tidal torque and frictional dissipation. The principle of wave-mean flow non-interaction is preserved. Bernoulli's Theorem replaces the energy equation. The potential temperature structure is determined by the balance between work done against friction and heat transfer by convection and radiation. An equation of state and the traditional momentum equations in the meridional plane are sufficient to complete the model. Based on the assumption that the final state vertical and meridional winds are small compared to the zonal wind (in any case they are impossible to predict ab initio as they are driven by wave flux convergences), these last equations determine the pressure and density (and hence gravity) fields of the basic state. The thermal wind relation (in its most general form with the axial derivative of the zonal wind balancing the baroclinicity) is preserved. The model is not hydrostatic (in the sense used in planetary modeling) and the zonal wind is not constant on cylinders. Rather, the zonal wind falls off more rapidly with depth --- at least as fast as r3. A similar reformulation of the equations of magnetohydrodynamics is possible. It is found that wave-mean flow non-interaction extends to Alfven waves. Bernoulli's Theorem is augmented by the Poynting Theorem. The components of the traditional dynamo equation can be written as conservation laws. Only a single element of the alpha tensor contributes to the generation of axisymmetric magnetic fields and the mean meridional circulation provides a significant feedback, quenching the omega effect and limiting the amplitudes of non-axisymmetric fields. Thus analytic models are available for all the state variables of Jupiter and Saturn. The unknown independent variables are terms in the equation of state, the eddy viscosity and heat transport coefficients, the magnetic resistivity, and the strength of the tidal torques (which are dependent on the vertical structure of the planet's troposphere). By making new measurements of the atmospheric structure and higher order gravitational moments of Jupiter, JUNO has the potential to constrain these unknowns and contribute greatly to our understanding of the interior of that planet.

A well-balanced meshless tsunami propagation and inundation model

NASA Astrophysics Data System (ADS)

Brecht, Rüdiger; Bihlo, Alexander; MacLachlan, Scott; Behrens, Jörn

2018-05-01

We present a novel meshless tsunami propagation and inundation model. We discretize the nonlinear shallow-water equations using a well-balanced scheme relying on radial basis function based finite differences. For the inundation model, radial basis functions are used to extrapolate the dry region from nearby wet points. Numerical results against standard one- and two-dimensional benchmarks are presented.

Top 10 Research Questions Related to Energy Balance

ERIC Educational Resources Information Center

Shook, Robin P.; Hand, Gregory A.; Blair, Steven N.

2014-01-01

Obesity is the result of a mismatch between the amount of calories consumed and the amount of calories expended during an extended period of time. This relationship is described by the energy balance equation, which states the rate of change in energy storage depots in the body are equal to the rate of energy intake minus the rate of energy…

Can weighing lysimeter ET represent surrounding field ET well enough to test flux station measurements of daily and sub-daily ET?

USDA-ARS?s Scientific Manuscript database

Weighing lysimeters and neutron probes are two tools used to determine the change in soil water storage that is needed to solve for evapotranspiration (ET) using the soil water balance equation. Errors in the soil water balance due to errors in determination of precipitation and irrigation are commo...

An evaluation of fluid bed drying of aqueous granulations.

PubMed

Hlinak, A J; Saleki-Gerhardt, A

2000-01-01

The purpose of the work described was twofold: (a) to apply heat and mass balance approaches to evaluate the fluid bed drying cycle of an aqueous granulation, and (b) to determine the effect of the temperature and relative humidity of the drying air on the ability to meet a predetermined moisture content specification. Water content determinations were performed using Karl Fischer titration, and Computrac and Mark 1 moisture analyzers. The water vapor sorption isotherms were measured using a gravimetric moisture sorption apparatus with vacuum-drying capability. Temperature, relative humidity, and air flow were measured during the drying cycle of a production-scale fluid bed dryer. Heat and mass balance equations were used to calculate the evaporation rates. Evaporation rates calculated from heat and mass balance equations agreed well with the experimental data, whereas equilibrium moisture content values provided useful information for determination of the upper limit for inlet air humidity. Increasing the air flow rate and inlet temperature reduced the drying time through the effect on the primary driving force. As expected, additional drying of granules during the equilibration period did not show a significant impact on reducing the final moisture content of granules. Reducing the drying temperature resulted in measurement of higher equilibrium moisture content for the granules, which was in good agreement with the water vapor sorption data. Heat and mass balance equations can be used to successfully model the fluid bed drying cycle of aqueous granulations. The water vapor sorption characteristics of granules dictate the final moisture content at a given temperature and relative humidity.

Theory and computation of general force balance in non-axisymmetric tokamak equilibria

NASA Astrophysics Data System (ADS)

Park, Jong-Kyu; Logan, Nikolas; Wang, Zhirui; Kim, Kimin; Boozer, Allen; Liu, Yueqiang; Menard, Jonathan

2014-10-01

Non-axisymmetric equilibria in tokamaks can be effectively described by linearized force balance. In addition to the conventional isotropic pressure force, there are three important components that can strongly contribute to the force balance; rotational, anisotropic tensor pressure, and externally given forces, i.e. ∇ --> p + ρv-> . ∇ --> v-> + ∇ --> . <-->Π + f-> = j-> × B-> , especially in, but not limited to, high β and rotating plasmas. Within the assumption of nested flux surfaces, Maxwell equations and energy minimization lead to the modified-generalized Newcomb equation for radial displacements with simple algebraic relations for perpendicular and parallel displacements, including an inhomogeneous term if any of the forces are not explicitly dependent on displacements. The general perturbed equilibrium code (GPEC) solves this force balance consistent with energy and torque given by external perturbations. Local and global behaviors of solutions will be discussed when ∇ --> . <-->Π is solved by the semi-analytic code PENT and will be compared with MARS-K. Any first-principle transport code calculating ∇ --> . <-->Π or f-> , e.g. POCA, can also be incorporated without demanding iterations. This work was supported by DOE Contract DE-AC02-09CH11466.

Position-dependent effective masses in semiconductor theory. II

NASA Technical Reports Server (NTRS)

Von Roos, O.; Mavromatis, H.

1985-01-01

A compound semiconductor possessing a slowly varying position-dependent chemical composition is considered. An effective-mass equation governing the dynamics of electron (or hole) motion using the Kohn-Luttinger representation and canonical transformations is derived. It is shown that, as long as the variation in chemical composition may be treated as a perturbation, the effective masses become constant, position-independent quantities. The effective-mass equation derived here is identical to the effective-mass equation derived previously by von Roos (1983), using a Wannier representation.

Well-balanced Schemes for Gravitationally Stratified Media

NASA Astrophysics Data System (ADS)

Käppeli, R.; Mishra, S.

2015-10-01

We present a well-balanced scheme for the Euler equations with gravitation. The scheme is capable of maintaining exactly (up to machine precision) a discrete hydrostatic equilibrium without any assumption on a thermodynamic variable such as specific entropy or temperature. The well-balanced scheme is based on a local hydrostatic pressure reconstruction. Moreover, it is computationally efficient and can be incorporated into any existing algorithm in a straightforward manner. The presented scheme improves over standard ones especially when flows close to a hydrostatic equilibrium have to be simulated. The performance of the well-balanced scheme is demonstrated on an astrophysically relevant application: a toy model for core-collapse supernovae.

Results of the Lake Michigan Mass Balance Project: Atrazine Modeling Report

EPA Science Inventory

This report covers an overview of chemical properties, measurements in air and water, model construct and assumptions, and results of mathematical mass balance modeling of the herbicide atrazine in the Lake Michigan basin. Within the context of the mass balance, an overview of a...

Regional Screening Levels (RSLs) - Equations

EPA Pesticide Factsheets

Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.

Estimation of chemical carcass composition from 8th rib characteristics with Belgian blue double-muscled bulls.

PubMed

De Campeneere, S; Fiems, L O; Van de Voorde, G; Vanacker, J M; Boucque, C V; Demeyer, D I

1999-01-01

Characteristics from the 8th rib cut: chemical composition, tissue composition after dissection, specific gravity (SG) and m. longissimus thoracis (LT) composition, collected on 17 Belgian Blue double-muscled fattening bulls were used to generate equations for predicting chemical carcass composition. Carcass composition was best predicted from chemical analysis of the 8th rib cut and the empty body weight (EBW) of the bull. Carcass chemical fat content (CCF, kg) was predicted from the 8th rib cut fat content (ether extract, 8RF, kg) by the following regression: CCF=1.94+27.37 8RF (R(2)=0.957, RSD =9.89%). A higher coefficient was found for carcass water (CCW, kg) predicted from 8RF and EBW: CCW=-2.26+0.28 EBW-34.28 8RF (R(2)=0.997, RSD=1.48%). No parameter was found to improve the prediction of CCP from EBW solely: CCP=-0.86+0.08 EBW (R(2) =0.992, RSD=2.61%). Prediction equations based solely on LT composition had low R(2) values of between 0.38 and 0.67, whereas no significant equations were found using SG. However, equations based on EBW had R(2) values between 0.78 and 0.99. Chemical components of the 8th rib cut in combination with EBW are most useful in predicting the chemical composition of the carcass of Belgian-Blue double-muscled bulls.

Low-pass filtered continuum streambed and bedload sediment mass balance laws for an alluvial, gravel-bed stream

NASA Astrophysics Data System (ADS)

DeTemple, B.; Wilcock, P.

2011-12-01

In an alluvial, gravel-bed stream governed by a plane-bed bedload transport regime, the physicochemical properties, size distribution, and granular architecture of the sediment grains that constitute the streambed surface influence many hydrodynamic, geomorphic, chemical, and ecological processes. Consequently, the abilities to accurately characterize the morphology and model the morphodynamics of the streambed surface and its interaction with the bedload above and subsurface below are necessary for a more complete understanding of how sediment, flow, organisms, and biogeochemistry interact. We report on our progress in the bottom-up development of low-pass filtered continuum streambed and bedload sediment mass balance laws for an alluvial, gravel-bed stream. These balance laws are assembled in a four stage process. First, the stream sediment-water system is conceptually abstracted as a nested, multi-phase, multi-species, structured continuum. Second, the granular surface of an aggregate of sediment grains is mathematically defined. Third, an integral approach to mass balance, founded in the continuum theory of multiphase flow, is used to formulate primordial, differential, instantaneous, local, continuum, mass balance laws applicable at any material point within a gravel-bed stream. Fourth, area averaging and time-after-area averaging, employing planform, low-pass filtering expressed as correlation or convolution integrals and based on the spatial and temporal filtering techniques found in the fields of multiphase flow, porous media flow, and large eddy simulation of turbulent fluid flow, are applied to smooth the primordial equations while maximizing stratigraphic resolution and preserving the definitions of relevant morphodynamic surfaces. Our approach unifies, corrects, contextualizes, and generalizes prior efforts at developing stream sediment continuity equations, including the top-down derivations of the surface layer (or "active layer") approach of Hirano [1971a,b] and probabilistic approach of Parker et al. [2000], as well as the bottom-up, low-pass filtered continuum approach of Coleman & Nikora [2009] which employed volume and volume-after-time averaging. It accommodates partial transport (e.g., Wilcock & McArdell [1997], Wilcock [1997a,b]). Additionally, it provides: (1) precise definitions of the geometry and kinematics of sediment in a gravel-bed stream required to collect and analyze the high resolution spatial and temporal datasets that are becoming ever more present in both laboratory and field investigations, (2) a mathematical framework for the use of tracer grains in gravel-bed streams, including the fate of streambed-emplaced tracers as well as the dispersion of tracers in the bedload, (3) spatial and temporal averaging uncompromised by the Reynolds rules necessary to assess the nature of scale separation, and (4) a kinematic foundation for hybrid Langrangian-Eulerian models of sediment morphodynamics.

Modelling and Inverse-Modelling: Experiences with O.D.E. Linear Systems in Engineering Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor

2009-01-01

In engineering careers courses, differential equations are widely used to solve problems concerned with modelling. In particular, ordinary differential equations (O.D.E.) linear systems appear regularly in Chemical Engineering, Food Technology Engineering and Environmental Engineering courses, due to the usefulness in modelling chemical kinetics,…

Artificial acoustic stiffness reduction in fully compressible, direct numerical simulation of combustion

NASA Astrophysics Data System (ADS)

Wang, Yi; Trouvé, Arnaud

2004-09-01

A pseudo-compressibility method is proposed to modify the acoustic time step restriction found in fully compressible, explicit flow solvers. The method manipulates terms in the governing equations of order Ma2, where Ma is a characteristic flow Mach number. A decrease in the speed of acoustic waves is obtained by adding an extra term in the balance equation for total energy. This term is proportional to flow dilatation and uses a decomposition of the dilatational field into an acoustic component and a component due to heat transfer. The present method is a variation of the pressure gradient scaling (PGS) method proposed in Ramshaw et al (1985 Pressure gradient scaling method for fluid flow with nearly uniform pressure J. Comput. Phys. 58 361-76). It achieves gains in computational efficiencies similar to PGS: at the cost of a slightly more involved right-hand-side computation, the numerical time step increases by a full order of magnitude. It also features the added benefit of preserving the hydrodynamic pressure field. The original and modified PGS methods are implemented into a parallel direct numerical simulation solver developed for applications to turbulent reacting flows with detailed chemical kinetics. The performance of the pseudo-compressibility methods is illustrated in a series of test problems ranging from isothermal sound propagation to laminar premixed flame problems.

Study of parameters affecting the conversion in a plug flow reactor for reactions of the type 2A→B

NASA Astrophysics Data System (ADS)

Beltran-Prieto, Juan Carlos; Long, Nguyen Huynh Bach Son

2018-04-01

Modeling of chemical reactors is an important tool to quantify reagent conversion, product yield and selectivity towards a specific compound and to describe the behavior of the system. Proposal of differential equations describing the mass and energy balance are among the most important steps required during the modeling process as they play a special role in the design and operation of the reactor. Parameters governing transfer of heat and mass have a strong relevance in the rate of the reaction. Understanding this information is important for the selection of reactor and operating regime. In this paper we studied the irreversible gas-phase reaction 2A→B. We model the conversion that can be achieved as function of the reactor volume and feeding temperature. Additionally, we discuss the effect of activation energy and the heat of reaction on the conversion achieved in the tubular reactor. Furthermore, we considered that dimerization occurs instantaneously in the catalytic surface to develop equations for the determination of rate of reaction per unit area of three different catalytic surface shapes. This data can be combined with information about the global rate of conversion in the reactor to improve regent conversion and yield of product.

Chemical oscillator as a generalized Rayleigh oscillator.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2013-10-28

We derive the conditions under which a set of arbitrary two dimensional autonomous kinetic equations can be reduced to the form of a generalized Rayleigh oscillator which admits of limit cycle solution. This is based on a linear transformation of field variables which can be found by inspection of the kinetic equations. We illustrate the scheme with the help of several chemical and bio-chemical oscillator models to show how they can be cast as a generalized Rayleigh oscillator.

General criteria for the validity of the Buckingham-Darcy Flow Law

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

Sposito, G.

A detailed, first-principles study is undertaken on the exact equation of linear momentum balance for water in an unsaturated soil. An approximate momentum balance equation (Raats and Klute) demonstrates that the flow of water through a rigid, homogeneous, isotropic, unsaturated soil will obey the Buckingham-Darcy Law within 10/sup -12/ to 10/sup -5/ sec after a gradient in the total potential of soil water has been applied. The Raats-Klute equation will be accurate if (1) the water mass density and mass flux density vector constitute a complete set of strongly coupled, macroscopic dynamical variables, and (2) the time scale over whichmore » these 2 variables change significantly is much longer than that over which any other dynamic quantities vary. If these 2 conditions are met, then, according to statistical mechanics, the flow of water through unsaturated soil will be described accurately over all macroscopic intervals by the Buckingham-Darcy law.« less

Modeling of chemical inhibition from amyloid protein aggregation kinetics.

PubMed

Vázquez, José Antonio

2014-02-27

The process of amyloid proteins aggregation causes several human neuropathologies. In some cases, e.g. fibrillar deposits of insulin, the problems are generated in the processes of production and purification of protein and in the pump devices or injectable preparations for diabetics. Experimental kinetics and adequate modelling of chemical inhibition from amyloid aggregation are of practical importance in order to study the viable processing, formulation and storage as well as to predict and optimize the best conditions to reduce the effect of protein nucleation. In this manuscript, experimental data of insulin, Aβ42 amyloid protein and apomyoglobin fibrillation from recent bibliography were selected to evaluate the capability of a bivariate sigmoid equation to model them. The mathematical functions (logistic combined with Weibull equation) were used in reparameterized form and the effect of inhibitor concentrations on kinetic parameters from logistic equation were perfectly defined and explained. The surfaces of data were accurately described by proposed model and the presented analysis characterized the inhibitory influence on the protein aggregation by several chemicals. Discrimination between true and apparent inhibitors was also confirmed by the bivariate equation. EGCG for insulin (working at pH = 7.4/T = 37°C) and taiwaniaflavone for Aβ42 were the compounds studied that shown the greatest inhibition capacity. An accurate, simple and effective model to investigate the inhibition of chemicals on amyloid protein aggregation has been developed. The equation could be useful for the clear quantification of inhibitor potential of chemicals and rigorous comparison among them.

Nitrogen balance and transformation in the nitrification process of coking wastewater and the influence on nitrification kinetics.

PubMed

Shan, Mingjun; Zhang, Yan; Kou, Lihong

2014-01-01

This paper describes the total nitrogen balance, and the direction and degree of nitrogen transformation during the nitrification process of coking wastewater. According to the actual nitrification process, the conventional nitrification kinetic equation was amended. After 48 h of nitrification, the total nitrogen content remained almost the same with error less than 0.6%. The total removal efficiency of NH4(+)-N was 91.1%, in which blow-off, producing cells and transforming to nitrate nitrogen accounted for 1.1, 17.8 and 72.2% respectively. Considering the influences of NH4(+)-N blow-off and conversion from cyanide, thiocyanide and organic nitrogen, the nitrification kinetic equation was amended as μ'=0.82·S/(0.48+S).

Improvements to water use and water stress estimates with the addition of IR and net radiometers to weather stations

USDA-ARS?s Scientific Manuscript database

Evapotranspiration (ET) is often estimated with the Penman-Monteith (P-M) equation. Net radiation (Rn) is a major component of the surface energy balance and an input to the P-M equation, but it is challenging and expensive to measure accurately. For these reasons, most weather stations do not inclu...

Systematic Constraint Selection Strategy for Rate-Controlled Constrained-Equilibrium Modeling of Complex Nonequilibrium Chemical Kinetics

NASA Astrophysics Data System (ADS)

Beretta, Gian Paolo; Rivadossi, Luca; Janbozorgi, Mohammad

2018-04-01

Rate-Controlled Constrained-Equilibrium (RCCE) modeling of complex chemical kinetics provides acceptable accuracies with much fewer differential equations than for the fully Detailed Kinetic Model (DKM). Since its introduction by James C. Keck, a drawback of the RCCE scheme has been the absence of an automatable, systematic procedure to identify the constraints that most effectively warrant a desired level of approximation for a given range of initial, boundary, and thermodynamic conditions. An optimal constraint identification has been recently proposed. Given a DKM with S species, E elements, and R reactions, the procedure starts by running a probe DKM simulation to compute an S-vector that we call overall degree of disequilibrium (ODoD) because its scalar product with the S-vector formed by the stoichiometric coefficients of any reaction yields its degree of disequilibrium (DoD). The ODoD vector evolves in the same (S-E)-dimensional stoichiometric subspace spanned by the R stoichiometric S-vectors. Next we construct the rank-(S-E) matrix of ODoD traces obtained from the probe DKM numerical simulation and compute its singular value decomposition (SVD). By retaining only the first C largest singular values of the SVD and setting to zero all the others we obtain the best rank-C approximation of the matrix of ODoD traces whereby its columns span a C-dimensional subspace of the stoichiometric subspace. This in turn yields the best approximation of the evolution of the ODoD vector in terms of only C parameters that we call the constraint potentials. The resulting order-C RCCE approximate model reduces the number of independent differential equations related to species, mass, and energy balances from S+2 to C+E+2, with substantial computational savings when C ≪ S-E.

A Novel Approach for Modeling Chemical Reaction in Generalized Fluid System Simulation Program

NASA Technical Reports Server (NTRS)

Sozen, Mehmet; Majumdar, Alok

2002-01-01

The Generalized Fluid System Simulation Program (GFSSP) is a computer code developed at NASA Marshall Space Flight Center for analyzing steady state and transient flow rates, pressures, temperatures, and concentrations in a complex flow network. The code, which performs system level simulation, can handle compressible and incompressible flows as well as phase change and mixture thermodynamics. Thermodynamic and thermophysical property programs, GASP, WASP and GASPAK provide the necessary data for fluids such as helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, water, a hydrogen, isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, several refrigerants, nitrogen trifluoride and ammonia. The program which was developed out of need for an easy to use system level simulation tool for complex flow networks, has been used for the following purposes to name a few: Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump Secondary Flow Circuits, Axial Thrust Balance of the Fastrac Engine Turbopump, Pressurized Propellant Feed System for the Propulsion Test Article at Stennis Space Center, X-34 Main Propulsion System, X-33 Reaction Control System and Thermal Protection System, and International Space Station Environmental Control and Life Support System design. There has been an increasing demand for implementing a combustion simulation capability into GFSSP in order to increase its system level simulation capability of a liquid rocket propulsion system starting from the propellant tanks up to the thruster nozzle for spacecraft as well as launch vehicles. The present work was undertaken for addressing this need. The chemical equilibrium equations derived from the second law of thermodynamics and the energy conservation equation derived from the first law of thermodynamics are solved simultaneously by a Newton-Raphson method. The numerical scheme was implemented as a User Subroutine in GFSSP.

Using Improved Equation of State to Model Simultaneous Nucleation and Bubble Growth in Thermoplastic Foams

NASA Astrophysics Data System (ADS)

Khan, Irfan; Costeux, Stephane; Adrian, David; Cristancho, Diego

2013-11-01

Due to environmental regulations carbon-dioxide (CO2) is increasingly being used to replace traditional blowing agents in thermoplastic foams. CO2 is dissolved in the polymer matrix under supercritical conditions. In order to predict the effect of process parameters on foam properties using numerical modeling, the P-V-T relationship of the blowing agents should accurately be represented at the supercritical state. Previous studies in the area of foam modeling have all used ideal gas equation of state to predict the behavior of the blowing agent. In this work the Peng-Robinson equation of state is being used to model the blowing agent during its diffusion into the growing bubble. The model is based on the popular ``Influence Volume Approach,'' which assumes a growing boundary layer with depleted blowing agent surrounds each bubble. Classical nucleation theory is used to predict the rate of nucleation of bubbles. By solving the mass balance, momentum balance and species conservation equations for each bubble, the model is capable of predicting average bubble size, bubble size distribution and bulk porosity. The effect of the improved model on the bubble growth and foam properties are discussed.

Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed

NASA Astrophysics Data System (ADS)

Canestrelli, Alberto; Dumbser, Michael; Siviglia, Annunziato; Toro, Eleuterio F.

2010-03-01

In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space-time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data.

VUV Emission of Microwave Driven Argon Plasma Source

NASA Astrophysics Data System (ADS)

Henriques, Julio; Espinho, Susana; Felizardo, Edgar; Tatarova, Elena; Dias, Francisco; Ferreira, Carlos

2013-09-01

An experimental and kinetic modeling investigation of a low-pressure (0.1-1.2 mbar), surface wave (2.45 GHz) induced Ar plasma as a source vacuum ultraviolet (VUV) light is presented, using visible and VUV optical spectroscopy. The electron density and the relative VUV emission intensities of excited Ar atoms (at 104.8 nm and 106.6 nm) and ions (at 92.0 nm and 93.2 nm) were determined as a function of the microwave power and pressure. The experimental results were analyzed using a 2D self-consistent theoretical model based on a set of coupled equations including the electron Boltzmann equation, the rate balance equations for the most important electronic excited species and for charged particles, the gas thermal balance equation, and the wave electrodynamics. The principal collisional and radiative processes for neutral Ar(3p54s) and Ar(3p54p) and ionized Ar(3s3p6 2S1/2) levels are accounted for. Model predictions are in good agreement with the experimental measurements. This study was funded by the Foundation for Science and Technology, Portuguese Ministry of Education and Science, under the research contract PTDC/FIS/108411/2008.

In vivo stationary flux analysis by 13C labeling experiments.

PubMed

Wiechert, W; de Graaf, A A

1996-01-01

Stationary flux analysis is an invaluable tool for metabolic engineering. In the last years the metabolite balancing technique has become well established in the bioengineering community. On the other hand metabolic tracer experiments using 13C isotopes have long been used for intracellular flux determination. Only recently have both techniques been fully combined to form a considerably more powerful flux analysis method. This paper concentrates on modeling and data analysis for the evaluation of such stationary 13C labeling experiments. After reviewing recent experimental developments, the basic equations for modeling carbon labeling in metabolic systems, i.e. metabolite, carbon label and isotopomer balances, are introduced and discussed in some detail. Then the basics of flux estimation from measured extracellular fluxes combined with carbon labeling data are presented and, finally, this method is illustrated by using an example from C. glutamicum. The main emphasis is on the investigation of the extra information that can be obtained with tracer experiments compared with the metabolite balancing technique alone. As a principal result it is shown that the combined flux analysis method can dispense with some rather doubtful assumptions on energy balancing and that the forward and backward flux rates of bidirectional reaction steps can be simultaneously determined in certain situations. Finally, it is demonstrated that the variant of fractional isotopomer measurement is even more powerful than fractional labeling measurement but requires much higher numerical effort to solve the balance equations.

Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models

NASA Astrophysics Data System (ADS)

Ghosh, Pijush K.; Sinha, Debdeep

2018-01-01

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

Regional Screening Levels (RSLs) - Equations (November 2017 )

EPA Pesticide Factsheets

Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.

Computations of Torque-Balanced Coaxial Rotor Flows

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Chan, William M.; Pulliam, Thomas H.

2017-01-01

Interactional aerodynamics has been studied for counter-rotating coaxial rotors in hover. The effects of torque balancing on the performance of coaxial-rotor systems have been investigated. The three-dimensional unsteady Navier-Stokes equations are solved on overset grids using high-order accurate schemes, dual-time stepping, and a hybrid turbulence model. Computational results for an experimental model are compared to available data. The results for a coaxial quadcopter vehicle with and without torque balancing are discussed. Understanding interactions in coaxial-rotor flows would help improve the design of next-generation autonomous drones.

Enhancing the calculation accuracy of performance characteristics of power-generating units by correcting general measurands based on matching energy balances

NASA Astrophysics Data System (ADS)

Shchinnikov, P. A.; Safronov, A. V.

2014-12-01

General principles of a procedure for matching energy balances of thermal power plants (TPPs), whose use enhances the accuracy of information-measuring systems (IMSs) during calculations of performance characteristics (PCs), are stated. To do this, there is the possibility for changing values of measured and calculated variables within intervals determined by measurement errors and regulations. An example of matching energy balances of the thermal power plants with a T-180 turbine is made. The proposed procedure allows one to reduce the divergence of balance equations by 3-4 times. It is shown also that the equipment operation mode affects the profit deficiency. Dependences for the divergence of energy balances on the deviation of input parameters and calculated data for the fuel economy before and after matching energy balances are represented.

Destruction of VX by aqueous-phase oxidation using peroxydisulfate (direct chemical oxidation)

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

Cooper, J.F.; Krueger, R.; Farmer, J.C.

1995-10-11

Chemical warfare agents may be completely destroyed (converted to H{sub 2}O, CO{sub 2}, salts) by oxidation at 90--100 C using acidified ammonium peroxydisulfate, with recycle of NH{sub 4}SO{sub 4} byproduct. The process requires no toxic or expended catalysts and produces no secondary wastes other than the precipitated inorganic content of the agents. To determine oxidative capability of peroxydisulfate at low reductant contents, we measured rate data for oxidation of 20 diverse compounds with diverse functional groups; 4 of these have bonds similar to those found in VX, HD, and GB. On an equivalence basis, integral first-order rate constants for 100more » C oxidation are 0.012{plus_minus}0.005 min{sup {minus}1} for di-isopropyl-methyl-phosphonate, methyl phosphonic acid, triethylamine, and 2,2{prime}-thiodiethanol at low initial concentrations of 50 ppM(as carbon) and pH 1.5. To provide scale-up equations for a bulk chemical agent destruction process, we measured time-dependent oxidation of bulk model chemicals at high concentrations (0.5 N) and developed and tested a quantitative model. A practical process for bulk VX destruction would begin with chemical detoxification by existing techniques (eg, hydrolysis or mild oxidation using oxone), followed by mineralization of the largely detoxified products by peroxydisulfate. Secondary wastes would be avoided by use of commercial electrolysis equipment to regenerate the oxidant. Reagent requirements, mass balance and scaleup parameters are given for VX destruction, using peroxydisulfate alone, or supplemented with hydrogen peroxide. For the use of 2.5 N peroxydisulfate as the oxidant, a 1 m{sup 3} digester will process about 200 kg (as C) per day. The process may be extended to total destruction of HD and hydrolysis products of G agents.« less

Simulation of heat storages and associated heat budgets in the Pacific Ocean: 2. Interdecadal timescale

NASA Astrophysics Data System (ADS)

Auad, Guillermo; Miller, Arthur J.; White, Warren B.

1998-11-01

We use a primitive equation isopycnal model of the Pacific Ocean to simulate and diagnose the anomalous heat balance on interdecadal timescales associated with heat storage changes observed from 1970-1988 in the expendable bathythermograph (XBT) data set. Given the smallness of the interdecadal signals compared to the El Niño-Southern Oscillation (ENSO) signal, the agreement between model and observations is remarkably good. The total anomalous heat balance is made up of two parts, the diabatic part (from the model temperature equation) and the adiabatic part (from the model mass conservation equation) due to thermocline heave. We therefore describe our analysis of both the total and diabatic anomalous heat balances in four areas of the tropical and subtropical North Pacific Ocean in the upper 400 m. The interdecadal total (diabatic plus adiabatic) heat balance in the North Pacific Ocean is characterized by a complicated interplay of different physical processes, especially revealed in basin-scale averages of the heat budget components that have comparable amounts of variance. In smaller subregions, simpler balances hold. For example, in the western equatorial Pacific (area 1) the total heat content tendency term is nearly zero, so that a simple balance exists between surface heat flux, vertical heat transport, and horizontal mixing. In the western subtropical Pacific the total heat content tendency balances the three-dimensional divergence of the heat flux. We speculate that this complexity is indicative of multiple physical mechanisms involved in the generation of North Pacific interdecadal variability. The diabatic heat balance north of 24°N, a region of special interest to The World Ocean Circulation Experiment (WOCE), can be simplified to a balance between the tendency term, surface heat flux, and meridional advection, the last term dominated by anomalous advection of mean temperature gradients. For the western equatorial region the diabatic heat content tendency is nearly zero and the steady balance involves simply horizontal advection and the surface heat flux, which at these latitudes has a damping role in the model. An important finding of this study is the identification of two interdecadal timescales, roughly 10 and 20 years, both similar to those reported by other investigators in recent years. [Tourre et al., 1998; Latif and Barnett, 1994; Robertson, 1995; White et al, 1997; Gu and Philander, 1997; Jacobs et al., 1994]. The 20-year timescale is only present in diabatic heat budget components, while the 10-year timescale is present in both diabatic and adiabatic components. The 10-year timescale can also be seen in the surface heat flux time series, but it occurs in the ocean adiabatic components which demonstrates the importance of oceanic adjustment through Rossby wave dynamics on decadal timescales.

Direct Discrete Method for Neutronic Calculations

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

Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for amore » cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)« less

Sensitivity of a Chemical Mass Balance model for PM2.5 to source profiles for differing styles of cooking

NASA Astrophysics Data System (ADS)

Abdullahi, K. L.; Delgado-Saborit, J. M.; Harrison, Roy M.

2018-04-01

Use of a Chemical Mass Balance model is one of the two most commonly used approaches to estimating atmospheric concentrations of cooking aerosol. Such models require the input of chemical profiles for each of the main sources contributing to particulate matter mass and there is appreciable evidence from the literature that not only the mass emission but also the chemical composition of particulate matter varies according to the food being prepared and the style of cooking. In this study, aerosol has been sampled in the laboratory from four different styles of cooking, i.e. Indian, Chinese, Western and African cooking. The chemical profiles of molecular markers have been quantified and are used individually within a Chemical Mass Balance model applied to air samples collected in a multi-ethnic area of Birmingham, UK. The model results give a source contribution estimate for cooking aerosol which is consistent with other comparable UK studies, but also shows a very low sensitivity of the model to the cooking aerosol profile utilised. A survey of local restaurants suggested a wide range of cooking styles taking place which may explain why no one profile gives an appreciably better fit in the CMB model.

Five-Junction Solar Cell Optimization Using Silvaco Atlas

DTIC Science & Technology

2017-09-01

experimental sources [1], [4], [6]. f. Numerical Method The method selected for solving the non -linear equations that make up the simulation can be...and maximize efficiency. Optimization of solar cell efficiency is carried out via nearly orthogonal balanced design of experiments methodology . Silvaco...Optimization of solar cell efficiency is carried out via nearly orthogonal balanced design of experiments methodology . Silvaco ATLAS is utilized to

Uncertainty analysis on simple mass balance model to calculate critical loads for soil acidity

Treesearch

Harbin Li; Steven G. McNulty

2007-01-01

Simple mass balance equations (SMBE) of critical acid loads (CAL) in forest soil were developed to assess potential risks of air pollutants to ecosystems. However, to apply SMBE reliably at large scales, SMBE must be tested for adequacy and uncertainty. Our goal was to provide a detailed analysis of uncertainty in SMBE so that sound strategies for scaling up CAL...

Linear systems on balancing chemical reaction problem

NASA Astrophysics Data System (ADS)

Kafi, R. A.; Abdillah, B.

2018-01-01

The concept of linear systems appears in a variety of applications. This paper presents a small sample of the wide variety of real-world problems regarding our study of linear systems. We show that the problem in balancing chemical reaction can be described by homogeneous linear systems. The solution of the systems is obtained by performing elementary row operations. The obtained solution represents the finding coefficients of chemical reaction. In addition, we present a computational calculation to show that mathematical software such as Matlab can be used to simplify completion of the systems, instead of manually using row operations.

Is the difference between chemical and numerical estimates of baseflow meaningful?

NASA Astrophysics Data System (ADS)

Cartwright, Ian; Gilfedder, Ben; Hofmann, Harald

2014-05-01

Both chemical and numerical techniques are commonly used to calculate baseflow inputs to gaining rivers. In general the chemical methods yield lower estimates of baseflow than the numerical techniques. In part, this may be due to the techniques assuming two components (event water and baseflow) whereas there may also be multiple transient stores of water. Bank return waters, interflow, or waters stored on floodplains are delayed components that may be geochemically similar to the surface water from which they are derived; numerical techniques may record these components as baseflow whereas chemical mass balance studies are likely to aggregate them with the surface water component. This study compares baseflow estimates using chemical mass balance, local minimum methods, and recursive digital filters in the upper reaches of the Barwon River, southeast Australia. While more sophisticated techniques exist, these methods of estimating baseflow are readily applied with the available data and have been used widely elsewhere. During the early stages of high-discharge events, chemical mass balance overestimates groundwater inflows, probably due to flushing of saline water from wetlands and marshes, soils, or the unsaturated zone. Overall, however, estimates of baseflow from the local minimum and recursive digital filters are higher than those from chemical mass balance using Cl calculated from continuous electrical conductivity. Between 2001 and 2011, the baseflow contribution to the upper Barwon River calculated using chemical mass balance is between 12 and 25% of annual discharge. Recursive digital filters predict higher baseflow contributions of 19 to 52% of annual discharge. These estimates are similar to those from the local minimum method (16 to 45% of annual discharge). These differences most probably reflect how the different techniques characterise the transient water sources in this catchment. The local minimum and recursive digital filters aggregate much of the water from delayed sources as baseflow. However, as many of these delayed transient water stores (such as bank return flow, floodplain storage, or interflow) have Cl concentrations that are similar to surface runoff, chemical mass balance calculations aggregate them with the surface runoff component. The difference between the estimates is greatest following periods of high discharge in winter, implying that these transient stores of water feed the river for several weeks to months at that time. Cl vs. discharge variations during individual flow events also demonstrate that inflows of high-salinity older water occurs on the rising limbs of hydrographs followed by inflows of low-salinity water from the transient stores as discharge falls. The use of complementary techniques allows a better understanding of the different components of water that contribute to river flow, which is important for the management and protection of water resources.

Wave propagation in a quasi-chemical equilibrium plasma

NASA Technical Reports Server (NTRS)

Fang, T.-M.; Baum, H. R.

1975-01-01

Wave propagation in a quasi-chemical equilibrium plasma is studied. The plasma is infinite and without external fields. The chemical reactions are assumed to result from the ionization and recombination processes. When the gas is near equilibrium, the dominant role describing the evolution of a reacting plasma is played by the global conservation equations. These equations are first derived and then used to study the small amplitude wave motion for a near-equilibrium situation. Nontrivial damping effects have been obtained by including the conduction current terms.

Use of Chemistry Software to Teach and Assess Model-Based Reaction and Equation Knowledge

ERIC Educational Resources Information Center

Pyatt, Kevin

2014-01-01

This study investigated the challenges students face when learning chemical reactions in a first-year chemistry course and the effectiveness of a curriculum and software implementation that was used to teach and assess student understanding of chemical reactions and equations. This study took place over a two year period in a public suburban…

GCKP84-general chemical kinetics code for gas-phase flow and batch processes including heat transfer effects

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1984-01-01

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

A modified dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

NASA Technical Reports Server (NTRS)

Cooke, C. H.

1981-01-01

A revised version of a split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three-dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard successive overrelaxation iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition.

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

NASA Technical Reports Server (NTRS)

Chao, Winston C.; Chen, Baode

2002-01-01

The dominant role of the latitudinal peak of the sea surface temperature (SST) in determining the latitudinal location of the intertropical convergence zone (ITCZ) is well-known. However, the roles of the other factors are less well-known and are the topic of this study. These other factors include the inertial stability, the interaction between convection and surface fluxes and the interaction between convection and radiation. Since these interactions involve convection, in a model they involve the cumulus parameterization scheme. These factors are studied with a general circulation model with uniform SST and solar angle. Under the aforementioned model settings, the latitudinal location of the ITCZ is the latitude where the balance of two types of attraction on the ITCZ, both due to earth's rotation, exists. Directly related to the Coriolis parameter, the first type pulls the ITCZ toward the equator and is not sensitive to model design changes. Related to the convective circulation, the second type pulls the ITCZ poleward and is sensitive to model design changes. Due to the shape and the magnitude of the attractors, the balance of the two types of attractions is reached either at the equator or more than 10 degrees away from the equator. The former case results in a single ITCZ over the equator and the latter case a double ITCZ straddling the equator.

Statistical summary of selected physical, chemical, and toxicity characteristics and estimates of annual constituent loads in urban stormwater, Maricopa County, Arizona

USGS Publications Warehouse

Fossum, Kenneth D.; O'Day, Christie M.; Wilson, Barbara J.; Monical, Jim E.

2001-01-01

Stormwater and streamflow in Maricopa County were monitored to (1) describe the physical, chemical, and toxicity characteristics of stormwater from areas having different land uses, (2) describe the physical, chemical, and toxicity characteristics of streamflow from areas that receive urban stormwater, and (3) estimate constituent loads in stormwater. Urban stormwater and streamflow had similar ranges in most constituent concentrations. The mean concentration of dissolved solids in urban stormwater was lower than in streamflow from the Salt River and Indian Bend Wash. Urban stormwater, however, had a greater chemical oxygen demand and higher concentrations of most nutrients. Mean seasonal loads and mean annual loads of 11 constituents and volumes of runoff were estimated for municipalities in the metropolitan Phoenix area, Arizona, by adjusting regional regression equations of loads. This adjustment procedure uses the original regional regression equation and additional explanatory variables that were not included in the original equation. The adjusted equations had standard errors that ranged from 161 to 196 percent. The large standard errors of the prediction result from the large variability of the constituent concentration data used in the regression analysis. Adjustment procedures produced unsatisfactory results for nine of the regressions?suspended solids, dissolved solids, total phosphorus, dissolved phosphorus, total recoverable cadmium, total recoverable copper, total recoverable lead, total recoverable zinc, and storm runoff. These equations had no consistent direction of bias and no other additional explanatory variables correlated with the observed loads. A stepwise-multiple regression or a three-variable regression (total storm rainfall, drainage area, and impervious area) and local data were used to develop local regression equations for these nine constituents. These equations had standard errors from 15 to 183 percent.

A Gas-Kinetic Scheme for Reactive Flows

NASA Technical Reports Server (NTRS)

Lian,Youg-Sheng; Xu, Kun

1998-01-01

In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.

Investigation of a Mercury-Argon Hot Cathode Discharge

NASA Astrophysics Data System (ADS)

Wamsley, Robert Charles

Classical absorption and laser induced fluorescence (LIF) experiments are used to investigate processes in the cathode region of a Hg-Ar hot cathode discharge. The absorption and LIF measurements are used to test the qualitative understanding and develop a quantitative model of a hot cathode discharge. The main contribution of this thesis is a model of the negative glow region that demonstrates the importance of Penning ionization to the ionization balance in the negative glow. We modeled the excited argon balance equation using a Monte Carlo simulation. In this simulation we used the trapped radiative decay rate of the resonance levels and the Penning ionization rate as the dominant loss terms in the balance equation. The simulated data is compared to and found to agree with absolute excited argon densities measured in a classical absorption experiment. We found the primary production rate per unit volume of excited Ar atoms in the simulation is sharply peaked near the cathode hot spot. We used the ion production rate from this simulation and a Green's function solution to the ambipolar diffusion equation to calculate the contribution of Penning ionization to the total ion density. We compared the results of this calculation to our experimental values of the Hg ^+ densities in the negative glow. We found that Penning ionization is an important and possibly the dominant ionization process in the negative glow.

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

Majda, Andrew J.; Xing, Yulong; Mohammadian, Majid

Determining the finite-amplitude preconditioned states in the hurricane embryo, which lead to tropical cyclogenesis, is a central issue in contemporary meteorology. In the embryo there is competition between different preconditioning mechanisms involving hydrodynamics and moist thermodynamics, which can lead to cyclogenesis. Here systematic asymptotic methods from applied mathematics are utilized to develop new simplified moist multi-scale models starting from the moist anelastic equations. Three interesting multi-scale models emerge in the analysis. The balanced mesoscale vortex (BMV) dynamics and the microscale balanced hot tower (BHT) dynamics involve simplified balanced equations without gravity waves for vertical vorticity amplification due to moist heatmore » sources and incorporate nonlinear advective fluxes across scales. The BMV model is the central one for tropical cyclogenesis in the embryo. The moist mesoscale wave (MMW) dynamics involves simplified equations for mesoscale moisture fluctuations, as well as linear hydrostatic waves driven by heat sources from moisture and eddy flux divergences. A simplified cloud physics model for deep convection is introduced here and used to study moist axisymmetric plumes in the BHT model. A simple application in periodic geometry involving the effects of mesoscale vertical shear and moist microscale hot towers on vortex amplification is developed here to illustrate features of the coupled multi-scale models. These results illustrate the use of these models in isolating key mechanisms in the embryo in a simplified content.« less

PM2.5 source apportionment with organic markers in the Southeastern Aerosol Research and Characterization (SEARCH) study.

PubMed

Watson, John G; Chow, Judith C; Lowenthal, Douglas H; Antony Chen, L-W; Shaw, Stephanie; Edgerton, Eric S; Blanchard, Charles L

2015-09-01

Positive matrix factorization (PMF) and effective variance (EV) solutions to the chemical mass balance (CMB) were applied to PM(2.5) (particulate matter with an aerodynamic diameter <2.5 μm) mass and chemically speciated measurements for samples taken from 2008 to 2010 at the Atlanta, Georgia, and Birmingham, Alabama, sites. Commonly measured PM(2.5) mass, elemental, ionic, and thermal carbon fraction concentrations were supplemented with detailed nonpolar organic speciation by thermal desorption-gas chromatography/mass spectrometry (TD-GC/MS). Source contribution estimates were calculated for motor vehicle exhaust, biomass burning, cooking, coal-fired power plants, road dust, vegetative detritus, and secondary sulfates and nitrates for Atlanta. Similar sources were found for Birmingham, with the addition of an industrial source and the separation of biomass burning into open burning and residential wood combustion. EV-CMB results based on conventional species were qualitatively similar to those estimated by PMF-CMB. Secondary ammonium sulfate was the largest contributor, accounting for 27-38% of PM(2.5), followed by biomass burning (21-24%) and motor vehicle exhaust (9-24%) at both sites, with 4-6% of PM(2.5) attributed to coal-fired power plants by EV-CMB. Including organic compounds in the EV-CMB reduced the motor vehicle exhaust and biomass burning contributions at both sites, with a 13-23% deficit for PM(2.5) mass. The PMF-CMB solution showed mixing of sources within the derived factors, both with and without the addition of speciated organics, as is often the case with complex source mixtures such as those at these urban-scale sites. The nonpolar TD-GC/MS compounds can be obtained from existing filter samples and are a useful complement to the elements, ions, and carbon fractions. However, they should be supplemented with other methods, such as TD-GC/MS on derivitized samples, to obtain a wider range of polar compounds such as sterols, sugars, and organic acids. The PMF and EV solutions to the CMB equations are complementary to, rather than replacements for, each other, as comparisons of their results reveal uncertainties that are not otherwise evident. Organic markers can be measured on currently acquired PM(2.5) filter samples by thermal methods. These markers can complement element, ion, and carbon fraction measurements from long-term speciation networks. Applying the positive matrix factorization and effective variance solutions for the chemical mass balance equations provides useful information on the accuracy of the source contribution estimates. Nonpolar compounds need to be complemented with polar compounds to better apportion cooking and secondary organic aerosol contributors.

Turbulence modeling and experiments

NASA Technical Reports Server (NTRS)

Shabbir, Aamir

1992-01-01

The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat flux equations for the buoyant plume.

Temporal 222Rn distributions to reveal groundwater discharge into desert lakes: Implication of water balance in the Badain Jaran Desert, China

NASA Astrophysics Data System (ADS)

Luo, Xin; Jiao, Jiu Jimmy; Wang, Xu-sheng; Liu, Kun

2016-03-01

How lake systems are maintained and water is balanced in the lake areas in the Badain Jaran Desert (BJD), northeast of China have been debated for about a decade. In this study, continuous 222Rn measurement is used to quantify groundwater discharge into two representative fresh and brine water lakes in the desert using a steady-state mass-balance model. Two empirical equations are used to calculate atmospheric evasion loss crossing the water-air interface of the lakes. Groundwater discharge rates yielded from the radon mass balance model based on the two empirical equations are well correlated and of almost the same values, confirming the validity of the model. The fresh water and brine lakes have a daily averaged groundwater discharge rate of 7.6 ± 1.7 mm d-1 and 6.4 ± 1.8 mm d-1, respectively. The temporal fluctuations of groundwater discharge show similar patterns to those of the lake water level, suggesting that the lakes are recharged from nearby groundwater. Assuming that all the lakes have the same discharge rate as the two studied lakes, total groundwater discharge into all the lakes in the desert is estimated to be 1.59 × 105 m3 d-1. A conceptual model of water balance within a desert lake catchment is proposed to characterize water behaviors within the catchment. This study sheds lights on the water balance in the BJD and is of significance in sustainable regional water resource utilization in such an ecologically fragile area.

Solving the chemical master equation using sliding windows

PubMed Central

2010-01-01

Background The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species. Results In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy. Conclusions The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori. PMID:20377904

Analysis of Large Quasistatic Deformations of Inelastic Solids by a New Stress Based Finite Element Method. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Reed, Kenneth W.

1992-01-01

A new hybrid stress finite element algorithm suitable for analyses of large quasistatic deformation of inelastic solids is presented. Principal variables in the formulation are the nominal stress rate and spin. The finite element equations which result are discrete versions of the equations of compatibility and angular momentum balance. Consistent reformulation of the constitutive equation and accurate and stable time integration of the stress are discussed at length. Examples which bring out the feasibility and performance of the algorithm conclude the work.

Exergy Analysis of Rocket Systems

NASA Technical Reports Server (NTRS)

Gilbert, Andrew; Mesmer, Bryan; Watson, Michael D.

2015-01-01

Exergy is defined as the useful work available from a system in a specified environment. Exergy analysis allows for comparison between different system designs, and allows for comparison of subsystem efficiencies within system designs. The proposed paper explores the relationship between the fundamental rocket equation and an exergy balance equation. A previously derived exergy equation related to rocket systems is investigated, and a higher fidelity analysis will be derived. The exergy assessments will enable informed, value-based decision making when comparing alternative rocket system designs, and will allow the most efficient configuration among candidate configurations to be determined.

Selection of Oil Coolers to Avoid Congealing

DTIC Science & Technology

1943-07-01

from one fluid to another, there is a resistance to heat transfer l/ htSt . The total resistance to the flow of heat is the sum of the...total thermal resistance equation is, htst hasa hoso n v \\hasa Vo/ (W The generally accepted equations for correlating heat...1 -. 1 htSt n v Da jS u Do Ho •a°l|.ki (5i2jLS 8oc3lc0/ W^ V \\SAafa; ^ fa^Z/yfij tM: (7) The heat-balance equation is. H

Comparisons of Flutter Analyses for an Experimental Fan

NASA Technical Reports Server (NTRS)

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

2010-01-01

Two propulsion aeroelasticity codes were used to model the aeroelastic characteristics of an experimental forward-swept fan that encountered flutter during wind tunnel testing. Both of these three-dimensional codes model the unsteady flowfield due to blade vibrations using the Navier-Stokes equations. In the first approach, the unsteady flow equations are solved using an implicit time-marching approach. In the second approach, the unsteady flow equations are converted to a harmonic balance form and solved using a pseudo-time marching method. This paper describes the flutter calculations and compares the results to experimental measurements.

Autobalancing of a rigid rotor in viscoelastic orthotropic supports considering eccentricity of the automatic ball balancer

NASA Astrophysics Data System (ADS)

Bykov, V. G.; Kovachev, A. S.

2018-05-01

A statically unbalanced rotor in viscoelastic orthotropic supports equipped with an automatic ball balancer (ABB), the axis of symmetry of which does not coincide with the symmetry axis of the rotor, is considered. Based on an analysis of the equations describing the stationary modes of motion of the system, the principal impossibility of complete balancing of the rotor is shown. The possibility of the existence of two types of stationary modes is established, one of which has a constant average amplitude of residual vibration equal to the eccentricity of the ABB. The solution corresponding to this almost balanced mode is constructed analytically. A study is made of its asymptotic stability.

40 CFR Table A-7 to Subpart A of... - Data Elements That Are Inputs to Emission Equations and for Which the Reporting Deadline Is March...

Code of Federal Regulations, 2012 CFR

2012-07-01

... mass balance equation. K 98.116(b) Only annual production by product from each EAF (No CEMS). K 98.116... carbon content values, molecular weights for gaseous feedstocks, molecular weights for gaseous products... of gas flared, average molecular weight, carbon content of the flare, and molar volume conversion...

Similarity of the Outer Region of the Turbulent Boundary

DTIC Science & Technology

2009-02-09

comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE...DISTRIBUTION / AVAILABILITY STATEMENT DISTRIBUTION A : APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED 13. SUPPLEMENTARY NOTES The U.S. Government...terms by a stream function approach using the transformed x-momentum balance equation and the transformed Reynolds stress transport equation. The

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

PubMed

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

Toward a Turbulence Constitutive Relation for Rotating Flows

NASA Technical Reports Server (NTRS)

Ristorcelli, J. R.

1996-01-01

In rapidly rotating turbulent flows the largest scales of the motion are in approximate geostrophic balance. Single-point turbulence closures, in general, cannot attain a geostrophic balance. This article addresses and resolves the possibility of constitutive relation procedures for single-point second order closures for a specific class of rotating or stratified flows. Physical situations in which the geostrophic balance is attained are described. Closely related issues of frame-indifference, horizontal nondivergence, Taylor-Proudman theorem and two-dimensionality are, in the context of both the instantaneous and averaged equations, discussed. It is shown, in the absence of vortex stretching along the axis of rotation, that turbulence is frame-indifferent. A derivation and discussion of a geostrophic constraint which the prognostic equations for second-order statistics must satisfy for turbulence approaching a frame-indifferent limit is given. These flow situations, which include rotating and nonrotating stratified flows, are slowly evolving flows in which the constitutive relation procedures are useful. A nonlinear non-constant coefficient representation for the rapid-pressure strain covariance appearing in the Reynolds stress and heat flux equations consistent with the geostrophic balance is described. The rapid-pressure strain model coefficients are not constants determined by numerical optimization but are functions of the state of the turbulence as parameterized by the Reynolds stresses and the turbulent heat fluxes. The functions are valid for all states of the turbulence attaining their limiting values only when a limit state is achieved. These issues are relevant to strongly vortical flows as well as flows such as the planetary boundary layers, in which there is a transition from a three-dimensional shear driven turbulence to a geostrophic or horizontal turbulence.

Agradient velocity, vortical motion and gravity waves in a rotating shallow-water model

NASA Astrophysics Data System (ADS)

Sutyrin Georgi, G.

2004-07-01

A new approach to modelling slow vortical motion and fast inertia-gravity waves is suggested within the rotating shallow-water primitive equations with arbitrary topography. The velocity is exactly expressed as a sum of the gradient wind, described by the Bernoulli function,B, and the remaining agradient part, proportional to the velocity tendency. Then the equation for inverse potential vorticity,Q, as well as momentum equations for agradient velocity include the same source of intrinsic flow evolution expressed as a single term J (B, Q), where J is the Jacobian operator (for any steady state J (B, Q) = 0). Two components of agradient velocity are responsible for the fast inertia-gravity wave propagation similar to the traditionally used divergence and ageostrophic vorticity. This approach allows for the construction of balance relations for vortical dynamics and potential vorticity inversion schemes even for moderate Rossby and Froude numbers assuming the characteristic value of |J(B, Q)| = to be small. The components of agradient velocity are used as the fast variables slaved to potential vorticity that allows for diagnostic estimates of the velocity tendency, the direct potential vorticity inversion with the accuracy of 2 and the corresponding potential vorticity-conserving agradient velocity balance model (AVBM). The ultimate limitations of constructing the balance are revealed in the form of the ellipticity condition for balanced tendency of the Bernoulli function which incorporates both known criteria of the formal stability: the gradient wind modified by the characteristic vortical Rossby wave phase speed should be subcritical. The accuracy of the AVBM is illustrated by considering the linear normal modes and coastal Kelvin waves in the f-plane channel with topography.

Something New from the Past.

ERIC Educational Resources Information Center

Schmuckler, Joseph S., Ed.

1980-01-01

Includes annotations of articles from previous issues of this periodical on the following topics: balancing equations and nomenclature, the mole, the silver tree experiment, and history of the periodic table. (CS)

Idea Bank.

ERIC Educational Resources Information Center

Bisbee, Gregory D.; Fritz, Jane K.; Zurenda, Deb

1997-01-01

Presents three science activities: (1) Pizza Quadrants, a tool for estimating population size; (2) Ion Models, to assist students in understanding how to balance equations; and (3) Endangered Species Project, an interdisciplinary unit. (DDR)

Analysis techniques for momentum transport

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

Scott, S.D.

1991-08-01

This report discusses the following topics on momentum analysis in tokamaks and stellarators: the momentum balance equation; deposition of torque by neutral beams; effects of toroidal rotation; and experimental observations. (LSP)

An Analytical Tool to Determine Undergraduate Students' Use of Volume and Pressure when Describing Expansion Work and Technical Work

ERIC Educational Resources Information Center

Nilsson, Tor; Niedderer, Hans

2012-01-01

In undergraduate chemical thermodynamics teachers often include equations and view manipulations of variables as understanding. Undergraduate students are often not able to describe the meaning of these equations. In chemistry, enthalpy and its change are introduced to describe some features of chemical reactions. In the process of measuring heat…

The prediction of the cavitation phenomena including population balance modeling

NASA Astrophysics Data System (ADS)

Bannari, Rachid; Hliwa, Ghizlane Zineb; Bannari, Abdelfettah; Belghiti, Mly Taib

2017-07-01

Cavitation is the principal reason behind the behavior's modification of the hydraulic turbines. However, the experimental observations can not be appropriate to all cases due to the limitations in the measurement techniques. The mathematical models which have been implemented, use the mixture multiphase frame. As well as, most of the published work is limited by considering a constant bubble size distribution. However, this assumption is not realist. The aim of this article is the implementation and the use of a non-homogeneous multiphase model which solve two phases transport equation. The evolution of bubble size is considered by the population balance equation. This study is based on the eulerian-eulerian model, associated to the cavitation model. All the inter-phase forces such as drag, lift and virtual mass are used.

The method of perturbation-harmonic balance for analysing nonlinear free vibration of MDOF systems and structures

NASA Astrophysics Data System (ADS)

Tang, Qiangang; Sun, Shixian

1992-03-01

In this paper, the perturbation technique is introduced into the method of harmonic balance. A new method used for analyzing nonlinear free vibration of multidegree-of-freedom systems and structures is obtained. The form of solution is expanded into a series of small parameters and harmonics, so no term will be lost in the solution and the algebraic equations are linear. With the linear transformations, the matrices of the equations become diagonal. As soon as the modes related to linear vibration are found, the solution can be obtained. This method is superior to the method of linearized iteration. The examples show that the method has high accuracy for small-amplitude problems and the results for rather large amplitudes are satisfactory.

Regression Analysis and Calibration Recommendations for the Characterization of Balance Temperature Effects

NASA Technical Reports Server (NTRS)

Ulbrich, N.; Volden, T.

2018-01-01

Analysis and use of temperature-dependent wind tunnel strain-gage balance calibration data are discussed in the paper. First, three different methods are presented and compared that may be used to process temperature-dependent strain-gage balance data. The first method uses an extended set of independent variables in order to process the data and predict balance loads. The second method applies an extended load iteration equation during the analysis of balance calibration data. The third method uses temperature-dependent sensitivities for the data analysis. Physical interpretations of the most important temperature-dependent regression model terms are provided that relate temperature compensation imperfections and the temperature-dependent nature of the gage factor to sets of regression model terms. Finally, balance calibration recommendations are listed so that temperature-dependent calibration data can be obtained and successfully processed using the reviewed analysis methods.

The monetary approach to the balance of payments: The case of the oil-based, small, open, developing economies of Libya, Kuwait and Saudi Arabia

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

Buzakuk, M.R.

1988-01-01

This study explores the determinants of foreign reserves flow in light of the oil-based small open economies of Libya, Kuwait, and Saudi Arabia. The period of study encompasses the major oil price increases of the 1970s and early 1980s, which had led to the huge transfers of foreign exchanges towards these, among other, developing economies. The framework of analysis is basically a monetary approach to the balance of payments. This study is of both a theoretical and empirical nature. It utilizes the monetary forces in the domestic money market to derive a basic balance of payments (BOP) equation that explainsmore » the monetary nature of the balance of payments. The study found that the data from those countries support the monetary relationships as hypothesized by the monetary approach, especially the negative one-to-one relation between domestic credit (DC) and the BOP. Results from the simultaneous estimations of the BOP and DC reported better estimates than the single-equation model. Findings from the reaction function indicated that the monetary authorities of these oil-based economies were actively sterilizing the effect of foreign reserve flows. Findings supported the integrated market hypothesis in Kuwait and Libya, but not in the Saudi case.« less

Adaptive mesh refinement and load balancing based on multi-level block-structured Cartesian mesh

NASA Astrophysics Data System (ADS)

Misaka, Takashi; Sasaki, Daisuke; Obayashi, Shigeru

2017-11-01

We developed a framework for a distributed-memory parallel computer that enables dynamic data management for adaptive mesh refinement and load balancing. We employed simple data structure of the building cube method (BCM) where a computational domain is divided into multi-level cubic domains and each cube has the same number of grid points inside, realising a multi-level block-structured Cartesian mesh. Solution adaptive mesh refinement, which works efficiently with the help of the dynamic load balancing, was implemented by dividing cubes based on mesh refinement criteria. The framework was investigated with the Laplace equation in terms of adaptive mesh refinement, load balancing and the parallel efficiency. It was then applied to the incompressible Navier-Stokes equations to simulate a turbulent flow around a sphere. We considered wall-adaptive cube refinement where a non-dimensional wall distance y+ near the sphere is used for a criterion of mesh refinement. The result showed the load imbalance due to y+ adaptive mesh refinement was corrected by the present approach. To utilise the BCM framework more effectively, we also tested a cube-wise algorithm switching where an explicit and implicit time integration schemes are switched depending on the local Courant-Friedrichs-Lewy (CFL) condition in each cube.

Delay chemical master equation: direct and closed-form solutions

PubMed Central

Leier, Andre; Marquez-Lago, Tatiana T.

2015-01-01

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived. PMID:26345616

Delay chemical master equation: direct and closed-form solutions.

PubMed

Leier, Andre; Marquez-Lago, Tatiana T

2015-07-08

The stochastic simulation algorithm (SSA) describes the time evolution of a discrete nonlinear Markov process. This stochastic process has a probability density function that is the solution of a differential equation, commonly known as the chemical master equation (CME) or forward-Kolmogorov equation. In the same way that the CME gives rise to the SSA, and trajectories of the latter are exact with respect to the former, trajectories obtained from a delay SSA are exact representations of the underlying delay CME (DCME). However, in contrast to the CME, no closed-form solutions have so far been derived for any kind of DCME. In this paper, we describe for the first time direct and closed solutions of the DCME for simple reaction schemes, such as a single-delayed unimolecular reaction as well as chemical reactions for transcription and translation with delayed mRNA maturation. We also discuss the conditions that have to be met such that such solutions can be derived.

On the origins of approximations for stochastic chemical kinetics.

PubMed

Haseltine, Eric L; Rawlings, James B

2005-10-22

This paper considers the derivation of approximations for stochastic chemical kinetics governed by the discrete master equation. Here, the concepts of (1) partitioning on the basis of fast and slow reactions as opposed to fast and slow species and (2) conditional probability densities are used to derive approximate, partitioned master equations, which are Markovian in nature, from the original master equation. Under different conditions dictated by relaxation time arguments, such approximations give rise to both the equilibrium and hybrid (deterministic or Langevin equations coupled with discrete stochastic simulation) approximations previously reported. In addition, the derivation points out several weaknesses in previous justifications of both the hybrid and equilibrium systems and demonstrates the connection between the original and approximate master equations. Two simple examples illustrate situations in which these two approximate methods are applicable and demonstrate the two methods' efficiencies.

Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.

PubMed

Martirosyan, A; Saakian, David B

2011-08-01

We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics of the chemical master equation (CME). We found exact analytical expressions (in large system-size limit) for the probability distribution, including explicit expression for the dynamics of variance of distribution. We also give the solution for some simple cases of the model with time-dependent rates. We derived the results of the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.

Study of travelling wave solutions for some special-type nonlinear evolution equations

NASA Astrophysics Data System (ADS)

Song, Junquan; Hu, Lan; Shen, Shoufeng; Ma, Wen-Xiu

2018-07-01

The tanh-function expansion method has been improved and used to construct travelling wave solutions of the form U={\\sum }j=0n{a}j{\\tanh }jξ for some special-type nonlinear evolution equations, which have a variety of physical applications. The positive integer n can be determined by balancing the highest order linear term with the nonlinear term in the evolution equations. We improve the tanh-function expansion method with n = 0 by introducing a new transform U=-W\\prime (ξ )/{W}2. A nonlinear wave equation with source terms, and mKdV-type equations, are considered in order to show the effectiveness of the improved scheme. We also propose the tanh-function expansion method of implicit function form, and apply it to a Harry Dym-type equation as an example.

Sensor fault detection and isolation system for a condensation process.

PubMed

Castro, M A López; Escobar, R F; Torres, L; Aguilar, J F Gómez; Hernández, J A; Olivares-Peregrino, V H

2016-11-01

This article presents the design of a sensor Fault Detection and Isolation (FDI) system for a condensation process based on a nonlinear model. The condenser is modeled by dynamic and thermodynamic equations. For this work, the dynamic equations are described by three pairs of differential equations which represent the energy balance between the fluids. The thermodynamic equations consist in algebraic heat transfer equations and empirical equations, that allow for the estimation of heat transfer coefficients. The FDI system consists of a bank of two nonlinear high-gain observers, in order to detect, estimate and to isolate the fault in any of both outlet temperature sensors. The main contributions of this work were the experimental validation of the condenser nonlinear model and the FDI system. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Balanced N and C input recommendations for rain-fed maize production in northern China based on N balances and grain yields.

PubMed

Wang, Xiaobin; Cai, Dianxiong; Zhao, Quansheng; Xie, Xiaohong; Hoogmoed, Willem B; Oenema, Oene

2018-02-01

This study aimed to assess longer-term (1993-2009) effects of combined applications of fertiliser, maize stover, and cattle manure on maize yields, partial nitrogen (N) and carbon (C) balances, and water and N-use efficiencies, to guide N and C input recommendations for rain-fed maize production in northern China. The field trial, with three factors at five levels and 12 treatments, was conducted at Shouyang Dryland-Farming Experimental Station, Shanxi, China. Data analysis revealed higher N balances but lower C balances significantly occurred in a dry year than in a wet year. Positive N balances related to higher N inputs resulted in higher soil available N, even downward to deep layers with increasing N inputs, while positive C balances due to higher C inputs could be benefit to increase soil organic C. Based on partial N balances and grain yields, N and C inputs at ranges of 100 kg N ha -1 and 1.9-2.9 Mg C ha -1 could be recommended for target yields of 6.7-7.2 Mg ha -1 in rain-fed maize production. The study suggests that N balances close to neutral be given priority to improving N-use efficiency, and more positive C balances also be important for sustaining target yields and soil fertility levels. © 2017 Society of Chemical Industry. © 2017 Society of Chemical Industry.

Prediction of hydrodynamics and chemistry of confined turbulent methane-air flames with attention to formation of oxides of nitrogen

NASA Technical Reports Server (NTRS)

Elghobashi, S.; Spalding, D. B.; Srivatsa, S. K.

1977-01-01

A formulation of the governing partial differential equations for fluid flow and reacting chemical species in a tubular combustor is presented. A numerical procedure for the solution of the governing differential equations is described, and models for chemical equilibrium and chemical kinetics calculations are presented. The chemical equilibrium model is used to characterize the hydrocarbon reactions. The chemical kinetics model is used to predict the concentrations of the oxides of nitrogen. The combustor consists of a cylindrical duct of varying cross sections with concentric streams of gaseous fuel and air entering the duct at one end. Four sample cases with specified inlet and boundary conditions are considered, and the results are discussed

Dissipative solitons with energy and matter flows: Fundamental building blocks for the world of living organisms

NASA Astrophysics Data System (ADS)

Akhmediev, N.; Soto-Crespo, J. M.; Brand, H. R.

2013-05-01

We consider a combined model of dissipative solitons that are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. The system is governed by the generic complex Ginzburg-Landau equation, which is coupled to a common reaction-diffusion (RD) system. Such a composite dynamical system may describe nerve pulses with a significant part of electromagnetic energy involved. We present examples of such composite dissipative solitons and analyse their internal balances between energy and matter generation and dissipation.

Comprehensive metabolic panel

MedlinePlus

A comprehensive metabolic panel is a group of blood tests. They provide an overall picture of your body's chemical balance and metabolism. Metabolism refers to all the physical and chemical processes ...

Ring current-energy balance during intense magnetic storms

NASA Astrophysics Data System (ADS)

Clua de Gonzalez, A. L.; Gonzalez, W. D.

2013-12-01

The energy-rate balance that governs the storm-time ring current is analyzed in terms of the Burton-McPherron-Russell equation (Burton et al., 1975). This is a first order differential equation relating the time variation of the pressure corrected Dst index, with the energy input to the magnetosphere. Based on the Burton et al. equation, we have analyzed in detail the geomagnetic storm of February 11, 2004. The energy input is taken proportional to the interplanetary electric field, Q(t) = αBsV, where Bs is the southward component of the interplanetary magnetic field in GSM coordinates, V is the flow speed of the solar wind and α a constant. The equation is integrated using the OMNI-combined interplanetary data and, the value of the decay time is estimated from a best fit of the response to the observed curve. For this storm we also use a rectangular approximation for the energy input function, thus allowing an analytical solution of the Burton et al. equation. The results from this approximation are then compared to the numerical solution. The study is also extended to the geomagnetic storm of April 22, 2001. This analysis seems to indicate that the Burton et al. equation should contain also a corrective term proportional to the second time derivative of the Dst index. This corrective term might become important for intense storms, with an effect of counteracting the growth of |Dst| before the energy input from the interplanetary medium declines, such that the value of |Dst| starts to decrease instead of continuing to grow.

A structural equation model of the relationship between muscle strength, balance performance, walking endurance and community integration in stroke survivors

PubMed Central

2017-01-01

Purpose To use structural equation modelling (SEM) to determine (1) the direct and indirect associations of strength of paretic lower limb muscles with the level of community integration, and (2) the direct association of walking endurance and balance performance with the level of community integration in community-dwelling stroke survivors. Materials and methods In this cross-sectional study of 105 stroke survivors, the Subjective Index of Physical and Social Outcome (SIPSO) was used to measure the level of community integration. Lower-limb strength measures included isometric paretic ankle strength and isokinetic paretic knee peak torque. The Berg Balance Scale (BBS) and the 6-minute walk test (6MWT) were used to evaluate balance performance and walking endurance, respectively. Results SEM revealed that the distance walked on the 6MWT had the strongest direct association with the SIPSO score (β = 0.41, p <0.001). An increase of one standard deviation in the 6MWT distance resulted in an increase of 0.41 standard deviations in the SIPSO score. Moreover, dorsiflexion strength (β = 0.18, p = 0.044) and the BBS score (β = 0.21, p = 0.021) had direct associations with the SIPSO score. Conclusions The results of the proposed model suggest that rehabilitation training of community-dwelling stroke survivors could focus on walking endurance, balance performance and dorsiflexor muscle strengthening if the aim is to augment the level of community integration. PMID:29049293

Iterative Strain-Gage Balance Calibration Data Analysis for Extended Independent Variable Sets

NASA Technical Reports Server (NTRS)

Ulbrich, Norbert Manfred

2011-01-01

A new method was developed that makes it possible to use an extended set of independent calibration variables for an iterative analysis of wind tunnel strain gage balance calibration data. The new method permits the application of the iterative analysis method whenever the total number of balance loads and other independent calibration variables is greater than the total number of measured strain gage outputs. Iteration equations used by the iterative analysis method have the limitation that the number of independent and dependent variables must match. The new method circumvents this limitation. It simply adds a missing dependent variable to the original data set by using an additional independent variable also as an additional dependent variable. Then, the desired solution of the regression analysis problem can be obtained that fits each gage output as a function of both the original and additional independent calibration variables. The final regression coefficients can be converted to data reduction matrix coefficients because the missing dependent variables were added to the data set without changing the regression analysis result for each gage output. Therefore, the new method still supports the application of the two load iteration equation choices that the iterative method traditionally uses for the prediction of balance loads during a wind tunnel test. An example is discussed in the paper that illustrates the application of the new method to a realistic simulation of temperature dependent calibration data set of a six component balance.

Diagnosis of boundary-layer circulations.

PubMed

Beare, Robert J; Cullen, Michael J P

2013-05-28

Diagnoses of circulations in the vertical plane provide valuable insights into aspects of the dynamics of the climate system. Dynamical theories based on geostrophic balance have proved useful in deriving diagnostic equations for these circulations. For example, semi-geostrophic theory gives rise to the Sawyer-Eliassen equation (SEE) that predicts, among other things, circulations around mid-latitude fronts. A limitation of the SEE is the absence of a realistic boundary layer. However, the coupling provided by the boundary layer between the atmosphere and the surface is fundamental to the climate system. Here, we use a theory based on Ekman momentum balance to derive an SEE that includes a boundary layer (SEEBL). We consider a case study of a baroclinic low-level jet. The SEEBL solution shows significant benefits over Ekman pumping, including accommodating a boundary-layer depth that varies in space and structure, which accounts for buoyancy and momentum advection. The diagnosed low-level jet is stronger than that determined by Ekman balance. This is due to the inclusion of momentum advection. Momentum advection provides an additional mechanism for enhancement of the low-level jet that is distinct from inertial oscillations.

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.

1984-01-01

This paper describes DIGTEM (digital turbofan engine model), a computer program that simulates two spool, two stream (turbofan) engines. DIGTEM was developed to support the development of a real time multiprocessor based engine simulator being designed at the Lewis Research Center. The turbofan engine model in DIGTEM contains steady state performance maps for all the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. DIGTEM features an implicit integration scheme for integrating stiff systems and trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off design points and iterates to a balanced engine condition. Transients are generated by defining the engine inputs as functions of time in a user written subroutine (TMRSP). Closed loop controls can also be simulated. DIGTEM is generalized in the aerothermodynamic treatment of components. This feature, along with DIGTEM's trimming at a design point, make it a very useful tool for developing a model of a specific turbofan engine.

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.

1983-01-01

This paper describes DIGTEM (digital turbofan engine model), a computer program that simulates two spool, two stream (turbofan) engines. DIGTEM was developed to support the development of a real time multiprocessor based engine simulator being designed at the Lewis Research Center. The turbofan engine model in DIGTEM contains steady state performance maps for all the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. DIGTEM features an implicit integration scheme for integrating stiff systems and trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off design points and iterates to a balanced engine condition. Transients are generated by defining the engine inputs as functions of time in a user written subroutine (TMRSP). Closed loop controls can also be simulated. DIGTEM is generalized in the aerothermodynamic treatment of components. This feature, along with DIGTEM's trimming at a design point, make it a very useful tool for developing a model of a specific turbofan engine.

Accelerating Subsurface Transport Simulation on Heterogeneous Clusters

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

Villa, Oreste; Gawande, Nitin A.; Tumeo, Antonino

Reactive transport numerical models simulate chemical and microbiological reactions that occur along a flowpath. These models have to compute reactions for a large number of locations. They solve the set of ordinary differential equations (ODEs) that describes the reaction for each location through the Newton-Raphson technique. This technique involves computing a Jacobian matrix and a residual vector for each set of equation, and then solving iteratively the linearized system by performing Gaussian Elimination and LU decomposition until convergence. STOMP, a well known subsurface flow simulation tool, employs matrices with sizes in the order of 100x100 elements and, for numerical accuracy,more » LU factorization with full pivoting instead of the faster partial pivoting. Modern high performance computing systems are heterogeneous machines whose nodes integrate both CPUs and GPUs, exposing unprecedented amounts of parallelism. To exploit all their computational power, applications must use both the types of processing elements. For the case of subsurface flow simulation, this mainly requires implementing efficient batched LU-based solvers and identifying efficient solutions for enabling load balancing among the different processors of the system. In this paper we discuss two approaches that allows scaling STOMP's performance on heterogeneous clusters. We initially identify the challenges in implementing batched LU-based solvers for small matrices on GPUs, and propose an implementation that fulfills STOMP's requirements. We compare this implementation to other existing solutions. Then, we combine the batched GPU solver with an OpenMP-based CPU solver, and present an adaptive load balancer that dynamically distributes the linear systems to solve between the two components inside a node. We show how these approaches, integrated into the full application, provide speed ups from 6 to 7 times on large problems, executed on up to 16 nodes of a cluster with two AMD Opteron 6272 and a Tesla M2090 per node.« less

The Effect of Shock on the Amorphous Component in Altered Basalt

NASA Technical Reports Server (NTRS)

Eckley, S. A.; Wright, S. P.; Rampe, E. B.; Niles, P. B.

2017-01-01

Investigation of the geochemical and mineralogical composition of the Martian surface provides insight into the geologic history of the predominantly basaltic crust. The Chemistry and Mineralogy (CheMin) instrument onboard the Curiosity rover has returned the first X-Ray diffraction data from the Martian surface. However, large proportions (27 +/- 14 with some estimates as high as 50 weight percentage) of an amorphous component have been reported. As a remedy to this problem, mass balance equations using geochemistry, volatile chemistry, and mineralogy have been employed to constrain the geochemistry of the amorphous component. However, "the nature and number of amorphous phases that constitute the amorphous component is not unequivocally known". Multiple hypotheses have been proposed to explain the origin of this amorphous component: Allophane (Al2O); Basaltic glass (Volcanic and impact); Palagonite (Altered basaltic glass); Hisingerite (Fe (sup 3 plus)-bearing phyllosilicate); S/Cl-rich component (sulfates and/or akaganeite); Nanophase ferric oxide component (npOx). Establishing a multi-phase amorphous component from a basaltic precursor that has undergone physical and chemical weathering within geochemical constraints is of paramount importance to better understand the composition of a large portion of the Martian surface (up to 50 weight percentage). Shocked basalts from Lonar Crater in India are valuable analogs for the Martian surface because it is a well-preserved impact crater in a basaltic target. Having undergone pre- and post-shock aqueous alteration, these rocks provide crucial data regarding the effect of shock on the amorphous component in altered basalt. By conducting mass balance equations similar to what has been performed for Gale crater materials, we attempt to calculate the geochemistry of the amorphous component in altered basalts ranging from unshocked to Class 5 (Table 1). This has the potential to reveal the nature and origin (i.e. primary igneous, shock metamorphic, and/or aqueous alteration occurring before or after the impact event) of the amorphous component in shocked basalt with the goal of unravelling the history of the Martian surface.

Chemical and isotopic methods for quantifying ground-water recharge in a regional, semiarid environment

USGS Publications Warehouse

Wood, Warren W.; Sanford, Ward E.

1995-01-01

The High Plains aquifer underlying the semiarid Southern High Plains of Texas and New Mexico, USA was used to illustrate solute and isotopic methods for evaluating recharge fluxes, runoff, and spatial and temporal distribution of recharge. The chloride mass-balance method can provide, under certain conditions, a time-integrated technique for evaluation of recharge flux to regional aquifers that is independent of physical parameters. Applying this method to the High Plains aquifer of the Southern High Plains suggests that recharge flux is approximately 2% of precipitation, or approximately 11 ± 2 mm/y, consistent with previous estimates based on a variety of physically based measurements. The method is useful because long-term average precipitation and chloride concentrations in rain and ground water have less uncertainty and are generally less expensive to acquire than physically based parameters commonly used in analyzing recharge. Spatial and temporal distribution of recharge was evaluated by use of δ2H, δ18O, and tritium concentrations in both ground water and the unsaturated zone. Analyses suggest that nearly half of the recharge to the Southern High Plains occurs as piston flow through playa basin floors that occupy approximately 6% of the area, and that macropore recharge may be important in the remaining recharge. Tritium and chloride concentrations in the unsaturated zone were used in a new equation developed to quantify runoff. Using this equation and data from a representative basin, runoff was found to be 24 ± 3 mm/y; that is in close agreement with values obtained from water-balance measurements on experimental watersheds in the area. Such geochemical estimates are possible because tritium is used to calculate a recharge flux that is independent of precipitation and runoff, whereas recharge flux based on chloride concentration in the unsaturated zone is dependent upon the amount of runoff. The difference between these two estimates yields the amount of runoff to the basin.

Dynamic power balance analysis in JET

NASA Astrophysics Data System (ADS)

Matthews, G. F.; Silburn, S. A.; Challis, C. D.; Eich, T.; Iglesias, D.; King, D.; Sieglin, B.; Contributors, JET

2017-12-01

The full scale realisation of nuclear fusion as an energy source requires a detailed understanding of power and energy balance in current experimental devices. In this we explore whether a global power balance model in which some of the calibration factors applied to the source or sink terms are fitted to the data can provide insight into possible causes of any discrepancies in power and energy balance seen in the JET tokamak. We show that the dynamics in the power balance can only be properly reproduced by including the changes in the thermal stored energy which therefore provides an additional opportunity to cross calibrate other terms in the power balance equation. Although the results are inconclusive with respect to the original goal of identifying the source of the discrepancies in the energy balance, we do find that with optimised parameters an extremely good prediction of the total power measured at the outer divertor target can be obtained over a wide range of pulses with time resolution up to ∼25 ms.

Groundwater and surface-water interactions and impacts of human activities in the Hailiutu catchment, northwest China

NASA Astrophysics Data System (ADS)

Yang, Zhi; Zhou, Yangxiao; Wenninger, Jochen; Uhlenbrook, Stefan; Wang, Xusheng; Wan, Li

2017-08-01

The interactions between groundwater and surface water have been significantly affected by human activities in the semi-arid Hailiutu catchment, northwest China. Several methods were used to investigate the spatial and temporal interactions between groundwater and surface water. Isotopic and chemical analyses of water samples determined that groundwater discharges to the Hailiutu River, and mass balance equations were employed to estimate groundwater seepage rates along the river using chemical profiles. The hydrograph separation method was used to estimate temporal variations of groundwater discharges to the river. A numerical groundwater model was constructed to simulate groundwater discharges along the river and to analyze effects of water use in the catchment. The simulated seepage rates along the river compare reasonably well with the seepage estimates derived from a chemical profile in 2012. The impacts of human activities (river-water diversion and groundwater abstraction) on the river discharge were analyzed by calculating the differences between the simulated natural groundwater discharge and the measured river discharge. Water use associated with the Hailiutu River increased from 1986 to 1991, reached its highest level from 1992 to 2000, and decreased from 2001 onwards. The reduction of river discharge might have negative impacts on the riparian ecosystem and the water availability for downstream users. The interactions between groundwater and surface water as well as the consequences of human activities should be taken into account when implementing sustainable water resources management in the Hailiutu catchment.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients.

PubMed

Saleem, M Rehan; Ashraf, Waqas; Zia, Saqib; Ali, Ishtiaq; Qamar, Shamsul

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme.

A kinetic flux vector splitting scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients

PubMed Central

2018-01-01

This paper is concerned with the derivation of a well-balanced kinetic scheme to approximate a shallow flow model incorporating non-flat bottom topography and horizontal temperature gradients. The considered model equations, also called as Ripa system, are the non-homogeneous shallow water equations considering temperature gradients and non-uniform bottom topography. Due to the presence of temperature gradient terms, the steady state at rest is of primary interest from the physical point of view. However, capturing of this steady state is a challenging task for the applied numerical methods. The proposed well-balanced kinetic flux vector splitting (KFVS) scheme is non-oscillatory and second order accurate. The second order accuracy of the scheme is obtained by considering a MUSCL-type initial reconstruction and Runge-Kutta time stepping method. The scheme is applied to solve the model equations in one and two space dimensions. Several numerical case studies are carried out to validate the proposed numerical algorithm. The numerical results obtained are compared with those of staggered central NT scheme. The results obtained are also in good agreement with the recently published results in the literature, verifying the potential, efficiency, accuracy and robustness of the suggested numerical scheme. PMID:29851978

A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

Chemical Mass Balance (CMB) Model

EPA Pesticide Factsheets

The EPA-CMB Version 8.2 uses source profiles and speciated ambient data to quantify source contributions. Contributions are quantified from chemically distinct source-types rather than from individual emitters.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

A coupled implicit method for chemical non-equilibrium flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun; Chen, Kuo-Huey; Choi, Yunho

1993-01-01

The present time-accurate coupled-solution procedure addresses the chemical nonequilibrium Navier-Stokes equations over a wide Mach-number range uses, in conjunction with the strong conservation form of the governing equations, five unknown primitive variables. The numerical tests undertaken address steady convergent-divergent nozzle flows with air dissociation/recombination, dump combustor flows with n-pentane/air chemistry, and unsteady nonreacting cavity flows.

A novel method for multifactorial bio-chemical experiments design based on combinational design theory.

PubMed

Wang, Xun; Sun, Beibei; Liu, Boyang; Fu, Yaping; Zheng, Pan

2017-01-01

Experimental design focuses on describing or explaining the multifactorial interactions that are hypothesized to reflect the variation. The design introduces conditions that may directly affect the variation, where particular conditions are purposely selected for observation. Combinatorial design theory deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry. In this work, borrowing the concept of "balance" in combinatorial design theory, a novel method for multifactorial bio-chemical experiments design is proposed, where balanced templates in combinational design are used to select the conditions for observation. Balanced experimental data that covers all the influencing factors of experiments can be obtianed for further processing, such as training set for machine learning models. Finally, a software based on the proposed method is developed for designing experiments with covering influencing factors a certain number of times.

Linear models for calculating digestibile energy for sheep diets.

PubMed

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

1981-05-01

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

Harmonic Balance Computations of Fan Aeroelastic Stability

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Reddy, T. S. R.

2010-01-01

A harmonic balance (HB) aeroelastic analysis, which has been recently developed, was used to determine the aeroelastic stability (flutter) characteristics of an experimental fan. To assess the numerical accuracy of this HB aeroelastic analysis, a time-domain aeroelastic analysis was also used to determine the aeroelastic stability characteristics of the same fan. Both of these three-dimensional analysis codes model the unsteady flowfield due to blade vibrations using the Reynolds-averaged Navier-Stokes (RANS) equations. In the HB analysis, the unsteady flow equations are converted to a HB form and solved using a pseudo-time marching method. In the time-domain analysis, the unsteady flow equations are solved using an implicit time-marching approach. Steady and unsteady computations for two vibration modes were carried out at two rotational speeds: 100 percent (design) and 70 percent (part-speed). The steady and unsteady results obtained from the two analysis methods compare well, thus verifying the recently developed HB aeroelastic analysis. Based on the results, the experimental fan was found to have no aeroelastic instability (flutter) at the conditions examined in this study.

The influence of pressure relaxation on the structure of an axial vortex

NASA Astrophysics Data System (ADS)

Ash, Robert L.; Zardadkhan, Irfan; Zuckerwar, Allan J.

2011-07-01

Governing equations including the effects of pressure relaxation have been utilized to study an incompressible, steady-state viscous axial vortex with specified far-field circulation. When sound generation is attributed to a velocity gradient tensor-pressure gradient product, the modified conservation of momentum equations that result yield an exact solution for a steady, incompressible axial vortex. The vortex velocity profile has been shown to closely approximate experimental vortex measurements in air and water over a wide range of circulation-based Reynolds numbers. The influence of temperature and humidity on the pressure relaxation coefficient in air has been examined using theoretical and empirical approaches, and published axial vortex experiments have been employed to estimate the pressure relaxation coefficient in water. Non-equilibrium pressure gradient forces have been shown to balance the viscous stresses in the vortex core region, and the predicted pressure deficits that result from this non-equilibrium balance can be substantially larger than the pressure deficits predicted using a Bernoulli equation approach. Previously reported pressure deficit distributions for dust devils and tornados have been employed to validate the non-equilibrium pressure deficit predictions.

Kinetic study on non-thermal volumetric plasma decay in the early afterglow of air discharge generated by a short pulse microwave or laser

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

Yang, Wei, E-mail: yangwei861212@126.com; Zhou, Qianhong; Dong, Zhiwei

This paper reports a kinetic study on non-thermal plasma decay in the early afterglow of air discharge generated by short pulse microwave or laser. A global self-consistent model is based on the particle balance of complex plasma chemistry, electron energy equation, and gas thermal balance equation. Electron-ion Coulomb collision is included in the steady state Boltzmann equation solver to accurately describe the electron mobility and other transport coefficients. The model is used to simulate the afterglow of microsecond to nanosecond pulse microwave discharge in N{sub 2}, O{sub 2}, and air, as well as femtosecond laser filament discharge in dry andmore » humid air. The simulated results for electron density decay are in quantitative agreement with the available measured ones. The evolution of plasma decay under an external electric field is also investigated, and the effect of gas heating is considered. The underlying mechanism of plasma density decay is unveiled through the above kinetic modeling.« less

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.

Two- and three-dimensional natural and mixed convection simulation using modular zonal models

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

Wurtz, E.; Nataf, J.M.; Winkelmann, F.

We demonstrate the use of the zonal model approach, which is a simplified method for calculating natural and mixed convection in rooms. Zonal models use a coarse grid and use balance equations, state equations, hydrostatic pressure drop equations and power law equations of the form {ital m} = {ital C}{Delta}{sup {ital n}}. The advantage of the zonal approach and its modular implementation are discussed. The zonal model resolution of nonlinear equation systems is demonstrated for three cases: a 2-D room, a 3-D room and a pair of 3-D rooms separated by a partition with an opening. A sensitivity analysis withmore » respect to physical parameters and grid coarseness is presented. Results are compared to computational fluid dynamics (CFD) calculations and experimental data.« less

Generalized heat-transport equations: parabolic and hyperbolic models

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Skylab water balance error analysis

NASA Technical Reports Server (NTRS)

Leonard, J. I.

1977-01-01

Estimates of the precision of the net water balance were obtained for the entire Skylab preflight and inflight phases as well as for the first two weeks of flight. Quantitative estimates of both total sampling errors and instrumentation errors were obtained. It was shown that measurement error is minimal in comparison to biological variability and little can be gained from improvement in analytical accuracy. In addition, a propagation of error analysis demonstrated that total water balance error could be accounted for almost entirely by the errors associated with body mass changes. Errors due to interaction between terms in the water balance equation (covariances) represented less than 10% of the total error. Overall, the analysis provides evidence that daily measurements of body water changes obtained from the indirect balance technique are reasonable, precise, and relaible. The method is not biased toward net retention or loss.

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

NASA Astrophysics Data System (ADS)

Wang, D.

2017-12-01

The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

BETR North America: A regionally segmented multimedia contaminant fate model for North America

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

MacLeod, M.; Woodfine, D.G.; Mackay, D.

We present the Berkeley-Trent North American contaminant fate model (BETR North America), a regionally segmented multimedia contaminant fate model based on the fugacity concept. The model is built on a framework that links contaminant fate models of individual regions, and is generally applicable to large, spatially heterogeneous areas. The North American environment is modeled as 24 ecological regions, within each region contaminant fate is described using a 7 compartment multimedia fugacity model including a vertically segmented atmosphere, freshwater, freshwater sediment, soil, coastal water and vegetation compartments. Inter-regional transport of contaminants in the atmosphere, freshwater and coastal water is described usingmore » a database of hydrological and meteorological data compiled with Geographical Information Systems (GIS) techniques. Steady-state and dynamic solutions to the 168 mass balance equations that make up the linked model for North America are discussed, and an illustrative case study of toxaphene transport from the southern United States to the Great Lakes Basin is presented. Regionally segmented models such as BETR North America can provide a critical link between evaluative models of long-range transport potential and contaminant concentrations observed in remote regions. The continent-scale mass balance calculated by the model provides a sound basis for evaluating long-range transport potential of organic pollutants, and formulation of continent scale management and regulatory strategies for chemicals.« less

Balanced Flow Measurement and Conditioning Technology (Balanced Orifice Plate 7,051,765 B1) for NASA Inventions and Contributions Board Invention of the Year Evaluation

NASA Technical Reports Server (NTRS)

Kelley, Anthony R.

2008-01-01

This viewgraph document reviews the Balanced Flow Measurement (BFM) and Conditioning Technology, and makes the case for this as the NASA Invention of the Year. The BFM technology makes use of a thin, multi-hole orifice plate with holes sized and placed per a unique set of equations. It produces mass flow, volumetric flow,kinelic energy,or momentum BALANCE across the face of the plate. The flow is proportional.to the square root of upstream to downstream differential pressure. Multiple holes lead to smoother pressure measurement. Measures and conditions or can limit fluid flow. This innovation has many uses in and out of NASA.

Balancing the Equation: Public Radio Comes of Age.

ERIC Educational Resources Information Center

Avery, Robert K.; Pepper, Robert

1979-01-01

The national development of public radio as a noncommercial medium is traced through the history of its national organizations, ending with the formation of its single programing and representational entity. (Author)

Silicon production process evaluations

NASA Technical Reports Server (NTRS)

1982-01-01

Chemical engineering analyses involving the preliminary process design of a plant (1,000 metric tons/year capacity) to produce silicon via the technology under consideration were accomplished. Major activities in the chemical engineering analyses included base case conditions, reaction chemistry, process flowsheet, material balance, energy balance, property data, equipment design, major equipment list, production labor and forward for economic analysis. The process design package provided detailed data for raw materials, utilities, major process equipment and production labor requirements necessary for polysilicon production in each process.

Managing Quality and Productivity in Aerospace and Defense

DTIC Science & Technology

1989-11-01

subject of The VPC at Virginia Tech. The Maryland excellence. We hope they will be of value to Center for Productivity and Quality of Worklife your...Budget drives the plan • Plan drives the budget I nvolves only top management * Participation at all levels * Finance and operations imbalanced * Balance ...to create a better tend to cause us to drive the equation left-to- balance . The Planning Process discussed in right, focusing on the levels of

Design Tools for Assessing Manufacturing Environmental Impact.

DTIC Science & Technology

1997-11-26

the material report alone. In order to more easily design, update and verify the output report, many of the cells which contained the information...needed for the material balance calculations were named. The cell name was then used in the calculations. Where possible the same names that were used in...Material balance information was used extensively to ensure all the equations were correct and were put into the appropriate cells . A summary of the

Simultaneous thermodynamic and geochemical analyses for P-T-time and mass transport toward comprehensive understanding of metamorphism

NASA Astrophysics Data System (ADS)

Uno, M.; Nakamura, H.; Iwamori, H.

2011-12-01

Individual parcel of regional metamorphic rock records physico-chemical conditions such as P-T path, mass transfer and deformation with the Lagrangian specification. On the other hand, a metamorphic belt as an ensemble of such parcels may provide a large-scale flow field of energy (e.g., temperature, entropy) and mass (including both solid and fluid phases with elements and isotopes) with the Eulerian specification. However, there is so far few model that integrates all the variables stated above. Phase petrology provides mostly the intensive variables (e.g., P-T path), whereas geochemistry provides mostly the extensive variables (time-integrated mass transfer), and these two have been treated separately. Here we combine phase petrology and geochemistry from a scale of mineral grain, and solve them under a simultaneous and consistent set of thermodynamic and mass balance equation. For this sake, the Sanbagawa metamorphic belt in Japan has been surveyed. To understand the nature of fluid during rehydration, we analyzed both basic rocks and pelitic rocks that record retrograde reactions. Major and trace element compositions of each mineral, and bulk rock chemistry have been analyzed with EPMA, LA-ICP-MS, XRF and ICP-MS, respectively. Retrograde P-T path and the extent of rehydration of each rock have been obtained by applying the Gibbs' method (e.g. Spear, 1993; Okamoto&Toriumi, 2001) to amphiboles. Trace element budget along a specific P-T path were calculated by equating differential mass balance equation for major and trace elements as follows; XfluiddMfluid = ⊙MsolidXsolid + ⊙XsoliddMsolid Where the X and M denotes compositions and modes of minerals and dX and dM are their changes along a specific P-T change. The mineral compositions (Xsolid), mineral modes (Msolid), mineral growths (dMsolid) for zoned minerals (amphibole and/or garnet) and fluid compositions (Xfluid) were derived from the results of Gibbs' method, X-ray map and fluid/mineral partition coefficients, respectively. Thus, the unknowns are dMs, and the equations are solved for them. As a result, the mass transfer during the specific P-T change (Xfluid dMfluid) can be specified. It is revealed that fluid mobile elements such as LIL elements, Sr and Pb are mostly proportional to LOI (loss on ignition). LOI and extent of rehydration is proportional in the Sanbagawa belt (Okamoto&Toriumi, 2005), thus the observed enrichment of LILE, Sr and Pb are interpreted to be associated with rehydration. The Sr isotope ratios of the basic shists also increase with LOI, implying that the differences in bulk rock chemistry are not attributed to differences in mineral modes,but addition and/or reaction with external source of fluids with high 87Sr/86Sr. The estimated fluid composition is similar to calculated compositions of slab-derived fluids (Nakamura et al., 2008). From mass balance calculation, trace element budget associated with rehydration reactions and their spatial distribution will be presented, and the mechanisms of mass and fluid transfer will be discussed.

Mass fluctuation kinetics: Capturing stochastic effects in systems of chemical reactions through coupled mean-variance computations

NASA Astrophysics Data System (ADS)

Gómez-Uribe, Carlos A.; Verghese, George C.

2007-01-01

The intrinsic stochastic effects in chemical reactions, and particularly in biochemical networks, may result in behaviors significantly different from those predicted by deterministic mass action kinetics (MAK). Analyzing stochastic effects, however, is often computationally taxing and complex. The authors describe here the derivation and application of what they term the mass fluctuation kinetics (MFK), a set of deterministic equations to track the means, variances, and covariances of the concentrations of the chemical species in the system. These equations are obtained by approximating the dynamics of the first and second moments of the chemical master equation. Apart from needing knowledge of the system volume, the MFK description requires only the same information used to specify the MAK model, and is not significantly harder to write down or apply. When the effects of fluctuations are negligible, the MFK description typically reduces to MAK. The MFK equations are capable of describing the average behavior of the network substantially better than MAK, because they incorporate the effects of fluctuations on the evolution of the means. They also account for the effects of the means on the evolution of the variances and covariances, to produce quite accurate uncertainty bands around the average behavior. The MFK computations, although approximate, are significantly faster than Monte Carlo methods for computing first and second moments in systems of chemical reactions. They may therefore be used, perhaps along with a few Monte Carlo simulations of sample state trajectories, to efficiently provide a detailed picture of the behavior of a chemical system.

Estimating the effective rate of fast chemical reactions with turbulent mixing of reactants

NASA Astrophysics Data System (ADS)

Vorotilin, V. P.; Yanovskii, Yu. G.

2015-07-01

On the basis of representation of a turbulent fluid as an aggregation of independent turbulent particles (vortexes), we derive relations for the effective rate of chemical reactions and obtain a closed system of equations describing reactions with turbulent mixing of reactants. A variant of instantaneous reactions is considered that explains the proposed approach simply. In particular, the turbulent mixing events according to this approach are uniquely related to the acts of chemical interaction, which makes it possible to exclude from consideration the mixing of inert impurities-the most difficult point of the theory formulated using classical notions. The obtained system of equations is closed without introducing arbitrarily adopted correlations, by naturally introducing the concept of effective reaction and writing the equations of conservation for both the concentrations of reactants and their volumes.

Interior. Balance room for chemistry laboratory. Storage room for glassware ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Interior. Balance room for chemistry laboratory. Storage room for glassware and reference room with frequently used chemistry and chemical engineering texts. - Thomas A. Edison Laboratories, Building No. 2, Main Street & Lakeside Avenue, West Orange, Essex County, NJ

A continuous time random walk (CTRW) integro-differential equation with chemical interaction

NASA Astrophysics Data System (ADS)

Ben-Zvi, Rami; Nissan, Alon; Scher, Harvey; Berkowitz, Brian

2018-01-01

A nonlocal-in-time integro-differential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M ( t), which includes the source of non-Fickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is non-linear and second-order, relevant for a bimolecular reaction A + B → C. The interaction term ΓP A ( s, t) P B ( s, t) is symmetric in the concentrations of A and B (i.e. P A and P B ); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M ( t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRW-PT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media.

A moment projection method for population balance dynamics with a shrinkage term

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

Wu, Shaohua; Yapp, Edward K.Y.; Akroyd, Jethro

A new method of moments for solving the population balance equation is developed and presented. The moment projection method (MPM) is numerically simple and easy to implement and attempts to address the challenge of particle shrinkage due to processes such as oxidation, evaporation or dissolution. It directly solves the moment transport equation for the moments and tracks the number of the smallest particles using the algorithm by Blumstein and Wheeler (1973) . The performance of the new method is measured against the method of moments (MOM) and the hybrid method of moments (HMOM). The results suggest that MPM performs muchmore » better than MOM and HMOM where shrinkage is dominant. The new method predicts mean quantities which are almost as accurate as a high-precision stochastic method calculated using the established direct simulation algorithm (DSA).« less

Dynamic analysis of a magnetic bearing system with flux control

NASA Technical Reports Server (NTRS)

Knight, Josiah; Walsh, Thomas; Virgin, Lawrence

1994-01-01

Using measured values of two-dimensional forces in a magnetic actuator, equations of motion for an active magnetic bearing are presented. The presence of geometric coupling between coordinate directions causes the equations of motion to be nonlinear. Two methods are used to examine the unbalance response of the system: simulation by direct integration in time; and determination of approximate steady state solutions by harmonic balance. For relatively large values of the derivative control coefficient, the system behaves in an essentially linear manner, but for lower values of this parameter, or for higher values of the coupling coefficient, the response shows a split of amplitudes in the two principal directions. This bifurcation is sensitive to initial conditions. The harmonic balance solution shows that the separation of amplitudes actually corresponds to a change in stability of multiple coexisting solutions.

AN ANALYTIC MODEL OF DUSTY, STRATIFIED, SPHERICAL H ii REGIONS

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

Rodríguez-Ramírez, J. C.; Raga, A. C.; Lora, V.

2016-12-20

We study analytically the effect of radiation pressure (associated with photoionization processes and with dust absorption) on spherical, hydrostatic H ii regions. We consider two basic equations, one for the hydrostatic balance between the radiation-pressure components and the gas pressure, and another for the balance among the recombination rate, the dust absorption, and the ionizing photon rate. Based on appropriate mathematical approximations, we find a simple analytic solution for the density stratification of the nebula, which is defined by specifying the radius of the external boundary, the cross section of dust absorption, and the luminosity of the central star. Wemore » compare the analytic solution with numerical integrations of the model equations of Draine, and find a wide range of the physical parameters for which the analytic solution is accurate.« less