An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties

PubMed Central

Mehmandoust, Babak; Sanjari, Ehsan; Vatani, Mostafa

2013-01-01

The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes. In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances. This equation is a function of normal boiling temperature, critical temperature, and critical pressure. The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range. The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3–722 K). PMID:25685493

An efficient reliable method to estimate the vaporization enthalpy of pure substances according to the normal boiling temperature and critical properties.

PubMed

Mehmandoust, Babak; Sanjari, Ehsan; Vatani, Mostafa

2014-03-01

The heat of vaporization of a pure substance at its normal boiling temperature is a very important property in many chemical processes. In this work, a new empirical method was developed to predict vaporization enthalpy of pure substances. This equation is a function of normal boiling temperature, critical temperature, and critical pressure. The presented model is simple to use and provides an improvement over the existing equations for 452 pure substances in wide boiling range. The results showed that the proposed correlation is more accurate than the literature methods for pure substances in a wide boiling range (20.3-722 K).

Errors in calculated oncotic pressure of dog plasma.

PubMed

Gabel, J C; Scott, R L; Adair, T H; Drake, R E; Traber, D L

1980-12-01

Several equations to calculate plasma oncotic pressure (pi) from the total protein concentration (C) have been previously described. These equations were derived empirically from samples with a wide range of C obtained by diluting or concentrating normal plasma samples. To test these equations over a range of naturally occurring C, we measured C and pi of plasma samples from 40 dogs. C ranged from 5.3 to 8.7 g/dl and averaged 6.5 +/- 0.1 (mean +/- SE) and pi averaged 17.9 +/- 0.3 mmHg. The regression equation was pi = 78.14 + 1.67 C (r = 0.74). pi increased with C much less than predicted with the commonly used equations. The albumin-to-globulin concentration ratios (A/G), determined in 27 of the dogs, decreased with increasing C (A/G = 1.56-0.128 C, r = 0.62). The lower A/G at the higher C's could cause the lower than predicted increase in pi with C, because the equations were developed from data in which A/G was constant.

Double-Plate Penetration Equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

2000-01-01

This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.

Reliability of tanoak volume equations when applied to different areas

Treesearch

Norman H. Pillsbury; Philip M. McDonald; Victor Simon

1995-01-01

Tree volume equations for tanoak (Lithocarpus densiflorus) were developed for seven stands throughout its natural range and compared by a volume prediction and a parameter difference method. The objective was to test if volume estimates from a species growing in a local, relatively uniform habitat could be applied more widely. Results indicated...

Hierarchical coarse-graining model for photosystem II including electron and excitation-energy transfer processes.

PubMed

Matsuoka, Takeshi; Tanaka, Shigenori; Ebina, Kuniyoshi

2014-03-01

We propose a hierarchical reduction scheme to cope with coupled rate equations that describe the dynamics of multi-time-scale photosynthetic reactions. To numerically solve nonlinear dynamical equations containing a wide temporal range of rate constants, we first study a prototypical three-variable model. Using a separation of the time scale of rate constants combined with identified slow variables as (quasi-)conserved quantities in the fast process, we achieve a coarse-graining of the dynamical equations reduced to those at a slower time scale. By iteratively employing this reduction method, the coarse-graining of broadly multi-scale dynamical equations can be performed in a hierarchical manner. We then apply this scheme to the reaction dynamics analysis of a simplified model for an illuminated photosystem II, which involves many processes of electron and excitation-energy transfers with a wide range of rate constants. We thus confirm a good agreement between the coarse-grained and fully (finely) integrated results for the population dynamics. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Evaluation of Piecewise Polynomial Equations for Two Types of Thermocouples

PubMed Central

Chen, Andrew; Chen, Chiachung

2013-01-01

Thermocouples are the most frequently used sensors for temperature measurement because of their wide applicability, long-term stability and high reliability. However, one of the major utilization problems is the linearization of the transfer relation between temperature and output voltage of thermocouples. The linear calibration equation and its modules could be improved by using regression analysis to help solve this problem. In this study, two types of thermocouple and five temperature ranges were selected to evaluate the fitting agreement of different-order polynomial equations. Two quantitative criteria, the average of the absolute error values |e|ave and the standard deviation of calibration equation estd, were used to evaluate the accuracy and precision of these calibrations equations. The optimal order of polynomial equations differed with the temperature range. The accuracy and precision of the calibration equation could be improved significantly with an adequate higher degree polynomial equation. The technique could be applied with hardware modules to serve as an intelligent sensor for temperature measurement. PMID:24351627

The shape parameter and its modification for defining coastal profiles

NASA Astrophysics Data System (ADS)

Türker, Umut; Kabdaşli, M. Sedat

2009-03-01

The shape parameter is important for the theoretical description of the sandy coastal profiles. This parameter has previously been defined as a function of the sediment-settling velocity. However, the settling velocity cannot be characterized over a wide range of sediment grains. This, in turn, limits the calculation of the shape parameter over a wide range. This paper provides a simpler and faster analytical equation to describe the shape parameter. The validity of the equation has been tested and compared with the previously estimated values given in both graphical and tabular forms. The results of this study indicate that the analytical solutions of the shape parameter improved the usability of profile better than graphical solutions, predicting better results both at the surf zone and offshore.

Wide-range simulation of elastoplastic wave fronts and failure of solids under high-speed loading

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

Saveleva, Natalia, E-mail: saveleva@icmm.ru; Bayandin, Yuriy, E-mail: buv@icmm.ru; Naimark, Oleg, E-mail: naimark@icmm.ru

2015-10-27

The aim of this paper is numerical study of deformation processes and failure of vanadium under shock-wave loading. According developed statistical theory of solid with mesoscopic defects the constitutive equations were proposed in terms of two structural variables characterizing behavior of defects ensembles: defect density tensor and structural scaling parameter. On the basis of wide-range constitutive equations the mathematical model of deformation behavior and failure of vanadium was developed taking into account the bond relaxation mechanisms, multistage of fracture and nonlinearity kinetic of defects. Results of numerical simulation allow the description of the major effects of shock wave propagation (elasticmore » precursor decay, grow of spall strength under grow strain rate)« less

The acoustic power of a vibrating clamped circular plate revisited in the wide low frequency range using expansion into the radial polynomials.

PubMed

Rdzanek, Wojciech P

2016-06-01

This study deals with the classical problem of sound radiation of an excited clamped circular plate embedded into a flat rigid baffle. The system of the two coupled differential equations is solved, one for the excited and damped vibrations of the plate and the other one-the Helmholtz equation. An approach using the expansion into radial polynomials leads to results for the modal impedance coefficients useful for a comprehensive numerical analysis of sound radiation. The results obtained are accurate and efficient in a wide low frequency range and can easily be adopted for a simply supported circular plate. The fluid loading is included providing accurate results in resonance.

Program for solution of ordinary differential equations

NASA Technical Reports Server (NTRS)

Sloate, H.

1973-01-01

A program for the solution of linear and nonlinear first order ordinary differential equations is described and user instructions are included. The program contains a new integration algorithm for the solution of initial value problems which is particularly efficient for the solution of differential equations with a wide range of eigenvalues. The program in its present form handles up to ten state variables, but expansion to handle up to fifty state variables is being investigated.

1/f Noise from nonlinear stochastic differential equations.

PubMed

Ruseckas, J; Kaulakys, B

2010-03-01

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

NASA Astrophysics Data System (ADS)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

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…

Buckling Analysis for Stiffened Anisotropic Circular Cylinders Based on Sanders Nonlinear Shell Theory

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2014-01-01

Nonlinear and bifurcation buckling equations for elastic, stiffened, geometrically perfect, right-circular cylindrical, anisotropic shells subjected to combined loads are presented that are based on Sanders' shell theory. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated-composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discrepancies between the results obtained by using Donnell's equations and variants of Sanders' equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.

Methane storage in nanoporous material at supercritical temperature over a wide range of pressures

PubMed Central

Wu, Keliu; Chen, Zhangxin; Li, Xiangfang; Dong, Xiaohu

2016-01-01

The methane storage behavior in nanoporous material is significantly different from that of a bulk phase, and has a fundamental role in methane extraction from shale and its storage for vehicular applications. Here we show that the behavior and mechanisms of the methane storage are mainly dominated by the ratio of the interaction between methane molecules and nanopores walls to the methane intermolecular interaction, and a geometric constraint. By linking the macroscopic properties of the methane storage to the microscopic properties of a system of methane molecules-nanopores walls, we develop an equation of state for methane at supercritical temperature over a wide range of pressures. Molecular dynamic simulation data demonstrates that this equation is able to relate very well the methane storage behavior with each of the key physical parameters, including a pore size and shape and wall chemistry and roughness. Moreover, this equation only requires one fitted parameter, and is simple, reliable and powerful in application. PMID:27628747

Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities.

PubMed

Hernández-Andrés, J; Lee, R L; Romero, J

1999-09-20

Natural outdoor illumination daily undergoes large changes in its correlated color temperature (CCT), yet existing equations for calculating CCT from chromaticity coordinates span only part of this range. To improve both the gamut and accuracy of these CCT calculations, we use chromaticities calculated from our measurements of nearly 7000 daylight and skylight spectra to test an equation that accurately maps CIE 1931 chromaticities x and y into CCT. We extend the work of McCamy [Color Res. Appl. 12, 285-287 (1992)] by using a chromaticity epicenter for CCT and the inverse slope of the line that connects it to x and y. With two epicenters for different CCT ranges, our simple equation is accurate across wide chromaticity and CCT ranges (3000-10(6) K) spanned by daylight and skylight.

General equations for the motions of ice crystals and water drops in gravitational and electric fields

NASA Technical Reports Server (NTRS)

Nisbet, John S.

1988-01-01

General equations for the Reynolds number of a variety of types of ice crystals and water drops are given in terms of the Davies, Bond, and Knudsen numbers. The equations are in terms of the basic physical parameters of the system and are valid for calculating velocities in gravitational and electric fields over a very wide range of sizes and atmospheric conditions. The equations are asymptotically matched at the bottom and top of the size spectrum, useful when checking large computer codes. A numerical system for specifying the dimensional properties of ice crystals is introduced. Within the limits imposed by such variables as particle density, which have large deviations, the accuracy of velocities appears to be within 10 percent over the entire range of sizes of interest.

Calculation of thermodynamic functions of aluminum plasma for high-energy-density systems

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

Shumaev, V. V., E-mail: shumaev@student.bmstu.ru

The results of calculating the degree of ionization, the pressure, and the specific internal energy of aluminum plasma in a wide temperature range are presented. The TERMAG computational code based on the Thomas–Fermi model was used at temperatures T > 105 K, and the ionization equilibrium model (Saha model) was applied at lower temperatures. Quantitatively similar results were obtained in the temperature range where both models are applicable. This suggests that the obtained data may be joined to produce a wide-range equation of state.

Simulation of Flow for an Immersed Sphere

DTIC Science & Technology

2016-12-01

Problem Set-Up .................................................................................................... 18 4.0 Results...CFD computer codes are now widely applied in the commercial world for aircraft design with little requirement for wind tunnel testing. A wide range of...as the burning of fuel in gas turbine combustors. Intricate multiphase physics equations couple the behavior of gas phase CFD algorithms with

Solving Second-Order Ordinary Differential Equations without Using Complex Numbers

ERIC Educational Resources Information Center

Kougias, Ioannis E.

2009-01-01

Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex…

Ionic channels: natural nanotubes described by the drift diffusion equations

NASA Astrophysics Data System (ADS)

Eisenberg, Bob

2000-05-01

Ionic channels are a large class of proteins with holes down their middle that control a wide range of cellular functions important in health and disease. Ionic channels can be analysed using a combination of the Poisson and drift diffusion equations familiar from computational electronics because their behavior is dominated by the electrical properties of their simple structure.

Linearized lattice Boltzmann method for micro- and nanoscale flow and heat transfer.

PubMed

Shi, Yong; Yap, Ying Wan; Sader, John E

2015-07-01

Ability to characterize the heat transfer in flowing gases is important for a wide range of applications involving micro- and nanoscale devices. Gas flows away from the continuum limit can be captured using the Boltzmann equation, whose analytical solution poses a formidable challenge. An efficient and accurate numerical simulation of the Boltzmann equation is thus highly desirable. In this article, the linearized Boltzmann Bhatnagar-Gross-Krook equation is used to develop a hierarchy of thermal lattice Boltzmann (LB) models based on half-space Gaussian-Hermite (GH) quadrature ranging from low to high algebraic precision, using double distribution functions. Simplified versions of the LB models in the continuum limit are also derived, and are shown to be consistent with existing thermal LB models for noncontinuum heat transfer reported in the literature. Accuracy of the proposed LB hierarchy is assessed by simulating thermal Couette flows for a wide range of Knudsen numbers. Effects of the underlying quadrature schemes (half-space GH vs full-space GH) and continuum-limit simplifications on computational accuracy are also elaborated. The numerical findings in this article provide direct evidence of improved computational capability of the proposed LB models for modeling noncontinuum flows and heat transfer at small length scales.

Rigorous derivation of porous-media phase-field equations

NASA Astrophysics Data System (ADS)

Schmuck, Markus; Kalliadasis, Serafim

2017-11-01

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

Mathematical model of one-man air revitalization system

NASA Technical Reports Server (NTRS)

1976-01-01

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

An examination of the rheology of flocculated clay suspensions

NASA Astrophysics Data System (ADS)

Spearman, Jeremy

2017-04-01

A dense cohesive sediment suspension, sometimes referred to as fluid mud, is a thixotropic fluid with a true yield stress. Current rheological formulations struggle to reconcile the structural dynamics of cohesive sediment suspensions with the equilibrium behaviour of these suspensions across the range of concentrations and shear. This paper is concerned with establishing a rheological framework for the range of sediment concentrations from the yield point to Newtonian flow. The shear stress equation is based on floc fractal theory, put forward by Mills and Snabre (1988). This results in a Casson-like rheology equation. Additional structural dynamics is then added, using a theory on the self-similarity of clay suspensions proposed by Coussot (1995), giving an equation which has the ability to match the equilibrium and time-dependent viscous rheology of a wide range of suspensions of different concentration and mineralogy.

Statistical Extremes of Turbulence and a Cascade Generalisation of Euler's Gyroscope Equation

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, Ioulia; Scherzer, Daniel

2016-04-01

Turbulence refers to a rather well defined hydrodynamical phenomenon uncovered by Reynolds. Nowadays, the word turbulence is used to designate the loss of order in many different geophysical fields and the related fundamental extreme variability of environmental data over a wide range of scales. Classical statistical techniques for estimating the extremes, being largely limited to statistical distributions, do not take into account the mechanisms generating such extreme variability. An alternative approaches to nonlinear variability are based on a fundamental property of the non-linear equations: scale invariance, which means that these equations are formally invariant under given scale transforms. Its specific framework is that of multifractals. In this framework extreme variability builds up scale by scale leading to non-classical statistics. Although multifractals are increasingly understood as a basic framework for handling such variability, there is still a gap between their potential and their actual use. In this presentation we discuss how to dealt with highly theoretical problems of mathematical physics together with a wide range of geophysical applications. We use Euler's gyroscope equation as a basic element in constructing a complex deterministic system that preserves not only the scale symmetry of the Navier-Stokes equations, but some more of their symmetries. Euler's equation has been not only the object of many theoretical investigations of the gyroscope device, but also generalised enough to become the basic equation of fluid mechanics. Therefore, there is no surprise that a cascade generalisation of this equation can be used to characterise the intermittency of turbulence, to better understand the links between the multifractal exponents and the structure of a simplified, but not simplistic, version of the Navier-Stokes equations. In a given way, this approach is similar to that of Lorenz, who studied how the flap of a butterfly wing could generate a cyclone with the help of a 3D ordinary differential system. Being well supported by the extensive numerical results, the cascade generalisation of Euler's gyroscope equation opens new horizons for predictability and predictions of processes having long-range dependences.

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.

Osmotic potential calculations of inorganic and organic aqueous solutions over wide solute concentration levels and temperatures.

PubMed

Cochrane, T T; Cochrane, T A

2016-01-01

To demonstrate that the authors' new "aqueous solution vs pure water" equation to calculate osmotic potential may be used to calculate the osmotic potentials of inorganic and organic aqueous solutions over wide ranges of solute concentrations and temperatures. Currently, the osmotic potentials of solutions used for medical purposes are calculated from equations based on the thermodynamics of the gas laws which are only accurate at low temperature and solute concentration levels. Some solutions used in medicine may need their osmotic potentials calculated more accurately to take into account solute concentrations and temperatures. The authors experimented with their new equation for calculating the osmotic potentials of inorganic and organic aqueous solutions up to and beyond body temperatures by adjusting three of its factors; (a) the volume property of pure water, (b) the number of "free" water molecules per unit volume of solution, "Nf," and (c) the "t" factor expressing the cooperative structural relaxation time of pure water at given temperatures. Adequate information on the volume property of pure water at different temperatures is available in the literature. However, as little information on the relative densities of inorganic and organic solutions, respectively, at varying temperatures needed to calculate Nf was available, provisional equations were formulated to approximate values. Those values together with tentative t values for different temperatures chosen from values calculated by different workers were substituted into the authors' equation to demonstrate how osmotic potentials could be estimated over temperatures up to and beyond bodily temperatures. The provisional equations formulated to calculate Nf, the number of free water molecules per unit volume of inorganic and organic solute solutions, respectively, over wide concentration ranges compared well with the calculations of Nf using recorded relative density data at 20 °C. They were subsequently used to estimate Nf values at temperatures up to and excess of body temperatures. Those values, together with t values at temperatures up to and in excess of body temperatures recorded in the literature, were substituted in the authors' equation for the provisional calculation of osmotic potentials. The calculations indicated that solution temperatures and solute concentrations have a marked effect on osmotic potentials. Following work to measure the relative densities of aqueous solutions for the calculation of Nf values and the determination of definitive t values up to and beyond bodily temperatures, the authors' equation would enable the accurate estimations of the osmotic potentials of wide concentrations of aqueous solutions of inorganic and organic solutes over the temperature range. The study illustrates that not only solute concentrations but also temperatures have a marked effect on osmotic potentials, an observation of medical and biological significance.

A Computational Fluid Dynamics Study of Transitional Flows in Low-Pressure Turbines under a Wide Range of Operating Conditions

NASA Technical Reports Server (NTRS)

Suzen, Y. B.; Huang, P. G.; Ashpis, D. E.; Volino, R. J.; Corke, T. C.; Thomas, F. O.; Huang, J.; Lake, J. P.; King, P. I.

2007-01-01

A transport equation for the intermittency factor is employed to predict the transitional flows in low-pressure turbines. The intermittent behavior of the transitional flows is taken into account and incorporated into computations by modifying the eddy viscosity, mu(sub p) with the intermittency factor, gamma. Turbulent quantities are predicted using Menter's two-equation turbulence model (SST). The intermittency factor is obtained from a transport equation model which can produce both the experimentally observed streamwise variation of intermittency and a realistic profile in the cross stream direction. The model had been previously validated against low-pressure turbine experiments with success. In this paper, the model is applied to predictions of three sets of recent low-pressure turbine experiments on the Pack B blade to further validate its predicting capabilities under various flow conditions. Comparisons of computational results with experimental data are provided. Overall, good agreement between the experimental data and computational results is obtained. The new model has been shown to have the capability of accurately predicting transitional flows under a wide range of low-pressure turbine conditions.

Accuracy of perturbative master equations.

PubMed

Fleming, C H; Cummings, N I

2011-03-01

We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.

New explicit equations for the accurate calculation of the growth and evaporation of hydrometeors by the diffusion of water vapor

NASA Technical Reports Server (NTRS)

Srivastava, R. C.; Coen, J. L.

1992-01-01

The traditional explicit growth equation has been widely used to calculate the growth and evaporation of hydrometeors by the diffusion of water vapor. This paper reexamines the assumptions underlying the traditional equation and shows that large errors (10-30 percent in some cases) result if it is used carelessly. More accurate explicit equations are derived by approximating the saturation vapor-density difference as a quadratic rather than a linear function of the temperature difference between the particle and ambient air. These new equations, which reduce the error to less than a few percent, merit inclusion in a broad range of atmospheric models.

Three dimensional iterative beam propagation method for optical waveguide devices

NASA Astrophysics Data System (ADS)

Ma, Changbao; Van Keuren, Edward

2006-10-01

The finite difference beam propagation method (FD-BPM) is an effective model for simulating a wide range of optical waveguide structures. The classical FD-BPMs are based on the Crank-Nicholson scheme, and in tridiagonal form can be solved using the Thomas method. We present a different type of algorithm for 3-D structures. In this algorithm, the wave equation is formulated into a large sparse matrix equation which can be solved using iterative methods. The simulation window shifting scheme and threshold technique introduced in our earlier work are utilized to overcome the convergence problem of iterative methods for large sparse matrix equation and wide-angle simulations. This method enables us to develop higher-order 3-D wide-angle (WA-) BPMs based on Pade approximant operators and the multistep method, which are commonly used in WA-BPMs for 2-D structures. Simulations using the new methods will be compared to the analytical results to assure its effectiveness and applicability.

CFD comparison with centrifugal compressor measurements on a wide operating range

NASA Astrophysics Data System (ADS)

Le Sausse, P.; Fabrie, P.; Arnou, D.; Clunet, F.

2013-04-01

Centrifugal compressors are widely used in industrial applications thanks to their high efficiency. They are able to provide a wide operating range before reaching the flow barrier or surge limits. Performances and range are described by compressor maps obtained experimentally. After a description of performance test rig, this article compares measured centrifugal compressor performances with computational fluid dynamics results. These computations are performed at steady conditions with R134a refrigerant as fluid. Navier-Stokes equations, coupled with k-ɛ turbulence model, are solved by the commercial software ANSYS-CFX by means of volume finite method. Input conditions are varied in order to calculate several speed lines. Theoretical isentropic efficiency and theoretical surge line are finally compared to experimental data.

Single wall penetration equations

NASA Technical Reports Server (NTRS)

Hayashida, K. B.; Robinson, J. H.

1991-01-01

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

The Noble-Abel Stiffened-Gas equation of state

NASA Astrophysics Data System (ADS)

Le Métayer, Olivier; Saurel, Richard

2016-04-01

Hyperbolic two-phase flow models have shown excellent ability for the resolution of a wide range of applications ranging from interfacial flows to fluid mixtures with several velocities. These models account for waves propagation (acoustic and convective) and consist in hyperbolic systems of partial differential equations. In this context, each phase is compressible and needs an appropriate convex equation of state (EOS). The EOS must be simple enough for intensive computations as well as boundary conditions treatment. It must also be accurate, this being challenging with respect to simplicity. In the present approach, each fluid is governed by a novel EOS named "Noble Abel stiffened gas," this formulation being a significant improvement of the popular "Stiffened Gas (SG)" EOS. It is a combination of the so-called "Noble-Abel" and "stiffened gas" equations of state that adds repulsive effects to the SG formulation. The determination of the various thermodynamic functions and associated coefficients is the aim of this article. We first use thermodynamic considerations to determine the different state functions such as the specific internal energy, enthalpy, and entropy. Then we propose to determine the associated coefficients for a liquid in the presence of its vapor. The EOS parameters are determined from experimental saturation curves. Some examples of liquid-vapor fluids are examined and associated parameters are computed with the help of the present method. Comparisons between analytical and experimental saturation curves show very good agreement for wide ranges of temperature for both liquid and vapor.

Visualization in mechanics: the dynamics of an unbalanced roller

NASA Astrophysics Data System (ADS)

Cumber, Peter S.

2017-04-01

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 user interface for its numerical solution in MATLAB. This allows a student's focus to be on the influence of different parameters on the system dynamics. The simulation tool can be used as a dynamics demonstrator in a lecture or as an educational tool driven by the imagination of the student. By way of demonstration the simulation tool has been applied to a range of roller-pivot arm configurations. In addition, approximations to the equations of motion are explored and a second-order model is shown to be accurate for a limited range of parameters.

Incomplete augmented Lagrangian preconditioner for steady incompressible Navier-Stokes equations.

PubMed

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.

Theory of a general class of dissipative processes.

NASA Technical Reports Server (NTRS)

Hale, J. K.; Lasalle, J. P.; Slemrod, M.

1972-01-01

Development of a theory of periodic processes that is of sufficient generality for being applied to systems defined by partial differential equations (distributed parameter systems) and functional differential equations of the retarded and neutral type (hereditary systems), as well as to systems arising in the theory of elasticity. In particular, the attempt is made to develop a meaningful general theory of dissipative periodic systems with a wide range of applications.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Impact of charge transport on current–voltage characteristics and power-conversion efficiency of organic solar cells

PubMed Central

Würfel, Uli; Neher, Dieter; Spies, Annika; Albrecht, Steve

2015-01-01

This work elucidates the impact of charge transport on the photovoltaic properties of organic solar cells. Here we show that the analysis of current–voltage curves of organic solar cells under illumination with the Shockley equation results in values for ideality factor, photocurrent and parallel resistance, which lack physical meaning. Drift-diffusion simulations for a wide range of charge-carrier mobilities and illumination intensities reveal significant carrier accumulation caused by poor transport properties, which is not included in the Shockley equation. As a consequence, the separation of the quasi Fermi levels in the organic photoactive layer (internal voltage) differs substantially from the external voltage for almost all conditions. We present a new analytical model, which considers carrier transport explicitly. The model shows excellent agreement with full drift-diffusion simulations over a wide range of mobilities and illumination intensities, making it suitable for realistic efficiency predictions for organic solar cells. PMID:25907581

A time-accurate implicit method for chemical non-equilibrium flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun

1992-01-01

A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

Ignition delay times of benzene and toluene with oxygen in argon mixtures

NASA Technical Reports Server (NTRS)

Burcat, A.; Snyder, C.; Brabbs, T.

1985-01-01

The ignition delay times of benzene and toluene with oxygen diluted in argon were investigated over a wide range of conditions. For benzene the concentration ranges were 0.42 to 1.69 percent fuel and 3.78 to 20.3 percent oxygen. The temperature range was 1212 to 1748 K and the reflected shock pressures were 1.7 to 7.89 atm. Statistical evaluation of the benzene experiments provided an overall equation which is given. For toluene the concentration ranges were 0.5 to 1.5 percent fuel and 4.48 to 13.45 percent oxygen. The temperature range was 1339 to 1797 K and the reflected shock pressures were 1.95 to 8.85 atm. The overall ignition delay equation for toluene after a statistical evaluation is also given. Detailed experimental information is provided.

Scour assessments and sediment-transport simulation for selected bridge sites in South Dakota

USGS Publications Warehouse

Niehus, C.A.

1996-01-01

Scour at bridges is a major concern in the design of new bridges and in the evaluation of structural stability of existing bridges. Equations for estimating pier, contraction, and abutment scour have been developed from numerous laboratory studies using sand-bed flumes, but little verification of these scour equations has been done for actual rivers with various bed conditions. This report describes the results of reconnaissance and detailed scour assessments and a sediment-transport simulation for selected bridge sites in South Dakota. Reconnaissance scour assessments were done during 1991 for 32 bridge sites. The reconnaissance assessments for each bridge site included compilation of general and structural data, field inspection to record and measure pertinent scour variables, and evaluation of scour susceptibility using various scour-index forms. Observed pier scour at the 32 sites ranged from 0 to 7 feet, observed contraction scour ranged from 0 to 4 feet, and observed abutment scour ranged from 0 to 10 feet. Thirteen bridge sites having high potential for scour were selected for detailed assessments, which were accomplished during 1992-95. These detailed assessments included prediction of scour depths for 2-, 100-, and 500-year flows using selected published scour equations; measurement of scour during high flows; comparison of measured and predicted scour; and identification of which scour equations best predict actual scour. The medians of predicted pier-scour depth at each of the 13 bridge sites (using 13 scour equations) ranged from 2.4 to 6.8 feet for the 2-year flows and ranged from 3.4 to 13.3 feet for the 500-year flows. The maximum pier scour measured during high flows ranged from 0 to 8.5 feet. Statistical comparison (Spearman rank correlation) of predicted pier-scour depths (using flow data col- lected during scour measurements) indicate that the Laursen, Shen (method b), Colorado State University, and Blench (method b) equations correlate closer with measured scour than do the other prediction equations. The predicted pier-scour depths using the Varzeliotis and Carstens equations have weak statistical rela- tions with measured scour depths. Medians of predicted pier-scour depth from the Shen (method a), Chitale, Bata, and Carstens equations are statistically equal to the median of measured pier-scour depths, based on the Wilcoxon signed-ranks test. The medians of contraction scour depth at each of the 13 bridge sites (using one equation) ranged from -0.1 foot for the 2- year flows to 23.2 feet for the 500-year flows. The maximum contraction scour measured during high flows ranged from 0 to 3.0 feet. The contraction- scour prediction equation substantially overestimated the scour depths in almost all comparisons with the measured scour depths. A significant reason for this discrepancy is due to the wide flood plain (as wide as 5,000 feet) at most of the bridge sites that were investigated. One possible way to reduce this effect for bridge design is to make a decision on what is the effective approach section and thereby limit the size of the bridge flow approach width. The medians of abutment-scour depth at each of the 13 bridge sites (using five equations) ranged from 8.2 to 16.5 feet for the 2-year flows and ranged from 5.7 to 41 feet for the 500-year flows. The maximum abutment scour measured during high flows ranged from 0 to 4.0 feet. The abutment-scour prediction equations also substantially overestimated the scour depths in almost all comparisons with the measured scour depths. The Liu and others (live bed) equation predicted abutment-scour depths substantially lower than the other four abutment-scour equations and closer to the actual measured scour depths. However, this equation at times predicted greater scour depths for 2-year flows than it did for 500-year flows, making its use highly questionable. Again, limiting the bridge flow approach width would produce more reasonable predicted abutment scour.

New collector efficiency equation for colloid filtration in both natural and engineered flow conditions

NASA Astrophysics Data System (ADS)

Nelson, Kirk E.; Ginn, Timothy R.

2011-05-01

A new equation for the collector efficiency (η) of the colloid filtration theory (CFT) is developed via nonlinear regression on the numerical data generated by a large number of Lagrangian simulations conducted in Happel's sphere-in-cell porous media model over a wide range of environmentally relevant conditions. The new equation expands the range of CFT's applicability in the natural subsurface primarily by accommodating departures from power law dependence of η on the Peclet and gravity numbers, a necessary but as of yet unavailable feature for applying CFT to large-scale field transport (e.g., of nanoparticles, radionuclides, or genetically modified organisms) under low groundwater velocity conditions. The new equation also departs from prior equations for colloids in the nanoparticle size range at all fluid velocities. These departures are particularly relevant to subsurface colloid and colloid-facilitated transport where low permeabilities and/or hydraulic gradients lead to low groundwater velocities and/or to nanoparticle fate and transport in porous media in general. We also note the importance of consistency in the conceptualization of particle flux through the single collector model on which most η equations are based for the purpose of attaining a mechanistic understanding of the transport and attachment steps of deposition. A lack of sufficient data for small particles and low velocities warrants further experiments to draw more definitive and comprehensive conclusions regarding the most significant discrepancies between the available equations.

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

PubMed Central

Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun

2013-01-01

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888

Bimolecular Recombination Kinetics of an Exciton-Trion Gas

DTIC Science & Technology

2015-07-01

3-D systems. Whereas a linear time-dependent system of first-order differential equations has only trivial steady- state solutions (all carrier...derivatives to zero, which reduces the system (Eq. 9) to the following set of 3 algebraic equations: ( ) ( ) ( ) ( ) 1 2 210 2 110...crossover around 20 ns. The exciton curve is nearly linear over a wide range from 10 ns to 50 ns. Fig. 2 Time dependence of carrier species for Λ = 4

Osmotic potential calculations of inorganic and organic aqueous solutions over wide solute concentration levels and temperatures

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

Cochrane, T. T., E-mail: agteca@hotmail.com; Cochrane, T. A., E-mail: tom.cochrane@canterbury.ac.nz

Purpose: To demonstrate that the authors’ new “aqueous solution vs pure water” equation to calculate osmotic potential may be used to calculate the osmotic potentials of inorganic and organic aqueous solutions over wide ranges of solute concentrations and temperatures. Currently, the osmotic potentials of solutions used for medical purposes are calculated from equations based on the thermodynamics of the gas laws which are only accurate at low temperature and solute concentration levels. Some solutions used in medicine may need their osmotic potentials calculated more accurately to take into account solute concentrations and temperatures. Methods: The authors experimented with their newmore » equation for calculating the osmotic potentials of inorganic and organic aqueous solutions up to and beyond body temperatures by adjusting three of its factors; (a) the volume property of pure water, (b) the number of “free” water molecules per unit volume of solution, “N{sub f},” and (c) the “t” factor expressing the cooperative structural relaxation time of pure water at given temperatures. Adequate information on the volume property of pure water at different temperatures is available in the literature. However, as little information on the relative densities of inorganic and organic solutions, respectively, at varying temperatures needed to calculate N{sub f} was available, provisional equations were formulated to approximate values. Those values together with tentative t values for different temperatures chosen from values calculated by different workers were substituted into the authors’ equation to demonstrate how osmotic potentials could be estimated over temperatures up to and beyond bodily temperatures. Results: The provisional equations formulated to calculate N{sub f}, the number of free water molecules per unit volume of inorganic and organic solute solutions, respectively, over wide concentration ranges compared well with the calculations of N{sub f} using recorded relative density data at 20 °C. They were subsequently used to estimate N{sub f} values at temperatures up to and excess of body temperatures. Those values, together with t values at temperatures up to and in excess of body temperatures recorded in the literature, were substituted in the authors’ equation for the provisional calculation of osmotic potentials. The calculations indicated that solution temperatures and solute concentrations have a marked effect on osmotic potentials. Conclusions: Following work to measure the relative densities of aqueous solutions for the calculation of N{sub f} values and the determination of definitive t values up to and beyond bodily temperatures, the authors’ equation would enable the accurate estimations of the osmotic potentials of wide concentrations of aqueous solutions of inorganic and organic solutes over the temperature range. The study illustrates that not only solute concentrations but also temperatures have a marked effect on osmotic potentials, an observation of medical and biological significance.« less

Determination of transport wind speed in the gaussian plume diffusion equation for low-lying point sources

NASA Astrophysics Data System (ADS)

Wang, I. T.

A general method for determining the effective transport wind speed, overlineu, in the Gaussian plume equation is discussed. Physical arguments are given for using the generalized overlineu instead of the often adopted release-level wind speed with the plume diffusion equation. Simple analytical expressions for overlineu applicable to low-level point releases and a wide range of atmospheric conditions are developed. A non-linear plume kinematic equation is derived using these expressions. Crosswind-integrated SF 6 concentration data from the 1983 PNL tracer experiment are used to evaluate the proposed analytical procedures along with the usual approach of using the release-level wind speed. Results of the evaluation are briefly discussed.

Multiphase Equations of State for Polymer Materials at High Dynamic Pressures

NASA Astrophysics Data System (ADS)

Khishchenko, Konstantin V.

2015-06-01

Equations of state for materials over a wide range of pressures and temperatures are necessary for numerical simulations of shock-wave processes in condensed matter. Accuracy of calculation results is determined mainly by adequacy of equation of state of a medium. In this work, a new multiphase equation-of-state model is proposed with taking into account the polymorphic phase transformations, melting and evaporation. Thermodynamic calculations are carried out for 2 polymer materials (polymethylmethacrylate and polytetrafluoroethylene) in a broad region of the phase diagram. Obtained results are presented in comparison with available data of experiments at high dynamic pressures in shock and release waves. This work is supported by RSF, Grant 14-50-00124.

Spatial Stochastic Intracellular Kinetics: A Review of Modelling Approaches.

PubMed

Smith, Stephen; Grima, Ramon

2018-05-21

Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers.

The Noble-Abel Stiffened-Gas equation of state

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

Le Métayer, Olivier, E-mail: olivier.lemetayer@univ-amu.fr; Saurel, Richard, E-mail: richard.saurel@univ-amu.fr; RS2N, 371 Chemin de Gaumin, 83640 Saint-Zacharie

2016-04-15

Hyperbolic two-phase flow models have shown excellent ability for the resolution of a wide range of applications ranging from interfacial flows to fluid mixtures with several velocities. These models account for waves propagation (acoustic and convective) and consist in hyperbolic systems of partial differential equations. In this context, each phase is compressible and needs an appropriate convex equation of state (EOS). The EOS must be simple enough for intensive computations as well as boundary conditions treatment. It must also be accurate, this being challenging with respect to simplicity. In the present approach, each fluid is governed by a novel EOSmore » named “Noble Abel stiffened gas,” this formulation being a significant improvement of the popular “Stiffened Gas (SG)” EOS. It is a combination of the so-called “Noble-Abel” and “stiffened gas” equations of state that adds repulsive effects to the SG formulation. The determination of the various thermodynamic functions and associated coefficients is the aim of this article. We first use thermodynamic considerations to determine the different state functions such as the specific internal energy, enthalpy, and entropy. Then we propose to determine the associated coefficients for a liquid in the presence of its vapor. The EOS parameters are determined from experimental saturation curves. Some examples of liquid-vapor fluids are examined and associated parameters are computed with the help of the present method. Comparisons between analytical and experimental saturation curves show very good agreement for wide ranges of temperature for both liquid and vapor.« less

PAB3D: Its History in the Use of Turbulence Models in the Simulation of Jet and Nozzle Flows

NASA Technical Reports Server (NTRS)

Abdol-Hamid, Khaled S.; Pao, S. Paul; Hunter, Craig A.; Deere, Karen A.; Massey, Steven J.; Elmiligui, Alaa

2006-01-01

This is a review paper for PAB3D s history in the implementation of turbulence models for simulating jet and nozzle flows. We describe different turbulence models used in the simulation of subsonic and supersonic jet and nozzle flows. The time-averaged simulations use modified linear or nonlinear two-equation models to account for supersonic flow as well as high temperature mixing. Two multiscale-type turbulence models are used for unsteady flow simulations. These models require modifications to the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k-epsilon) model with a RANS/LES transition function, dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) formulation. All of these models are implemented in the three-dimensional Navier-Stokes code PAB3D. This paper discusses computational methods, code implementation, computed results for a wide range of nozzle configurations at various operating conditions, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions.

Simple Formulas and Results for Buckling-Resistance and Stiffness Design of Compression-Loaded Laminated-Composite Cylinders

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Mikulas, Martin M., Jr.

2009-01-01

Simple formulas for the buckling stress of homogeneous, specially orthotropic, laminated-composite cylinders are presented. The formulas are obtained by using nondimensional parameters and equations that facilitate general validation, and are validated against the exact solution for a wide range of cylinder geometries and laminate constructions. Results are presented that establish the ranges of the nondimensional parameters and coefficients used. General results, given in terms of the nondimensional parameters, are presented that encompass a wide range of geometries and laminate constructions. These general results also illustrate a wide spectrum of behavioral trends. Design-oriented results are also presented that provide a simple, clear indication of laminate composition on critical stress, critical strain, and axial stiffness. An example is provided to demonstrate the application of these results to thin-walled column designs.

The Drake Equation revisited

NASA Astrophysics Data System (ADS)

Konesky, Gregory

2009-08-01

In the almost half century since the Drake Equation was first conceived, a number of profound discoveries have been made that require each of the seven variables of this equation to be reconsidered. The discovery of hydrothermal vents on the ocean floor, for example, as well as the ever-increasing extreme conditions in which life is found on Earth, suggest a much wider range of possible extraterrestrial habitats. The growing consensus that life originated very early in Earth's history also supports this suggestion. The discovery of exoplanets with a wide range of host star types, and attendant habitable zones, suggests that life may be possible in planetary systems with stars quite unlike our Sun. Stellar evolution also plays an important part in that habitable zones are mobile. The increasing brightness of our Sun over the next few billion years, will place the Earth well outside the present habitable zone, but will then encompass Mars, giving rise to the notion that some Drake Equation variables, such as the fraction of planets on which life emerges, may have multiple values.

Capillary Rise: Validity of the Dynamic Contact Angle Models.

PubMed

Wu, Pingkeng; Nikolov, Alex D; Wasan, Darsh T

2017-08-15

The classical Lucas-Washburn-Rideal (LWR) equation, using the equilibrium contact angle, predicts a faster capillary rise process than experiments in many cases. The major contributor to the faster prediction is believed to be the velocity dependent dynamic contact angle. In this work, we investigated the dynamic contact angle models for their ability to correct the dynamic contact angle effect in the capillary rise process. We conducted capillary rise experiments of various wetting liquids in borosilicate glass capillaries and compared the model predictions with our experimental data. The results show that the LWR equations modified by the molecular kinetic theory and hydrodynamic model provide good predictions on the capillary rise of all the testing liquids with fitting parameters, while the one modified by Joos' empirical equation works for specific liquids, such as silicone oils. The LWR equation modified by molecular self-layering model predicts well the capillary rise of carbon tetrachloride, octamethylcyclotetrasiloxane, and n-alkanes with the molecular diameter or measured solvation force data. The molecular self-layering model modified LWR equation also has good predictions on the capillary rise of silicone oils covering a wide range of bulk viscosities with the same key parameter W(0), which results from the molecular self-layering. The advantage of the molecular self-layering model over the other models reveals the importance of the layered molecularly thin wetting film ahead of the main meniscus in the energy dissipation associated with dynamic contact angle. The analysis of the capillary rise of silicone oils with a wide range of bulk viscosities provides new insights into the capillary dynamics of polymer melts.

A New Wide-Range Equation of State for Xenon

NASA Astrophysics Data System (ADS)

Carpenter, John H.

2011-06-01

We describe the development of a new wide-range equation of state (EOS) for xenon. Three different prior EOS models predicted significant variations in behavior along the high pressure Hugoniot from an initial liquid state at 163.5 K and 2.97 g/cm3, which is near the triple point. Experimental measurements on Sandia's Z machine as well as density functional theory based molecular dynamics calculations both invalidate the prior EOS models in the pressure range from 200 to 840 GPa. The reason behind these EOS model disagreements is found to lie in the contribution from the thermal electronic models. A new EOS, based upon the standard separation of the Helmholtz free energy into ionic and electronic components, is constructed by combining the successful parts of prior models with a semi-empirical electronic model. Both the fluid and fcc solid phases are combined in a wide-range, multi-phase table. The new EOS is tabulated on a fine temperature and density grid, to preserve phase boundary information, and is available as table number 5191 in the LANL SESAME database. Improvements over prior EOS models are found not only along the Hugoniot, but also along the melting curve and in the region of the liquid-vapor critical point. *Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems

NASA Astrophysics Data System (ADS)

Plestenjak, Bor; Gheorghiu, Călin I.; Hochstenbach, Michiel E.

2015-10-01

In numerous science and engineering applications a partial differential equation has to be solved on some fairly regular domain that allows the use of the method of separation of variables. In several orthogonal coordinate systems separation of variables applied to the Helmholtz, Laplace, or Schrödinger equation leads to a multiparameter eigenvalue problem (MEP); important cases include Mathieu's system, Lamé's system, and a system of spheroidal wave functions. Although multiparameter approaches are exploited occasionally to solve such equations numerically, MEPs remain less well known, and the variety of available numerical methods is not wide. The classical approach of discretizing the equations using standard finite differences leads to algebraic MEPs with large matrices, which are difficult to solve efficiently. The aim of this paper is to change this perspective. We show that by combining spectral collocation methods and new efficient numerical methods for algebraic MEPs it is possible to solve such problems both very efficiently and accurately. We improve on several previous results available in the literature, and also present a MATLAB toolbox for solving a wide range of problems.

A study of numerical methods for hyperbolic conservation laws with stiff source terms

NASA Technical Reports Server (NTRS)

Leveque, R. J.; Yee, H. C.

1988-01-01

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

Optical soliton solutions of the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term

NASA Astrophysics Data System (ADS)

Kaplan, Melike; Hosseini, Kamyar; Samadani, Farzan; Raza, Nauman

2018-07-01

A wide range of problems in different fields of the applied sciences especially non-linear optics is described by non-linear Schrödinger's equations (NLSEs). In the present paper, a specific type of NLSEs known as the cubic-quintic non-linear Schrödinger's equation including an anti-cubic term has been studied. The generalized Kudryashov method along with symbolic computation package has been exerted to carry out this objective. As a consequence, a series of optical soliton solutions have formally been retrieved. It is corroborated that the generalized form of Kudryashov method is a direct, effectual, and reliable technique to deal with various types of non-linear Schrödinger's equations.

Prediction of high frequency core loss for electrical steel using the data provided by manufacturer

NASA Astrophysics Data System (ADS)

Roy, Rakesh; Dalal, Ankit; Kumar, Praveen

2016-07-01

This paper describes a technique to determine the core loss data, at high frequencies, using the loss data provided by the lamination manufacturer. Steinmetz equation is used in this proposed method to determine core loss at high frequency. This Steinmetz equation consists of static hysteresis and eddy current loss. The presented technique considers the coefficients of Steinmetz equation as variable with frequency and peak magnetic flux density. The high frequency core loss data, predicted using this model is compared with the catalogue data given by manufacturer and very good accuracy has been obtained for a wide range of frequency.

Stability and bifurcation analysis of a generalized scalar delay differential equation.

PubMed

Bhalekar, Sachin

2016-08-01

This paper deals with the stability and bifurcation analysis of a general form of equation D(α)x(t)=g(x(t),x(t-τ)) involving the derivative of order α ∈ (0, 1] and a constant delay τ ≥ 0. The stability of equilibrium points is presented in terms of the stability regions and critical surfaces. We provide a necessary condition to exist chaos in the system also. A wide range of delay differential equations involving a constant delay can be analyzed using the results proposed in this paper. The illustrative examples are provided to explain the theory.

Evolution of statistical averages: An interdisciplinary proposal using the Chapman-Enskog method

NASA Astrophysics Data System (ADS)

Mariscal-Sanchez, A.; Sandoval-Villalbazo, A.

2017-08-01

This work examines the idea of applying the Chapman-Enskog (CE) method for approximating the solution of the Boltzmann equation beyond the realm of physics, using an information theory approach. Equations describing the evolution of averages and their fluctuations in a generalized phase space are established up to first-order in the Knudsen parameter which is defined as the ratio of the time between interactions (mean free time) and a characteristic macroscopic time. Although the general equations here obtained may be applied in a wide range of disciplines, in this paper, only a particular case related to the evolution of averages in speculative markets is examined.

Development of One-Group and Two-Group Interfacial Area Transport Equation

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

Ishii, M.; Kim, S.

A dynamic approach employing the interfacial area transport equation is presented to replace the static flow regime dependent correlations for the interfacial area concentration. The current study derives the transport equations for the bubble number, volume, and interfacial area concentration. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, both one-group and two-group interfacial area transport equations are developed along with the necessary constitutive relations. The framework for the complicated source and sink terms in the two-group transport equation is also presented by identifying the major intragroup and intergroup bubble interaction mechanisms. In view ofmore » evaluating the theoretical model, the one-group interfacial area transport equation is benchmarked based on the available data obtained in a wide range of air-water bubbly flow in round tubes of various diameters. In general, the results show good agreement within the measurement error of {+-}10%.« less

Determination of the glass-transition temperature of proteins from a viscometric approach.

PubMed

Monkos, Karol

2015-03-01

All fully hydrated proteins undergo a distinct change in their dynamical properties at glass-transition temperature Tg. To determine indirectly this temperature for dry albumins, the viscosity measurements of aqueous solutions of human, equine, ovine, porcine and rabbit serum albumin have been conducted at a wide range of concentrations and at temperatures ranging from 278 K to 318 K. Viscosity-temperature dependence of the solutions is discussed on the basis of the three parameters equation resulting from Avramov's model. One of the parameter in the Avramov's equation is the glass-transition temperature. For all studied albumins, Tg of a solution monotonically increases with increasing concentration. The glass-transition temperature of a solution depends both on Tg for a dissolved dry protein Tg,p and water Tg,w. To obtain Tg,p for each studied albumin the modified Gordon-Taylor equation was applied. This equation describes the dependence of Tg of a solution on concentration, and Tg,p and a parameter depending on the strength of the protein-solvent interaction are the fitting parameters. Thus determined the glass-transition temperature for the studied dry albumins is in the range (215.4-245.5)K. Copyright © 2014 Elsevier B.V. All rights reserved.

Get Your Wishes Granted: Supplementary Funds for School Music Programs Are Available from a Wide Array of Sources, but Tapping into Them Requires Time, Effort, and Savvy

ERIC Educational Resources Information Center

Randall, Mac

2009-01-01

Music teachers across the country are taking advantage of a wide range of grants from any number of sources--cities and towns, states, the federal government, nonprofit foundations, businesses, even generous individuals--to lend extra strength to their programs. Finding the right grantor for one's program is a major part of the equation. Before…

A time-accurate algorithm for chemical non-equilibrium viscous flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, J.-S.; Chen, K.-H.; Choi, Y.

1992-01-01

A time-accurate, coupled solution procedure is described for the chemical nonequilibrium Navier-Stokes equations over a wide range of Mach numbers. This method employs the strong conservation form of the governing equations, but uses primitive variables as unknowns. Real gas properties and equilibrium chemistry are considered. Numerical tests include steady convergent-divergent nozzle flows with air dissociation/recombination chemistry, dump combustor flows with n-pentane-air chemistry, nonreacting flow in a model double annular combustor, and nonreacting unsteady driven cavity flows. Numerical results for both the steady and unsteady flows demonstrate the efficiency and robustness of the present algorithm for Mach numbers ranging from the incompressible limit to supersonic speeds.

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

A tabulation of pipe length to diameter ratios as a function of Mach number and pressure ratios for compressible flow

NASA Technical Reports Server (NTRS)

Dixon, G. V.; Barringer, S. R.; Gray, C. E.; Leatherman, A. D.

1975-01-01

Computer programs and resulting tabulations are presented of pipeline length-to-diameter ratios as a function of Mach number and pressure ratios for compressible flow. The tabulations are applicable to air, nitrogen, oxygen, and hydrogen for compressible isothermal flow with friction and compressible adiabatic flow with friction. Also included are equations for the determination of weight flow. The tabulations presented cover a wider range of Mach numbers for choked, adiabatic flow than available from commonly used engineering literature. Additional information presented, but which is not available from this literature, is unchoked, adiabatic flow over a wide range of Mach numbers, and choked and unchoked, isothermal flow for a wide range of Mach numbers.

Efficiency of laser beam utilization in gas laser cutting of materials

NASA Astrophysics Data System (ADS)

Galushkin, M. G.; Grishaev, R. V.

2018-02-01

Relying on the condition of dynamic matching of the process parameters in gas laser cutting, the dependence of the beam utilization factor on the cutting speed and the beam power has been determined. An energy balance equation has been derived for a wide range of cutting speed values.

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory.

PubMed

Danwanichakul, Panu; Glandt, Eduardo D

2004-11-15

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

Particle connectedness and cluster formation in sequential depositions of particles: Integral-equation theory

NASA Astrophysics Data System (ADS)

Danwanichakul, Panu; Glandt, Eduardo D.

2004-11-01

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

Seafloor identification in sonar imagery via simulations of Helmholtz equations and discrete optimization

NASA Astrophysics Data System (ADS)

Engquist, Björn; Frederick, Christina; Huynh, Quyen; Zhou, Haomin

2017-06-01

We present a multiscale approach for identifying features in ocean beds by solving inverse problems in high frequency seafloor acoustics. The setting is based on Sound Navigation And Ranging (SONAR) imaging used in scientific, commercial, and military applications. The forward model incorporates multiscale simulations, by coupling Helmholtz equations and geometrical optics for a wide range of spatial scales in the seafloor geometry. This allows for detailed recovery of seafloor parameters including material type. Simulated backscattered data is generated using numerical microlocal analysis techniques. In order to lower the computational cost of the large-scale simulations in the inversion process, we take advantage of a pre-computed library of representative acoustic responses from various seafloor parameterizations.

An Application of Gröbner Basis in Differential Equations of Physics

NASA Astrophysics Data System (ADS)

Chaharbashloo, Mohammad Saleh; Basiri, Abdolali; Rahmany, Sajjad; Zarrinkamar, Saber

2013-11-01

We apply the Gröbner basis to the ansatz method in quantum mechanics to obtain the energy eigenvalues and the wave functions in a very simple manner. There are important physical potentials such as the Cornell interaction which play significant roles in particle physics and can be treated via this technique. As a typical example, the algorithm is applied to the semi-relativistic spinless Salpeter equation under the Cornell interaction. Many other applications of the idea in a wide range of physical fields are listed as well.

A new variant of a scaling hypothesis and a fundamental equation of state based on it

NASA Astrophysics Data System (ADS)

Kudryavtseva, I. V.; Rykov, V. A.; Rykov, S. V.; Ustyuzhanin, E. E.

2018-01-01

This paper deals with a fundamental equation of state (FEOS) for substances. We have suggested a new method. It allows constructing FEOS that is based on the scaling theory of critical phenomena and describes thermodynamic properties related to liquid and gas phases of a substance in a wide range of the pressures and temperatures. In the framework of the methodological approach, we have provided: (i) a transition of FEOS in a virial equation of state in the low density region; (ii) a transition of FEOS in a Widom equation of state in the critical region. The method has been tested on the example of FEOS of R218. The area of applicability of FEOS is 0 < ρ/ρ c < 3.2 in the density and 133 < T < 440 K in the temperature. We have compared FEOS with some equations of state and discussed the results.

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

NASA Astrophysics Data System (ADS)

Nagano, Y.; Kim, C.

1988-08-01

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

Regional Regression Equations to Estimate Flow-Duration Statistics at Ungaged Stream Sites in Connecticut

USGS Publications Warehouse

Ahearn, Elizabeth A.

2010-01-01

Multiple linear regression equations for determining flow-duration statistics were developed to estimate select flow exceedances ranging from 25- to 99-percent for six 'bioperiods'-Salmonid Spawning (November), Overwinter (December-February), Habitat Forming (March-April), Clupeid Spawning (May), Resident Spawning (June), and Rearing and Growth (July-October)-in Connecticut. Regression equations also were developed to estimate the 25- and 99-percent flow exceedances without reference to a bioperiod. In total, 32 equations were developed. The predictive equations were based on regression analyses relating flow statistics from streamgages to GIS-determined basin and climatic characteristics for the drainage areas of those streamgages. Thirty-nine streamgages (and an additional 6 short-term streamgages and 28 partial-record sites for the non-bioperiod 99-percent exceedance) in Connecticut and adjacent areas of neighboring States were used in the regression analysis. Weighted least squares regression analysis was used to determine the predictive equations; weights were assigned based on record length. The basin characteristics-drainage area, percentage of area with coarse-grained stratified deposits, percentage of area with wetlands, mean monthly precipitation (November), mean seasonal precipitation (December, January, and February), and mean basin elevation-are used as explanatory variables in the equations. Standard errors of estimate of the 32 equations ranged from 10.7 to 156 percent with medians of 19.2 and 55.4 percent to predict the 25- and 99-percent exceedances, respectively. Regression equations to estimate high and median flows (25- to 75-percent exceedances) are better predictors (smaller variability of the residual values around the regression line) than the equations to estimate low flows (less than 75-percent exceedance). The Habitat Forming (March-April) bioperiod had the smallest standard errors of estimate, ranging from 10.7 to 20.9 percent. In contrast, the Rearing and Growth (July-October) bioperiod had the largest standard errors, ranging from 30.9 to 156 percent. The adjusted coefficient of determination of the equations ranged from 77.5 to 99.4 percent with medians of 98.5 and 90.6 percent to predict the 25- and 99-percent exceedances, respectively. Descriptive information on the streamgages used in the regression, measured basin and climatic characteristics, and estimated flow-duration statistics are provided in this report. Flow-duration statistics and the 32 regression equations for estimating flow-duration statistics in Connecticut are stored on the U.S. Geological Survey World Wide Web application ?StreamStats? (http://water.usgs.gov/osw/streamstats/index.html). The regression equations developed in this report can be used to produce unbiased estimates of select flow exceedances statewide.

Liquid film drag out in the presence of molecular forces

NASA Astrophysics Data System (ADS)

Schmidhalter, I.; Cerro, R. L.; Giavedoni, M. D.; Saita, F. A.

2013-03-01

From a practical as well as a conceptual point of view, one of the most interesting problems of physicochemical hydrodynamics is the drag out of a liquid film by a moving solid out of a pool of liquid. The basic problem, sometimes denoted the Landau-Levich problem [L. Landau and B. Levich, "Dragging of a liquid by a moving plate," Acta Physicochim. USSR 17, 42-54 (1942)], involves an interesting blend of capillary and viscous forces plus a matching of the static solution for capillary rise with a numerical solution of the film evolution equation, neglecting gravity, on the downstream region of the flow field. The original solution describes experimental data for a wide range of Capillary numbers but fails to match results for large and very small Capillary numbers. Molecular level forces are introduced to create an augmented version of the film evolution equation to show the effect of van der Waals forces at the lower range of Capillary numbers. A closed form solution for static capillary rise, including molecular forces, was matched with a numerical solution of the augmented film evolution equation in the dynamic meniscus region. Molecular forces do not sensibly modify the static capillary rise region, since film thicknesses are larger than the range of influence of van der Waals forces, but are determinant in shaping the downstream dynamic meniscus of the very thin liquid films. As expected, a quantitatively different level of disjoining pressure for different values of molecular constants remains in the very thin liquid film far downstream. Computational results for a wide range of Capillary numbers and Hamaker constants show a clear transition towards a region where the film thickness becomes independent of the coating speed.

Analytical description of concentration dependence of surface tension in multicomponent systems

NASA Astrophysics Data System (ADS)

R, Dadashev; R, Kutuev; D, Elimkhanov

2008-02-01

From the basic fundamental thermodynamic expressions the equation of isotherms of the surface tension of a ternary system is received. Various assumptions concerning the concentration dependence of molar areas are usually made when the equation is derived. The dependence of the molar areas is calculated as an additive function of the structure of a volumetric phase or the structure of a surface layer. To define the concentration dependence of the molar areas we used a stricter thermodynamic expression offered by Butler. In the received equation the dependence of molar areas on the structure of the solution is taken into account. Therefore, the equation can be applied for the calculation of surface tension over a wide concentration range of the components. Unlike the known expressions, the equation includes the surface tension properties of lateral binary systems, which makes the accuracy of the calculated values considerably higher. Thus, among the advantages of the offered equation we can point out the mathematical simplicity of the received equation and the fact that the equation includes physical parameters the experimental definition of which does not present any special difficulties.

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material.

PubMed

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-04-13

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173-1573 K) and strain rates (10 -4 -10 -2 s -1 ) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations.

An analytic performance model of disk arrays and its application

NASA Technical Reports Server (NTRS)

Lee, Edward K.; Katz, Randy H.

1991-01-01

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

A parameter study of the two-fluid solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

1992-01-01

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

Molar mass, radius of gyration and second virial coefficient from new static light scattering equations for dilute solutions: application to 21 (macro)molecules.

PubMed

Illien, Bertrand; Ying, Ruifeng

2009-05-11

New static light scattering (SLS) equations for dilute binary solutions are derived. Contrarily to the usual SLS equations [Carr-Zimm (CZ)], the new equations have no need for the experimental absolute Rayleigh ratio of a reference liquid and solely rely on the ratio of scattered intensities of solutions and solvent. The new equations, which are based on polarizability equations, take into account the usual refractive index increment partial differential n/partial differential rho(2) complemented by the solvent specific polarizability and a term proportional to the slope of the solution density rho versus the solute mass concentration rho(2) (density increment). Then all the equations are applied to 21 (macro)molecules with a wide range of molar mass (0.2500 kg mol(-1)), for which the scattered intensity is no longer independent of the scattering angle, the new equations give the same value of the radius of gyration as the CZ equation and consistent values of the second virial coefficient.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

REVIEWS OF TOPICAL PROBLEMS: Analytic calculations on digital computers for applications in physics and mathematics

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Tarasov, O. V.; Shirkov, Dmitrii V.

1980-01-01

The present state of analytic calculations on computers is reviewed. Several programming systems which are used for analytic calculations are discussed: SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK, MACSYMA, etc. It is shown that these systems can be used to solve a wide range of problems in physics and mathematics. Some physical applications are discussed in celestial mechanics, the general theory of relativity, quantum field theory, plasma physics, hydrodynamics, atomic and molecular physics, and quantum chemistry. Some mathematical applications which are discussed are evaluating indefinite integrals, solving differential equations, and analyzing mathematical expressions. This review is addressed to physicists and mathematicians working in a wide range of fields.

The consentaneous model of the financial markets exhibiting spurious nature of long-range memory

NASA Astrophysics Data System (ADS)

Gontis, V.; Kononovicius, A.

2018-09-01

It is widely accepted that there is strong persistence in the volatility of financial time series. The origin of the observed persistence, or long-range memory, is still an open problem as the observed phenomenon could be a spurious effect. Earlier we have proposed the consentaneous model of the financial markets based on the non-linear stochastic differential equations. The consentaneous model successfully reproduces empirical probability and power spectral densities of volatility. This approach is qualitatively different from models built using fractional Brownian motion. In this contribution we investigate burst and inter-burst duration statistics of volatility in the financial markets employing the consentaneous model. Our analysis provides an evidence that empirical statistical properties of burst and inter-burst duration can be explained by non-linear stochastic differential equations driving the volatility in the financial markets. This serves as an strong argument that long-range memory in finance can have spurious nature.

Equation of state of solid, liquid and gaseous tantalum from first principles

DOE PAGES

Miljacic, Ljubomir; Demers, Steven; Hong, Qi-Jun; ...

2015-09-18

Here, we present ab initio calculations of the phase diagram and the equation of state of Ta in a wide range of volumes and temperatures, with volumes from 9 to 180 Å 3/atom, temperature as high as 20000 K, and pressure up to 7 Mbars. The calculations are based on first principles, in combination with techniques of molecular dynamics, thermodynamic integration, and statistical modeling. Multiple phases are studied, including the solid, fluid, and gas single phases, as well as two-phase coexistences. We calculate the critical point by direct molecular dynamics sampling, and extend the equation of state to very lowmore » density through virial series fitting. The accuracy of the equation of state is assessed by comparing both the predicted melting curve and the critical point with previous experimental and theoretical investigations.« less

Predicting maximal strength in trained postmenopausal woman.

PubMed

Kemmler, Wolfgang K; Lauber, Dirk; Wassermann, Alfred; Mayhew, Jerry L

2006-11-01

The purpose of this study was to present an equation that accurately predicts 1 repetition maximum (RM) over a wide range of repetitions to fatigue (RTF) for 4 different machine resistance exercises in postmenopausal women. Seventy trained women (age = 57.4 +/- 3.1 years) performed maximal and submaximal repetitions on leg press, bench press, rowing, and leg adduction machines at the conclusion of a 2-year training program. Maximal repetitions were performed on each exercise in the following ranges: 3-5RM, 6-10RM, 11-15RM, and 16-20RM. Special regard was taken to maintain the identical execution of each test (i.e., range of motion, starting angle, speed of movement). One cubic polynomial (w(i) [0.988-0.0000584 r(i)(3) + 0.00190 r(i)(2) + 0.0104 r(i),] where w(i) is the load of measurement I, and r(i) is the number of repetitions) accurately predicted 1RM from RTF with mean absolute differences between actual 1RM and predicted 1RM for the 4 exercises of 1.5-3.1% and with coefficients of variation of <3.3%. Equation accuracy was independent of the exercise type or the number of RTF. Thus, this study supported the validity of RTF to adequately estimate 1RM over a wide range of repetitions and within different exercises in trained, older female subjects.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor.

PubMed

Du, Yuhuan; Guo, Yingqing

2016-07-15

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter.

Theoretical and Experimental Study on Wide Range Optical Fiber Turbine Flow Sensor

PubMed Central

Du, Yuhuan; Guo, Yingqing

2016-01-01

In this paper, a novel fiber turbine flow sensor was proposed and demonstrated for liquid measurement with optical fiber, using light intensity modulation to measure the turbine rotational speed for converting to flow rate. The double-circle-coaxial (DCC) fiber probe was introduced in frequency measurement for the first time. Through the divided ratio of two rings light intensity, the interference in light signals acquisition can be eliminated. To predict the characteristics between the output frequency and flow in the nonlinear range, the turbine flow sensor model was built. Via analyzing the characteristics of turbine flow sensor, piecewise linear equations were achieved in expanding the flow measurement range. Furthermore, the experimental verification was tested. The results showed that the flow range ratio of DN20 turbine flow sensor was improved 2.9 times after using piecewise linear in the nonlinear range. Therefore, combining the DCC fiber sensor and piecewise linear method, it can be developed into a strong anti-electromagnetic interference(anti-EMI) and wide range fiber turbine flowmeter. PMID:27428976

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations.

PubMed

Schüler, D; Alonso, S; Torcini, A; Bär, M

2014-12-01

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions

DOE PAGES

Hu, S. X.; Collins, L. A.; Goncharov, V. N.; ...

2015-10-14

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. Thus, with first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ = 0.1 to 100 g/cm 3 and T = 1,000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic targetmore » implosions on OMEGA using the FPEOS table of CH have predicted ~5% reduction in implosion velocity and ~30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ~10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered lights from ICF implosions.« less

First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions.

PubMed

Hu, S X; Collins, L A; Goncharov, V N; Kress, J D; McCrory, R L; Skupsky, S

2015-10-01

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. With first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ=0.1to100g/cm(3) and T=1000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ∼30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ∼5% reduction in implosion velocity that is caused by the ∼10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered light from ICF implosions.

Cumulative Clearness Index Frequency Distributions on the Territory of the Russian Federation

NASA Astrophysics Data System (ADS)

Frid, S. E.; Lisitskaya, N. V.; Popel, O. S.

2018-02-01

Cumulative distributions of clearness index values are constructed for the territory of Russia based on ground observation results and NASA POWER data. The obtained distributions lie close to each other, which means that the NASA POWER data can be used in solar power installations simulation at temperate and high latitudes. Approximation of the obtained distributions is carried out. The values of equation coefficients for the cumulative clearness index distributions constructed for a wide range of climatic conditions are determined. Equations proposed for a tropical climate are used in the calculations, so they can be regarded as universal ones.

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2003-01-01

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters

NASA Astrophysics Data System (ADS)

Kruglov, Vladimir I.; Harvey, John D.

2006-12-01

We present exact asymptotic similariton solutions of the generalized nonlinear Schrödinger equation (NLSE) with gain or loss terms for a normal-dispersion fiber amplifier with dispersion, nonlinearity, and gain profiles that depend on the propagation distance. Our treatment is based on the mapping of the NLSE with varying parameters to the NLSE with constant dispersion and nonlinearity coefficients and an arbitrary varying gain function. We formulate an effective procedure that leads directly, under appropriate conditions, to a wide range of exact asymptotic similariton solutions of NLSE demonstrating self-similar propagating regimes with linear chirp.

Teaching Creative Thinking and Transitioning Students to the Workplace in an Academic Setting

ERIC Educational Resources Information Center

Senra, Michael; Fogler, H. Scott

2014-01-01

In their collegiate studies, students are given a wide range of concepts, theories, and equations to assist them in their future endeavors. However, students have not been sufficiently exposed to practical critical thinking methodologies that will benefit them as they encounter open-ended problems. A course developed at the University of Michigan…

Programmable calculator uses equation to figure steady-state gas-pipeline flow

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

Holmberg, E.

Because it is accurate and consistent over a wide range of variables, the Colebrook-White (C-W) formula serves as the basis for many methods of calculating turbulent flow in gas pipelines. Oilconsult reveals a simple way to adapt the C-W formula to calculate steady-state pipeline flow using the TI-59 programmable calculator.

An evaluation of MODIS 250-m data for green LAI estimation in crops

NASA Astrophysics Data System (ADS)

Gitelson, Anatoly A.; Wardlow, Brian D.; Keydan, Galina P.; Leavitt, Bryan

2007-10-01

Green leaf area index (LAI) is an important variable for climate modeling, estimates of primary production, agricultural yield forecasting, and many other diverse applications. Remotely sensed data provide considerable potential for estimating LAI at local, regional, and global scales. The goal of this study was to retrieve green LAI from MODIS 250-m vegetation index (VI) data for irrigated and rainfed maize and soybeans. The performance of both MODIS-derived NDVI and Wide Dynamic Range Vegetation Index (WDRVI) were evaluated across three growing seasons (2002 through 2004) over a wide range of LAI and also compared to the performance of NDVI and WDRVI derived from reflectance data collected at close-range across the same field locations. The NDVI vs. LAI relationship showed asymptotic behavior with a sharp decrease in the sensitivity of the NDVI to LAI exceeding 2 m2/m2 for both crops. WDRVI vs. LAI relation was linear across the entire range of LAI variation with determination coefficients above 0.93. Importantly, the coefficients of the close-range WDRVI vs. LAI equation and the MODIS-retrieved WDRVI vs. LAI equation were very close. The WDRVI was found to be capable of accurately estimating LAI across a much greater LAI range than the NDVI and can be used for assessing even slight variations in LAI, which are indicative of the early stages of plant stress. These results demonstrate the new possibilities for analyzing the spatio-temporal variation of the LAI of crops using multi-temporal MODIS 250-m imagery.

The adsorption properties of short chain alcohols and Triton X-100 mixtures at the water-air interface.

PubMed

Zdziennicka, Anna

2009-07-15

The adsorption behaviour at the water-air interface of aqueous solutions of Triton X-100 and methanol (ethanol) mixtures at constant Triton X-100 (TX-100) concentration equal to 10(-7), 10(-6), 10(-5), 10(-4), 6x10(-4) and 10(-3)M, respectively, in a wide range of alcohol concentration was investigated by surface tension measurements of solutions. The obtained values of the surface tension of aqueous solutions of "pure" methanol and ethanol and their mixtures with TX-100, as well as the values of propanol solutions and their mixtures with TX-100 as a function of alcohol concentration taken from the literature were compared with those calculated from the Szyszkowski, Connors and Fainerman and Miller equations. On the basis of this comparison it was stated that these equations can be useful for description of the solution surface tension in the wide range of alcohol concentration, but only at the concentrations of Triton X-100 corresponding to its unsaturated layer in the absence of alcohol. It was also stated that the Connors equation is more adequate for concentrated aqueous organic solutions. The measured values of the surface tension were used in the Gibbs equation to determine the surface excess concentration of Triton X-100 and alcohol. Next, on the basis of Gibbs adsorption isotherms those of Guggenheim and Adam and real adsorption isotherms were established. From the obtained adsorption isotherms it results that alcohol influences the shape of TX-100 isotherms in the whole range of alcohol and TX-100 concentration, but TX-100 influences the alcohol isotherms only at TX-100 concentration at which the saturated monolayer at the solution-air interface is formed in the absence of alcohol. This conclusion was confirmed by analysis of the composition of the surface layer in comparison to the composition of the bulk phase in the equilibrium state.

Investigation of a Coupled Arrhenius-Type/Rossard Equation of AH36 Material

PubMed Central

Qin, Qin; Tian, Ming-Liang; Zhang, Peng

2017-01-01

High-temperature tensile testing of AH36 material in a wide range of temperatures (1173–1573 K) and strain rates (10−4–10−2 s−1) has been obtained by using a Gleeble system. These experimental stress-strain data have been adopted to develop the constitutive equation. The constitutive equation of AH36 material was suggested based on the modified Arrhenius-type equation and the modified Rossard equation respectively. The results indicate that the constitutive equation is strongly influenced by temperature and strain, especially strain. Moreover, there is a good agreement between the predicted data of the modified Arrhenius-type equation and the experimental results when the strain is greater than 0.02. There is also good agreement between the predicted data of the Rossard equation and the experimental results when the strain is less than 0.02. Therefore, a coupled equation where the modified Arrhenius-type equation and Rossard equation are combined has been proposed to describe the constitutive equation of AH36 material according to the different strain values in order to improve the accuracy. The correlation coefficient between the computed and experimental flow stress data was 0.998. The minimum value of the average absolute relative error shows the high accuracy of the coupled equation compared with the two modified equations. PMID:28772767

Virial series expansion and Monte Carlo studies of equation of state for hard spheres in narrow cylindrical pores

NASA Astrophysics Data System (ADS)

Mon, K. K.

2018-05-01

In this paper, the virial series expansion and constant pressure Monte Carlo method are used to study the longitudinal pressure equation of state for hard spheres in narrow cylindrical pores. We invoke dimensional reduction and map the model into an effective one-dimensional fluid model with interacting internal degrees of freedom. The one-dimensional model is extensive. The Euler relation holds, and longitudinal pressure can be probed with the standard virial series expansion method. Virial coefficients B2 and B3 were obtained analytically, and numerical quadrature was used for B4. A range of narrow pore widths (2 Rp) , Rp<(√{3 }+2 ) /4 =0.9330 ... (in units of the hard sphere diameter) was used, corresponding to fluids in the important single-file formations. We have also computed the virial pressure series coefficients B2', B3', and B4' to compare a truncated virial pressure series equation of state with accurate constant pressure Monte Carlo data. We find very good agreement for a wide range of pressures for narrow pores. These results contribute toward increasing the rather limited understanding of virial coefficients and the equation of state of hard sphere fluids in narrow cylindrical pores.

Constraining the equation of state with identified particle spectra

NASA Astrophysics Data System (ADS)

Monnai, Akihiko; Ollitrault, Jean-Yves

2017-10-01

We show that in a central nucleus-nucleus collision, the variation of the mean transverse mass with the multiplicity is determined, up to a rescaling, by the variation of the energy over entropy ratio as a function of the entropy density, thus providing a direct link between experimental data and the equation of state. Each colliding energy thus probes the equation of state at an effective entropy density, whose approximate value is 19 fm-3 for Au+Au collisions at 200 GeV and 41 fm-3 for Pb+Pb collisions at 2.76 TeV, corresponding to temperatures of 227 and 279 MeV if the equation of state is taken from lattice calculations. The relative change of the mean transverse mass as a function of the colliding energy gives a direct measure of the pressure over energy density ratio P /ɛ , at the corresponding effective density. Using Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) data, we obtain P /ɛ =0.21 ±0.10 , in agreement with the lattice value P /ɛ =0.23 in the corresponding temperature range. Measurements over a wide range of colliding energies using a single detector with good particle identification would help reduce the error.

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

NASA Technical Reports Server (NTRS)

Kleb, William L.; Wood, William A.; vanLeer, Bram

1999-01-01

A new method has been developed to accelerate the convergence of explicit time-marching, laminar, Navier-Stokes codes through the combination of local preconditioning and multi-stage time marching optimization. Local preconditioning is a technique to modify the time-dependent equations so that all information moves or decays at nearly the same rate, thus relieving the stiffness for a system of equations. Multi-stage time marching can be optimized by modifying its coefficients to account for the presence of viscous terms, allowing larger time steps. We show it is possible to optimize the time marching scheme for a wide range of cell Reynolds numbers for the scalar advection-diffusion equation, and local preconditioning allows this optimization to be applied to the Navier-Stokes equations. Convergence acceleration of the new method is demonstrated through numerical experiments with circular advection and laminar boundary-layer flow over a flat plate.

Hydration of nonelectrolytes in binary aqueous solutions

NASA Astrophysics Data System (ADS)

Rudakov, A. M.; Sergievskii, V. V.

2010-10-01

Literature data on the thermodynamic properties of binary aqueous solutions of nonelectrolytes that show negative deviations from Raoult's law due largely to the contribution of the hydration of the solute are briefly surveyed. Attention is focused on simulating the thermodynamic properties of solutions using equations of the cluster model. It is shown that the model is based on the assumption that there exists a distribution of stoichiometric hydrates over hydration numbers. In terms of the theory of ideal associated solutions, the equations for activity coefficients, osmotic coefficients, vapor pressure, and excess thermodynamic functions (volume, Gibbs energy, enthalpy, entropy) are obtained in analytical form. Basic parameters in the equations are the hydration numbers of the nonelectrolyte (the mathematical expectation of the distribution of hydrates) and the dispersions of the distribution. It is concluded that the model equations adequately describe the thermodynamic properties of a wide range of nonelectrolytes partly or completely soluble in water.

Acquisition and correlation of cryogenic nitrogen mass flow data through a multiple orifice Joule-Thomson device

NASA Astrophysics Data System (ADS)

Papell, S. Stephen; Saiyed, Naseem H.; Nyland, Ted W.

1990-05-01

Liquid nitrogen mass flow rate, pressure drop, and temperature drop data were obtained for a series of multiple orifice Joule-Thomson devices, known as Visco Jets, over a wide range of flow resistance. The test rig used to acquire the data was designed to minimize heat transfer so that fluid expansion through the Visco Jets would be isenthalpic. The data include a range of fluid inlet pressures from 30 to 60 psia, fluid inlet temperatures from 118 to 164 R, outlet pressures from 2.8 to 55.8 psia, outlet temperatures from 117 to 162 R and flow rate from 0.04 to 4.0 lbm/hr of nitrogen. A flow rate equation supplied by the manufacturer was found to accurately predict single-phase (noncavitating) liquid nitrogen flow through the Visco Jets. For cavitating flow, the manufacturer's equation was found to be inaccurate. Greatly improved results were achieved with a modified version of the single-phase equation. The modification consists of a multiplication factor to the manufacturer's equation equal to one minus the downstream quality on an isenthalpic expansion of the fluid across the Visco Jet. For a range of flow resistances represented by Visco Jet Lohm ratings between 17,600 and 80,000, 100 percent of the single-phase data and 85 percent of the two-phase data fall within + or - 10 percent of predicted values.

H theorem for generalized entropic forms within a master-equation framework

NASA Astrophysics Data System (ADS)

Casas, Gabriela A.; Nobre, Fernando D.; Curado, Evaldo M. F.

2016-03-01

The H theorem is proven for generalized entropic forms, in the case of a discrete set of states. The associated probability distributions evolve in time according to a master equation, for which the corresponding transition rates depend on these entropic forms. An important equation describing the time evolution of the transition rates and probabilities in such a way as to drive the system towards an equilibrium state is found. In the particular case of Boltzmann-Gibbs entropy, it is shown that this equation is satisfied in the microcanonical ensemble only for symmetric probability transition rates, characterizing a single path to the equilibrium state. This equation fulfils the proof of the H theorem for generalized entropic forms, associated with systems characterized by complex dynamics, e.g., presenting nonsymmetric probability transition rates and more than one path towards the same equilibrium state. Some examples considering generalized entropies of the literature are discussed, showing that they should be applicable to a wide range of natural phenomena, mainly those within the realm of complex systems.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

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

Raman spectroscopic characterization of CH4 density over a wide range of temperature and pressure

USGS Publications Warehouse

Shang, Linbo; Chou, I-Ming; Burruss, Robert; Hu, Ruizhong; Bi, Xianwu

2014-01-01

The positions of the CH4 Raman ν1 symmetric stretching bands were measured in a wide range of temperature (from −180 °C to 350 °C) and density (up to 0.45 g/cm3) using high-pressure optical cell and fused silica capillary capsule. The results show that the Raman band shift is a function of both methane density and temperature; the band shifts to lower wavenumbers as the density increases and the temperature decreases. An equation representing the observed relationship among the CH4 ν1 band position, temperature, and density can be used to calculate the density in natural or synthetic CH4-bearing inclusions.

Throttle pneumatic impact mechanism equipped with afterburner idle-stroke chamber

NASA Astrophysics Data System (ADS)

Dedov, Alexey; Frantseva, Eleanor; Dmitriev, Mikhail

2017-01-01

Pneumatic impact mechanisms are widely used in construction, mining and other economic sectors of a country. Such mechanisms are a base for a wide range of machines of various types and dimensions from hand-held tools to mounted piling hammers with impact energy up to 10 000 J. This paper is aimed at creation of pneumatic impact mechanism with the improved characteristics, including operation, energy use, weight and size which is especially important in space-limited working conditions. The research methods include development of computer mathematical model that can solve equations system and test a prototype model at the experimental stand. As a result of conducted research the pneumatic impact mechanism with the improved characteristics was developed. An engineering method for calculating throttle pneumatic impact mechanisms with a preset value of impact energy from 1 to 20 000 was investigated. This method allows creating percussive machines of a wide range of application.

Comparison of up-scaling methods in poroelasticity and its generalizations

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

Berryman, J G

2003-12-13

Four methods of up-scaling coupled equations at the microscale to equations valid at the mesoscale and/or macroscale for fluid-saturated and partially saturated porous media will be discussed, compared, and contrasted. The four methods are: (1) effective medium theory, (2) mixture theory, (3) two-scale and multiscale homogenization, and (4) volume averaging. All these methods have advantages for some applications and disadvantages for others. For example, effective medium theory, mixture theory, and homogenization methods can all give formulas for coefficients in the up-scaled equations, whereas volume averaging methods give the form of the up-scaled equations but generally must be supplemented with physicalmore » arguments and/or data in order to determine the coefficients. Homogenization theory requires a great deal of mathematical insight from the user in order to choose appropriate scalings for use in the resulting power-law expansions, while volume averaging requires more physical insight to motivate the steps needed to find coefficients. Homogenization often is performed on periodic models, while volume averaging does not require any assumption of periodicity and can therefore be related very directly to laboratory and/or field measurements. Validity of the homogenization process is often limited to specific ranges of frequency - in order to justify the scaling hypotheses that must be made - and therefore cannot be used easily over wide ranges of frequency. However, volume averaging methods can quite easily be used for wide band data analysis. So, we learn from these comparisons that a researcher in the theory of poroelasticity and its generalizations needs to be conversant with two or more of these methods to solve problems generally.« less

Quantum-mechanical transport equation for atomic systems.

NASA Technical Reports Server (NTRS)

Berman, P. R.

1972-01-01

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

From the GKLS Equation to the Theory of Solar and Fuel Cells

NASA Astrophysics Data System (ADS)

Alicki, R.

The mathematically sound theory of quantum open systems, formulated in the ’70s and highlighted by the discovery of Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) equation, found a wide range of applications in various branches of physics and chemistry, notably in the field of quantum information and quantum thermodynamics. However, it took 40 years before this formalism has been applied to explain correctly the operation principles of long existing energy transducers like photovoltaic, thermoelectric and fuel cells. This long path is briefly reviewed from the author’s perspective. Finally, the new, fully quantum model of chemical engine based on GKLS equation and applicable to fuel cells or replicators is outlined. The model illustrates the difficulty with an entirely quantum operational definition of work, comparable to the problem of quantum measurement.

One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes

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

Ishii, M.

1977-10-01

In view of the practical importance of the drift-flux model for two-phase flow analysis in general and in the analysis of nuclear-reactor transients and accidents in particular, the kinematic constitutive equation for the drift velocity has been studied for various two-phase flow regimes. The constitutive equation that specifies the relative motion between phases in the drift-flux model has been derived by taking into account the interfacial geometry, the body-force field, shear stresses, and the interfacial momentum transfer, since these macroscopic effects govern the relative velocity between phases. A comparison of the model with various experimental data over various flow regimesmore » and a wide range of flow parameters shows a satisfactory agreement.« less

Flow stabilization with active hydrodynamic cloaks.

PubMed

Urzhumov, Yaroslav A; Smith, David R

2012-11-01

We demonstrate that fluid flow cloaking solutions, based on active hydrodynamic metamaterials, exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers (Re's), up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for Re's in the range of 5-119. The first highly efficient method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigenperturbations; the second method is a direct numerical integration in the time domain. We show that, by suppressing the von Kármán vortex street in the weakly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120 or five times greater than for a bare uncloaked cylinder.

Numerical simulation of separated flows. Ph.D. Thesis - Stanford Univ., Calif.

NASA Technical Reports Server (NTRS)

Spalart, P. R.; Leonard, A.; Baganoff, D.

1983-01-01

A new numerical method, based on the Vortex Method, for the simulation of two-dimensional separated flows, was developed and tested on a wide range of gases. The fluid is incompressible and the Reynolds number is high. A rigorous analytical basis for the representation of the Navier-Stokes equation in terms of the vorticity is used. An equation for the control of circulation around each body is included. An inviscid outer flow (computed by the Vortex Method) was coupled with a viscous boundary layer flow (computed by an Eulerian method). This version of the Vortex Method treats bodies of arbitrary shape, and accurately computes the pressure and shear stress at the solid boundary. These two quantities reflect the structure of the boundary layer. Several versions of the method are presented and applied to various problems, most of which have massive separation. Comparison of its results with other results, generally experimental, demonstrates the reliability and the general accuracy of the new method, with little dependence on empirical parameters. Many of the complex features of the flow past a circular cylinder, over a wide range of Reynolds numbers, are correctly reproduced.

Testing Mercury Porosimetry with 3D Printed Porosity Models

NASA Astrophysics Data System (ADS)

Hasiuk, F.; Ewing, R. P.; Hu, Q.

2014-12-01

Mercury intrusion porosimetry is one of the most widely used techniques to study the porous nature of a geological and man-made materials. In the geosciences, it is commonly used to describe petroleum reservoir and seal rocks as well as to grade aggregates for the design of asphalt and portland cement concretes. It's wide utility stems from its ability to characterize a wide range of pore throat sizes (from nanometers to around a millimeter). The fundamental physical model underlying mercury intrusion porosimetry, the Washburn Equation, is based on the assumption that rock porosity can be described as a bundle of cylindrical tubes. 3D printing technology, also known as rapid prototyping, allows the construction of intricate and accurate models, exactly what is required to build models of rock porosity. We evaluate the applicability of the Washburn Equation by comparing properties (like porosity, pore and pore throat size distribution, and surface area) computed on digital porosity models (built from CT data, CAD designs, or periodic geometries) to properties measured via mercury intrusion porosimetry on 3D printed versions of the same digital porosity models.

Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

NASA Astrophysics Data System (ADS)

Zhang, Chuang; Guo, Zhaoli; Chen, Songze

2017-12-01

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

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

Schüler, D.; Alonso, S.; Bär, M.

2014-12-15

Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexistingmore » static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.« less

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

A numerical study of coarsening in the two-dimensional complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Liu, Weigang; Tauber, Uwe

The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems: coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability; spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations; and driven-dissipative Bose-Einstein condensation, realized in open systems on the interface of quantum optics and many-body physics. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate the coarsening dynamics following a quench from a strongly fluctuating defect turbulence phase to a long-range ordered phase. We start from a simplified amplitude equation, solve it numerically, and then study the spatio-temporal behavior characterized by the spontaneous creation and annihilation of topological defects (spiral waves). We check our simulation results against the known dynamical phase diagram in this non-equilibrium system, tentatively analyze the coarsening kinetics following sudden quenches, and characterize the ensuing aging scaling behavior. In addition, we aim to use Voronoi triangulation to study the cellular structure in the phase turbulence and frozen states. This research is supported by the U. S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-FG02-09ER46613.

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.

An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Srivastava, Akanksha

2013-01-01

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.

Heat transfer characteristics of an emergent strand

NASA Technical Reports Server (NTRS)

Simon, W. E.; Witte, L. C.; Hedgcoxe, P. G.

1974-01-01

A mathematical model was developed to describe the heat transfer characteristics of a hot strand emerging into a surrounding coolant. A stable strand of constant efflux velocity is analyzed, with a constant (average) heat transfer coefficient on the sides and leading surface of the strand. After developing a suitable governing equation to provide an adequate description of the physical system, the dimensionless governing equation is solved with Laplace transform methods. The solution yields the temperature within the strand as a function of axial distance and time. Generalized results for a wide range of parameters are presented, and the relationship of the results and experimental observations is discussed.

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

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

Large-Amplitude, High-Rate Roll Oscillations of a 65 deg Delta Wing at High Incidence

NASA Technical Reports Server (NTRS)

Chaderjian, Neal M.; Schiff, Lewis B.

2000-01-01

The IAR/WL 65 deg delta wing experimental results provide both detail pressure measurements and a wide range of flow conditions covering from simple attached flow, through fully developed vortex and vortex burst flow, up to fully-stalled flow at very high incidence. Thus, the Computational Unsteady Aerodynamics researchers can use it at different level of validating the corresponding code. In this section a range of CFD results are provided for the 65 deg delta wing at selected flow conditions. The time-dependent, three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate the unsteady vertical flow. Two sting angles and two large- amplitude, high-rate, forced-roll motions and a damped free-to-roll motion are presented. The free-to-roll motion is computed by coupling the time-dependent RANS equations to the flight dynamic equation of motion. The computed results are compared with experimental pressures, forces, moments and roll angle time history. In addition, surface and off-surface flow particle streaks are also presented.

Proceedings of the International Symposium on Frozen Soil Impacts on Agricultural, Range, and Forest Lands Held at Spokane, Washington on March 21-22, 1990

DTIC Science & Technology

1990-03-01

Antecedent soil water conditions were measured during the preceding fall using a neutron probe at three locations within each plot to a depth of 1.0 m. A...interrelated heat, water , and solute transfer through snow, residue and soil for a wide range of conditions . Because the model uses fundamental equations... water content profiles at the other sites were measured weekly. Frost depth was measured using cylindrical gypsum moisture blocks read every three hours

Body fat from body density: Underwater weighing vs. dual-photon absorptiometry

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

Wang, J.; Heymsfield, S.B.; Aulet, M.

1989-06-01

We measured fat in 286 healthy volunteers by underwater weighing (FUWW) and dual-photon absorptiometry (FDPA) to develop a translation table for the differing results from these entirely different techniques and to study the sources of these differences. In 99 males and 187 females aged 19-94 yr, fatness was 7-47%. Prediction equations are presented for FUWW-FDPA (delta F), density of lean body mass (DLBM), and FDPA. FUWW and FDPA were significantly different from each other (P less than 0.01). Calculated DLBM is less than the assumed constant of 1.10 (P less than 0.01), ranging widely from 1.05 to 1.13 and beingmore » highly correlated with the ratio of total body bone mineral to lean body mass (TBBM/LBM). delta F, the differences between FUWW and FDPA measurements in individual subjects, varied widely (-7 to +11% in males and -18 to +13% in females). The difference was positively correlated with the DLBM. FUWW was no better than anthropometrics in equations for predicting FDPA. The FDPA predicted from anthropometrics showed smaller standard errors than when FUWW was used. Neither anthropometrics nor FUWW equations are clearly superior to those previously available.« less

Density-Functional-Theory-Based Equation-of-State Table of Beryllium for Inertial Confinement Fusion Applications

NASA Astrophysics Data System (ADS)

Ding, Y. H.; Hu, S. X.

2017-10-01

Beryllium has been considered a superior ablator material for inertial confinement fusion target designs. Based on density-functional-theory calculations, we have established a wide-range beryllium equation-of-state (EOS) table of density ρ = 0.001 to ρ = 500 g/cm3 and temperature T = 2000 to 108 K. Our first-principles equation-of-state (FPEOS) table is in better agreement with widely used SESAMEEOS table (SESAME2023) than the average-atom INFERNOmodel and the Purgatoriomodel. For the principal Hugoniot, our FPEOS prediction shows 10% stiffer behavior than the last two models at maximum compression. Comparisons between FPEOS and SESAMEfor off-Hugoniot conditions show that both the pressure and internal energy differences are within 20% between two EOS tables. By implementing the FPEOS table into the 1-D radiation-hydrodynamics code LILAC, we studied the EOS effects on beryllium target-shell implosions. The FPEOS simulation predicts up to an 15% higher neutron yield compared to the simulation using the SESAME2023 EOS table. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.

A pressure flux-split technique for computation of inlet flow behavior

NASA Technical Reports Server (NTRS)

Pordal, H. S.; Khosla, P. K.; Rubin, S. G.

1991-01-01

A method for calculating the flow field in aircraft engine inlets is presented. The phenomena of inlet unstart and restart are investigated. Solutions of the reduced Navier-Stokes (RNS) equations are obtained with a time consistent direct sparse matrix solver that computes the transient flow field both internal and external to the inlet. Time varying shocks and time varying recirculation regions can be efficiently analyzed. The code is quite general and is suitable for the computation of flow for a wide variety of geometries and over a wide range of Mach and Reynolds numbers.

Limits of applicability of a two-temperature model under nonuniform heating of metal by an ultrashort laser pulse

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

Polyakov, D S; Yakovlev, E B

The heating of metals (silver and aluminium) by ultrashort laser pulses is analysed proceeding from a spatially nonuniform kinetic equation for the electron distribution function. The electron subsystem thermalisation is estimated in a wide range of absorbed pulse energy density. The limits of applicability are determined for the two-temperature model. (interaction of laser radiation with matter)

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli

1997-01-01

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Analysis and Sizing for Transient Thermal Heating of Insulated Aerospace Vehicle Structures

NASA Technical Reports Server (NTRS)

Blosser, Max L.

2012-01-01

An analytical solution was derived for the transient response of an insulated structure subjected to a simplified heat pulse. The solution is solely a function of two nondimensional parameters. Simpler functions of these two parameters were developed to approximate the maximum structural temperature over a wide range of parameter values. Techniques were developed to choose constant, effective thermal properties to represent the relevant temperature and pressure-dependent properties for the insulator and structure. A technique was also developed to map a time-varying surface temperature history to an equivalent square heat pulse. Equations were also developed for the minimum mass required to maintain the inner, unheated surface below a specified temperature. In the course of the derivation, two figures of merit were identified. Required insulation masses calculated using the approximate equation were shown to typically agree with finite element results within 10%-20% over the relevant range of parameters studied.

Development of reference equations for spirometry in Japanese children aged 6-18 years.

PubMed

Takase, Masato; Sakata, Hiroshi; Shikada, Masahiro; Tatara, Katsuyoshi; Fukushima, Takayoshi; Miyakawa, Tomoo

2013-01-01

Spirometry is the most widely used pulmonary function test and the measured values of spirometric parameters need to be evaluated using reference values predicted for the corresponding race, sex, age, and height. However, none of the existing reference equations for Japanese children covers the entire age range of 6-18 years. The Japanese Society of Pediatric Pulmonology had organized a working group in 2006, in order to develop a new set of national standard reference equations for commonly used spirometric parameters that are applicable through the age range of 6-18 years. Quality assured spirometric data were collected through 2006-2008, from 14 institutions in Japan. We applied multiple regression analysis, using age in years (A), square of age (A(2)), height in meters (H), square of height (H(2)), and the product of age and height (AH) as explanatory variables to predict forced vital capacity (FVC), forced expiratory volume in 1 sec (FEV(1)), peak expiratory flow (PEF), forced expiratory flow between 25% and 75% of the FVC (FEF(25-75%)), instantaneous forced expiratory flow when 50% (FEF(50%)) or 75% (FEF(75%)) of the FVC have been expired. Finally, 1,296 tests (674 boys, 622 girls) formed the reference data set. Distributions of the percent predicted values did not differ by ages, confirming excellent fit of the prediction equations throughout the entire age range from 6 to 18 years. Cut-off values (around 5 percentile points) for the parameters were also determined. We recommend the use of this new set of prediction equations together with suggested cut-off values, for assessment of spirometry in Japanese children and adolescents. Copyright © 2012 Wiley Periodicals, Inc.

Flow model for open-channel reach or network

USGS Publications Warehouse

Schaffranek, R.W.

1987-01-01

Formulation of a one-dimensional model for simulating unsteady flow in a single open-channel reach or in a network of interconnected channels is presented. The model is both general and flexible in that it can be used to simulate a wide range of flow conditions for various channel configurations. It is based on a four-point (box), implicit, finite-difference approximation of the governing nonlinear flow equations with user-definable weighting coefficients to permit varying the solution scheme from box-centered to fully forward. Unique transformation equations are formulated that permit correlation of the unknowns at the extremities of the channels, thereby reducing coefficient matrix and execution time requirements. Discharges and water-surface elevations computed at intermediate locations within a channel are determined following solution of the transformation equations. The matrix of transformation and boundary-condition equations is solved by Gauss elimination using maximum pivot strategy. Two diverse applications of the model are presented to illustrate its broad utility. (USGS)

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport.

PubMed

Garzó, Vicente; Dufty, James W; Hrenya, Christine M

2007-09-01

A hydrodynamic description for an s -component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In this first part of the two-part series, the macroscopic balance equations for mass, momentum, and energy are derived. Constitutive equations are calculated from exact expressions for the fluxes by a Chapman-Enskog expansion carried out to first order in spatial gradients, thereby resulting in a Navier-Stokes order theory. Within this context of small gradients, the theory is applicable to a wide range of restitution coefficients and densities. The resulting integral-differential equations for the zeroth- and first-order approximations of the distribution functions are given in exact form. An approximate solution to these equations is required for practical purposes in order to cast the constitutive quantities as algebraic functions of the macroscopic variables; this task is described in the companion paper.

Generating a Multiphase Equation of State with Swarm Intelligence

NASA Astrophysics Data System (ADS)

Cox, Geoffrey

2017-06-01

Hydrocode calculations require knowledge of the variation of pressure of a material with density and temperature, which is given by the equation of state. An accurate model needs to account for discontinuities in energy, density and properties of a material across a phase boundary. When generating a multiphase equation of state the modeller attempts to balance the agreement between the available data for compression, expansion and phase boundary location. However, this can prove difficult because minor adjustments in the equation of state for a single phase can have a large impact on the overall phase diagram. Recently, Cox and Christie described a method for combining statistical-mechanics-based condensed matter physics models with a stochastic analysis technique called particle swarm optimisation. The models produced show good agreement with experiment over a wide range of pressure-temperature space. This talk details the general implementation of this technique, shows example results, and describes the types of analysis that can be performed with this method.

The Effect of Orifice Eccentricity on Instability of Liquid Jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-11-01

The hydrodynamic instability of inviscid jets issuing from elliptic orifices is studied. A linear stability analysis is presented for liquid jets that includes the effect of the surrounding gas and an explicit dispersion equation is derived for waves on an infinite uniform jet column. Elliptic configuration has two extreme cases; round jet when ratio of minor to major axis is unity and plane sheet when this ratio approaches zero. Dispersion equation of elliptic jet is approximated for large and small aspect ratios considering asymptotic of the dispersion equation. In case of aspect ratio equal to one, the dispersion equation is analogous to one of the circular jets derived by Yang. In case of aspect ratio approaches zero, the behavior of waves is qualitatively similar to that of long waves on a two dimensional liquid jets and the varicose and sinuous modes are predicted. The growth rate of initial disturbances for various azimuthal modes has been presented in a wide range of disturbances. PhD Candidate.

A Unified Equation of State on a Microscopic Basis : Implications for Neutron Stars Structure and Cooling

NASA Astrophysics Data System (ADS)

Burgio, G. F.

2018-03-01

We discuss the structure of Neutron Stars by modelling the homogeneous nuclear matter of the core by a suitable microscopic Equation of State, based on the Brueckner-Hartree-Fock many-body theory, and the crust, including the pasta phase, by the BCPM energy density functional which is based on the same Equation of State. This allows for a uni ed description of the Neutron Star matter over a wide density range. A comparison with other uni ed approaches is discussed. With the same Equation of State, which features strong direct Urca processes and using consistent nuclear pairing gaps as well as effective masses, we model neutron star cooling, in particular the current rapid cooldown of the neutron star Cas A. We nd that several scenarios are possible to explain the features of Cas A, but only large and extended proton 1 S 0 gaps and small neutron 3 PF 2 gaps can accommodate also the major part of the complete current cooling data.

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

NASA Astrophysics Data System (ADS)

Yousefvand, Hossein Reza

2017-12-01

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

The Hugoniot adiabat of crystalline copper based on molecular dynamics simulation and semiempirical equation of state

NASA Astrophysics Data System (ADS)

Gubin, S. A.; Maklashova, I. V.; Mel'nikov, I. N.

2018-01-01

The molecular dynamics (MD) method was used for prediction of properties of copper under shock-wave compression and clarification of the melting region of crystal copper. The embedded atom potential was used for the interatomic interaction. Parameters of Hugonoit adiabats of solid and liquid phases of copper calculated by the semiempirical Grüneisen equation of state are consistent with the results of MD simulations and experimental data. MD simulation allows to visualize the structure of cooper on the atomistic level. The analysis of the radial distribution function and the standard deviation by MD modeling allows to predict the melting area behind the shock wave front. These MD simulation data are required to verify the wide-range equation of state of metals. The melting parameters of copper based on MD simulations and semiempirical equations of state are consistent with experimental and theoretical data, including the region of the melting point of copper.

Empirical improvements for estimating earthquake response spectra with random‐vibration theory

USGS Publications Warehouse

Boore, David; Thompson, Eric M.

2012-01-01

The stochastic method of ground‐motion simulation is often used in combination with the random‐vibration theory to directly compute ground‐motion intensity measures, thereby bypassing the more computationally intensive time‐domain simulations. Key to the application of random‐vibration theory to simulate response spectra is determining the duration (Drms) used in computing the root‐mean‐square oscillator response. Boore and Joyner (1984) originally proposed an equation for Drms , which was improved upon by Liu and Pezeshk (1999). Though these equations are both substantial improvements over using the duration of the ground‐motion excitation for Drms , we document systematic differences between the ground‐motion intensity measures derived from the random‐vibration and time‐domain methods for both of these Drms equations. These differences are generally less than 10% for most magnitudes, distances, and periods of engineering interest. Given the systematic nature of the differences, however, we feel that improved equations are warranted. We empirically derive new equations from time‐domain simulations for eastern and western North America seismological models. The new equations improve the random‐vibration simulations over a wide range of magnitudes, distances, and oscillator periods.

Modeling the radiation pattern of LEDs.

PubMed

Moreno, Ivan; Sun, Ching-Cherng

2008-02-04

Light-emitting diodes (LEDs) come in many varieties and with a wide range of radiation patterns. We propose a general, simple but accurate analytic representation for the radiation pattern of the light emitted from an LED. To accurately render both the angular intensity distribution and the irradiance spatial pattern, a simple phenomenological model takes into account the emitting surfaces (chip, chip array, or phosphor surface), and the light redirected by both the reflecting cup and the encapsulating lens. Mathematically, the pattern is described as the sum of a maximum of two or three Gaussian or cosine-power functions. The resulting equation is widely applicable for any kind of LED of practical interest. We accurately model a wide variety of radiation patterns from several world-class manufacturers.

Whispering--a single-subject study of glottal configuration and aerodynamics.

PubMed

Sundberg, Johan; Scherer, Ronald; Hess, Markus; Müller, Frank

2010-09-01

Whisper productions were produced by a single adult male subject over a wide range of subglottal pressures, glottal areas, and glottal flows. Dimensional measurements were made of these three variables, including glottal perimeter. Subglottal pressure was directly obtained by a pressure transducer in a tracheal catheter, and wide-band flow with a pneumotach mask. Four types of whispers were used-hyperfunctional, hypofunctional, neutral, and postphonation-in addition to three levels of loudness (soft, medium, loud). Sequences of the /pae/ syllable were used. Video recordings of the larynx were made. The glottis was outlined by hand with extrapolation for unseen parts, and area and perimeter were obtained through image analysis software. The whisper tokens resulted in the following wide ranges: subglottal pressure: 1.3-17 cm H2O; glottal flow: 0.9-1.71 L/s; glottal area: 0.065-1.76 m2; and glottal perimeter: 1.09-6.55 cm. Hyperfunctional whisper tended to have higher subglottal pressures and lower areas and flows than hypofunctional whisper, with neutral and postphonation whisper values in between. An important finding is that glottal flow changed more for small changes of area when the area was already small, and did not create much flow change when area was changed for already larger areas; that is, whisper is "more sensitive" to airflow changes for smaller glottal areas. A general equation for whisper aerodynamics was obtained, namely, P (subglottal pressure [cm H2O])=C X F (glottal flow [cm(3)/s]), where C = 0.052 x A(4) - 0.1913 x A(3) + 0.2577 x A(2) - 0.1523 x A+0.0388, where A is the glottal area (cm(2)). Another general equation for nondimensional terms (pressure coefficient vs Reynolds number) also is offered. Implications for whisper flow resistance and aerodynamic power are given. These results give insight into whisper aerodynamics and offer equations relevant to speech synthesis. Copyright © 2010 The Voice Foundation. Published by Mosby, Inc. All rights reserved.

Stress-intensity factors and crack-opening displacements for round compact specimens. [fracture toughness of metallic materials

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.

1979-01-01

A two dimensional, boundary collocation stress analysis was used to analyze various round compact specimens. The influence of the round external boundary and of pin-loaded holes on stress intensity factors and crack opening displacements was determined as a function of crack-length-to-specimen-width ratios. A wide-range equation for the stress intensity factors was developed. Equations for crack-surface displacements and load-point displacements were also developed. In addition, stress intensity factors were calculated from compliance methods to demonstrate that load-displacement records must be made at the loading points and not along the crack line for crack-length-to-specimen-width ratios less than about 0.4.

Constraint Force Equation Methodology for Modeling Multi-Body Stage Separation Dynamics

NASA Technical Reports Server (NTRS)

Toniolo, Matthew D.; Tartabini, Paul V.; Pamadi, Bandu N.; Hotchko, Nathaniel

2008-01-01

This paper discusses a generalized approach to the multi-body separation problems in a launch vehicle staging environment based on constraint force methodology and its implementation into the Program to Optimize Simulated Trajectories II (POST2), a widely used trajectory design and optimization tool. This development facilitates the inclusion of stage separation analysis into POST2 for seamless end-to-end simulations of launch vehicle trajectories, thus simplifying the overall implementation and providing a range of modeling and optimization capabilities that are standard features in POST2. Analysis and results are presented for two test cases that validate the constraint force equation methodology in a stand-alone mode and its implementation in POST2.

SIMD Optimization of Linear Expressions for Programmable Graphics Hardware

PubMed Central

Bajaj, Chandrajit; Ihm, Insung; Min, Jungki; Oh, Jinsang

2009-01-01

The increased programmability of graphics hardware allows efficient graphical processing unit (GPU) implementations of a wide range of general computations on commodity PCs. An important factor in such implementations is how to fully exploit the SIMD computing capacities offered by modern graphics processors. Linear expressions in the form of ȳ = Ax̄ + b̄, where A is a matrix, and x̄, ȳ and b̄ are vectors, constitute one of the most basic operations in many scientific computations. In this paper, we propose a SIMD code optimization technique that enables efficient shader codes to be generated for evaluating linear expressions. It is shown that performance can be improved considerably by efficiently packing arithmetic operations into four-wide SIMD instructions through reordering of the operations in linear expressions. We demonstrate that the presented technique can be used effectively for programming both vertex and pixel shaders for a variety of mathematical applications, including integrating differential equations and solving a sparse linear system of equations using iterative methods. PMID:19946569

Methods for compressible multiphase flows and their applications

NASA Astrophysics Data System (ADS)

Kim, H.; Choe, Y.; Kim, H.; Min, D.; Kim, C.

2018-06-01

This paper presents an efficient and robust numerical framework to deal with multiphase real-fluid flows and their broad spectrum of engineering applications. A homogeneous mixture model incorporated with a real-fluid equation of state and a phase change model is considered to calculate complex multiphase problems. As robust and accurate numerical methods to handle multiphase shocks and phase interfaces over a wide range of flow speeds, the AUSMPW+_N and RoeM_N schemes with a system preconditioning method are presented. These methods are assessed by extensive validation problems with various types of equation of state and phase change models. Representative realistic multiphase phenomena, including the flow inside a thermal vapor compressor, pressurization in a cryogenic tank, and unsteady cavitating flow around a wedge, are then investigated as application problems. With appropriate physical modeling followed by robust and accurate numerical treatments, compressible multiphase flow physics such as phase changes, shock discontinuities, and their interactions are well captured, confirming the suitability of the proposed numerical framework to wide engineering applications.

Methods for estimating flood frequency in Montana based on data through water year 1998

USGS Publications Warehouse

Parrett, Charles; Johnson, Dave R.

2004-01-01

Annual peak discharges having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (T-year floods) were determined for 660 gaged sites in Montana and in adjacent areas of Idaho, Wyoming, and Canada, based on data through water year 1998. The updated flood-frequency information was subsequently used in regression analyses, either ordinary or generalized least squares, to develop equations relating T-year floods to various basin and climatic characteristics, equations relating T-year floods to active-channel width, and equations relating T-year floods to bankfull width. The equations can be used to estimate flood frequency at ungaged sites. Montana was divided into eight regions, within which flood characteristics were considered to be reasonably homogeneous, and the three sets of regression equations were developed for each region. A measure of the overall reliability of the regression equations is the average standard error of prediction. The average standard errors of prediction for the equations based on basin and climatic characteristics ranged from 37.4 percent to 134.1 percent. Average standard errors of prediction for the equations based on active-channel width ranged from 57.2 percent to 141.3 percent. Average standard errors of prediction for the equations based on bankfull width ranged from 63.1 percent to 155.5 percent. In most regions, the equations based on basin and climatic characteristics generally had smaller average standard errors of prediction than equations based on active-channel or bankfull width. An exception was the Southeast Plains Region, where all equations based on active-channel width had smaller average standard errors of prediction than equations based on basin and climatic characteristics or bankfull width. Methods for weighting estimates derived from the basin- and climatic-characteristic equations and the channel-width equations also were developed. The weights were based on the cross correlation of residuals from the different methods and the average standard errors of prediction. When all three methods were combined, the average standard errors of prediction ranged from 37.4 percent to 120.2 percent. Weighting of estimates reduced the standard errors of prediction for all T-year flood estimates in four regions, reduced the standard errors of prediction for some T-year flood estimates in two regions, and provided no reduction in average standard error of prediction in two regions. A computer program for solving the regression equations, weighting estimates, and determining reliability of individual estimates was developed and placed on the USGS Montana District World Wide Web page. A new regression method, termed Region of Influence regression, also was tested. Test results indicated that the Region of Influence method was not as reliable as the regional equations based on generalized least squares regression. Two additional methods for estimating flood frequency at ungaged sites located on the same streams as gaged sites also are described. The first method, based on a drainage-area-ratio adjustment, is intended for use on streams where the ungaged site of interest is located near a gaged site. The second method, based on interpolation between gaged sites, is intended for use on streams that have two or more streamflow-gaging stations.

Multiplicative Quaternion Extended Kalman Filtering for Nonspinning Guided Projectiles

DTIC Science & Technology

2013-07-01

tactical applications are inertial. The advantages of using quaternions rather than Euler angles to represent projectile attitude are discussed, and...projectiles generally don’t experience a wide range of heading angles , this has not a primary concern. The other major advantage of quaternions (or...DCMs) over Euler angles is their propagation equations are linear with respect to the quaternion and only depend on the IMU’s angular velocity. This

Dibaryons in neutron stars

NASA Technical Reports Server (NTRS)

Olinto, Angela V.; Haensel, Pawel; Frieman, Joshua A.

1991-01-01

The effects are studied of H-dibaryons on the structure of neutron stars. It was found that H particles could be present in neutron stars for a wide range of dibaryon masses. The appearance of dibaryons softens the equations of state, lowers the maximum neutron star mass, and affects the transport properties of dense matter. The parameter space is constrained for dibaryons by requiring that a 1.44 solar mass neutron star be gravitationally stable.

Development and verification of real-time, hybrid computer simulation of F100-PW-100(3) turbofan engine

NASA Technical Reports Server (NTRS)

Szuch, J. R.; Seldner, K.; Cwynar, D. S.

1977-01-01

A real time, hybrid computer simulation of a turbofan engine is described. Controls research programs involving that engine are supported by the simulation. The real time simulation is shown to match the steady state and transient performance of the engine over a wide range of flight conditions and power settings. The simulation equations, FORTRAN listing, and analog patching diagrams are included.

Solving PDEs with Intrepid

DOE PAGES

Bochev, P.; Edwards, H. C.; Kirby, R. C.; ...

2012-01-01

Intrepid is a Trilinos package for advanced discretizations of Partial Differential Equations (PDEs). The package provides a comprehensive set of tools for local, cell-based construction of a wide range of numerical methods for PDEs. This paper describes the mathematical ideas and software design principles incorporated in the package. We also provide representative examples showcasing the use of Intrepid both in the context of numerical PDEs and the more general context of data analysis.

Density Functional Methods for Shock Physics and High Energy Density Science

NASA Astrophysics Data System (ADS)

Desjarlais, Michael

2017-06-01

Molecular dynamics with density functional theory has emerged over the last two decades as a powerful and accurate framework for calculating thermodynamic and transport properties with broad application to dynamic compression, high energy density science, and warm dense matter. These calculations have been extensively validated against shock and ramp wave experiments, are a principal component of high-fidelity equation of state generation, and are having wide-ranging impacts on inertial confinement fusion, planetary science, and shock physics research. In addition to thermodynamic properties, phase boundaries, and the equation of state, one also has access to electrical conductivity, thermal conductivity, and lower energy optical properties. Importantly, all these properties are obtained within the same theoretical framework and are manifestly consistent. In this talk I will give a brief history and overview of molecular dynamics with density functional theory and its use in calculating a wide variety of thermodynamic and transport properties for materials ranging from ambient to extreme conditions and with comparisons to experimental data. I will also discuss some of the limitations and difficulties, as well as active research areas. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Individualized correction of insulin measurement in hemolyzed serum samples.

PubMed

Wu, Zhi-Qi; Lu, Ju; Chen, Huanhuan; Chen, Wensen; Xu, Hua-Guo

2017-06-01

Insulin measurement plays a key role in the investigation of patients with hypoglycemia, subtype classification of diabetes mellitus, insulin resistance, and impaired beta cell function. However, even slight hemolysis can negatively affect insulin measurement due to RBC insulin-degrading enzyme (IDE). Here, we derived and validated an individualized correction equation in an attempt to eliminate the effects of hemolysis on insulin measurement. The effects of hemolysis on insulin measurement were studied by adding lysed self-RBCs to serum. A correction equation was derived, accounting for both percentage and exposure time of hemolysis. The performance of this individualized correction was evaluated in intentionally hemolyzed samples. Insulin concentration decreased with increasing percentage and exposure time of hemolysis. Based on the effects of hemolysis on insulin measurement of 17 donors (baseline insulin concentrations ranged from 156 to 2119 pmol/L), the individualized hemolysis correction equation was derived: INS corr  = INS meas /(0.705lgHb plasma /Hb serum  - 0.001Time - 0.612). This equation can revert insulin concentrations of the intentionally hemolyzed samples to values that were statistically not different from the corresponding insulin baseline concentrations (p = 0.1564). Hemolysis could lead to a negative interference on insulin measurement; by individualized hemolysis correction equation for insulin measurement, we can correct and report reliable serum insulin results for a wide range of degrees of sample hemolysis. This correction would increase diagnostic accuracy, reduce inappropriate therapeutic decisions, and improve patient satisfaction with care.

Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

NASA Astrophysics Data System (ADS)

Abdulwahhab, Muhammad Alim

2016-10-01

Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

Predicting herbivore faecal nitrogen using a multispecies near-infrared reflectance spectroscopy calibration.

PubMed

Villamuelas, Miriam; Serrano, Emmanuel; Espunyes, Johan; Fernández, Néstor; López-Olvera, Jorge R; Garel, Mathieu; Santos, João; Parra-Aguado, María Ángeles; Ramanzin, Maurizio; Fernández-Aguilar, Xavier; Colom-Cadena, Andreu; Marco, Ignasi; Lavín, Santiago; Bartolomé, Jordi; Albanell, Elena

2017-01-01

Optimal management of free-ranging herbivores requires the accurate assessment of an animal's nutritional status. For this purpose 'near-infrared reflectance spectroscopy' (NIRS) is very useful, especially when nutritional assessment is done through faecal indicators such as faecal nitrogen (FN). In order to perform an NIRS calibration, the default protocol recommends starting by generating an initial equation based on at least 50-75 samples from the given species. Although this protocol optimises prediction accuracy, it limits the use of NIRS with rare or endangered species where sample sizes are often small. To overcome this limitation we tested a single NIRS equation (i.e., multispecies calibration) to predict FN in herbivores. Firstly, we used five herbivore species with highly contrasting digestive physiologies to build monospecies and multispecies calibrations, namely horse, sheep, Pyrenean chamois, red deer and European rabbit. Secondly, the equation accuracy was evaluated by two procedures using: (1) an external validation with samples from the same species, which were not used in the calibration process; and (2) samples from different ungulate species, specifically Alpine ibex, domestic goat, European mouflon, roe deer and cattle. The multispecies equation was highly accurate in terms of the coefficient of determination for calibration R2 = 0.98, standard error of validation SECV = 0.10, standard error of external validation SEP = 0.12, ratio of performance to deviation RPD = 5.3, and range error of prediction RER = 28.4. The accuracy of the multispecies equation to predict other herbivore species was also satisfactory (R2 > 0.86, SEP < 0.27, RPD > 2.6, and RER > 8.1). Lastly, the agreement between multi- and monospecies calibrations was also confirmed by the Bland-Altman method. In conclusion, our single multispecies equation can be used as a reliable, cost-effective, easy and powerful analytical method to assess FN in a wide range of herbivore species.

Expanded prediction equations of human sweat loss and water needs.

PubMed

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

2009-08-01

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

Vertical distribution of ozone: a new method of determination using satellite measurements.

PubMed

Aruga, T; Igarashi, T

1976-01-01

A new method to determine the vertical distribution of atmospheric ozone over a wide range from the spectral measurement of backscattered solar uv radiation is proposed. Equations for the diffuse reflection in an inhomogeneous atmosphere are introduced, and some theoretical approximations are discussed. An inversion equation is formulated in such a way that the change of radiance at each wavelength, caused by the minute relative increment of ozone density at each altitude, is obtained exactly. The equation is solved by an iterative procedure using the weight function obtained in this work. The results of computer simulation indicate that the ozone distribution from the mesopause to the tropopause can be determined, and that although it is impossible to suggest exactly the complicated profile with fine structure, the smoothed ozone distribution and the total content can be determined with almost the same accuracy as the accuracies of measurement and theoretical calculation of the spectral intensity.

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

NASA Astrophysics Data System (ADS)

Heye, Colin; Raman, Venkat

2012-11-01

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

Compressible convection in geophysical fluids: comparison of anelastic, anelastic liquid and full numerical simulations

NASA Astrophysics Data System (ADS)

Curbelo, Jezabel; Alboussiere, Thierry; Labrosse, Stephane; Dubuffet, Fabien; Ricard, Yanick

2015-11-01

In this talk we describe the numerical method implemented to study convection in a fully compressible two-dimensional model, which may be reduced to the different simplifications such as the anelastic approximation and the anelastic liquid approximation. Various equations of state are considered, from the ideal gas equation to equations related to liquid or solid condensed matter. We are particularly interested in the total value and spatial distribution of viscous dissipation. We analyze the solutions obtained with each approximation in a wide range of dimensionless parameters and compare the domain of validity of each of them. The authors are grateful to the LABEX Lyon Institute of Origins (ANR-10-LABX-0066) of the Universite de Lyon for its financial support ``Investissements d'Avenir'' (ANR-11-IDEX-0007) of the French government operated by the National Research Agency (ANR).

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

NASA Technical Reports Server (NTRS)

Dlugach, Janna M.; Mishchenko, Michael I.

2017-01-01

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

A general mixture theory. I. Mixtures of spherical molecules

NASA Astrophysics Data System (ADS)

Hamad, Esam Z.

1996-08-01

We present a new general theory for obtaining mixture properties from the pure species equations of state. The theory addresses the composition and the unlike interactions dependence of mixture equation of state. The density expansion of the mixture equation gives the exact composition dependence of all virial coefficients. The theory introduces multiple-index parameters that can be calculated from binary unlike interaction parameters. In this first part of the work, details are presented for the first and second levels of approximations for spherical molecules. The second order model is simple and very accurate. It predicts the compressibility factor of additive hard spheres within simulation uncertainty (equimolar with size ratio of three). For nonadditive hard spheres, comparison with compressibility factor simulation data over a wide range of density, composition, and nonadditivity parameter, gave an average error of 2%. For mixtures of Lennard-Jones molecules, the model predictions are better than the Weeks-Chandler-Anderson perturbation theory.

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

NASA Astrophysics Data System (ADS)

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

1993-11-01

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

Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method

NASA Astrophysics Data System (ADS)

Assi, I. A.; Sous, A. J.

2018-05-01

The goal of this work is to derive a new class of short-range potentials that could have a wide range of physical applications, specially in molecular physics. The tridiagonal representation approach has been developed beyond its limitations to produce new potentials by requiring the representation of the Schrödinger wave operator to be multidiagonal and symmetric. This produces a family of Hulthén potentials that has a specific structure, as mentioned in the introduction. As an example, we have solved the nonrelativistic wave equation for the new four-parameter short-range screening potential numerically using the asymptotic iteration method, where we tabulated the eigenvalues for both s -wave and arbitrary l -wave cases in tables.

Reference Correlation for the Viscosity of Ammonia from the Triple Point to 725 K and up to 50 MPa

NASA Astrophysics Data System (ADS)

Monogenidou, S. A.; Assael, M. J.; Huber, M. L.

2018-06-01

This paper presents a new wide-ranging correlation for the viscosity of ammonia based on critically evaluated experimental data. The correlation is designed to be used with a recently developed equation of state, and it is valid from the triple point to 725 K at pressures up to 50 MPa. The estimated uncertainty varies depending on the temperature and pressure, from 0.6% to 5%. The correlation behaves in a physically reasonable manner when extrapolated to 100 MPa; however, care should be taken when using the correlation outside of the validated range.

Anisotropic light diffraction in crystals with a large acoustic-energy walk-off

NASA Astrophysics Data System (ADS)

Balakshy, V. I.; Voloshin, A. S.; Molchanov, V. Ya.

2014-11-01

The influence of energy walk-off in an acoustic beam on the characteristic of anisotropic Bragg diffraction of light has been investigated by the example of paratellurite crystal. The angular and frequency characteristics of acousto-optic diffraction have been calculated in wide ranges of ultrasound frequencies and Bragg angles using the modified Raman-Nath equations. It is shown that the walk-off of an acoustic beam may change (either widen or narrow) significantly the frequency and angular ranges. The calculation results have been experimentally checked on an acousto-optic cell made of 10.5°-cut paratellurite crystal.

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

PubMed

Mills, Edmund Martin; Kim, Sangtae

2016-12-15

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

Frequency Response Calculations of Input Characteristics of Cavity-Backed Aperture Antennas Using AWE with Hybrid FEM/MoM Technique

NASA Technical Reports Server (NTRS)

Reddy, C. J.; Deshpande, M. D.

1997-01-01

Application of Asymptotic Waveform Evaluation (AWE) is presented in conjunction with a hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique to calculate the input characteristics of cavity-backed aperture antennas over a frequency range. The hybrid FEM/MoM technique is used to form an integro-partial-differential equation to compute the electric field distribution of the cavity-backed aperture antenna. The electric field, thus obtained, is expanded in a Taylor series around the frequency of interest. The coefficients of 'Taylor series (called 'moments') are obtained using the frequency derivatives of the integro-partial-differential Equation formed by the hybrid FEM/MoM technique. Using the moments, the electric field in the cavity is obtained over a frequency range. Using the electric field at different frequencies, the input characteristics of the antenna are obtained over a wide frequency band. Numerical results for an open coaxial line, probe fed cavity, and cavity-backed microstrip patch antennas are presented. Good agreement between AWE and the exact solution over the frequency range is observed.

Application of Model Based Parameter Estimation for Fast Frequency Response Calculations of Input Characteristics of Cavity-Backed Aperture Antennas Using Hybrid FEM/MoM Technique

NASA Technical Reports Server (NTRS)

Reddy C. J.

1998-01-01

Model Based Parameter Estimation (MBPE) is presented in conjunction with the hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique for fast computation of the input characteristics of cavity-backed aperture antennas over a frequency range. The hybrid FENI/MoM technique is used to form an integro-partial- differential equation to compute the electric field distribution of a cavity-backed aperture antenna. In MBPE, the electric field is expanded in a rational function of two polynomials. The coefficients of the rational function are obtained using the frequency derivatives of the integro-partial-differential equation formed by the hybrid FEM/ MoM technique. Using the rational function approximation, the electric field is obtained over a frequency range. Using the electric field at different frequencies, the input characteristics of the antenna are obtained over a wide frequency range. Numerical results for an open coaxial line, probe-fed coaxial cavity and cavity-backed microstrip patch antennas are presented. Good agreement between MBPE and the solutions over individual frequencies is observed.

Verification of a VRF Heat Pump Computer Model in EnergyPlus

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

Nigusse, Bereket; Raustad, Richard

2013-06-15

This paper provides verification results of the EnergyPlus variable refrigerant flow (VRF) heat pump computer model using manufacturer's performance data. The paper provides an overview of the VRF model, presents the verification methodology, and discusses the results. The verification provides quantitative comparison of full and part-load performance to manufacturer's data in cooling-only and heating-only modes of operation. The VRF heat pump computer model uses dual range bi-quadratic performance curves to represent capacity and Energy Input Ratio (EIR) as a function of indoor and outdoor air temperatures, and dual range quadratic performance curves as a function of part-load-ratio for modeling part-loadmore » performance. These performance curves are generated directly from manufacturer's published performance data. The verification compared the simulation output directly to manufacturer's performance data, and found that the dual range equation fit VRF heat pump computer model predicts the manufacturer's performance data very well over a wide range of indoor and outdoor temperatures and part-load conditions. The predicted capacity and electric power deviations are comparbale to equation-fit HVAC computer models commonly used for packaged and split unitary HVAC equipment.« less

Out-of-equilibrium dynamical mean-field equations for the perceptron model

NASA Astrophysics Data System (ADS)

Agoritsas, Elisabeth; Biroli, Giulio; Urbani, Pierfrancesco; Zamponi, Francesco

2018-02-01

Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their applicability and importance, a detailed study of their Langevin dynamics has never been performed yet. Here we derive the mean-field dynamical equations that describe the continuous random perceptron in the thermodynamic limit, in a very general setting with arbitrary noise and friction kernels, not necessarily related by equilibrium relations. We derive the equations in two ways: via a dynamical cavity method, and via a path-integral approach in its supersymmetric formulation. The end point of both approaches is the reduction of the dynamics of the system to an effective stochastic process for a representative dynamical variable. Because the perceptron is formally very close to a system of interacting particles in a high dimensional space, the methods we develop here can be transferred to the study of liquid and glasses in high dimensions. Potentially interesting applications are thus the study of the glass transition in active matter, the study of the dynamics around the jamming transition, and the calculation of rheological properties in driven systems.

Modeling techniques for quantum cascade lasers

NASA Astrophysics Data System (ADS)

Jirauschek, Christian; Kubis, Tillmann

2014-03-01

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Modeling techniques for quantum cascade lasers

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

Jirauschek, Christian; Kubis, Tillmann

2014-03-15

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation ofmore » quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrödinger equation and Schrödinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.« less

Effects of high-frequency damping on iterative convergence of implicit viscous solver

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko

2017-11-01

This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.

Radial Photonic Crystal for Detection of Frequency and Position of Radiation Sources

DTIC Science & Technology

2012-08-06

Dehesa, J. Acoustic resonances in two-dimensional radial sonic crystal shells. New J. Phys. 12, 073034 (2010). 15. Kurs, A. et al. Wireless power...microstructured materials, i.e. metamaterials, we present here the first practical realization of a radial wave crystal . This type of device was...parameters, those that define the solution of the wave propagation equations, has opened a very wide range of possibilities going from negative

Models of Anisotropic Creep in Integral Wing Panel Forming Processes

NASA Astrophysics Data System (ADS)

Oleinikov, A. I.; Oleinikov, A. A.

2016-08-01

For a sufficiently wide range of stresses the titanic and aluminummagnesium alloys, as a rule, strained differently in the process of creep under tension and compression along a fixed direction. There are suggested constitutive relations for the description of the steady-state creep of transversely isotropic materials with different tension and compression characteristics. Experimental justification is given to the proposed constitutive equations. Modeling of forming of wing panels of the aircraft are considered.

An Analysis of an Implicit Factored Scheme for Simulating Shock Waves

DTIC Science & Technology

1988-05-01

can cope with a wide range of boundary conditions and equations of state, For modelling -( shock waves in solids, elastic- plastic terms must also be...positive caracteristic speeds. One-sided schemes have superior dissipative and dispersive properties compared to those of centered schemes (Steger and...Elastic- plastic con. ditions must be- incorporated into the problem and usually the addition of suitable bource or sink terms to c-’ustion (1

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

DTIC Science & Technology

2010-03-01

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

PETOOL: MATLAB-based one-way and two-way split-step parabolic equation tool for radiowave propagation over variable terrain

NASA Astrophysics Data System (ADS)

Ozgun, Ozlem; Apaydin, Gökhan; Kuzuoglu, Mustafa; Sevgi, Levent

2011-12-01

A MATLAB-based one-way and two-way split-step parabolic equation software tool (PETOOL) has been developed with a user-friendly graphical user interface (GUI) for the analysis and visualization of radio-wave propagation over variable terrain and through homogeneous and inhomogeneous atmosphere. The tool has a unique feature over existing one-way parabolic equation (PE)-based codes, because it utilizes the two-way split-step parabolic equation (SSPE) approach with wide-angle propagator, which is a recursive forward-backward algorithm to incorporate both forward and backward waves into the solution in the presence of variable terrain. First, the formulation of the classical one-way SSPE and the relatively-novel two-way SSPE is presented, with particular emphasis on their capabilities and the limitations. Next, the structure and the GUI capabilities of the PETOOL software tool are discussed in detail. The calibration of PETOOL is performed and demonstrated via analytical comparisons and/or representative canonical tests performed against the Geometric Optic (GO) + Uniform Theory of Diffraction (UTD). The tool can be used for research and/or educational purposes to investigate the effects of a variety of user-defined terrain and range-dependent refractivity profiles in electromagnetic wave propagation. Program summaryProgram title: PETOOL (Parabolic Equation Toolbox) Catalogue identifier: AEJS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 143 349 No. of bytes in distributed program, including test data, etc.: 23 280 251 Distribution format: tar.gz Programming language: MATLAB (MathWorks Inc.) 2010a. Partial Differential Toolbox and Curve Fitting Toolbox required Computer: PC Operating system: Windows XP and Vista Classification: 10 Nature of problem: Simulation of radio-wave propagation over variable terrain on the Earth's surface, and through homogeneous and inhomogeneous atmosphere. Solution method: The program implements one-way and two-way Split-Step Parabolic Equation (SSPE) algorithm, with wide-angle propagator. The SSPE is, in general, an initial-value problem starting from a reference range (typically from an antenna), and marching out in range by obtaining the field along the vertical direction at each range step, through the use of step-by-step Fourier transformations. The two-way algorithm incorporates the backward-propagating waves into the standard one-way SSPE by utilizing an iterative forward-backward scheme for modeling multipath effects over a staircase-approximated terrain. Unusual features: This is the first software package implementing a recursive forward-backward SSPE algorithm to account for the multipath effects during radio-wave propagation, and enabling the user to easily analyze and visualize the results of the two-way propagation with GUI capabilities. Running time: Problem dependent. Typically, it is about 1.5 ms (for conducting ground) and 4 ms (for lossy ground) per range step for a vertical field profile of vector length 1500, on Intel Core 2 Duo 1.6 GHz with 2 GB RAM under Windows Vista.

A near-wall two-equation model for compressible turbulent flows

NASA Technical Reports Server (NTRS)

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

1991-01-01

A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

Effective equations governing an active poroelastic medium

PubMed Central

2017-01-01

In this work, we consider the spatial homogenization of a coupled transport and fluid–structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation and transport in an active poroelastic medium. The ‘active’ nature of the material results from a morphoelastic response to a chemical stimulant, in which the growth time scale is strongly separated from other elastic time scales. The resulting effective model is broadly relevant to the study of biological tissue growth, geophysical flows (e.g. swelling in coals and clays) and a wide range of industrial applications (e.g. absorbant hygiene products). The key contribution of this work is the derivation of a system of homogenized partial differential equations describing macroscale growth, coupled to transport of solute, that explicitly incorporates details of the structure and dynamics of the microscopic system, and, moreover, admits finite growth and deformation at the pore scale. The resulting macroscale model comprises a Biot-type system, augmented with additional terms pertaining to growth, coupled to an advection–reaction–diffusion equation. The resultant system of effective equations is then compared with other recent models under a selection of appropriate simplifying asymptotic limits. PMID:28293138

Learning Qualitative Differential Equation models: a survey of algorithms and applications.

PubMed

Pang, Wei; Coghill, George M

2010-03-01

Over the last two decades, qualitative reasoning (QR) has become an important domain in Artificial Intelligence. QDE (Qualitative Differential Equation) model learning (QML), as a branch of QR, has also received an increasing amount of attention; many systems have been proposed to solve various significant problems in this field. QML has been applied to a wide range of fields, including physics, biology and medical science. In this paper, we first identify the scope of this review by distinguishing QML from other QML systems, and then review all the noteworthy QML systems within this scope. The applications of QML in several application domains are also introduced briefly. Finally, the future directions of QML are explored from different perspectives.

Equation of state survey of black hole-neutron star mergers

NASA Astrophysics Data System (ADS)

Brege, Wyatt

2016-03-01

By varying across several realistic equations of state in the regime in which most neutron star masses are most likely to appear, we can study how important a role these EOS's play in the properties of the post-merger accretion disk in mixed binary systems. In each system considered, the black hole has a mass of MBH = 7M⊙ and a spin of a* = 0 . 9 , and the neutron star has a mass of 1.2 or 1.4 M⊙. The realistic EOS's chosen satisfy experimental and observational constraints, and explore a wide range of neutron star compactnesses. We will address remaining uncertainties in the NS high-density EOS's and, principally, examine differences in the dynamical ejecta and consider implications for nucleosynthesis.

Coexisting rogue waves within the (2+1)-component long-wave-short-wave resonance.

PubMed

Chen, Shihua; Soto-Crespo, Jose M; Grelu, Philippe

2014-09-01

The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics.

Professor Thomas J. Ahrens and Shock Wave Physics in Russia

NASA Astrophysics Data System (ADS)

Fortov, Vladimir E.; Kanel, Gennady I.

2011-06-01

Since his earlier works on the equations of state and dynamic mechanical properties of rocks and other materials Prof. T.J. Ahrens furnished large influence on development of the shock wave physics in Russia. He always demonstrates a choice of excellent problems and a level of productivity in the field of shock compression science which is unparalleled. In recognition of his great contribution into science and international scientific collaboration Prof. Ahrens has been elected in Russian Academy of Sciences as its foreign member. In the presentation, emphasis will be done on the Comet Shoemaker-Levy project in which we had fruitful informal collaboration, on the problem of wide-range equations of state, and on stress relaxation at shock compression of solids.

Heat transfer to the transpired turbulent boundary layer.

NASA Technical Reports Server (NTRS)

Kays, W. M.

1972-01-01

This paper contains a summarization of five years work on an investigation on heat transfer to the transpired turbulent boundary layer. Experimental results are presented for friction coefficient and Stanton number over a wide range of blowing and suction for the case of constant free-stream velocity, holding certain blowing parameters constant. The problem of the accelerated turbulent boundary layer with transpiration is considered, experimental data are presented and discussed, and theoretical models for solution of the momentum equation under these conditions are presented. Data on turbulent Prandtl number are presented so that solutions to the energy equation may be obtained. Some examples of boundary layer heat transfer and friction coefficient predictions are presented using one of the models discussed, employing a finite difference solution method.

The electron Boltzmann equation in a plasma generated by fission fragments

NASA Technical Reports Server (NTRS)

Hassan, H. A.; Deese, J. E.

1976-01-01

A Boltzmann equation formulation is presented for the determination of the electron distribution function in a plasma generated by fission fragments. The formulation takes into consideration ambipolar diffusion, elastic and inelastic collisions, recombination and ionization, and allows for the fact that the primary electrons are not monoenergetic. Calculations for He in a tube coated with fissionable material show that, over a wide pressure and neutron flux range, the distribution function is non-Maxwellian, but the electrons are essentially thermal. Moreover, about a third of the energy of the primary electrons is transferred into the inelastic levels of He. This fraction of energy transfer is almost independent of pressure and neutron flux but increases sharply in the presence of a sustainer electric field.

Learning Qualitative Differential Equation models: a survey of algorithms and applications

PubMed Central

PANG, WEI; COGHILL, GEORGE M.

2013-01-01

Over the last two decades, qualitative reasoning (QR) has become an important domain in Artificial Intelligence. QDE (Qualitative Differential Equation) model learning (QML), as a branch of QR, has also received an increasing amount of attention; many systems have been proposed to solve various significant problems in this field. QML has been applied to a wide range of fields, including physics, biology and medical science. In this paper, we first identify the scope of this review by distinguishing QML from other QML systems, and then review all the noteworthy QML systems within this scope. The applications of QML in several application domains are also introduced briefly. Finally, the future directions of QML are explored from different perspectives. PMID:23704803

Unified first principles description from warm dense matter to ideal ionized gas plasma: electron-ion collisions induced friction.

PubMed

Dai, Jiayu; Hou, Yong; Yuan, Jianmin

2010-06-18

Electron-ion interactions are central to numerous phenomena in the warm dense matter (WDM) regime and at higher temperature. The electron-ion collisions induced friction at high temperature is introduced in the procedure of ab initio molecular dynamics using the Langevin equation based on density functional theory. In this framework, as a test for Fe and H up to 1000 eV, the equation of state and the transition of electronic structures of the materials with very wide density and temperature can be described, which covers a full range of WDM up to high energy density physics. A unified first principles description from condensed matter to ideal ionized gas plasma is constructed.

Accurate atomistic first-principles calculations of electronic stopping

DOE PAGES

Schleife, André; Kanai, Yosuke; Correa, Alfredo A.

2015-01-20

In this paper, we show that atomistic first-principles calculations based on real-time propagation within time-dependent density functional theory are capable of accurately describing electronic stopping of light projectile atoms in metal hosts over a wide range of projectile velocities. In particular, we employ a plane-wave pseudopotential scheme to solve time-dependent Kohn-Sham equations for representative systems of H and He projectiles in crystalline aluminum. This approach to simulate nonadiabatic electron-ion interaction provides an accurate framework that allows for quantitative comparison with experiment without introducing ad hoc parameters such as effective charges, or assumptions about the dielectric function. Finally, our work clearlymore » shows that this atomistic first-principles description of electronic stopping is able to disentangle contributions due to tightly bound semicore electrons and geometric aspects of the stopping geometry (channeling versus off-channeling) in a wide range of projectile velocities.« less

Introduction, comparison, and validation of Meta‐Essentials: A free and simple tool for meta‐analysis

PubMed Central

van Rhee, Henk; Hak, Tony

2017-01-01

We present a new tool for meta‐analysis, Meta‐Essentials, which is free of charge and easy to use. In this paper, we introduce the tool and compare its features to other tools for meta‐analysis. We also provide detailed information on the validation of the tool. Although free of charge and simple, Meta‐Essentials automatically calculates effect sizes from a wide range of statistics and can be used for a wide range of meta‐analysis applications, including subgroup analysis, moderator analysis, and publication bias analyses. The confidence interval of the overall effect is automatically based on the Knapp‐Hartung adjustment of the DerSimonian‐Laird estimator. However, more advanced meta‐analysis methods such as meta‐analytical structural equation modelling and meta‐regression with multiple covariates are not available. In summary, Meta‐Essentials may prove a valuable resource for meta‐analysts, including researchers, teachers, and students. PMID:28801932

Development of a One-Equation Eddy Viscosity Turbulence Model for Application to Complex Turbulent Flows

NASA Astrophysics Data System (ADS)

Wray, Timothy J.

Computational fluid dynamics (CFD) is routinely used in performance prediction and design of aircraft, turbomachinery, automobiles, and in many other industrial applications. Despite its wide range of use, deficiencies in its prediction accuracy still exist. One critical weakness is the accurate simulation of complex turbulent flows using the Reynolds-Averaged Navier-Stokes equations in conjunction with a turbulence model. The goal of this research has been to develop an eddy viscosity type turbulence model to increase the accuracy of flow simulations for mildly separated flows, flows with rotation and curvature effects, and flows with surface roughness. It is accomplished by developing a new zonal one-equation turbulence model which relies heavily on the flow physics; it is now known in the literature as the Wray-Agarwal one-equation turbulence model. The effectiveness of the new model is demonstrated by comparing its results with those obtained by the industry standard one-equation Spalart-Allmaras model and two-equation Shear-Stress-Transport k - o model and experimental data. Results for subsonic, transonic, and supersonic flows in and about complex geometries are presented. It is demonstrated that the Wray-Agarwal model can provide the industry and CFD researchers an accurate, efficient, and reliable turbulence model for the computation of a large class of complex turbulent flows.

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.

A new perspective for quintic B-spline based Crank-Nicolson-differential quadrature method algorithm for numerical solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Başhan, Ali; Uçar, Yusuf; Murat Yağmurlu, N.; Esen, Alaattin

2018-01-01

In the present paper, a Crank-Nicolson-differential quadrature method (CN-DQM) based on utilizing quintic B-splines as a tool has been carried out to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. For this purpose, first of all, the Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using both the forward difference formula and the Crank-Nicolson method. After that, Rubin and Graves linearization techniques have been utilized and the differential quadrature method has been applied to obtain an algebraic equation system. Next, in order to be able to test the efficiency of the newly applied method, the error norms, L2 and L_{∞}, as well as the two lowest invariants, I1 and I2, have been computed. Besides those, the relative changes in those invariants have been presented. Finally, the newly obtained numerical results have been compared with some of those available in the literature for similar parameters. This comparison clearly indicates that the currently utilized method, namely CN-DQM, is an effective and efficient numerical scheme and allows us to propose to solve a wide range of nonlinear equations.

Journal: A Review of Some Tracer-Test Design Equations for ...

EPA Pesticide Factsheets

Determination of necessary tracer mass, initial sample-collection time, and subsequent sample-collection frequency are the three most difficult aspects to estimate for a proposed tracer test prior to conducting the tracer test. To facilitate tracer-mass estimation, 33 mass-estimation equations are reviewed here, 32 of which were evaluated using previously published tracer-test design examination parameters. Comparison of the results produced a wide range of estimated tracer mass, but no means is available by which one equation may be reasonably selected over the others. Each equation produces a simple approximation for tracer mass. Most of the equations are based primarily on estimates or measurements of discharge, transport distance, and suspected transport times. Although the basic field parameters commonly employed are appropriate for estimating tracer mass, the 33 equations are problematic in that they were all probably based on the original developers' experience in a particular field area and not necessarily on measured hydraulic parameters or solute-transport theory. Suggested sampling frequencies are typically based primarily on probable transport distance, but with little regard to expected travel times. This too is problematic in that tends to result in false negatives or data aliasing. Simulations from the recently developed efficient hydrologic tracer-test design methodology (EHTD) were compared with those obtained from 32 of the 33 published tracer-

Computations of Complex Three-Dimensional Turbulent Free Jets

NASA Technical Reports Server (NTRS)

Wilson, Robert V.; Demuren, Ayodeji O.

1997-01-01

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets.

Effective Inflow Conditions for Turbulence Models in Aerodynamic Calculations

NASA Technical Reports Server (NTRS)

Spalart, Philippe R.; Rumsey, Christopher L.

2007-01-01

The selection of inflow values at boundaries far upstream of an aircraft is considered, for one- and two-equation turbulence models. Inflow values are distinguished from the ambient values near the aircraft, which may be much smaller. Ambient values should be selected first, and inflow values that will lead to them after the decay second; this is not always possible, especially for the time scale. The two-equation decay during the approach to the aircraft is shown; often, the time scale has been set too short for this decay to be calculated accurately on typical grids. A simple remedy for both issues is to impose floor values for the turbulence variables, outside the viscous sublayer, and it is argued that overriding the equations in this manner is physically justified. Selecting laminar ambient values is easy, if the boundary layers are to be tripped, but a more common practice is to seek ambient values that will cause immediate transition in boundary layers. This opens up a wide range of values, and selection criteria are discussed. The turbulent Reynolds number, or ratio of eddy viscosity to laminar viscosity has a huge dynamic range that makes it unwieldy; it has been widely mis-used, particularly by codes that set upper limits on it. The value of turbulent kinetic energy in a wind tunnel or the atmosphere is also of dubious value as an input to the model. Concretely, the ambient eddy viscosity must be small enough to preserve potential cores in small geometry features, such as flap gaps. The ambient frequency scale should also be small enough, compared with shear rates in the boundary layer. Specific values are recommended and demonstrated for airfoil flows

Revisiting Maxwell’s accommodation coefficient: A study of nitrogen flow in a silica microtube across all flow regimes

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

Lei, Wenwen, E-mail: wlei@physics.usyd.edu.au; McKenzie, David R., E-mail: d.mckenzie@physics.usyd.edu.au

2014-12-15

Gas flows have been studied quantitatively for more than a hundred years and have relevance in modern fields such as the control of gas inputs to processes, the measurement of leak rates and the separation of gaseous species. Cha and McCoy have derived a convenient formula for the flow of an ideal gas applicable across a wide range of Knudsen numbers (Kn) that approaches the Navier–Stokes equations at small Kn and the Smoluchowski extension of the Knudsen flow equation at large Kn. Smoluchowski’s result relies on the Maxwell definition of the tangential momentum accommodation coefficient α, recently challenged by Aryamore » et al. We measure the flow rate of nitrogen gas in a smooth walled silica tube across a wide range of Knudsen numbers from 0.0048 to 12.4583. We find that the nitrogen flow obeys the Cha and McCoy equation with a large value of α, unlike carbon nanotubes which show flows consistent with a small value of α. Silica capillaries are therefore not atomically smooth. The flow at small Kn has α=0.91 and at large Kn has α close to one, consistent with the redefinition of accommodation coefficient by Arya et al., which also resolves a problem in the literature where there are many observations of α of less than one at small Kn and many equal to one at large Kn. Silica capillaries are an excellent choice for an accurate flow control system. - Highlights: • First experimental study on flow rate across all flow regimes in a well-defined microtube. • Extend Cha and McCoy theory for molecular flow regime. • Demonstrate the Maxwell accommodation coefficient is different in the slip and molecular flow regimes.« less

The thermodynamics of dense granular flow and jamming

NASA Astrophysics Data System (ADS)

Lu, Shih Yu

The scope of the thesis is to propose, based on experimental evidence and theoretical validation, a quantifiable connection between systems that exhibit the jamming phenomenon. When jammed, some materials that flow are able to resist deformation so that they appear solid-like on the laboratory scale. But unlike ordinary fusion, which has a critically defined criterion in pressure and temperature, jamming occurs under a wide range of conditions. These condition have been rigorously investigated but at the moment, no self-consistent framework can apply to grains, foam and colloids that may have suddenly ceased to flow. To quantify the jamming behavior, a constitutive model of dense granular flows is deduced from shear-flow experiments. The empirical equations are then generalized, via a thermodynamic approach, into an equation-of-state for jamming. Notably, the unifying theory also predicts the experimental data on the behavior of molecular glassy liquids. This analogy paves a crucial road map for a unifying theoretical framework in condensed matter, for example, ranging from sand to fire retardants to toothpaste.

Effect of Reynolds and Grashof numbers on mixed convection inside a lid-driven square cavity filled with water-Al2O3 nanofluid

NASA Astrophysics Data System (ADS)

Jaman, Md. Shah; Islam, Showmic; Saha, Sumon; Hasan, Mohammad Nasim; Islam, Md. Quamrul

2016-07-01

A numerical analysis is carried out to study the performance of steady laminar mixed convection flow inside a square lid-driven cavity filled with water-Al2O3 nanofluid. The top wall of the cavity is moving at a constant velocity and is heated by an isothermal heat source. Two-dimensional Navier-stokes equations along with the energy equations are solved using Galerkin finite element method. Results are obtained for a range of Reynolds and Grashof numbers by considering with and without the presence of nanoparticles. The parametric studies for a wide range of governing parameters in case of pure mixed convective flow show significant features of the present problem in terms of streamline and isotherm contours, average Nusselt number and average temperature profiles. The computational results indicate that the heat transfer coeffcient is strongly influenced by the above governing parameters at the pure mixed convection regime.

Highly-Effective Purification of Air on the Fibrous Filtering Nozzles

NASA Astrophysics Data System (ADS)

Galtseva, O. V.; Bordunov, S. V.; Torgaev, S. N.

2016-02-01

A series of experiments by air purification on fibrous filtering nozzles was made. It is experimentally shown that the fibrous filter can operate in a wide rate range. The degree of trapping of fine aerosols of glass was 99% at a linear rate of 0.01 m/s. the degree of capture decreased to 85% at the increasing of filtration rate up to 0.06 m/s. Dustiness of the air ranged from 3 to 5 g/m3 at the course of the experiment. Hydraulic resistance changed from 5 to 25 mm of water column. The calculated data of resistance and falling of pressure on fibrous filters are given; these data were received on the equations from various sources in comparison with experimentally obtained data. According to the results of series of experiments the amendment of the well-known Fuchsian equation is calculated for calculation of the resistance of fibrous air filter. This amendment considers a form and defects of surface of the fibers received by centrifugal-spinneret method.

Optical properties of body-centered tetragonal C4: Insights from many-body perturbation and time-dependent density functional theories

NASA Astrophysics Data System (ADS)

Tarighi Ahmadpour, Mahdi; Rostamnejadi, Ali; Hashemifar, S. Javad

2018-04-01

We study the electronic structure and optical properties of a body-centered tetragonal phase of carbon (bct-C4) within the framework of time-dependent density functional theory and Bethe-Salpeter equation. The results indicate that the optical properties of bct-C4 are strongly affected by the electron-hole interaction. It is demonstrated that the long-range corrected exchange-correlation kernels could fairly reproduce the Bethe-Salpeter equation results. The effective carrier number reveals that at energies above 30 eV, the excitonic effects are not dominant any more and that the optical transitions originate mainly from electronic excitations. The emerged peaks in the calculated electron energy loss spectra are discussed in terms of plasmon excitations and interband transitions. The results of the research indicate that bct-C4 is an indirect wide-band-gap semiconductor, which is transparent in the visible region and opaque in the ultraviolet spectral range.

Large Eddy Simulation of a Supercritical Turbulent Mixing Layer

NASA Astrophysics Data System (ADS)

Sheikhi, Reza; Hadi, Fatemeh; Safari, Mehdi

2017-11-01

Supercritical turbulent flows are relevant to a wide range of applications such as supercritical power cycles, gas turbine combustors, rocket propulsion and internal combustion engines. Large eddy simulation (LES) analysis of such flows involves solving mass, momentum, energy and scalar transport equations with inclusion of generalized diffusion fluxes. These equations are combined with a real gas equation of state and the corresponding thermodynamic mixture variables. Subgrid scale models are needed for not only the conventional convective terms but also the additional high pressure effects arising due to the nonlinearity associated with generalized diffusion fluxes and real gas equation of state. In this study, LES is carried out to study the high pressure turbulent mixing of methane with carbon dioxide in a temporally developing mixing layer under supercritical condition. LES results are assessed by comparing with data obtained from direct numerical simulation (DNS) of the same layer. LES predictions agree favorably with DNS data and represent several key supercritical turbulent flow features such as high density gradient regions. Supported by DOE Grant SC0017097; computational support is provided by DOE National Energy Research Scientific Computing Center.

Towards a unified theory for morphomechanics

PubMed Central

Taber, Larry A.

2009-01-01

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

Gaussian closure technique applied to the hysteretic Bouc model with non-zero mean white noise excitation

NASA Astrophysics Data System (ADS)

Waubke, Holger; Kasess, Christian H.

2016-11-01

Devices that emit structure-borne sound are commonly decoupled by elastic components to shield the environment from acoustical noise and vibrations. The elastic elements often have a hysteretic behavior that is typically neglected. In order to take hysteretic behavior into account, Bouc developed a differential equation for such materials, especially joints made of rubber or equipped with dampers. In this work, the Bouc model is solved by means of the Gaussian closure technique based on the Kolmogorov equation. Kolmogorov developed a method to derive probability density functions for arbitrary explicit first-order vector differential equations under white noise excitation using a partial differential equation of a multivariate conditional probability distribution. Up to now no analytical solution of the Kolmogorov equation in conjunction with the Bouc model exists. Therefore a wide range of approximate solutions, especially the statistical linearization, were developed. Using the Gaussian closure technique that is an approximation to the Kolmogorov equation assuming a multivariate Gaussian distribution an analytic solution is derived in this paper for the Bouc model. For the stationary case the two methods yield equivalent results, however, in contrast to statistical linearization the presented solution allows to calculate the transient behavior explicitly. Further, stationary case leads to an implicit set of equations that can be solved iteratively with a small number of iterations and without instabilities for specific parameter sets.

An isothermal equation of state for solids

NASA Astrophysics Data System (ADS)

Bose Roy, Papiya; Bose Roy, Sushil

2004-07-01

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/ V0= f( P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B‧ ∞=(∂ Bs/∂ P) s( P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P= f( V/ V0), proposed by Birch-and also with those from the EOS model of Keane in which B‧ ∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B‧ ∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B‧ ∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B‧ ∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W-and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B0 and B‧ 0 constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach-a good agreement is observed with the predictions, and the values of B‧ ∞ inferred at different temperatures tend to converge to a constant value.

Effect of Production Process on Microstructure and Mechanical Properties of Copper Coatings of Jet Charges

NASA Astrophysics Data System (ADS)

Gleener, R. E.; Cheerova, M. N.; Shadiev, B. Sh.; Katyukhin, E. B.

2017-07-01

Special features of formation of the grain structure and mechanical properties of copper during recrystallization annealing after cold deformation with a wide range of reduction are studied. The constants of the Hall-Petch equation are determined for copper, the microstructure of which forms in the course of plastic deformation and subsequent heat treatment. The results of the study are allowed for in the process of production of claddings for jet charges.

Mesoscale Particle-Based Model of Electrophoresis

DOE PAGES

Giera, Brian; Zepeda-Ruiz, Luis A.; Pascall, Andrew J.; ...

2015-07-31

Here, we develop and evaluate a semi-empirical particle-based model of electrophoresis using extensive mesoscale simulations. We parameterize the model using only measurable quantities from a broad set of colloidal suspensions with properties that span the experimentally relevant regime. With sufficient sampling, simulated diffusivities and electrophoretic velocities match predictions of the ubiquitous Stokes-Einstein and Henry equations, respectively. This agreement holds for non-polar and aqueous solvents or ionic liquid colloidal suspensions under a wide range of applied electric fields.

Symposium on Numerical and Physical Aspects of Aerodynamic Flows

DTIC Science & Technology

1992-01-15

ReT/R. -1 wide range of Mach numbers including pressure gradient, a = - (a*) (10) surface roughness. surface heating and cooling . and surface 9 I + ReT...and specific heat at constant pressure, respectively. Favre equation is then obtained by contracting the Reynolds-stress decomposition is applied to...their near- wall behavior. In other words, if highly cooled -wall flows are to be predicted correctly, heat fluxes should be modeled e = 2ak + 4bky

Mesoscale Particle-Based Model of Electrophoresis

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

Giera, Brian; Zepeda-Ruiz, Luis A.; Pascall, Andrew J.

Here, we develop and evaluate a semi-empirical particle-based model of electrophoresis using extensive mesoscale simulations. We parameterize the model using only measurable quantities from a broad set of colloidal suspensions with properties that span the experimentally relevant regime. With sufficient sampling, simulated diffusivities and electrophoretic velocities match predictions of the ubiquitous Stokes-Einstein and Henry equations, respectively. This agreement holds for non-polar and aqueous solvents or ionic liquid colloidal suspensions under a wide range of applied electric fields.

TAIR: A transonic airfoil analysis computer code

NASA Technical Reports Server (NTRS)

Dougherty, F. C.; Holst, T. L.; Grundy, K. L.; Thomas, S. D.

1981-01-01

The operation of the TAIR (Transonic AIRfoil) computer code, which uses a fast, fully implicit algorithm to solve the conservative full-potential equation for transonic flow fields about arbitrary airfoils, is described on two levels of sophistication: simplified operation and detailed operation. The program organization and theory are elaborated to simplify modification of TAIR for new applications. Examples with input and output are given for a wide range of cases, including incompressible, subcritical compressible, and transonic calculations.

Modeling Protective Anti-Tumor Immunity via Preventative Cancer Vaccines Using a Hybrid Agent-based and Delay Differential Equation Approach

PubMed Central

Kim, Peter S.; Lee, Peter P.

2012-01-01

A next generation approach to cancer envisions developing preventative vaccinations to stimulate a person's immune cells, particularly cytotoxic T lymphocytes (CTLs), to eliminate incipient tumors before clinical detection. The purpose of our study is to quantitatively assess whether such an approach would be feasible, and if so, how many anti-cancer CTLs would have to be primed against tumor antigen to provide significant protection. To understand the relevant dynamics, we develop a two-compartment model of tumor-immune interactions at the tumor site and the draining lymph node. We model interactions at the tumor site using an agent-based model (ABM) and dynamics in the lymph node using a system of delay differential equations (DDEs). We combine the models into a hybrid ABM-DDE system and investigate dynamics over a wide range of parameters, including cell proliferation rates, tumor antigenicity, CTL recruitment times, and initial memory CTL populations. Our results indicate that an anti-cancer memory CTL pool of 3% or less can successfully eradicate a tumor population over a wide range of model parameters, implying that a vaccination approach is feasible. In addition, sensitivity analysis of our model reveals conditions that will result in rapid tumor destruction, oscillation, and polynomial rather than exponential decline in the tumor population due to tumor geometry. PMID:23133347

Interference, focusing and excitation of ultracold atoms

NASA Astrophysics Data System (ADS)

Kandes, M. C.; Fahy, B. M.; Williams, S. R.; Tally, C. H., IV; Bromley, M. W. J.

2011-05-01

One of the pressing technological challenges in atomic physics is to go orders-of-magnitude beyond the limits of photon-based optics by harnessing the wave-nature of dilute clouds of ultracold atoms. We have developed parallelised algorithms to perform numerical calculations of the Gross-Pitaevskii equation in up to three dimensions and with up to three components to simulate Bose-Einstein condensates. A wide-ranging array of the physics associated with atom optics-based systems will be presented including BEC-based Sagnac interferometry in circular waveguides, the focusing of BECs using Laguerre-Gauss beams, and the interactions between BECs and Ince-Gaussian laser beams and their potential applications. One of the pressing technological challenges in atomic physics is to go orders-of-magnitude beyond the limits of photon-based optics by harnessing the wave-nature of dilute clouds of ultracold atoms. We have developed parallelised algorithms to perform numerical calculations of the Gross-Pitaevskii equation in up to three dimensions and with up to three components to simulate Bose-Einstein condensates. A wide-ranging array of the physics associated with atom optics-based systems will be presented including BEC-based Sagnac interferometry in circular waveguides, the focusing of BECs using Laguerre-Gauss beams, and the interactions between BECs and Ince-Gaussian laser beams and their potential applications. Performed on computational resources via NSF grants PHY-0970127, CHE-0947087 and DMS-0923278.

The terminal velocity of volcanic particles with shape obtained from 3D X-ray microtomography

NASA Astrophysics Data System (ADS)

Dioguardi, Fabio; Mele, Daniela; Dellino, Pierfrancesco; Dürig, Tobias

2017-01-01

New experiments of falling volcanic particles were performed in order to define terminal velocity models applicable in a wide range of Reynolds number Re. Experiments were carried out with fluids of various viscosities and with particles that cover a wide range of size, density and shape. Particle shape, which strongly influences fluid drag, was measured in 3D by High-resolution X-ray microtomography, by which sphericity Φ3D and fractal dimension D3D were obtained. They are easier to measure and less operator dependent than the 2D shape parameters used in previous papers. Drag laws that make use of the new 3D parameters were obtained by fitting particle data to the experiments, and single-equation terminal velocity models were derived. They work well both at high and low Re (3 × 10- 2 < Re < 104), while earlier formulations made use of different equations at different ranges of Re. The new drag laws are well suited for the modelling of particle transportation both in the eruptive column, where coarse and fine particles are present, and also in the distal part of the umbrella region, where fine ash is involved in the large-scale domains of atmospheric circulation. A table of the typical values of Φ3D and D3D of particles from known plinian, subplinian and ash plume eruptions is presented. Graphs of terminal velocity as a function of grain size are finally proposed as tools to help volcanologists and atmosphere scientists to model particle transportation of explosive eruptions.

Control-structure ratings on the Chicago Sanitary and Ship Canal near Lockport, Illinois

USGS Publications Warehouse

Straub, Timothy D.; Johnson, Kevin K.; Hortness, Jon E.; Duncker, James J.

2012-01-01

The U.S. Army Corps of Engineers and the Metropolitan Water Reclamation District of Greater Chicago regulate flows through control structures along the Lake Michigan lakefront and the Chicago Sanitary and Ship Canal (CSSC) for Lake Michigan diversion accounting, flood control, sanitary, and navigation purposes. This report documents the measurement and computation of flow through the Lockport Controlling Works (LCW) and the Lockport Powerhouse. This analysis aided in evaluation of the ratings at both structures, and the development of new ratings at the controlling works. The LCW structure consists of seven 30-feet (ft) wide sluice gates and is used to divert water from the CSSC and into the Des Plaines River. The flow regimes for the sluice gate included both free and submerged weir. Forty and 491 flow values from U.S. Geological Survey streamflow-gaging stations were used to develop equations describing free- and submerged-weir flow, respectively, through the sluice gates. The equations were developed for canal headwater elevations ranging from -7.0 to -10.5 ft Chicago City Datum (CCD), and tailwater (Des Plaines River at Lockport) to headwater (CSSC-LCW-Base) ratios ranging from 0.31 to 0.66. The Lockport Powerhouse structure consists of nine 9-ft wide by 14-ft high sluice gates and two 10-ft diameter turbines. Both tailwater and no-tailwater effect flow regimes occurred during nine measurements. Also, the canal headwater elevations ranged from -2.74 to -8.45 ft CCD, and the gates were configured six different ways during the measurements.

ATMOSPHERIC DYNAMICS OF TERRESTRIAL EXOPLANETS OVER A WIDE RANGE OF ORBITAL AND ATMOSPHERIC PARAMETERS

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

Kaspi, Yohai; Showman, Adam P., E-mail: yohai.kaspi@weizmann.ac.il

The recent discoveries of terrestrial exoplanets and super-Earths extending over a broad range of orbital and physical parameters suggest that these planets will span a wide range of climatic regimes. Characterization of the atmospheres of warm super-Earths has already begun and will be extended to smaller and more distant planets over the coming decade. The habitability of these worlds may be strongly affected by their three-dimensional atmospheric circulation regimes, since the global climate feedbacks that control the inner and outer edges of the habitable zone—including transitions to Snowball-like states and runaway-greenhouse feedbacks—depend on the equator-to-pole temperature differences, patterns of relativemore » humidity, and other aspects of the dynamics. Here, using an idealized moist atmospheric general circulation model including a hydrological cycle, we study the dynamical principles governing the atmospheric dynamics on such planets. We show how the planetary rotation rate, stellar flux, atmospheric mass, surface gravity, optical thickness, and planetary radius affect the atmospheric circulation and temperature distribution on such planets. Our simulations demonstrate that equator-to-pole temperature differences, meridional heat transport rates, structure and strength of the winds, and the hydrological cycle vary strongly with these parameters, implying that the sensitivity of the planet to global climate feedbacks will depend significantly on the atmospheric circulation. We elucidate the possible climatic regimes and diagnose the mechanisms controlling the formation of atmospheric jet streams, Hadley and Ferrel cells, and latitudinal temperature differences. Finally, we discuss the implications for understanding how the atmospheric circulation influences the global climate.« less

CORE-COLLAPSE SUPERNOVA EQUATIONS OF STATE BASED ON NEUTRON STAR OBSERVATIONS

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

Steiner, A. W.; Hempel, M.; Fischer, T.

2013-09-01

Many of the currently available equations of state for core-collapse supernova simulations give large neutron star radii and do not provide large enough neutron star masses, both of which are inconsistent with some recent neutron star observations. In addition, one of the critical uncertainties in the nucleon-nucleon interaction, the nuclear symmetry energy, is not fully explored by the currently available equations of state. In this article, we construct two new equations of state which match recent neutron star observations and provide more flexibility in studying the dependence on nuclear matter properties. The equations of state are also provided in tabularmore » form, covering a wide range in density, temperature, and asymmetry, suitable for astrophysical simulations. These new equations of state are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics with three-flavor Boltzmann neutrino transport. The results are compared with commonly used equations of state in supernova simulations of 11.2 and 40 M{sub Sun} progenitors. We consider only equations of state which are fitted to nuclear binding energies and other experimental and observational constraints. We find that central densities at bounce are weakly correlated with L and that there is a moderate influence of the symmetry energy on the evolution of the electron fraction. The new models also obey the previously observed correlation between the time to black hole formation and the maximum mass of an s = 4 neutron star.« less

A third-order gas-kinetic CPR method for the Euler and Navier-Stokes equations on triangular meshes

NASA Astrophysics Data System (ADS)

Zhang, Chao; Li, Qibing; Fu, Song; Wang, Z. J.

2018-06-01

A third-order accurate gas-kinetic scheme based on the correction procedure via reconstruction (CPR) framework is developed for the Euler and Navier-Stokes equations on triangular meshes. The scheme combines the accuracy and efficiency of the CPR formulation with the multidimensional characteristics and robustness of the gas-kinetic flux solver. Comparing with high-order finite volume gas-kinetic methods, the current scheme is more compact and efficient by avoiding wide stencils on unstructured meshes. Unlike the traditional CPR method where the inviscid and viscous terms are treated differently, the inviscid and viscous fluxes in the current scheme are coupled and computed uniformly through the kinetic evolution model. In addition, the present scheme adopts a fully coupled spatial and temporal gas distribution function for the flux evaluation, achieving high-order accuracy in both space and time within a single step. Numerical tests with a wide range of flow problems, from nearly incompressible to supersonic flows with strong shocks, for both inviscid and viscous problems, demonstrate the high accuracy and efficiency of the present scheme.

Path integral Monte Carlo ground state approach: formalism, implementation, and applications

NASA Astrophysics Data System (ADS)

Yan, Yangqian; Blume, D.

2017-11-01

Monte Carlo techniques have played an important role in understanding strongly correlated systems across many areas of physics, covering a wide range of energy and length scales. Among the many Monte Carlo methods applicable to quantum mechanical systems, the path integral Monte Carlo approach with its variants has been employed widely. Since semi-classical or classical approaches will not be discussed in this review, path integral based approaches can for our purposes be divided into two categories: approaches applicable to quantum mechanical systems at zero temperature and approaches applicable to quantum mechanical systems at finite temperature. While these two approaches are related to each other, the underlying formulation and aspects of the algorithm differ. This paper reviews the path integral Monte Carlo ground state (PIGS) approach, which solves the time-independent Schrödinger equation. Specifically, the PIGS approach allows for the determination of expectation values with respect to eigen states of the few- or many-body Schrödinger equation provided the system Hamiltonian is known. The theoretical framework behind the PIGS algorithm, implementation details, and sample applications for fermionic systems are presented.

Linear and nonlinear spectroscopy from quantum master equations.

PubMed

Fetherolf, Jonathan H; Berkelbach, Timothy C

2017-12-28

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Linear and nonlinear spectroscopy from quantum master equations

NASA Astrophysics Data System (ADS)

Fetherolf, Jonathan H.; Berkelbach, Timothy C.

2017-12-01

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Modeling water vapor and heat transfer in the normal and the intubated airways.

PubMed

Tawhai, Merryn H; Hunter, Peter J

2004-04-01

Intubation of the artificially ventilated patient with an endotracheal tube bypasses the usual conditioning regions of the nose and mouth. In this situation any deficit in heat or moisture in the air is compensated for by evaporation and thermal transfer from the pulmonary airway walls. To study the dynamics of heat and water transport in the intubated airway, a coupled system of nonlinear equations is solved in airway models with symmetric geometry and anatomically based geometry. Radial distribution of heat, water vapor, and velocity in the airway are described by power-law equations. Solution of the time-dependent system of equations yields dynamic airstream and mucosal temperatures and air humidity. Comparison of model results with two independent experimental studies in the normal and intubated airway shows a close correlation over a wide range of minute ventilation. Using the anatomically based model a range of spatially distributed temperature paths is demonstrated, which highlights the model's ability to predict thermal behavior in airway regions currently inaccessible to measurement. Accurate representation of conducting airway geometry is shown to be necessary for simulating mouth-breathing at rates between 15 and 100 l x min(-1), but symmetric geometry is adequate for the low minute ventilation and warm inspired air conditions that are generally supplied to the intubated patient.

Use of Two-Body Correlated Basis Functions with van der Waals Interaction to Study the Shape-Independent Approximation for a Large Number of Trapped Interacting Bosons

NASA Astrophysics Data System (ADS)

Lekala, M. L.; Chakrabarti, B.; Das, T. K.; Rampho, G. J.; Sofianos, S. A.; Adam, R. M.; Haldar, S. K.

2017-05-01

We study the ground-state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small (˜ 3) to very large (˜ 10^7) particle numbers. We use the two-body correlated basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground-state energy and the one-body density for different values of the van der Waals parameter C6. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.

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

PubMed

Siettos, Constantinos; Starke, Jens

2016-09-01

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

Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

NASA Astrophysics Data System (ADS)

Bertini, L.; de Sole, A.; Gabrielli, D.; Jona-Lasinio, G.; Landim, C.

2002-05-01

We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within this theory we derive the following results: the modification of the Onsager-Machlup theory in the SNS; a general Hamilton-Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton-Jacobi equation, we obtain a logically independent derivation of this result.

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

PubMed

Mehta, Paras D

2018-01-01

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

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

NASA Astrophysics Data System (ADS)

Yousefvand, H. R.

2017-12-01

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

Molecular dynamics at low time resolution.

PubMed

Faccioli, P

2010-10-28

The internal dynamics of macromolecular systems is characterized by widely separated time scales, ranging from fraction of picoseconds to nanoseconds. In ordinary molecular dynamics simulations, the elementary time step Δt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale in order not to cut-off physical effects. We show that in systems obeying the overdamped Langevin equation, it is possible to systematically correct for such discretization errors. This is done by analytically averaging out the fast molecular dynamics which occurs at time scales smaller than Δt, using a renormalization group based technique. Such a procedure gives raise to a time-dependent calculable correction to the diffusion coefficient. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps Δt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy model and the denaturation of a protein.

Theoretical analysis of exponential transversal method of lines for the diffusion equation

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

Salazar, A.; Raydan, M.; Campo, A.

1996-12-31

Recently a new approximate technique to solve the diffusion equation was proposed by Campo and Salazar. This new method is inspired on the Method of Lines (MOL) with some insight coming from the method of separation of variables. The proposed method, the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this paper, the authors study the theoretical properties of ETMOL in depth. In particular, consistency,more » stability and convergence are established in the framework of the heat/mass diffusion equation. In most practical applications the method presents a very reduced truncation error in time and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the solutions is then established. The theory is corroborated by several analytical/numerical experiments.« less

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

PubMed

Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten

2016-08-09

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

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

Status and future of the 3D MAFIA group of codes

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

Ebeling, F.; Klatt, R.; Krawzcyk, F.

1988-12-01

The group of fully three dimensional computer codes for solving Maxwell's equations for a wide range of applications, MAFIA, is already well established. Extensive comparisons with measurements have demonstrated the accuracy of the computations. A large numer of components have been designed for accelerators, such as kicker magnets, non cyclindrical cavities, ferrite loaded cavities, vacuum chambers with slots and transitions, etc. The latest additions to the system include a new static solver that can calculate 3D magneto- and electrostatic fields, and a self consistent version of the 2D-BCI that solves the field equations and the equations of motion in parallel.more » Work on new eddy current modules has started, which will allow treatment of laminated and/or solid iron cores excited by low frequency currents. Based on our experience with the present releases 1 and 2, we have started a complete revision of the whole user interface and data structure, which will make the codes even more user-friendly and flexible.« less

Accurate radiative transfer calculations for layered media.

PubMed

Selden, Adrian C

2016-07-01

Simple yet accurate results for radiative transfer in layered media with discontinuous refractive index are obtained by the method of K-integrals. These are certain weighted integrals applied to the angular intensity distribution at the refracting boundaries. The radiative intensity is expressed as the sum of the asymptotic angular intensity distribution valid in the depth of the scattering medium and a transient term valid near the boundary. Integrated boundary equations are obtained, yielding simple linear equations for the intensity coefficients, enabling the angular emission intensity and the diffuse reflectance (albedo) and transmittance of the scattering layer to be calculated without solving the radiative transfer equation directly. Examples are given of half-space, slab, interface, and double-layer calculations, and extensions to multilayer systems are indicated. The K-integral method is orders of magnitude more accurate than diffusion theory and can be applied to layered scattering media with a wide range of scattering albedos, with potential applications to biomedical and ocean optics.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure

NASA Astrophysics Data System (ADS)

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

Colonization of a territory by a stochastic population under a strong Allee effect and a low immigration pressure.

PubMed

Be'er, Shay; Assaf, Michael; Meerson, Baruch

2015-06-01

We study the dynamics of colonization of a territory by a stochastic population at low immigration pressure. We assume a sufficiently strong Allee effect that introduces, in deterministic theory, a large critical population size for colonization. At low immigration rates, the average precolonization population size is small, thus invalidating the WKB approximation to the master equation. We circumvent this difficulty by deriving an exact zero-flux solution of the master equation and matching it with an approximate nonzero-flux solution of the pertinent Fokker-Planck equation in a small region around the critical population size. This procedure provides an accurate evaluation of the quasistationary probability distribution of population sizes in the precolonization state and of the mean time to colonization, for a wide range of immigration rates. At sufficiently high immigration rates our results agree with WKB results obtained previously. At low immigration rates the results can be very different.

A review of selected topics in physics based modeling for tunnel field-effect transistors

NASA Astrophysics Data System (ADS)

Esseni, David; Pala, Marco; Palestri, Pierpaolo; Alper, Cem; Rollo, Tommaso

2017-08-01

The research field on tunnel-FETs (TFETs) has been rapidly developing in the last ten years, driven by the quest for a new electronic switch operating at a supply voltage well below 1 V and thus delivering substantial improvements in the energy efficiency of integrated circuits. This paper reviews several aspects related to physics based modeling in TFETs, and shows how the description of these transistors implies a remarkable innovation and poses new challenges compared to conventional MOSFETs. A hierarchy of numerical models exist for TFETs covering a wide range of predictive capabilities and computational complexities. We start by reviewing seminal contributions on direct and indirect band-to-band tunneling (BTBT) modeling in semiconductors, from which most TCAD models have been actually derived. Then we move to the features and limitations of TCAD models themselves and to the discussion of what we define non-self-consistent quantum models, where BTBT is computed with rigorous quantum-mechanical models starting from frozen potential profiles and closed-boundary Schrödinger equation problems. We will then address models that solve the open-boundary Schrödinger equation problem, based either on the non-equilibrium Green’s function NEGF or on the quantum-transmitting-boundary formalism, and show how the computational burden of these models may vary in a wide range depending on the Hamiltonian employed in the calculations. A specific section is devoted to TFETs based on 2D crystals and van der Waals hetero-structures. The main goal of this paper is to provide the reader with an introduction to the most important physics based models for TFETs, and with a possible guidance to the wide and rapidly developing literature in this exciting research field.

Effective conductivity, dielectric constant, and diffusion coefficient of digitized composite media via first-passage-time equations

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

Torquato, S.; Kim, I.C.; Cule, D.

1999-02-01

We generalize the Brownian motion simulation method of Kim and Torquato [J. Appl. Phys. {bold 68}, 3892 (1990)] to compute the effective conductivity, dielectric constant and diffusion coefficient of digitized composite media. This is accomplished by first generalizing the {ital first-passage-time equations} to treat first-passage regions of arbitrary shape. We then develop the appropriate first-passage-time equations for digitized media: first-passage squares in two dimensions and first-passage cubes in three dimensions. A severe test case to prove the accuracy of the method is the two-phase periodic checkerboard in which conduction, for sufficiently large phase contrasts, is dominated by corners that joinmore » two conducting-phase pixels. Conventional numerical techniques (such as finite differences or elements) do not accurately capture the local fields here for reasonable grid resolution and hence lead to inaccurate estimates of the effective conductivity. By contrast, we show that our algorithm yields accurate estimates of the effective conductivity of the periodic checkerboard for widely different phase conductivities. Finally, we illustrate our method by computing the effective conductivity of the random checkerboard for a wide range of volume fractions and several phase contrast ratios. These results always lie within rigorous four-point bounds on the effective conductivity. {copyright} {ital 1999 American Institute of Physics.}« less

First-principles equation-of-state table of beryllium based on density-functional theory calculations

DOE PAGES

Ding, Y. H.; Hu, S. X.

2017-06-06

Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm 3 and temperature T = 2000 to 10 8 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ~10% stiffer than the lastmore » two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ~20%. By implementing the FPEOS table into the 1-D radiation–hydrodynamic code LILAC, we studied in this paper the EOS effects on beryllium-shell–target implosions. Finally, the FPEOS simulation predicts higher neutron yield (~15%) compared to the simulation using the SESAME 2023 EOS table.« less

First-principles equation-of-state table of beryllium based on density-functional theory calculations

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

Ding, Y. H.; Hu, S. X.

Beryllium has been considered a superior ablator material for inertial confinement fusion (ICF) target designs. An accurate equation-of-state (EOS) of beryllium under extreme conditions is essential for reliable ICF designs. Based on density-functional theory (DFT) calculations, we have established a wide-range beryllium EOS table of density ρ = 0.001 to 500 g/cm 3 and temperature T = 2000 to 10 8 K. Our first-principle equation-of-state (FPEOS) table is in better agreement with the widely used SESAME EOS table (SESAME 2023) than the average-atom INFERNO and Purgatorio models. For the principal Hugoniot, our FPEOS prediction shows ~10% stiffer than the lastmore » two models in the maximum compression. Although the existing experimental data (only up to 17 Mbar) cannot distinguish these EOS models, we anticipate that high-pressure experiments at the maximum compression region should differentiate our FPEOS from INFERNO and Purgatorio models. Comparisons between FPEOS and SESAME EOS for off-Hugoniot conditions show that the differences in the pressure and internal energy are within ~20%. By implementing the FPEOS table into the 1-D radiation–hydrodynamic code LILAC, we studied in this paper the EOS effects on beryllium-shell–target implosions. Finally, the FPEOS simulation predicts higher neutron yield (~15%) compared to the simulation using the SESAME 2023 EOS table.« less

Influence of the electromagnetic parameters on the surface wave attenuation in thin absorbing layers

NASA Astrophysics Data System (ADS)

Li, Yinrui; Li, Dongmeng; Wang, Xian; Nie, Yan; Gong, Rongzhou

2018-05-01

This paper describes the relationships between the surface wave attenuation properties and the electromagnetic parameters of radar absorbing materials (RAMs). In order to conveniently obtain the attenuation constant of TM surface waves over a wide frequency range, the simplified dispersion equations in thin absorbing materials were firstly deduced. The validity of the proposed method was proved by comparing with the classical dispersion equations. Subsequently, the attenuation constants were calculated separately for the absorbing layers with hypothetical relative permittivity and permeability. It is found that the surface wave attenuation properties can be strongly tuned by the permeability of RAM. Meanwhile, the permittivity should be appropriate so as to maintain high cutoff frequency. The present work provides specific methods and designs to improve the attenuation performances of radar absorbing materials.

Effect of Prestresses on the Dispersion of Quasi-Lamb Waves in the System Consisting of an Ideal Liquid Layer and a Compressible Elastic Layer

NASA Astrophysics Data System (ADS)

Bagno, A. M.

2017-03-01

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer interacting with a layer of an ideal compressible fluid is studied. The three-dimensional equations of linearized elasticity and the assumption of finite strains for the elastic layer and the three-dimensional linearized Euler equations for the fluid are used. The dispersion curves for the quasi-Lamb modes are plotted over a wide frequency range. The effect of prestresses and the thickness of the elastic and liquid layers on the frequency spectrum of normal quasi-Lamb waves is analyzed. The localization properties of the lower quasi-Lamb modes in the elastic-fluid waveguides are studied. The numerical results are presented in the form of graphs and analyzed

Analytic theory of orbit contraction and ballistic entry into planetary atmospheres

NASA Technical Reports Server (NTRS)

Longuski, J. M.; Vinh, N. X.

1980-01-01

A space object traveling through an atmosphere is governed by two forces: aerodynamic and gravitational. On this premise, equations of motion are derived to provide a set of universal entry equations applicable to all regimes of atmospheric flight from orbital motion under the dissipate force of drag through the dynamic phase of reentry, and finally to the point of contact with the planetary surface. Rigorous mathematical techniques such as averaging, Poincare's method of small parameters, and Lagrange's expansion, applied to obtain a highly accurate, purely analytic theory for orbit contraction and ballistic entry into planetary atmospheres. The theory has a wide range of applications to modern problems including orbit decay of artificial satellites, atmospheric capture of planetary probes, atmospheric grazing, and ballistic reentry of manned and unmanned space vehicles.

A laboratory facility for electric vehicle propulsion system testing

NASA Technical Reports Server (NTRS)

Sargent, N. B.

1980-01-01

The road load simulator facility located at the NASA Lewis Research Center enables a propulsion system or any of its components to be evaluated under a realistic vehicle inertia and road loads. The load is applied to the system under test according to the road load equation: F(net)=K1F1+K2F2V+K3 sq V+K4(dv/dt)+K5 sin theta. The coefficient of each term in the equation can be varied over a wide range with vehicle inertial representative of vehicles up to 7500 pounds simulated by means of flywheels. The required torque is applied by the flywheels, a hydroviscous absorber and clutch, and a drive motor integrated by a closed loop control system to produce a smooth, continuous load up to 150 horsepower.

Recent advances in modeling Hugoniots with Cheetah

NASA Astrophysics Data System (ADS)

Glaesemann, Kurt

2005-07-01

The detonation of an energetic material is the result of a complex interaction between kinetic chemical reactions and thermodynamic chemical equilibrium. Unfortunately, little is known concerning the detailed chemical kinetics of reacting energetic materials. Cheetah uses rate laws to treat species with the slowest chemical reactions, while assuming other chemical species are in equilibrium. Cheetah supports a wide range of elements and condensed detonation products and can also be applied to gas phase reactions. Improvements have been made to Cheetah's equilibrium solver, that allow it to find a wider range of thermodynamic states. Many of the difficulties experienced by users in earlier versions of Cheetah have been fixed. New capabilities have also been added. The ultimate result is a code that can be applied to a wide range of shock problems involving both energetic and non-energetic materials. New experimental validations of Cheetah's equation of state methodology have been performed, including both reacted and unreacted Hugoniots. This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

A new dimension of organizational justice: procedural voice.

PubMed

Jepsen, Denise; Rodwell, John

2009-10-01

Dimensionality of the Colquitt justice measures was investigated across a wide range of service occupations. Structural equation modeling of data from 410 survey respondents found support for the 4-factor model of justice (procedural, distributive, interpersonal, and informational), although significant improvement of model fit was obtained by including a new latent variable, "procedural voice," which taps employees' desire to express their views and feelings and influence results. The model was confirmed in a second sample (N = 505) in the same organization six months later.

Eigenvalue Tests and Distributions for Small Sample Order Determination for Complex Wishart Matrices

DTIC Science & Technology

1994-08-13

theoretic order determination criteria for ARMA(p, q) models can be expressed in the form of equation 4.2. The word ARIMA should not be a distractor...subjectivity is not necessarily bad. It enables us to build tractable models and efficiently achieve reasonable results. The charge of "subjectivity" lodged...signal processing studies because it simplifies the mathematics involved and it is not a bad model for a wide range of situations. Wooding [293] is

Research procedure for buck-boost converter for small electric vehicles

NASA Astrophysics Data System (ADS)

Vacheva, Gergana; Hinov, Nikolay; Penev, Dimitar

2017-12-01

In the current paper is developed a mathematical model realized in Matlab for describing a buck-boost converter for control of small electric vehicle. The model is presented with differential equations which describes the processes in the converter. Through the research of this model it can be accomplished the optimal work mode of a small electric vehicles. The proposed converter can be used in a wide range of applications like small electric vehicles, smart grids and different systems for energy storage.

Rotative balance of the I.M.F. Lille and associated experimental techniques

NASA Technical Reports Server (NTRS)

Verbrugge, R.

1981-01-01

The study of aerodynamic effects at high incidence associated with motions of wide amplitude incorporating continuous rotations requires the consideration of coupled effects, which are generally nonlinear, in a formulation of equations of motion. A rotative balance designed to simulate such maneuvers in a windtunnel was created to form a test medium for analytical studies. A general description of the assembly is provided by considering two main ranges of application. The capacities and performance of the assembly are discussed.

A multiple-objective optimal exploration strategy

USGS Publications Warehouse

Christakos, G.; Olea, R.A.

1988-01-01

Exploration for natural resources is accomplished through partial sampling of extensive domains. Such imperfect knowledge is subject to sampling error. Complex systems of equations resulting from modelling based on the theory of correlated random fields are reduced to simple analytical expressions providing global indices of estimation variance. The indices are utilized by multiple objective decision criteria to find the best sampling strategies. The approach is not limited by geometric nature of the sampling, covers a wide range in spatial continuity and leads to a step-by-step procedure. ?? 1988.

Wideband Low-Reflection Inhomogeneous Dielectric Structures

NASA Astrophysics Data System (ADS)

Denisova, N. A.; Rezvov, A. V.

2017-08-01

We consider reflection of electromagnetic waves from two-layer dielectric films with finite thickness, whose refractive indices vary in the direction of wave propagation, which is perpendicular to the substrate boundary. The profiles of the refractive indices of the structures having low reflection coefficients in a wide frequency range are found. The obtained results are based on exact analytical solutions of the Helmholtz equation for one type of the layered inhomogeneous dielectric medium. The possibility of creating new low-reflection wideband inhomogeneous dielectric structures is demonstrated.

Solution of underdetermined systems of equations with gridded a priori constraints.

PubMed

Stiros, Stathis C; Saltogianni, Vasso

2014-01-01

The TOPINV, Topological Inversion algorithm (or TGS, Topological Grid Search) initially developed for the inversion of highly non-linear redundant systems of equations, can solve a wide range of underdetermined systems of non-linear equations. This approach is a generalization of a previous conclusion that this algorithm can be used for the solution of certain integer ambiguity problems in Geodesy. The overall approach is based on additional (a priori) information for the unknown variables. In the past, such information was used either to linearize equations around approximate solutions, or to expand systems of observation equations solved on the basis of generalized inverses. In the proposed algorithm, the a priori additional information is used in a third way, as topological constraints to the unknown n variables, leading to an R(n) grid containing an approximation of the real solution. The TOPINV algorithm does not focus on point-solutions, but exploits the structural and topological constraints in each system of underdetermined equations in order to identify an optimal closed space in the R(n) containing the real solution. The centre of gravity of the grid points defining this space corresponds to global, minimum-norm solutions. The rationale and validity of the overall approach are demonstrated on the basis of examples and case studies, including fault modelling, in comparison with SVD solutions and true (reference) values, in an accuracy-oriented approach.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

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

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

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

1988-01-01

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

AN INTEGRAL EQUATION REPRESENTATION OF WIDE-BAND ELECTROMAGNETIC SCATTERING BY THIN SHEETS

EPA Science Inventory

An efficient, accurate numerical modeling scheme has been developed, based on the integral equation solution to compute electromagnetic (EM) responses of thin sheets over a wide frequency band. The thin-sheet approach is useful for simulating the EM response of a fracture system ...

Maximizing noise energy for noise-masking studies.

PubMed

Jules Étienne, Cédric; Arleo, Angelo; Allard, Rémy

2017-08-01

Noise-masking experiments are widely used to investigate visual functions. To be useful, noise generally needs to be strong enough to noticeably impair performance, but under some conditions, noise does not impair performance even when its contrast approaches the maximal displayable limit of 100 %. To extend the usefulness of noise-masking paradigms over a wider range of conditions, the present study developed a noise with great masking strength. There are two typical ways of increasing masking strength without exceeding the limited contrast range: use binary noise instead of Gaussian noise or filter out frequencies that are not relevant to the task (i.e., which can be removed without affecting performance). The present study combined these two approaches to further increase masking strength. We show that binarizing the noise after the filtering process substantially increases the energy at frequencies within the pass-band of the filter given equated total contrast ranges. A validation experiment showed that similar performances were obtained using binarized-filtered noise and filtered noise (given equated noise energy at the frequencies within the pass-band) suggesting that the binarization operation, which substantially reduced the contrast range, had no significant impact on performance. We conclude that binarized-filtered noise (and more generally, truncated-filtered noise) can substantially increase the energy of the noise at frequencies within the pass-band. Thus, given a limited contrast range, binarized-filtered noise can display higher energy levels than Gaussian noise and thereby widen the range of conditions over which noise-masking paradigms can be useful.

A fluid-mechanic-based model for the sedimentation of flocculated suspensions

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

Chhabra, R.P.; Prasad, D.

1991-02-01

Due to the wide occurrence of the suspensions of fine particles in mineral and chemical processing industries, considerable interest has been shown in modeling the hydrodynamic behavior of such systems. A fluid-mechanic-based analysis is presented for the settling behavior of flocculated4d suspensions. Flocs have been modeled as composite spheres consisting of a solid core embedded in a shell of homogeneous and isotropic porous medium. Theoretical estimates of the rates of sedimentation for flocculated suspensions are obtained by solving the equations of continuity and of motion. The interparticle interactions are incorporated into the analysis by employing the Happel free surface cellmore » model. The results reported embrace wide ranges of conditions of floc size and concentration.« less

Electromagnetic Nanoparticles for Sensing and Medical Diagnostic Applications

PubMed Central

Vegni, Lucio

2018-01-01

A modeling and design approach is proposed for nanoparticle-based electromagnetic devices. First, the structure properties were analytically studied using Maxwell’s equations. The method provides us a robust link between nanoparticles electromagnetic response (amplitude and phase) and their geometrical characteristics (shape, geometry, and dimensions). Secondly, new designs based on “metamaterial” concept are proposed, demonstrating great performances in terms of wide-angle range functionality and multi/wide behavior, compared to conventional devices working at the same frequencies. The approach offers potential applications to build-up new advanced platforms for sensing and medical diagnostics. Therefore, in the final part of the article, some practical examples are reported such as cancer detection, water content measurements, chemical analysis, glucose concentration measurements and blood diseases monitoring. PMID:29652853

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TRIANGULATED SURFACES*

PubMed Central

Fu, Zhisong; Jeong, Won-Ki; Pan, Yongsheng; Kirby, Robert M.; Whitaker, Ross T.

2012-01-01

This paper presents an efficient, fine-grained parallel algorithm for solving the Eikonal equation on triangular meshes. The Eikonal equation, and the broader class of Hamilton–Jacobi equations to which it belongs, have a wide range of applications from geometric optics and seismology to biological modeling and analysis of geometry and images. The ability to solve such equations accurately and efficiently provides new capabilities for exploring and visualizing parameter spaces and for solving inverse problems that rely on such equations in the forward model. Efficient solvers on state-of-the-art, parallel architectures require new algorithms that are not, in many cases, optimal, but are better suited to synchronous updates of the solution. In previous work [W. K. Jeong and R. T. Whitaker, SIAM J. Sci. Comput., 30 (2008), pp. 2512–2534], the authors proposed the fast iterative method (FIM) to efficiently solve the Eikonal equation on regular grids. In this paper we extend the fast iterative method to solve Eikonal equations efficiently on triangulated domains on the CPU and on parallel architectures, including graphics processors. We propose a new local update scheme that provides solutions of first-order accuracy for both architectures. We also propose a novel triangle-based update scheme and its corresponding data structure for efficient irregular data mapping to parallel single-instruction multiple-data (SIMD) processors. We provide detailed descriptions of the implementations on a single CPU, a multicore CPU with shared memory, and SIMD architectures with comparative results against state-of-the-art Eikonal solvers. PMID:22641200

Second relativistic mean field and virial equation of state for astrophysical simulations

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

Shen, G.; Horowitz, C. J.; O'Connor, E.

2011-06-15

We generate a second equation of state (EOS) of nuclear matter for a wide range of temperatures, densities, and proton fractions for use in supernovae, neutron star mergers, and black hole formation simulations. We employ full relativistic mean field (RMF) calculations for matter at intermediate density and high density, and the virial expansion of a nonideal gas for matter at low density. For this EOS we use the RMF effective interaction FSUGold, whereas our earlier EOS was based on the RMF effective interaction NL3. The FSUGold interaction has a lower pressure at high densities compared to the NL3 interaction. Wemore » calculate the resulting EOS at over 100 000 grid points in the temperature range T=0 to 80 MeV, the density range n{sub B}=10{sup -8} to 1.6 fm{sup -3}, and the proton fraction range Y{sub p}=0 to 0.56. We then interpolate these data points using a suitable scheme to generate a thermodynamically consistent equation of state table on a finer grid. We discuss differences between this EOS, our NL3-based EOS, and previous EOSs by Lattimer-Swesty and H. Shen et al. for the thermodynamic properties, composition, and neutron star structure. The original FSUGold interaction produces an EOS, which we call FSU1.7, that has a maximum neutron star mass of 1.7 solar masses. A modification in the high-density EOS is introduced to increase the maximum neutron star mass to 2.1 solar masses and results in a slightly different EOS that we call FSU2.1. The EOS tables for FSU1.7 and FSU2.1 are available for download.« less

The Effectiveness of Circular Equating as a Criterion for Evaluating Equating.

ERIC Educational Resources Information Center

Wang, Tianyou; Hanson, Bradley A.; Harris, Deborah J.

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

On the die compaction of powders used in pharmaceutics.

PubMed

Aryanpour, Gholamreza; Farzaneh, Masoud

2018-07-01

Die compaction is widely used in the compaction of pharmaceutical powders (tableting). It is well known that the powder densification is a result of particle rearrangement and particle deformation. The former is considered to be the governing mechanism of densification in an initial stage of compaction and the latter is regarded as the governing mechanism in the compaction at the higher pressure range. As a more realistic assumption, one can consider that a simultaneous performance of both the rearrangement and deformation mechanisms takes place from the beginning of compaction. To mathematically formulate this assumption, a piston equation is presented where the material relative density is given as a function of the applied pressure on the powder. From the equation, it is possible to obtain the contribution of each mechanism to the material densification at each value of the applied pressure. In the continuation, the piston equation is applied to the tabletting of some pharmaceutical powders. These are the powders of Ascorbic Acid, Avicel ® PH 101, Avicel ® PH 301, Emcompress ® , Sodium Chloride, and Tablettose ® whose tableting results have been previously published in the literature. The results show the piston equation as a suitable approach to describe the tabletting of pharmaceutical powders.

Modeling Aerodynamically Generated Sound of Helicopter Rotors

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

2002-01-01

A great deal of progress has been made in the modeling of aerodynamically generated sound of rotors over the past decade. Although the modeling effort has focused on helicopter main rotors, the theory is generally valid for a wide range of rotor configurations. The Ffowcs Williams Hawkings (FW-H) equation has been the foundation for much of the development. The monopole and dipole source terms of the FW-H equation account for the thickness and loading noise, respectively. Bladevortex-interaction noise and broadband noise are important types of loading noise, hence much research has been directed toward the accurate modeling of these noise mechanisms. Both subsonic and supersonic quadrupole noise formulations have been developed for the prediction of high-speed impulsive noise. In an effort to eliminate the need to compute the quadrupole contribution, the FW-H equation has also been utilized on permeable surfaces surrounding all physical noise sources. Comparisons of the Kirchhoff formulation for moving surfaces with the FW-H equation have shown that the Kirchhoff formulation for moving surfaces can give erroneous results for aeroacoustic problems. Finally, significant progress has been made incorporating the rotor noise models into full vehicle noise prediction tools.

Discretization analysis of bifurcation based nonlinear amplifiers

NASA Astrophysics Data System (ADS)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show inmore » two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.« less

A molecular model for cohesive slip at polymer melt/solid interfaces.

PubMed

Tchesnokov, M A; Molenaar, J; Slot, J J M; Stepanyan, R

2005-06-01

A molecular model is proposed which predicts wall slip by disentanglement of polymer chains adsorbed on a wall from those in the polymer bulk. The dynamics of the near-wall boundary layer is found to be governed by a nonlinear equation of motion, which accounts for such mechanisms on surface chains as convection, retraction, constraint release, and thermal fluctuations. This equation is valid over a wide range of grafting regimes, including those in which interactions between neighboring adsorbed molecules become essential. It is not closed since the dynamics of adsorbed chains is shown to be coupled to that of polymer chains in the bulk via constraint release. The constitutive equations for the layer and bulk, together with continuity of stress and velocity, are found to form a closed system of equations which governs the dynamics of the whole "bulk+boundary layer" ensemble. Its solution provides a stick-slip law in terms of the molecular parameters and extruder geometry. The model is quantitative and contains only those parameters that can be measured directly, or extracted from independent rheological measurements. The model predictions show a good agreement with available experimental data.

Position-Dependent Mass Schrödinger Equation for the Morse Potential

NASA Astrophysics Data System (ADS)

Ovando, G.; Peña, J. J.; Morales, J.; López-Bonilla, J.

2017-01-01

The position dependent mass Schrödinger equation (PDMSE) has a wide range of quantum applications such as the study of semiconductors, quantum wells, quantum dots and impurities in crystals, among many others. On the other hand, the Morse potential is one of the most important potential models used to study the electronic properties of diatomic molecules. In this work, the solution of the effective mass one-dimensional Schrödinger equation for the Morse potential is presented. This is done by means of the canonical transformation method in algebraic form. The PDMSE is solved for any model of the proposed kinetic energy operators as for example the BenDaniel-Duke, Gora-Williams, Zhu-Kroemer or Li-Kuhn. Also, in order to solve the PDMSE with Morse potential, we consider a superpotential leading to a special form of the exactly solvable Schrödinger equation of constant mass for a class of multiparameter exponential-type potential along with a proper mass distribution. The proposed approach is general and can be applied in the search of new potentials suitable on science of materials by looking into the viable choices of the mass function.

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190

A quantitative investigation of the solar modulation of cosmic-ray protons and helium nuclei. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Garrard, T. L.

1972-01-01

The differential energy spectra of cosmic ray protons and He nuclei were measured at energies up to 315 MeV/nucleon using balloon-borne and satellite-borne instruments. These spectra are presented for solar quiet times for the years 1966 through 1970. The data analysis is verified by extensive accelerator calibrations of the detector systems and by calculations and measurements of the production of secondary protons in the atmosphere. The spectra of protons and He nuclei in this energy range are dominated by the solar modulation of the local interstellar spectra. Numerical solutions to the transport equation are presented for a wide range of parameters.

Dynamic principle for ensemble control tools.

PubMed

Samoletov, A; Vasiev, B

2017-11-28

Dynamical equations describing physical systems in contact with a thermal bath are commonly extended by mathematical tools called "thermostats." These tools are designed for sampling ensembles in statistical mechanics. Here we propose a dynamic principle underlying a range of thermostats which is derived using fundamental laws of statistical physics and ensures invariance of the canonical measure. The principle covers both stochastic and deterministic thermostat schemes. Our method has a clear advantage over a range of proposed and widely used thermostat schemes that are based on formal mathematical reasoning. Following the derivation of the proposed principle, we show its generality and illustrate its applications including design of temperature control tools that differ from the Nosé-Hoover-Langevin scheme.

The drag and terminal velocity of volcanic ash and lapilli with 3D shape obtained by X-ray microtomography

NASA Astrophysics Data System (ADS)

Dioguardi, Fabio; Mele, Daniela; Dellino, Pierfrancesco; Dürig, Tobias

2017-04-01

New experiments of falling volcanic particles were performed in order to define drag and terminal velocity models applicable in a wide range of Reynolds number Re. Experiments were carried out with fluids of various viscosities and with particles that cover a wide range of size, density and shape. Particle shape, which strongly influences fluid drag, was measured in 3D by High-resolution X-ray microtomography, by which sphericity and fractal dimension were obtained, the latter used for quantifying the aerodynamic drag of irregular particles for the first time. With this method, the measure of particle shape descriptors proved to be easier and less operator dependent than previously used 2D image particle analyses. Drag laws that make use of the new 3D parameters were obtained by fitting particle data to the experiments, and single-equation terminal velocity models were derived. They work well both at high and low Re (3x10-2 < Re < 104), while earlier formulations made use of different equations at different ranges of Re. The new drag laws are well suited for the modelling of particle transportation both in the eruptive column and pyroclastic density currents, where coarse and fine particles are present, and also in the distal part of the umbrella region, where fine ash is involved in the large-scale domains of atmospheric circulation. A table of the typical values of 3D sphericity and fractal dimension of particles from known plinian, subplinian and ash plume eruptions is presented. Graphs of terminal velocity as a function of grain size are proposed as tools to help volcanologists and atmosphere scientists to model particle transportation of explosive eruptions. Some volcanological application examples are finally presented.

High-throughput determination of octanol/water partition coefficients using a shake-flask method and novel two-phase solvent system.

PubMed

Morikawa, Go; Suzuka, Chihiro; Shoji, Atsushi; Shibusawa, Yoichi; Yanagida, Akio

2016-01-05

A high-throughput method for determining the octanol/water partition coefficient (P(o/w)) of a large variety of compounds exhibiting a wide range in hydrophobicity was established. The method combines a simple shake-flask method with a novel two-phase solvent system comprising an acetonitrile-phosphate buffer (0.1 M, pH 7.4)-1-octanol (25:25:4, v/v/v; AN system). The AN system partition coefficients (K(AN)) of 51 standard compounds for which log P(o/w) (at pH 7.4; log D) values had been reported were determined by single two-phase partitioning in test tubes, followed by measurement of the solute concentration in both phases using an automatic flow injection-ultraviolet detection system. The log K(AN) values were closely related to reported log D values, and the relationship could be expressed by the following linear regression equation: log D=2.8630 log K(AN) -0.1497(n=51). The relationship reveals that log D values (+8 to -8) for a large variety of highly hydrophobic and/or hydrophilic compounds can be estimated indirectly from the narrow range of log K(AN) values (+3 to -3) determined using the present method. Furthermore, log K(AN) values for highly polar compounds for which no log D values have been reported, such as amino acids, peptides, proteins, nucleosides, and nucleotides, can be estimated using the present method. The wide-ranging log D values (+5.9 to -7.5) of these molecules were estimated for the first time from their log K(AN) values and the above regression equation. Copyright © 2015 Elsevier B.V. All rights reserved.

Effects of system-bath coupling on a photosynthetic heat engine: A polaron master-equation approach

NASA Astrophysics Data System (ADS)

Qin, M.; Shen, H. Z.; Zhao, X. L.; Yi, X. X.

2017-07-01

Stimulated by suggestions of quantum effects in energy transport in photosynthesis, the fundamental principles responsible for the near-unit efficiency of the conversion of solar to chemical energy became active again in recent years. Under natural conditions, the formation of stable charge-separation states in bacteria and plant reaction centers is strongly affected by the coupling of electronic degrees of freedom to a wide range of vibrational motions. These inspire and motivate us to explore the effects of the environment on the operation of such complexes. In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect the exciton-transfer processes in the Photosystem II reaction center described by a quantum heat engine (QHE) model over a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in detail. We interpret these results in terms of noise-assisted transport effect and dynamical localization, which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is the dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms are manifestations of the dual role played by bath-induced fluctuations depending on the range of parameters. The origin and role of coherence are also discussed. It is the constructive interplay between noise and coherent dynamics, rather than the mere presence or absence of coherence or noise, that is responsible for the optimal heat engine performance. In addition, we find that the effective voltage of QHE exhibits superior robustness against the bath noise as long as the system-bath coupling is not very strong.

The stable carbon isotope ratios in benthic food webs of the gulf of Calvi, Corsica

NASA Astrophysics Data System (ADS)

Dauby, Patrick

1989-02-01

The Gulf of Calvi, Corsica, presents a wide diversity of biocoenoses, amongst which the seagrass Posidonia meadow is prevalent. More than 100 plant, animal and sediment samples from various biotopes were analysed for their stable carbon isotope ratios, to assess carbon flows within the food chains. Marine plants display a wide range of δ 13C values, from -6 to -32‰ but with three relatively well distinct peaks for Posidonia, brown algae and phytoplankton (-9, -19 and -23‰, respectively), which are the main carbon sources. The range of isotopic values of animals is narrower, from -14 to -24‰, suggesting that they feed mainly on algae and plankton. Computations based on simple equations show the proportion of each carbon source in the diet of the animals. Posidonia, notwithstanding their important biomass, appear to be a minor food source; this is possibly because of the transfer of their dead leaves, towards the shorelines, in winter.

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions.

PubMed

Karasiev, Valentin V; Dufty, James W; Trickey, S B

2018-02-16

Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (XC) free-energy functional accurate over a wide range of state conditions. Unlike the ground-state case, no such functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free-energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Its accuracy in the warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated T. Pressure shifts for hot electrons in compressed static fcc Al and for low-density Al demonstrate the combined magnitude of thermal and gradient effects handled well by this functional over a wide T range.

A microwave scattering model for layered vegetation

NASA Technical Reports Server (NTRS)

Karam, Mostafa A.; Fung, Adrian K.; Lang, Roger H.; Chauhan, Narinder S.

1992-01-01

A microwave scattering model was developed for layered vegetation based on an iterative solution of the radiative transfer equation up to the second order to account for multiple scattering within the canopy and between the ground and the canopy. The model is designed to operate over a wide frequency range for both deciduous and coniferous forest and to account for the branch size distribution, leaf orientation distribution, and branch orientation distribution for each size. The canopy is modeled as a two-layered medium above a rough interface. The upper layer is the crown containing leaves, stems, and branches. The lower layer is the trunk region modeled as randomly positioned cylinders with a preferred orientation distribution above an irregular soil surface. Comparisons of this model with measurements from deciduous and coniferous forests show good agreements at several frequencies for both like and cross polarizations. Major features of the model needed to realize the agreement include allowance for: (1) branch size distribution, (2) second-order effects, and (3) tree component models valid over a wide range of frequencies.

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

NASA Astrophysics Data System (ADS)

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

2018-02-01

Realizing the potential for predictive density functional calculations of matter under extreme conditions depends crucially upon having an exchange-correlation (X C ) free-energy functional accurate over a wide range of state conditions. Unlike the ground-state case, no such functional exists. We remedy that with systematic construction of a generalized gradient approximation X C free-energy functional based on rigorous constraints, including the free-energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T , high-T , and homogeneous electron gas limits. Its accuracy in the warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated T . Pressure shifts for hot electrons in compressed static fcc Al and for low-density Al demonstrate the combined magnitude of thermal and gradient effects handled well by this functional over a wide T range.

The rate dependent response of a bistable chain at finite temperature

NASA Astrophysics Data System (ADS)

Benichou, Itamar; Zhang, Yaojun; Dudko, Olga K.; Givli, Sefi

2016-10-01

We study the rate dependent response of a bistable chain subjected to thermal fluctuations. The study is motivated by the fact that the behavior of this model system is prototypical to a wide range of nonlinear processes in materials physics, biology and chemistry. To account for the stochastic nature of the system response, we formulate a set of governing equations for the evolution of the probability density of meta-stable configurations. Based on this approach, we calculate the behavior for a wide range of parametric values, such as rate, temperature, overall stiffness, and number of elements in the chain. Our results suggest that fundamental characteristics of the response, such as average transition stress and hysteresis, can be captured by a simple law which folds the influence of all these factors into a single non-dimensional quantity. We also show that the applicability of analytical results previously obtained for single-well systems can be extended to systems having multiple wells by proper definition of rate and of the transition stress.

Introduction, comparison, and validation of Meta-Essentials: A free and simple tool for meta-analysis.

PubMed

Suurmond, Robert; van Rhee, Henk; Hak, Tony

2017-12-01

We present a new tool for meta-analysis, Meta-Essentials, which is free of charge and easy to use. In this paper, we introduce the tool and compare its features to other tools for meta-analysis. We also provide detailed information on the validation of the tool. Although free of charge and simple, Meta-Essentials automatically calculates effect sizes from a wide range of statistics and can be used for a wide range of meta-analysis applications, including subgroup analysis, moderator analysis, and publication bias analyses. The confidence interval of the overall effect is automatically based on the Knapp-Hartung adjustment of the DerSimonian-Laird estimator. However, more advanced meta-analysis methods such as meta-analytical structural equation modelling and meta-regression with multiple covariates are not available. In summary, Meta-Essentials may prove a valuable resource for meta-analysts, including researchers, teachers, and students. © 2017 The Authors. Research Synthesis Methods published by John Wiley & Sons Ltd.

Development of liquid-environment frequency modulation atomic force microscope with low noise deflection sensor for cantilevers of various dimensions

NASA Astrophysics Data System (ADS)

Fukuma, Takeshi; Jarvis, Suzanne P.

2006-04-01

We have developed a liquid-environment frequency modulation atomic force microscope (FM-AFM) with a low noise deflection sensor for a wide range of cantilevers with different dimensions. A simple yet accurate equation describing the theoretical limit of the optical beam deflection method in air and liquid is presented. Based on the equation, we have designed a low noise deflection sensor. Replaceable microscope objective lenses are utilized for providing a high magnification optical view (resolution: <3μm) as well as for focusing a laser beam (laser spot size: ˜10μm). Even for a broad range of cantilevers with lengths from 35to125μm, the sensor provides deflection noise densities of less than 11fm/√Hz in air and 16fm/√Hz in water. In particular, a cantilever with a length of 50μm gives the minimum deflection noise density of 5.7fm/√Hz in air and 7.3fm/√Hz in water. True atomic resolution of the developed FM-AFM is demonstrated by imaging mica in water.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Unique Results and Lessons Learned from the TSS Missions

NASA Technical Reports Server (NTRS)

Stone, Nobie H.

2016-01-01

In 1924, Irvin Langmuir and H. M. Mott-Smith published a theoretical model for the complex plasma sheath phenomenon in which they identified some very special cases which greatly simplified the sheath and allowed a closed solution to the problem. The most widely used application is for an electrostatic, or "Langmuir," probe in laboratory plasma. Although the Langmuir probe is physically simple (a biased wire) the theory describing its functional behavior and its current-voltage characteristic is extremely complex and, accordingly, a number of assumptions and approximations are used in the LMS model. These simplifications, correspondingly, place limits on the model's range of application. Adapting the LMS model to real-life conditions is the subject of numerous papers and dissertations. The Orbit-Motion Limited (OML) model that is widely used today is one of these adaptions that is a convenient means of calculating sheath effects. The OML equation for electron current collection by a positively biased body is simply: I is approximately equal to A x j(sub eo) x 2/v??(phi)(exp ½) where A is the area of the body and phi is the electric potential on the body with respect to the plasma. Since the Langmuir probe is a simple biased wire immersed in plasma, it is particularly tempting to use the OML equation in calculating the characteristics of the long, highly biased wires of an Electric Sail in the solar wind plasma. However, in order to arrive at the OML equation, a number of additional simplifying assumptions and approximations (beyond those made by Langmuir-Mott-Smith) are necessary. The OML equation is a good approximation when all conditions are met, but it would appear that the Electric Sail problem lies outside of the limits of applicability.

A hybridized method for computing high-Reynolds-number hypersonic flow about blunt bodies

NASA Technical Reports Server (NTRS)

Weilmuenster, K. J.; Hamilton, H. H., II

1979-01-01

A hybridized method for computing the flow about blunt bodies is presented. In this method the flow field is split into its viscid and inviscid parts. The forebody flow field about a parabolic body is computed. For the viscous solution, the Navier-Stokes equations are solved on orthogonal parabolic coordinates using explicit finite differencing. The inviscid flow is determined by using a Moretti type scheme in which the Euler equations are solved, using explicit finite differences, on a nonorthogonal coordinate system which uses the bow shock as an outer boundary. The two solutions are coupled along a common data line and are marched together in time until a converged solution is obtained. Computed results, when compared with experimental and analytical results, indicate the method works well over a wide range of Reynolds numbers and Mach numbers.

Linear approximations of global behaviors in nonlinear systems with moderate or strong noise

NASA Astrophysics Data System (ADS)

Liang, Junhao; Din, Anwarud; Zhou, Tianshou

2018-03-01

While many physical or chemical systems can be modeled by nonlinear Langevin equations (LEs), dynamical analysis of these systems is challenging in the cases of moderate and strong noise. Here we develop a linear approximation scheme, which can transform an often intractable LE into a linear set of binomial moment equations (BMEs). This scheme provides a feasible way to capture nonlinear behaviors in the sense of probability distribution and is effective even when the noise is moderate or big. Based on BMEs, we further develop a noise reduction technique, which can effectively handle tough cases where traditional small-noise theories are inapplicable. The overall method not only provides an approximation-based paradigm to analysis of the local and global behaviors of nonlinear noisy systems but also has a wide range of applications.

A cell-vertex multigrid method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Radespiel, R.

1989-01-01

A cell-vertex scheme for the Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing, a multigrid method, and carefully controlled artificial dissipative terms, very good convergence rates are obtained for a wide range of two- and three-dimensional flows over airfoils and wings. The accuracy of the code is examined by grid refinement studies and comparison with experimental data. For an accurate prediction of turbulent flows with strong separations, a modified version of the nonequilibrium turbulence model of Johnson and King is introduced, which is well suited for an implementation into three-dimensional Navier-Stokes codes. It is shown that the solutions for three-dimensional flows with strong separations can be dramatically improved, when a nonequilibrium model of turbulence is used.

Calculation of the Pitot tube correction factor for Newtonian and non-Newtonian fluids.

PubMed

Etemad, S Gh; Thibault, J; Hashemabadi, S H

2003-10-01

This paper presents the numerical investigation performed to calculate the correction factor for Pitot tubes. The purely viscous non-Newtonian fluids with the power-law model constitutive equation were considered. It was shown that the power-law index, the Reynolds number, and the distance between the impact and static tubes have a major influence on the Pitot tube correction factor. The problem was solved for a wide range of these parameters. It was shown that employing Bernoulli's equation could lead to large errors, which depend on the magnitude of the kinetic energy and energy friction loss terms. A neural network model was used to correlate the correction factor of a Pitot tube as a function of these three parameters. This correlation is valid for most Newtonian, pseudoplastic, and dilatant fluids at low Reynolds number.

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

The Exact Solution for Linear Thermoelastic Axisymmetric Deformations of Generally Laminated Circular Cylindrical Shells

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.; Schultz, Marc R.

2012-01-01

A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.

Synchronous acceleration with tapered dielectric-lined waveguides

NASA Astrophysics Data System (ADS)

Lemery, F.; Floettmann, K.; Piot, P.; Kärtner, F. X.; Aßmann, R.

2018-05-01

We present a general concept to accelerate nonrelativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell's equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program astra and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of 100 MV /m . Numerical simulations indicate that a ˜200 -keV electron beam can be accelerated to an energy of ˜10 MeV over ˜10 cm with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.

Explicit 2-D Hydrodynamic FEM Program

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

Lin, Jerry

1996-08-07

DYNA2D* is a vectorized, explicit, two-dimensional, axisymmetric and plane strain finite element program for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. DYNA2D* contains 13 material models and 9 equations of state (EOS) to cover a wide range of material behavior. The material models implemented in all machine versions are: elastic, orthotropic elastic, kinematic/isotropic elastic plasticity, thermoelastoplastic, soil and crushable foam, linear viscoelastic, rubber, high explosive burn, isotropic elastic-plastic, temperature-dependent elastic-plastic. The isotropic and temperature-dependent elastic-plastic models determine only the deviatoric stresses. Pressure is determined by one of 9 equations of state including linear polynomial, JWL highmore » explosive, Sack Tuesday high explosive, Gruneisen, ratio of polynomials, linear polynomial with energy deposition, ignition and growth of reaction in HE, tabulated compaction, and tabulated.« less

Efficient Computation of Atmospheric Flows with Tempest: Validation of Next-Generation Climate and Weather Prediction Algorithms at Non-Hydrostatic Scales

NASA Astrophysics Data System (ADS)

Guerra, Jorge; Ullrich, Paul

2016-04-01

Tempest is a next-generation global climate and weather simulation platform designed to allow experimentation with numerical methods for a wide range of spatial resolutions. The atmospheric fluid equations are discretized by continuous / discontinuous finite elements in the horizontal and by a staggered nodal finite element method (SNFEM) in the vertical, coupled with implicit/explicit time integration. At horizontal resolutions below 10km, many important questions remain on optimal techniques for solving the fluid equations. We present results from a suite of idealized test cases to validate the performance of the SNFEM applied in the vertical with an emphasis on flow features and dynamic behavior. Internal gravity wave, mountain wave, convective bubble, and Cartesian baroclinic instability tests will be shown at various vertical orders of accuracy and compared with known results.

Explanation of climate and human impacts on sediment discharge change in Darwinian hydrology: Derivation of a differential equation

NASA Astrophysics Data System (ADS)

Zhang, Jianjun; Gao, Guangyao; Fu, Bojie; Zhang, Lu

2018-04-01

The assessment for impacts of climate variability and human activities on suspended sediment yield (SSY) change has long been a question of great interest. However, the sediment generation processes are sophisticated with high nonlinearity and great uncertainty, which give rise to extreme complexity for SSY change assessment in Newtonian approach. Consequently, few approaches can be simply but widely applied to decompose impacts of climatic variability and human activities on SSY change. Thus, it is an urgent need to develop advanced methods that are simple and robust. Since that the Newtonian approach is hardly achievable due to limitation of either observations or knowledge of mechanisms, there have been repeated calls to capture the hydrologic system in Darwinian approach for hydrological change prediction or explanation. As streamflow is the carrier of suspended sediment, SSY change are thus documented in changes of sediment concentrated flow and suspended sediment concentration - water discharge (C-Q) relationships. By deduced corollaries, a differential equation of sediment discharge change was derived to explicitly decompose impacts of climate variability and human activities in Darwinian hydrology. Besides, a new form of sediment rating curves was proposed and curved as C-Q relationships and probability distribution of sediment concentrated flow. River sediment flux can be revealed by this representation, which simply elucidates mechanism of SSY generation covering a range of time scales from finer than rainfall-event to long term. By the new sediment rating curves, the differential equation was partly solved using a segmentation algorithm proposed and validated in this paper, and then was submitted to water balance framework expressed by Budyko-type equation. Thus, for catchment management, hydrologists can obtain explicit explanation of how climate variation and human activities propagate through landscape and result in sediment discharge change. The differential equation is simple and robust for widely application in sediment discharge change assessment, as only discrete data of precipitation, potential evaporation and C-Q observed at gauging stations are required.

Absolute paleobathymetry of Upper Cretaceous chalks based on ostracodes - Evidence from the Demopolis Chalk (Campanian and Maastrichtian) of the northern Gulf Coastal Plain

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

Puckett, T.M.

1991-05-01

The presence of abundant and diverse sighted ostracodes in chalk and marl of the Demopolis Chalk (Campanian and Maastrichtian) in Alabama and Mississippi strongly suggests that the Late Cretaceous sea floor was within the photic zone. The maximum depth of deposition is calculated from an equation based on eye morphology and efficiency and estimates of the vertical light attenuation. In this equation, K, the vertical light attenuation coefficient, is the most critical variable because it is the divisor for the rest of the equation. Rates of accumulation of coccoliths during the Cretaceous are estimated and are on the same ordermore » as those in modern areas of high phytoplankton production, suggesting similar pigment and coccolith concentrations in the water column. Values of K are known for a wide range of water masses and pigment concentrations, including areas of high phytoplankton production; thus light attenuation through the Cretaceous seas can be estimated reliably. Waters in which attenuation is due only to biogenic matter-conditions that result in deposition of relatively pure chalk-have values of K ranging between 0.2 and 0.3. Waters rich in phytoplankton and mud-conditions that result in deposition of marl-have K values as great as 0.5. Substituting these values for K results in depth range of 65 to 90 m for deposition of chalk and depth of 35 m for deposition of marl. These depth values suggest that deposition of many Cretaceous chalks and marls around the world were deposited under relatively shallow conditions.« less

Model Comparison of Bayesian Semiparametric and Parametric Structural Equation Models

ERIC Educational Resources Information Center

Song, Xin-Yuan; Xia, Ye-Mao; Pan, Jun-Hao; Lee, Sik-Yum

2011-01-01

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

The compressive behaviour and constitutive equation of polyimide foam in wide strain rate and temperature

NASA Astrophysics Data System (ADS)

Yoshimoto, Akifumi; Kobayashi, Hidetoshi; Horikawa, Keitaro; Tanigaki, Kenichi

2015-09-01

These days, polymer foams, such as polyurethane foam and polystyrene foam, are used in various situations as a thermal insulator or shock absorber. In general, however, their strength is insufficient in high temperature environments because of their low glass transition temperature. Polyimide is a polymer which has a higher glass transition temperature and high strength. Its mechanical properties do not vary greatly, even in low temperature environments. Therefore, polyimide foam is expected to be used in the aerospace industry. Thus, the constitutive equation of polyimide foam that can be applied across a wide range of strain rates and ambient temperature is very useful. In this study, a series of compression tests at various strain rates, from 10-3 to 103 s-1 were carried out in order to examine the effect of strain rate on the compressive properties of polyimide foam. The flow stress of polyimide foam increased rapidly at dynamic strain rates. The effect of ambient temperature on the properties of polyimide foam was also investigated at temperature from - 190 °C to 270°∘C. The flow stress decreased with increasing temperature.

Experiences in Automated Calibration of a Nickel Equation of State

NASA Astrophysics Data System (ADS)

Carpenter, John H.

2017-06-01

Wide availability of large computers has led to increasing incorporation of computational data, such as from density functional theory molecular dynamics, in the development of equation of state (EOS) models. Once a grid of computational data is available, it is usually left to an expert modeler to model the EOS using traditional techniques. One can envision the possibility of using the increasing computing resources to perform black-box calibration of EOS models, with the goal of reducing the workload on the modeler or enabling non-experts to generate good EOSs with such a tool. Progress towards building such a black-box calibration tool will be explored in the context of developing a new, wide-range EOS for nickel. While some details of the model and data will be shared, the focus will be on what was learned by automatically calibrating the model in a black-box method. Model choices and ensuring physicality will also be discussed. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Calculating the Ionization Constant of Functional Groups of Carboxyl Ion Exchangers

NASA Astrophysics Data System (ADS)

Meychik, N. R.; Stepanov, S. I.; Nikolaeva, Yu. I.

2018-02-01

The potentiometric titration of a weakly basic carboxyl cation exchanger, obtained via alkaline hydrolysis of an acrylonitrile copolymer with divinyl benzene (degree of crosslinking, 12%) in a wide range of variation in a solution of pH (2-12) and NaCl (concentration 0.01, 0.1, 0.5, 1 M), is considered. The maximum ion-exchange capacity of the ion exchanger for Na+ is determined (10.10 ± 0.088 mmol/g of the dry mass) and found to be independent of the solution's ionic strength. It is established that in the investigated range of NaCl concentrations and pH, the acid-base balance is adequately described by Gregor's equation. The parameters of this equation are calculated as a function of the NaCl concentration: p K a = 8.13 ± 0.04, n = 1.50 ± 0.02 for 0.01 M; p K a = 6.56 ± 0.04, n = 2.60 ± 0.07 for 0.1 M; and p K a = 5.66 ± 0.6, n = 2.62 ± 0.06 for 0.5 and 1 M. It is shown that to describe the acid-base balance correctly within the proposed model we must estimate the adequacy of the experimental and calculated values of the ion exchanger's capacity at each pH value according to the calculated parameters of Gregor's equation.

Some New Lidar Equations for Laser Pulses Scattered Back from Optically Thick Media Such as Clouds, Dense Aerosol Plumes, Sea Ice, Snow, and Turbid Coastal Waters

NASA Technical Reports Server (NTRS)

Davis, Anthony B.

2013-01-01

I survey the theoretical foundations of the slowly-but-surely emerging field of multiple scattering lidar, which has already found applications in atmospheric and cryospheric optics that I also discuss. In multiple scattering lidar, returned pulses are stretched far beyond recognition, and there is no longer a one-to-one connection between range and return-trip timing. Moreover, one can exploit the radial profile of the diffuse radiance field excited by the laser source that, by its very nature, is highly concentrated in space and collimated in direction. One needs, however, a new class of lidar equations to explore this new phenomenology. A very useful set is derived from radiative diffusion theory, which is found at the opposite asymptotic limit of radiative transfer theory than the conventional (single-scattering) limit used to derive the standard lidar equation. In particular, one can use it to show that, even if the simple time-of-flight-to-range connection is irretrievably lost, multiply-scattered lidar light can be used to restore a unique profiling capability with coarser resolution but much deeper penetration into a wide variety of optical thick media in nature. Several new applications are proposed, including a laser bathymetry technique that should work for highly turbid coastal waters.

Rethinking Use of the OML Model in Electric Sail Development

NASA Technical Reports Server (NTRS)

Stone, Nobie H.

2016-01-01

In 1924, Irvin Langmuir and H. M. Mott-Smith published a theoretical model for the complex plasma sheath phenomenon in which they identified some very special cases which greatly simplified the sheath and allowed a closed solution to the problem. The most widely used application is for an electrostatic, or "Langmuir," probe in laboratory plasma. Although the Langmuir probe is physically simple (a biased wire) the theory describing its functional behavior and its current-voltage characteristic is extremely complex and, accordingly, a number of assumptions and approximations are used in the LMS model. These simplifications, correspondingly, place limits on the model's range of application. Adapting the LMS model to real-life conditions is the subject of numerous papers and dissertations. The Orbit-Motion Limited (OML) model that is widely used today is one of these adaptions that is a convenient means of calculating sheath effects. Since the Langmuir probe is a simple biased wire immersed in plasma, it is particularly tempting to use the OML equation in calculating the characteristics of the long, highly biased wires of an Electric Sail in the solar wind plasma. However, in order to arrive at the OML equation, a number of additional simplifying assumptions and approximations (beyond those made by Langmuir-Mott-Smith) are necessary. The OML equation is a good approximation when all conditions are met, but it would appear that the Electric Sail problem lies outside of the limits of applicability.

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

USGS Publications Warehouse

Franz, Delbert D.; Melching, Charles S.

1997-01-01

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

Generalized first-order kinetic model for biosolids decomposition and oxidation during hydrothermal treatment.

PubMed

Shanableh, A

2005-01-01

The main objective of this study was to develop generalized first-order kinetic models to represent hydrothermal decomposition and oxidation of biosolids within a wide range of temperatures (200-450 degrees C). A lumping approach was used in which oxidation of the various organic ingredients was characterized by the chemical oxygen demand (COD), and decomposition was characterized by the particulate (i.e., nonfilterable) chemical oxygen demand (PCOD). Using the Arrhenius equation (k = k(o)e(-Ea/RT)), activation energy (Ea) levels were derived from 42 continuous-flow hydrothermal treatment experiments conducted at temperatures in the range of 200-450 degrees C. Using predetermined values for k(o) in the Arrhenius equation, the activation energies of the various organic ingredients were separated into 42 values for oxidation and a similar number for decomposition. The activation energy values were then classified into levels representing the relative ease at which the organic ingredients of the biosolids were oxidized or decomposed. The resulting simple first-order kinetic models adequately represented, within the experimental data range, hydrothermal decomposition of the organic particles as measured by PCOD and oxidation of the organic content as measured by COD. The modeling approach presented in the paper provide a simple and general framework suitable for assessing the relative reaction rates of the various organic ingredients of biosolids.

Large perturbation flow field analysis and simulation for supersonic inlets

NASA Technical Reports Server (NTRS)

Varner, M. O.; Martindale, W. R.; Phares, W. J.; Kneile, K. R.; Adams, J. C., Jr.

1984-01-01

An analysis technique for simulation of supersonic mixed compression inlets with large flow field perturbations is presented. The approach is based upon a quasi-one-dimensional inviscid unsteady formulation which includes engineering models of unstart/restart, bleed, bypass, and geometry effects. Numerical solution of the governing time dependent equations of motion is accomplished through a shock capturing finite difference algorithm, of which five separate approaches are evaluated. Comparison with experimental supersonic wind tunnel data is presented to verify the present approach for a wide range of transient inlet flow conditions.

Reactive Flow Modeling of Liquid Explosives via ALE3D/Cheetah Simulations

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

Kuo, I W; Bastea, S; Fried, L E

2010-03-10

We carried out reactive flow simulations of liquid explosives such as nitromethane using the hydrodynamic code ALE3D coupled with equations of state and reaction kinetics modeled by the thermochemical code Cheetah. The simulation set-up was chosen to mimic cylinder experiments. For pure unconfined nitromethane we find that the failure diameter and detonation velocity dependence on charge diameter are in agreement with available experimental results. Such simulations are likely to be useful for determining detonability and failure behavior for a wide range of experimental conditions and explosive compounds.

Vecksler-Macmillan phase stability for neutral atoms accelerated by a laser beam

NASA Astrophysics Data System (ADS)

Mel'nikov, I. V.; Haus, J. W.; Kazansky, P. G.

2003-05-01

We use a Fokker-Planck equation to study the phenomenon of accelerating a neutral atom bunch by a chirped optical beam. This method enables us to obtain a semi-analytical solution to the problem in which a wide range of parameters can be studied. In addition it provides a simple physical interpretation where the problem is reduced to an analogous problem of charged particles accelerators, that is, the Vecksler-Macmillan principle of phase stability. A possible experimental scenario is suggested, which uses a photonic crystal fiber as the guiding medium.

Universal solution for the characteristic time and the degree of settlement in nonlinear soil consolidation scenarios. A deduction based on nondimensionalization

NASA Astrophysics Data System (ADS)

Alhama Manteca, Iván; García-Ros, Gonzalo; Alhama López, Francisco

2018-04-01

Using the mathematical-physical process of nondimensionalization of governing equations, the problem of nonlinear soil consolidation based on the Cornetti and Battaglio model removing some of the restrictive hypotheses assumed by these authors is studied for the search of the dimensionless groups that govern the characteristic time and the average degree of settlement. The derived groups, once verified by numerical simulations, allow the universal representation of the aforementioned unknowns for the wide range of properties of real soils.

Perturbation-iteration theory for analyzing microwave striplines

NASA Technical Reports Server (NTRS)

Kretch, B. E.

1985-01-01

A perturbation-iteration technique is presented for determining the propagation constant and characteristic impedance of an unshielded microstrip transmission line. The method converges to the correct solution with a few iterations at each frequency and is equivalent to a full wave analysis. The perturbation-iteration method gives a direct solution for the propagation constant without having to find the roots of a transcendental dispersion equation. The theory is presented in detail along with numerical results for the effective dielectric constant and characteristic impedance for a wide range of substrate dielectric constants, stripline dimensions, and frequencies.

Deducing noninductive current profile from surface voltage evolution

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

Litwin, C.; Wukitch, S.; Hershkowitz, N.

Solving the resistive diffusion equation in the presence of a noninductive current source determines the time-evolution of the surface voltage. By inverting the problem the current drive profile can be determined from the surface voltage evolution. We show that under wide range of conditions the deduced profile is unique. If the conductivity profile is known, this method can be employed to infer the noninductive current profile, and, ipso facto, the profile of the total current. We discuss the application of this method to analyze the Alfven wave current drive experiments in Phaedrus-T.

Low Temperature Kinetics of the First Steps of Water Cluster Formation

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

Bourgalais, J.; Roussel, V.; Capron, M.

2016-03-01

We present a combined experimental and theoretical low temperature kinetic study of water cluster formation. Water cluster growth takes place in low temperature (23-69 K) supersonic flows. The observed kinetics of formation of water clusters are reproduced with a kinetic model based on theoretical predictions for the first steps of clusterization. The temperature-and pressure-dependent association and dissociation rate coefficients are predicted with an ab initio transition state theory based master equation approach over a wide range of temperatures (20-100 K) and pressures (10(-6) - 10 bar).

Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.

PubMed

Banks, H Thomas; Robbins, Danielle; Sutton, Karyn L

2013-01-01

In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

Numerical simulation of the hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor

NASA Astrophysics Data System (ADS)

Fortova, S. V.; Shepelev, V. V.; Troshkin, O. V.; Kozlov, S. A.

2017-09-01

The paper presents the results of numerical simulation of the development of hydrodynamic instabilities of Richtmyer-Meshkov and Rayleigh-Taylor encountered in experiments [1-3]. For the numerical solution used the TPS software package (Turbulence Problem Solver) that implements a generalized approach to constructing computer programs for a wide range of problems of hydrodynamics, described by the system of equations of hyperbolic type. As numerical methods are used the method of large particles and ENO-scheme of the second order with Roe solver for the approximate solution of the Riemann problem.

Design of structure and simulation of the three-zone gasifier of dense layer of the inverted process

NASA Astrophysics Data System (ADS)

Zagrutdinov, R. Sh; Negutorov, V. N.; Maliykhin, D. G.; Nikishanin, M. S.; Senachin, P. K.

2017-11-01

Experts of LLC “New Energy Technologies” have developed gasifiers designs, with the implementation of the three-zone gasification method, which satisfy the following conditions: 1) the generated gas must be free from tar, soot and hydrocarbons, with a given ratio of CO/H2; 2) to use as the fuel source a wide range of low-grade low-value solid fuels, including biomass and various kinds of carbonaceous wastes; 3) have high reliability in operation, do not require qualified operating personnel, be relatively inexpensive to produce and use steam-air blowing instead of expensive steam-oxygen one; 4) the line of standard sizes should be sufficiently wide (with a single unit capacity of fuel from 1 to 50-70 MW). Two models of gas generators of the inverted gasification process with three combustion zones operating under pressure have been adopted for design: 1) gas generator with a remote combustion chamber type GOP-VKS (two-block version) and 2) a gas generator with a common combustion chamber of the GOP-OK type (single-block version), which is an almost ideal model for increasing the unit capacity. There have been worked out various schemes for the preparation of briquettes from practically the entire spectrum of low-grade fuel: high-ash and high-moisture coals, peat and biomass, including all types of waste - solid household waste, crop, livestock, poultry, etc. In the gas generators there are gasified the cylindrical briquettes with a diameter of 20-25 mm and a length of 25-35 mm. There have been developed a mathematical model and computer code for numerical simulation of synthesis gas generation processes in a gasifier of a dense layer of inverted process during a steam-air blast, including: continuity equations for the 8 gas phase components and for the solid phase; the equation of the heat balance for the entire heterogeneous system; the Darcy law equation (for porous media); equation of state for 8 components of the gas phase; equations for the rates of 3 gas-phase and 4 heterogeneous reactions; macro kinetics law of coke combustion; other equations and boundary conditions.

An analysis of fiber-matrix interface failure stresses for a range of ply stress states

NASA Technical Reports Server (NTRS)

Crews, J. H.; Naik, R. A.; Lubowinski, S. J.

1993-01-01

A graphite/bismaleimide laminate was prepared without the usual fiber treatment and was tested over a wide range of stress states to measure its ply cracking strength. These tests were conducted using off-axis flexure specimens and produced fiber-matrix interface failure data over a correspondingly wide range of interface stress states. The absence of fiber treatment, weakened the fiber-matrix interfaces and allowed these tests to be conducted at load levels that did not yield the matrix. An elastic micromechanics computer code was used to calculate the fiber-matrix interface stresses at failure. Two different fiber-array models (square and diamond) were used in these calculations to analyze the effects of fiber arrangement as well as stress state on the critical interface stresses at failure. This study showed that both fiber-array models were needed to analyze interface stresses over the range of stress states. A linear equation provided a close fit to these critical stress combinations and, thereby, provided a fiber-matrix interface failure criterion. These results suggest that prediction procedures for laminate ply cracking can be based on micromechanics stress analyses and appropriate fiber-matrix interface failure criteria. However, typical structural laminates may require elastoplastic stress analysis procedures that account for matrix yielding, especially for shear-dominated ply stress states.

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

PubMed Central

Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946

Modeling the initial mechanical response and yielding behavior of gelled crude oil

NASA Astrophysics Data System (ADS)

Lei, Chen; Gang, Liu; Xingguo, Lu; Minghai, Xu; Yuannan, Tang

2018-05-01

The initial mechanical response and yielding behavior of gelled crude oil under constant shear rate conditions were investigated. By putting the Maxwell mechanical analog and a special dashpot in parallel, a quasi-Jeffreys model was obtained. The kinetic equation of the structural parameter in the Houska model was simplified reasonably so that a simplified constitutive equation of the special dashpot was expressed. By introducing a damage factor into the constitutive equation of the special dashpot and the Maxwell mechanical analog, we established a constitutive equation of the quasi-Jeffreys model. Rheological tests of gelled crude oil were conducted by imposing constant shear rates and the relationship between the shear stress and shear strain under different shear rates was plotted. It is found that the constitutive equation can fit the experimental data well under a wide range of shear rates. Based on the fitted parameters in the quasi-Jeffreys model, the shear stress changing rules of the Maxwell mechanical analog and the special dashpot were calculated and analyzed. It is found that the critical yield strain and the corresponding shear strain where shear stress of the Maxwell analog is the maximum change slightly under different shear rates. And then a critical damage softening strain which is irrelevant to the shearing conditions was put forward to describe the yielding behavior of gelled crude oil.

Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

PubMed

Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2016-04-12

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

Analysis of finite-strain equations of state for solids under high pressures

NASA Astrophysics Data System (ADS)

Sushil, K.; Arunesh, K.; Singh, P. K.; Sharma, B. S.

2004-10-01

We have reformulated equations of state (EOS) for solids based on Lagrangian and Eulerian strains following the method developed by Stacey [Phys. Earth Planet. Inter. 128 (2001) 179]. The expressions thus obtained are used conveniently to assess the validity of various EOS for different types of solids. The logarithmic EOS based on the Hencky measure of finite-strain is also modified by including the higher terms arising from the fourth-order contribution in the Taylor series expansion of the free energy. The results are obtained for pressure (P), isothermal bulk modulus (KT) and its pressure derivative (dKT/dP) for Ne, Ar, Al, Cu, LiH and MgO solids for a wide range of compressions (V/V0) down to 0.5. The results determined from the finite-strain equations are compared with those obtained from the Vinet-Rydberg equation and the Shanker equation, which are based on the interatomic potential energy functions. The results are also compared with the ab inito values reported by Hama and Suito [J. Phys.: Condens. Matter 8 (1996) 67] determined from first-principles calculations using the augmented plane wave method and the quantum statistical model. The EOS based on the K‧ finite-strain theory due to Keane and Stacey are also discussed, emphasising the importance of K∞‧ , in the limit P→∞.

Nonextensive Thomas-Fermi model

NASA Astrophysics Data System (ADS)

Shivamoggi, Bhimsen; Martinenko, Evgeny

2007-11-01

Nonextensive Thomas-Fermi model was father investigated in the following directions: Heavy atom in strong magnetic field. following Shivamoggi work on the extension of Kadomtsev equation we applied nonextensive formalism to father generalize TF model for the very strong magnetic fields (of order 10e12 G). The generalized TF equation and the binding energy of atom were calculated which contain a new nonextensive term dominating the classical one. The binding energy of a heavy atom was also evaluated. Thomas-Fermi equations in N dimensions which is technically the same as in Shivamoggi (1998) ,but behavior is different and in interesting 2 D case nonextesivity prevents from becoming linear ODE as in classical case. Effect of nonextensivity on dielectrical screening reveals itself in the reduction of the envelope radius. It was shown that nonextesivity in each case is responsible for new term dominating classical thermal correction term by order of magnitude, which is vanishing in a limit q->1. Therefore it appears that nonextensive term is ubiquitous for a wide range of systems and father work is needed to understand the origin of it.

Equation of State of Ammonium Nitrate

NASA Astrophysics Data System (ADS)

Robbins, David L.; Sheffield, Stephen A.; Dattelbaum, Dana M.; Velisavljevic, Nenad; Stahl, David B.

2009-12-01

Ammonium nitrate (AN) is a widely used fertilizer and mining explosive. AN is commonly used in ammonium nitrate-fuel oil (ANFO), which is a mixture of explosive-grade AN prills and fuel oil in a 94:6 ratio by weight. ANFO is a non-ideal explosive with measured detonation velocities around 4 km/s. The equation of state properties and known initiation behavior of neat AN are limited. We present the results of a series of gas gun-driven plate impact experiments on pressed neat ammonium nitrate at 1.72 g/cm3. No evidence of initiation was observed under shock loading to 22 GPa. High pressure x-ray diffraction experiments in diamond anvil cells provided insight into the high pressure phase behavior over the same pressure range (to 25 GPa), as well as a static isotherm at ambient temperature. From the isotherm and thermodynamic properties at ambient conditions, a preliminary unreacted equation of state (EOS) has been developed based on the Murnaghan isotherm and Helmholtz formalism [1], which compares favorably with the available experimental Hugoniot data on several densities of AN.

Exact solutions of the Navier-Stokes equations generalized for flow in porous media

NASA Astrophysics Data System (ADS)

Daly, Edoardo; Basser, Hossein; Rudman, Murray

2018-05-01

Flow of Newtonian fluids in porous media is often modelled using a generalized version of the full non-linear Navier-Stokes equations that include additional terms describing the resistance to flow due to the porous matrix. Because this formulation is becoming increasingly popular in numerical models, exact solutions are required as a benchmark of numerical codes. The contribution of this study is to provide a number of non-trivial exact solutions of the generalized form of the Navier-Stokes equations for parallel flow in porous media. Steady-state solutions are derived in the case of flows in a medium with constant permeability along the main direction of flow and a constant cross-stream velocity in the case of both linear and non-linear drag. Solutions are also presented for cases in which the permeability changes in the direction normal to the main flow. An unsteady solution for a flow with velocity driven by a time-periodic pressure gradient is also derived. These solutions form a basis for validating computational models across a wide range of Reynolds and Darcy numbers.

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.

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

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

Mu, Lin; Wang, Junping; Ye, Xiu

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2017-08-17

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for bothmore » the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.« less

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

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

A reduced-dimensional model for near-wall transport in cardiovascular flows

PubMed Central

Hansen, Kirk B.

2015-01-01

Near-wall mass transport plays an important role in many cardiovascular processes, including the initiation of atherosclerosis, endothelial cell vasoregulation, and thrombogenesis. These problems are characterized by large Péclet and Schmidt numbers as well as a wide range of spatial and temporal scales, all of which impose computational difficulties. In this work, we develop an analytical relationship between the flow field and near-wall mass transport for high-Schmidt-number flows. This allows for the development of a wall-shear-stress-driven transport equation that lies on a codimension-one vessel-wall surface, significantly reducing computational cost in solving the transport problem. Separate versions of this equation are developed for the reaction-rate-limited and transport-limited cases, and numerical results in an idealized abdominal aortic aneurysm are compared to those obtained by solving the full transport equations over the entire domain. The reaction-rate-limited model matches the expected results well. The transport-limited model is accurate in the developed flow regions, but overpredicts wall flux at entry regions and reattachment points in the flow. PMID:26298313

Role of phase synchronisation in turbulence

NASA Astrophysics Data System (ADS)

Moradi, Sara; Teaca, Bogdan; Anderson, Johan

2017-11-01

The role of the phase dynamics in turbulence is investigated. As a demonstration of the importance of the phase dynamics, a simplified system is used, namely the one-dimensional Burgers equation, which is evolved numerically. The system is forced via a known external force, with two components that are added into the evolution equations of the amplitudes and the phase of the Fourier modes, separately. In this way, we are able to control the impact of the force on the dynamics of the phases. In the absence of the direct forcing in the phase equation, it is observed that the phases are not stochastic as assumed in the Random Phase Approximation (RPA) models, and in contrast, the non-linear couplings result in intermittent locking of the phases to ± π/2. The impact of the force, applied purely on the phases, is to increase the occurrence of the phase locking events in which the phases of the modes in a wide k range are now locked to ± π/2, leading to a change in the dynamics of both phases and amplitudes, with a significant localization of the real space flow structures.

Community-wide assessment of intensive care outcomes using a physiologically based prognostic measure: implications for critical care delivery from Cleveland Health Quality Choice.

PubMed

Sirio, C A; Shepardson, L B; Rotondi, A J; Cooper, G S; Angus, D C; Harper, D L; Rosenthal, G E

1999-03-01

To examine the applicability of a previously developed intensive care prognostic measure to a community-based sample of hospitals, and assess variations in severity-adjusted mortality across a major metropolitan region. Retrospective cohort study. Twenty-eight hospitals with 38 ICUs participating in a community-wide initiative to measure performance supported by the business community, hospitals, and physicians. Included in the study were 116,340 consecutive eligible patients admitted to medical, surgical, neurologic, and mixed medical/surgical ICUs between March 1, 1991, and March 31, 1995. The risk of hospital mortality was assessed using a previous risk prediction equation that was developed in a national sample, and a reestimated logistic regression model fit to the current sample. The standardized mortality ratio (SMR) (actual/predicted mortality) was used to describe hospital performance. Although discrimination of the previous national risk equation in the current sample was high (receiver operating characteristic [ROC] curve area = 0.90), the equation systematically overestimated the risk of death and was not as well calibrated (Hosmer-Lemeshow statistic, 2407.6, 8 df, p < 0.001). The locally derived equation had similar discrimination (ROC curve area = 0.91), but had improved calibration across all ranges of severity (Hosmer-Lemeshow statistic = 13.5, 8 df, p = 0.10). Hospital SMRs ranged from 0.85 to 1.21, and four hospitals had SMRs that were higher or lower (p < 0.01) than 1.0. Variation in SMRs tended to be greatest during the first year of data collection. SMRs also tended to decline over the 4 years (1.06, 1.02, 0.98, and 0.94 in years 1 to 4, respectively), as did mean hospital length of stay (13.0, 12.4, 11.6, and 11.1 days in years 1 to 4; p < 0.001). However, excluding the increasing (p < 0.001) number of patients discharged to skilled nursing facilities attenuated much of the decline in standardized mortality over time. A previously validated physiologically based prognostic measure successfully stratified patients in a large community-based sample by their risk of death. However, such methods may require recalibration when applied to new samples and to reflect changes in practice over time. Moreover, although significant variations in hospital standardized mortality were observed, changing hospital discharge practices suggest that in-hospital mortality may no longer be an adequate measure of ICU performance. Community-wide efforts with broad-based support from business, hospitals, and physicians can be sustained over time to assess outcomes associated with ICU care. Such efforts may provide important information about variations in patient outcomes and changes in practice patterns over time. Future efforts should assess the impact of such community-wide initiatives on health-care purchasing and institutional quality improvement programs.

Gravity and Heater Size Effects on Pool Boiling Heat Transfer

NASA Technical Reports Server (NTRS)

Kim, Jungho; Raj, Rishi

2014-01-01

The current work is based on observations of boiling heat transfer over a continuous range of gravity levels between 0g to 1.8g and varying heater sizes with a fluorinert as the test liquid (FC-72/n-perfluorohexane). Variable gravity pool boiling heat transfer measurements over a wide range of gravity levels were made during parabolic flight campaigns as well as onboard the International Space Station. For large heaters and-or higher gravity conditions, buoyancy dominated boiling and heat transfer results were heater size independent. The power law coefficient for gravity in the heat transfer equation was found to be a function of wall temperature under these conditions. Under low gravity conditions and-or for smaller heaters, surface tension forces dominated and heat transfer results were heater size dependent. A pool boiling regime map differentiating buoyancy and surface tension dominated regimes was developed along with a unified framework that allowed for scaling of pool boiling over a wide range of gravity levels and heater sizes. The scaling laws developed in this study are expected to allow performance quantification of phase change based technologies under variable gravity environments eventually leading to their implementation in space based applications.

Nonlinear and dissipative constitutive equations for coupled first-order acoustic field equations that are consistent with the generalized Westervelt equation

NASA Astrophysics Data System (ADS)

Verweij, Martin D.; Huijssen, Jacob

2006-05-01

In diagnostic medical ultrasound, it has become increasingly important to evaluate the nonlinear field of an acoustic beam that propagates in a weakly nonlinear, dissipative medium and that is steered off-axis up to very wide angles. In this case, computations cannot be based on the widely used KZK equation since it applies only to small angles. To benefit from successful computational schemes from elastodynamics and electromagnetics, we propose to use two first-order acoustic field equations, accompanied by two constitutive equations, as an alternative basis. This formulation quite naturally results in the contrast source formalism, makes a clear distinction between fundamental conservation laws and medium behavior, and allows for a straightforward inclusion of any medium inhomogenities. This paper is concerned with the derivation of relevant constitutive equations. We take a pragmatic approach and aim to find those constitutive equations that represent the same medium as implicitly described by the recognized, full wave, nonlinear equations such as the generalized Westervelt equation. We will show how this is achieved by considering the nonlinear case without attenuation, the linear case with attenuation, and the nonlinear case with attenuation. As a result we will obtain surprisingly simple constitutive equations for the full wave case.

Calculation of Linear Stability of a Stratified Gas-Liquid Flow in an Inclined Plane Channel

NASA Astrophysics Data System (ADS)

Trifonov, Yu. Ya.

2018-01-01

Linear stability of liquid and gas counterflows in an inclined channel is considered. The full Navier-Stokes equations for both phases are linearized, and the dynamics of periodic disturbances is determined by means of solving a spectral problem in wide ranges of Reynolds numbers for the liquid and vapor velocity. Two unstable modes are found in the examined ranges: surface mode (corresponding to the Kapitsa waves at small velocities of the gas) and shear mode in the gas phase. The wave length and the phase velocity of neutral disturbances of both modes are calculated as functions of the Reynolds number for the liquid. It is shown that these dependences for the surface mode are significantly affected by the gas velocity.

Infinite matter properties and zero-range limit of non-relativistic finite-range interactions

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

Davesne, D.; Becker, P., E-mail: pbecker@ipnl.in2p3.fr; Pastore, A.

2016-12-15

We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin–orbit terms from the spin–isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin–orbit ofmore » the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.« less

Three-dimensional fully-coupled electrical and thermal transport model of dynamic switching in oxide memristors

DOE PAGES

Gao, Xujiao; Mamaluy, Denis; Mickel, Patrick R.; ...

2015-09-08

In this paper, we present a fully-coupled electrical and thermal transport model for oxide memristors that solves simultaneously the time-dependent continuity equations for all relevant carriers, together with the time-dependent heat equation including Joule heating sources. The model captures all the important processes that drive memristive switching and is applicable to simulate switching behavior in a wide range of oxide memristors. The model is applied to simulate the ON switching in a 3D filamentary TaOx memristor. Simulation results show that, for uniform vacancy density in the OFF state, vacancies fill in the conduction filament till saturation, and then fill outmore » a gap formed in the Ta electrode during ON switching; furthermore, ON-switching time strongly depends on applied voltage and the ON-to-OFF current ratio is sensitive to the filament vacancy density in the OFF state.« less

Secular Orbit Evolution in Systems with a Strong External Perturber—A Simple and Accurate Model

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

Andrade-Ines, Eduardo; Eggl, Siegfried, E-mail: eandrade.ines@gmail.com, E-mail: siegfried.eggl@jpl.nasa.gov

We present a semi-analytical correction to the seminal solution for the secular motion of a planet’s orbit under gravitational influence of an external perturber derived by Heppenheimer. A comparison between analytical predictions and numerical simulations allows us to determine corrective factors for the secular frequency and forced eccentricity in the coplanar restricted three-body problem. The correction is given in the form of a polynomial function of the system’s parameters that can be applied to first-order forced eccentricity and secular frequency estimates. The resulting secular equations are simple, straight forward to use, and improve the fidelity of Heppenheimers solution well beyond higher-ordermore » models. The quality and convergence of the corrected secular equations are tested for a wide range of parameters and limits of its applicability are given.« less

Transcritical flow of a Bose-Einstein condensate through a penetrable barrier

NASA Astrophysics Data System (ADS)

Leszczyszyn, A. M.; El, G. A.; Gladush, Yu. G.; Kamchatnov, A. M.

2009-06-01

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the locally steady “hydraulic” solution of the one-dimensional Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters, the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train, and the drag force are determined in terms of the Bose-Einstein condensate oncoming flow velocity and the strength of the potential barrier. Good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.

Lee wave breaking region: the map of instability development scenarios

NASA Astrophysics Data System (ADS)

Yakovenko, S. N.

2017-10-01

Numerical study of a stably stratified flow above the two-dimensional cosine-shaped obstacle has been performed by DNS and LES. These methods were implemented to solve the three-dimensional Navier-Stokes equations in the Boussinesq approximation, together with by the scalar diffusion equation. The results of scanning in the wide ranges of physical parameters (Reynolds and Prandtl/Schmidt numbers relating to laboratory experiment cases and atmospheric or oceanic situations) are presented for instability and turbulence development scenarios in the overturning internal lee waves. The latter is generated by the obstacle in a flow with the constant inflow values of velocity and stable density gradient. Evolution of lee-wave breaking is explored by visualization of velocity and scalar (density) fields, and the analysis of spectra. Based on the numerical simulation results, the power-law dependence on Reynolds number is demonstrated for the wavelength of the most unstable perturbation.

Analytical study on the thermal performance of a partially wet constructal T-shaped fin

NASA Astrophysics Data System (ADS)

Hazarika, Saheera Azmi; Zeeshan, Mohd; Bhanja, Dipankar; Nath, Sujit

2017-07-01

The present paper addresses the thermal analysis of a T-shaped fin under partially wet condition by adopting a cubic variation of the humidity ratio of saturated air with the corresponding fin surface temperature. The point separating the dry and wet parts may lie either in the flange or stem part of the fin and so, two different cases having different governing equations and boundary conditions are analyzed in this paper. Since the governing equations are highly non-linear, they are solved by using an analytical technique called the Differential Transform Method and subsequently, the dry fin length, temperature distribution and fin performances are evaluated and analyzed for a wide range of the various psychometric, geometric and thermo-physical parameters. Finally, it can be highlighted that relative humidity has a pronounced effect on the performance parameters when the fin surface is partially wet whereas this effect is marginally small for fully wet surface.

An analytical drain current model for symmetric double-gate MOSFETs

NASA Astrophysics Data System (ADS)

Yu, Fei; Huang, Gongyi; Lin, Wei; Xu, Chuanzhong

2018-04-01

An analytical surface-potential-based drain current model of symmetric double-gate (sDG) MOSFETs is described as a SPICE compatible model in this paper. The continuous surface and central potentials from the accumulation to the strong inversion regions are solved from the 1-D Poisson's equation in sDG MOSFETs. Furthermore, the drain current is derived from the charge sheet model as a function of the surface potential. Over a wide range of terminal voltages, doping concentrations, and device geometries, the surface potential calculation scheme and drain current model are verified by solving the 1-D Poisson's equation based on the least square method and using the Silvaco Atlas simulation results and experimental data, respectively. Such a model can be adopted as a useful platform to develop the circuit simulator and provide the clear understanding of sDG MOSFET device physics.

Nonlinear longitudinal resonance interaction of energetic charged particles and VLF waves in the magnetosphere

NASA Technical Reports Server (NTRS)

Tkalcevic, S.

1982-01-01

The longitudinal resonance of waves and energetic electrons in the Earth's magnetosphere, and the possible role this resonance may play in generating various magnetospheric phenomena are studied. The derivation of time-averaged nonlinear equations of motion for energetic particles longitudinally resonant with a whistler mode wave propagating with nonzero wave normal is considered. It is shown that the wave magnetic forces can be neglected at lower particle pitch angles, while they become equal to or larger than the wave electric forces for alpha 20 deg. The time-averaged equations of motion were used in test particle simulation which were done for a wide range of wave amplitudes, wave normals, particle pitch angles, particle parallel velocities, and in an inhomogeneous medium such as the magnetosphere. It was found that there are two classes of particles, trapped and untrapped, and that the scattering and energy exchange for those two groups exhibit significantly different behavior.

Reconstruction of the Mesoscale Velocity Shear Seaward of Coastal Upwelling Regions from the Refraction of the Surface Wave Field

NASA Technical Reports Server (NTRS)

Flament, Pierre; Graber, Hans C.; Halpern, D.; Holt, B.

1996-01-01

The objective of this project is to study fronts that develop at the boundary between cold water recently upwelled to the surface through Ekman divergence, and warmer surrounding waters. This specific objective was suggested by studying the small scale structure of upwelling fronts (coastal, island, and equatorial) through shipboard surveys and infrared satellite images. Constraints on the shuttle equator crossing imposed by other land sites precluded a coverage of the area targeted in the initial SIR-C proposal, the California Current. The site was then relocated to the Equatorial Pacific upwelling tongue, that can be satisfactorily imaged for a wide range of longitudes of the equator crossing. Some limited data was nevertheless obtained over coastal upwelling off California in 1989, using the JPL AIRSAR in multifrequency mode, and over island upwelling off Hawaii in 1990, using the radar in along-track interferometric mode.

An Adiabatic Phase-Matching Accelerator

DOE PAGES

Lemery, Francois; Floettmann, Klaus; Piot, Philippe; ...

2018-05-25

We present a general concept to accelerate non-relativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell's equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program {\\sc astra} and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of 100~MV/m. The numerical simulations indicate that amore » $$\\sim 200$$-keV electron beam can be accelerated to an energy of $$\\sim10$$~MeV over $$\\sim 10$$~cm. The novel scheme is also found to form electron beams with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.« less

Growth, Quantitative Growth Analysis, and Applications of Graphene on γ-Al2O3 catalysts

PubMed Central

Park, Jaehyun; Lee, Joohwi; Choi, Jung-Hae; Hwang, Do Kyung; Song, Yong-Won

2015-01-01

The possibilities offered by catalytic γ-Al2O3 substrates are explored, and the mechanism governing graphene formation thereon is elucidated using both numerical simulations and experiments. The growth scheme offers metal-free synthesis at low temperature, grain-size customization, large-area uniformity of electrical properties, single-step preparation of graphene/dielectric structures, and readily detachable graphene. We quantify based on thermodynamic principles the activation energies associated with graphene nucleation/growth on γ-Al2O3, verifying the low physical and chemical barriers. Importantly, we derive a universal equation governing the adsorption-based synthesis of graphene over a wide range of temperatures in both catalytic and spontaneous growth regimes. Experimental results support the equation, highlighting the catalytic function of γ-Al2O3 at low temperatures. The synthesized graphene is manually incorporated as a ‘graphene sticker’ into an ultrafast mode-locked laser. PMID:26137994

PICASSO: an end-to-end image simulation tool for space and airborne imaging systems II. Extension to the thermal infrared: equations and methods

NASA Astrophysics Data System (ADS)

Cota, Stephen A.; Lomheim, Terrence S.; Florio, Christopher J.; Harbold, Jeffrey M.; Muto, B. Michael; Schoolar, Richard B.; Wintz, Daniel T.; Keller, Robert A.

2011-10-01

In a previous paper in this series, we described how The Aerospace Corporation's Parameterized Image Chain Analysis & Simulation SOftware (PICASSO) tool may be used to model space and airborne imaging systems operating in the visible to near-infrared (VISNIR). PICASSO is a systems-level tool, representative of a class of such tools used throughout the remote sensing community. It is capable of modeling systems over a wide range of fidelity, anywhere from conceptual design level (where it can serve as an integral part of the systems engineering process) to as-built hardware (where it can serve as part of the verification process). In the present paper, we extend the discussion of PICASSO to the modeling of Thermal Infrared (TIR) remote sensing systems, presenting the equations and methods necessary to modeling in that regime.

A mathematical model of nutrient influence on fungal competition.

PubMed

Jabed A Choudhury, M; M J Trevelyan, Philip; P Boswell, Graeme

2018-02-07

Fungi have a well-established role in nutrient cycling and are widely used as agents in biological control and in the remediation of polluted landscapes. Competition for resources between different fungal communities is common in these contexts and its outcome impacts on the success of such biotechnological applications. In this investigation a mathematical model is constructed to represent competition between two fungal colonies that have access to different resources. It is shown that the model equations display a multitude of travelling wave solutions and that the outcome of competition between two fungal biomasses can be controlled through the simple manipulation of the nutrient resources available to each. The model equations are also numerically integrated to illustrate the range of outcomes arising from fungal competition and these results are placed in context of established experimental observations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Investigation of nose bluntness and angle of attack effects on slender bodies in viscous hypersonic flows

NASA Technical Reports Server (NTRS)

Sehgal, A. K.; Tiwari, S. N.; Singh, D. J.

1991-01-01

Hypersonic flows over cones and straight biconic configurations are calculated for a wide range of free stream conditions in which the gas behind the shock is treated as perfect. Effect of angle of attack and nose bluntness on these slender cones in air is studied extensively. The numerical procedures are based on the solution of complete Navier-Stokes equations at the nose section and parabolized Navier-Stokes equations further downstream. The flow field variables and surface quantities show significant differences when the angle of attack and nose bluntness are varied. The complete flow field is thoroughly analyzed with respect to velocity, temperature, pressure, and entropy profiles. The post shock flow field is studied in detail from the contour plots of Mach number, density, pressure, and temperature. The effect of nose bluntness for slender cones persists as far as 200 nose radii downstream.

Synchronous acceleration with tapered dielectric-lined waveguides

DOE PAGES

Lemery, Francois; Floettmann, Klaus; Piot, Philippe; ...

2018-05-25

Here, we present a general concept to accelerate non-relativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell's equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program {\\sc astra} and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of 100~MV/m. The numerical simulations indicate that amore » $$\\sim 200$$-keV electron beam can be accelerated to an energy of $$\\sim10$$~MeV over $$\\sim 10$$~cm. The novel scheme is also found to form electron beams with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.« less

From Physics Model to Results: An Optimizing Framework for Cross-Architecture Code Generation

DOE PAGES

Blazewicz, Marek; Hinder, Ian; Koppelman, David M.; ...

2013-01-01

Starting from a high-level problem description in terms of partial differential equations using abstract tensor notation, the Chemora framework discretizes, optimizes, and generates complete high performance codes for a wide range of compute architectures. Chemora extends the capabilities of Cactus, facilitating the usage of large-scale CPU/GPU systems in an efficient manner for complex applications, without low-level code tuning. Chemora achieves parallelism through MPI and multi-threading, combining OpenMP and CUDA. Optimizations include high-level code transformations, efficient loop traversal strategies, dynamically selected data and instruction cache usage strategies, and JIT compilation of GPU code tailored to the problem characteristics. The discretization ismore » based on higher-order finite differences on multi-block domains. Chemora's capabilities are demonstrated by simulations of black hole collisions. This problem provides an acid test of the framework, as the Einstein equations contain hundreds of variables and thousands of terms.« less

Simulation of two-dimensional turbulent flows in a rotating annulus

NASA Astrophysics Data System (ADS)

Storey, Brian D.

2004-05-01

Rotating water tank experiments have been used to study fundamental processes of atmospheric and geophysical turbulence in a controlled laboratory setting. When these tanks are undergoing strong rotation the forced turbulent flow becomes highly two dimensional along the axis of rotation. An efficient numerical method has been developed for simulating the forced quasi-geostrophic equations in an annular geometry to model current laboratory experiments. The algorithm employs a spectral method with Fourier series and Chebyshev polynomials as basis functions. The algorithm has been implemented on a parallel architecture to allow modelling of a wide range of spatial scales over long integration times. This paper describes the derivation of the model equations, numerical method, testing and performance of the algorithm. Results provide reasonable agreement with the experimental data, indicating that such computations can be used as a predictive tool to design future experiments.

Beyond Cassie equation: Local structure of heterogeneous surfaces determines the contact angles of microdroplets

PubMed Central

Zhang, Bo; Wang, Jianjun; Liu, Zhiping; Zhang, Xianren

2014-01-01

The application of Cassie equation to microscopic droplets is recently under intense debate because the microdroplet dimension is often of the same order of magnitude as the characteristic size of substrate heterogeneities, and the mechanism to describe the contact angle of microdroplets is not clear. By representing real surfaces statistically as an ensemble of patterned surfaces with randomly or regularly distributed heterogeneities (patches), lattice Boltzmann simulations here show that the contact angle of microdroplets has a wide distribution, either continuous or discrete, depending on the patch size. The origin of multiple contact angles observed is ascribed to the contact line pinning effect induced by substrate heterogeneities. We demonstrate that the local feature of substrate structure near the contact line determines the range of contact angles that can be stabilized, while the certain contact angle observed is closely related to the contact line width. PMID:25059292

Regression analysis of traction characteristics of traction fluids

NASA Technical Reports Server (NTRS)

Loewenthal, S. H.; Rohn, D. A.

1983-01-01

Traction data for Santotrac 50 and TDF-88 over a wide range of operating conditions were analyzed. An eight term correlation equation to predict the maximum traction coefficient and a six term correlation equation to predict the initial slope of the traction curve were developed. The slope correlation was corrected for size effect considering the compliance of the disks. The effects of different operating conditions on the traction performance of each traction fluid were studied. Both fluids exhibited a loss in traction with increases in spin, but the losses with the TDF-88 fluid were not as severe as those with Santotrac 50. Overall, both fluids exhibited similar performance, showing an increase in traction with contact pressure up to about 2.0 GPa, and a reduction in traction with higher surface speeds up to about 100 m/sec. The apparent stiffness of the traction contact, that is, film disk combination, increases with contact pressure and decreases with speed.

Relativistic effects on acidities and basicities of Brønsted acids and bases containing gold.

PubMed

Koppel, Ilmar A; Burk, Peeter; Kasemets, Kalev; Koppel, Ivar

2013-11-07

It is usually believed that relativistic effects as described by the Dirac-Schrödinger equation (relative to the classical or time-independent Schrödinger equation) are of little importance in chemistry. A closer look, however, reveals that some important and widely known properties (e.g., gold is yellow, mercury is liquid at room temperature) stem from relativistic effects. So far the influence of relativistic effects on the acid-base properties has been mostly ignored. Here we show that at least for compounds of gold such omission is completely erroneous and would lead to too high basicity and too low acidity values with errors in the range of 25-55 kcal mol(-1) (or 20 to 44 powers of ten in pK(a) units) in the gas-phase. These findings have important implications for the design of new superstrong acids and bases, and for the understanding of gold-catalysed reactions.

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

PubMed Central

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

2012-01-01

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

Analytical solution of Luedeking-Piret equation for a batch fermentation obeying Monod growth kinetics.

PubMed

Garnier, Alain; Gaillet, Bruno

2015-12-01

Not so many fermentation mathematical models allow analytical solutions of batch process dynamics. The most widely used is the combination of the logistic microbial growth kinetics with Luedeking-Piret bioproduct synthesis relation. However, the logistic equation is principally based on formalistic similarities and only fits a limited range of fermentation types. In this article, we have developed an analytical solution for the combination of Monod growth kinetics with Luedeking-Piret relation, which can be identified by linear regression and used to simulate batch fermentation evolution. Two classical examples are used to show the quality of fit and the simplicity of the method proposed. A solution for the combination of Haldane substrate-limited growth model combined with Luedeking-Piret relation is also provided. These models could prove useful for the analysis of fermentation data in industry as well as academia. © 2015 Wiley Periodicals, Inc.

An Adiabatic Phase-Matching Accelerator

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

Lemery, Francois; Floettmann, Klaus; Piot, Philippe

2017-12-22

We present a general concept to accelerate non-relativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell's equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program {\\sc astra} and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of 100~MV/m. The numerical simulations indicate that amore » $$\\sim 200$$-keV electron beam can be accelerated to an energy of $$\\sim10$$~MeV over $$\\sim 10$$~cm. The novel scheme is also found to form electron beams with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.« less

Theoretical Study of Large-Angle Bending Transport of Microparticles by 2D Acoustic Half-Bessel Beams.

PubMed

Li, Yixiang; Qiu, Chunyin; Xu, Shengjun; Ke, Manzhu; Liu, Zhengyou

2015-08-17

Conventional microparticle transports by light or sound are realized along a straight line. Recently, this limit has been overcome in optics as the growing up of the self-accelerating Airy beams, which are featured by many peculiar properties, e.g., bending propagation, diffraction-free and self-healing. However, the bending angles of Airy beams are rather small since they are only paraxial solutions of the two-dimensional (2D) Helmholtz equation. Here we propose a novel micromanipulation by using acoustic Half-Bessel beams, which are strict solutions of the 2D Helmholtz equation. Compared with that achieved by Airy beams, the bending angle of the particle trajectory attained here is much steeper (exceeding 90(o)). The large-angle bending transport of microparticles, which is robust to complex scattering environment, enables a wide range of applications from the colloidal to biological sciences.

The reactants equation of state for the tri-amino-tri-nitro-benzene (TATB) based explosive PBX 9502

NASA Astrophysics Data System (ADS)

Aslam, Tariq D.

2017-07-01

The response of high explosives (HEs), due to mechanical and/or thermal insults, is of great importance for both safety and performance. A major component of how an HE responds to these stimuli stems from its reactant equation of state (EOS). Here, the tri-amino-tri-nitro-benzene based explosive PBX 9502 is investigated by examining recent experiments. Furthermore, a complete thermal EOS is calibrated based on the functional form devised by Wescott, Stewart, and Davis [J. Appl. Phys. 98, 053514 (2005)]. It is found, by comparing to earlier calibrations, that a variety of thermodynamic data are needed to sufficiently constrain the EOS response over a wide range of thermodynamic state space. Included in the calibration presented here is the specific heat as a function of temperature, isobaric thermal expansion, and shock Hugoniot response. As validation of the resulting model, isothermal compression and isentropic compression are compared with recent experiments.

Modified Lippmann--Schwinger equations for two-body scattering theory with long-range interactions

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

Prugovecki, E.; Zorbas, J.

Two kinds of modified Lippmann-Schwinger equations are derived for the case of long-range potentials. The equations of the first kind are homogeneous and are a direct result of the fact that the standard Lippmann-Schwinger equations do not hold when long-range forces are present. The equations of the second kind depend on the existence of an operator Z such that W/sub plus or minus /=s-lim exp(iHt)Z exp-(-iHot). A general recipe for constructing Z is given and ita computation is carried through for the case of asymptotically Coulombic potentials. The resulting equations are used to compare the long-range theory with the theorymore » with a space cutoff (i.e., screened potential) in the limit in which that cutoff is being removed. (auth)« less

Modelling ecological flow regime: an example from the Tennessee and Cumberland River basins

USGS Publications Warehouse

Knight, Rodney R.; Gain, W. Scott; Wolfe, William J.

2012-01-01

Predictive equations were developed for 19 ecologically relevant streamflow characteristics within five major groups of flow variables (magnitude, ratio, frequency, variability, and date) for use in the Tennessee and Cumberland River basins using stepbackward regression. Basin characteristics explain 50% or more of the variation for 12 of the 19 equations. Independent variables identified through stepbackward regression were statistically significant in 78 of 304 cases (α > 0.0001) and represent four major groups: climate, physical landscape features, regional indicators, and land use. Of these groups, the regional and climate variables were the most influential for determining hydrologic response. Daily temperature range, geologic factor, and rock depth were major factors explaining the variability in 17, 15, and 13 equations, respectively. The equations and independent datasets were used to explore the broad relation between basin properties and streamflow and the implication of streamflow to the study of ecological flow requirements. Key results include a high degree of hydrologic variability among least disturbed Blue Ridge streams, similar hydrologic behaviour for watersheds with widely varying degrees of forest cover, and distinct hydrologic profiles for streams in different geographic regions. Published in 2011. This article is a US Government work and is in the public domain in the USA.

Search algorithm complexity modeling with application to image alignment and matching

NASA Astrophysics Data System (ADS)

DelMarco, Stephen

2014-05-01

Search algorithm complexity modeling, in the form of penetration rate estimation, provides a useful way to estimate search efficiency in application domains which involve searching over a hypothesis space of reference templates or models, as in model-based object recognition, automatic target recognition, and biometric recognition. The penetration rate quantifies the expected portion of the database that must be searched, and is useful for estimating search algorithm computational requirements. In this paper we perform mathematical modeling to derive general equations for penetration rate estimates that are applicable to a wide range of recognition problems. We extend previous penetration rate analyses to use more general probabilistic modeling assumptions. In particular we provide penetration rate equations within the framework of a model-based image alignment application domain in which a prioritized hierarchical grid search is used to rank subspace bins based on matching probability. We derive general equations, and provide special cases based on simplifying assumptions. We show how previously-derived penetration rate equations are special cases of the general formulation. We apply the analysis to model-based logo image alignment in which a hierarchical grid search is used over a geometric misalignment transform hypothesis space. We present numerical results validating the modeling assumptions and derived formulation.

Implementation of an Associative Flow Rule Including Hydrostatic Stress Effects Into the High Strain Rate Deformation Analysis of Polymer Matrix Composites

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Roberts, Gary D.; Gilat, Amos

2003-01-01

A previously developed analytical formulation has been modified in order to more accurately account for the effects of hydrostatic stresses on the nonlinear, strain rate dependent deformation of polymer matrix composites. State variable constitutive equations originally developed for metals have been modified in order to model the nonlinear, strain rate dependent deformation of polymeric materials. To account for the effects of hydrostatic stresses, which are significant in polymers, the classical J2 plasticity theory definitions of effective stress and effective inelastic strain, along with the equations used to compute the components of the inelastic strain rate tensor, are appropriately modified. To verify the revised formulation, the shear and tensile deformation of two representative polymers are computed across a wide range of strain rates. Results computed using the developed constitutive equations correlate well with experimental data. The polymer constitutive equations are implemented within a strength of materials based micromechanics method to predict the nonlinear, strain rate dependent deformation of polymer matrix composites. The composite mechanics are verified by analyzing the deformation of a representative polymer matrix composite for several fiber orientation angles across a variety of strain rates. The computed values compare well to experimentally obtained results.

Unified Theory for Decoding the Signals from X-Ray Florescence and X-Ray Diffraction of Mixtures.

PubMed

Chung, Frank H

2017-05-01

For research and development or for solving technical problems, we often need to know the chemical composition of an unknown mixture, which is coded and stored in the signals of its X-ray fluorescence (XRF) and X-ray diffraction (XRD). X-ray fluorescence gives chemical elements, whereas XRD gives chemical compounds. The major problem in XRF and XRD analyses is the complex matrix effect. The conventional technique to deal with the matrix effect is to construct empirical calibration lines with standards for each element or compound sought, which is tedious and time-consuming. A unified theory of quantitative XRF analysis is presented here. The idea is to cancel the matrix effect mathematically. It turns out that the decoding equation for quantitative XRF analysis is identical to that for quantitative XRD analysis although the physics of XRD and XRF are fundamentally different. The XRD work has been published and practiced worldwide. The unified theory derives a new intensity-concentration equation of XRF, which is free from the matrix effect and valid for a wide range of concentrations. The linear decoding equation establishes a constant slope for each element sought, hence eliminating the work on calibration lines. The simple linear decoding equation has been verified by 18 experiments.

Effects of mean flow on transmission loss of orthogonally rib-stiffened aeroelastic plates.

PubMed

Xin, F X; Lu, T J

2013-06-01

This paper investigates the sound transmission loss (STL) of aeroelastic plates reinforced by two sets of orthogonal rib-stiffeners in the presence of external mean flow. Built upon the periodicity of the structure, a comprehensive theoretical model is developed by considering the convection effect of mean flow. The rib-stiffeners are modeled by employing the Bernoulli-Euler beam theory and the torsional wave equation. While the solution for the transmission loss of the structure based on plate displacement and acoustic pressures is given in the form of space-harmonic series, the corresponding coefficients are obtained from the solution of a system of linear equations derived from the plate-beam coupling vibration governing equation and Helmholtz equation. The model predictions are validated by comparing with existing theoretical and experimental results in the absence of mean flow. A parametric study is subsequently performed to quantify the effects of mean flow as well as structure geometrical parameters upon the transmission loss. It is demonstrated that the transmission loss of periodically rib-stiffened structure is increased significantly with increasing Mach number of mean flow over a wide frequency range. The STL value for the case of sound wave incident downstream is pronouncedly larger than that associated with sound wave incident upstream.

Numerical investigations on the characteristics of thermomagnetic instability in MgB2 bulks

NASA Astrophysics Data System (ADS)

Xia, Jing; Li, Maosheng; Zhou, Youhe

2017-07-01

This paper presents the characteristics of thermomagnetic instability in MgB2 bulks by numerically solving the macroscopic dynamics of thermomagnetic interaction governed by the coupled magnetic and heat diffusion equations in association with a modified E-J power-law relationship. The finite element method is used to discretize the system of partial differential equations. The calculated magnetization loops with flux jumps are consistent with the experimental results for MgB2 slabs bathed in a wide range of ambient temperatures. We reveal the evolution process of the thermomagnetic instability and present the distributions of the magnetic field, temperature, and current density before and after flux jumps. A 2D axisymmetric model is used to study the thermomagnetic instability in cylindrical MgB2 bulks. It is found that the number of flux jumps monotonously reduces as the ambient temperature rises and no flux jump appears when the ambient temperature exceeds a certain value. Moreover, the flux-jump phenomenon exists in a wide range of the ramp rate of the applied external field, i.e. 10-2-102 T s-1. Furthermore, the dependences of the first flux-jump field on the ambient temperature, ramp rate, and bulk thickness are investigated. The critical bulk thicknesses for stability are obtained for different ambient temperatures and sample radii. In addition, the influence of the capability of the interfacial heat transfer on the temporal response of the bulk temperature is discussed. We also find that the prediction of thermomagnetic instability is sensitive to the employment of the flux creep exponent in the simulations.

Equations for calculating hydrogeochemical reactions of minerals and gases such as CO2 at high pressures and temperatures

USGS Publications Warehouse

Appelo, C.A.J.; Parkhurst, David L.; Post, V.E.A.

2014-01-01

Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich–Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson–Kirkham–Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye–Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich–Rosenfeld equation were fitted by least-squares on measured solution densities.The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng–Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The coefficients for the Peng–Robinson equations are readily available in the literature.The required equations have been implemented in PHREEQC, version 3, and the parameters for calculating the partial molar volumes and fugacity coefficients have been added to the databases that are distributed with PHREEQC. The ease of use and power of the formulation are illustrated by calculating the solubility of CO2 at high pressures and temperatures, and comparing with well-known examples from the geochemical literature. The equations and parameterizations are suitable for wide application in hydrogeochemical systems, especially in the field of carbon capture and storage.

Equations for calculating hydrogeochemical reactions of minerals and gases such as CO2 at high pressures and temperatures

NASA Astrophysics Data System (ADS)

Appelo, C. A. J.; Parkhurst, D. L.; Post, V. E. A.

2014-01-01

Calculating the solubility of gases and minerals at the high pressures of carbon capture and storage in geological reservoirs requires an accurate description of the molar volumes of aqueous species and the fugacity coefficients of gases. Existing methods for calculating the molar volumes of aqueous species are limited to a specific concentration matrix (often seawater), have been fit for a limited temperature (below 60 °C) or pressure range, apply only at infinite dilution, or are defined for salts instead of individual ions. A more general and reliable calculation of apparent molar volumes of single ions is presented, based on a modified Redlich-Rosenfeld equation. The modifications consist of (1) using the Born equation to calculate the temperature dependence of the intrinsic volumes, following Helgeson-Kirkham-Flowers (HKF), but with Bradley and Pitzer’s expression for the dielectric permittivity of water, (2) using the pressure dependence of the extended Debye-Hückel equation to constrain the limiting slope of the molar volume with ionic strength, and (3) adopting the convention that the proton has zero volume at all ionic strengths, temperatures and pressures. The modifications substantially reduce the number of fitting parameters, while maintaining or even extending the range of temperature and pressure over which molar volumes can be accurately estimated. The coefficients in the HKF-modified-Redlich-Rosenfeld equation were fitted by least-squares on measured solution densities. The limiting volume and attraction factor in the Van der Waals equation of state can be estimated with the Peng-Robinson approach from the critical temperature, pressure, and acentric factor of a gas. The Van der Waals equation can then be used to determine the fugacity coefficients for pure gases and gases in a mixture, and the solubility of the gas can be calculated from the fugacity, the molar volume in aqueous solution, and the equilibrium constant. The coefficients for the Peng-Robinson equations are readily available in the literature. The required equations have been implemented in PHREEQC, version 3, and the parameters for calculating the partial molar volumes and fugacity coefficients have been added to the databases that are distributed with PHREEQC. The ease of use and power of the formulation are illustrated by calculating the solubility of CO2 at high pressures and temperatures, and comparing with well-known examples from the geochemical literature. The equations and parameterizations are suitable for wide application in hydrogeochemical systems, especially in the field of carbon capture and storage.

A method for predicting optimized processing parameters for surfacing

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

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

1994-12-31

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

Stream-temperature patterns of the Muddy Creek basin, Anne Arundel County, Maryland

USGS Publications Warehouse

Pluhowski, E.J.

1981-01-01

Using a water-balance equation based on a 4.25-year gaging-station record on North Fork Muddy Creek, the following mean annual values were obtained for the Muddy Creek basin: precipitation, 49.0 inches; evapotranspiration, 28.0 inches; runoff, 18.5 inches; and underflow, 2.5 inches. Average freshwater outflow from the Muddy Creek basin to the Rhode River estuary was 12.2 cfs during the period October 1, 1971, to December 31, 1975. Harmonic equations were used to describe seasonal maximum and minimum stream-temperature patterns at 12 sites in the basin. These equations were fitted to continuous water-temperature data obtained periodically at each site between November 1970 and June 1978. The harmonic equations explain at least 78 percent of the variance in maximum stream temperatures and 81 percent of the variance in minimum temperatures. Standard errors of estimate averaged 2.3C (Celsius) for daily maximum water temperatures and 2.1C for daily minimum temperatures. Mean annual water temperatures developed for a 5.4-year base period ranged from 11.9C at Muddy Creek to 13.1C at Many Fork Branch. The largest variations in stream temperatures were detected at thermograph sites below ponded reaches and where forest coverage was sparse or missing. At most sites the largest variations in daily water temperatures were recorded in April whereas the smallest were in September and October. The low thermal inertia of streams in the Muddy Creek basin tends to amplify the impact of surface energy-exchange processes on short-period stream-temperature patterns. Thus, in response to meteorologic events, wide ranging stream-temperature perturbations of as much as 6C have been documented in the basin. (USGS)

Explicit expressions for meromorphic solutions of autonomous nonlinear ordinary differential equations

NASA Astrophysics Data System (ADS)

Demina, Maria V.; Kudryashov, Nikolay A.

2011-03-01

Meromorphic solutions of autonomous nonlinear ordinary differential equations are studied. An algorithm for constructing meromorphic solutions in explicit form is presented. General expressions for meromorphic solutions (including rational, periodic, elliptic) are found for a wide class of autonomous nonlinear ordinary differential equations.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Nicholson, S.; Moore, J.

1986-01-01

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite volume, time marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier Stokes equations. The entire calculation is performed in the physical domain. The method is currently limited to the calculation of attached flows. The features of the current method can be summarized as follows. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is now needed. Different time steps are used in the different governing equations to improve the convergence speed of the viscous calculations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes. A special discretization technique is also used to stabilize these calculations. A special formulation of the energy equation is used to provide improved transient behavior of solutions which use the full energy equation. The method is then compared with a wide variety of test cases. The freestream Mach numbers range from 0.075 to 2.8 in the calculations. Transonic viscous flow in a converging diverging nozzle is calculated with the method; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good. Essentially incompressible turbulent boundary layer flow in a adverse pressure gradient is calculated and the computed distribution of mean velocity and shear stress are in good agreement with the measurements. At the other end of the Mach number range, a flat plate turbulent boundary layer with a freestream Mach number of 2.8 is calculated using the full energy equation; the computed total temperature distribution and recovery factor agree well with the measurements when a variable Prandtl number is used through the boundary layer.

Equation of state of pyrite to 85 GPa and 2400 K

NASA Astrophysics Data System (ADS)

Thompson, E. C.; Chidester, B.; Campbell, A. J.; Prakapenka, V.

2014-12-01

Pyrite (FeS2), a Pa3 space group non-magnetic semiconductor, is the most abundant iron sulfide in nature, yet the high cosmic abundance of sulfur is not reflected in the terrestrial crust, implying it is either sequestered in the Earth's interior or was volatilized during accretion. As it has widely been suggested that sulfur could be one of the contributing light elements leading to the density deficit of Earth's core, a robust thermal equation of state of FeS2 is vital for understanding the evolution and properties of Earth's interior. We performed X-ray diffraction measurements on FeS2 at the GSECARS sector 13-ID-D and HPCAT sector 16-ID-B beamlines at the Advanced Photon Source. Pressures from 17 to 85 GPa and temperatures up to 2400 K were achieved using laser-heated diamond anvil cells. Pressures were determined from the lattice parameters of KBr [1], which served as an insulator and pressure medium, and temperatures were determined by spectroradiometry. No phase transitions were observed in the pyrite structure over the pressure and temperature ranges investigated. By combining our new P-V-T data with previously published room temperature compression data [2], we have determined a thermal equation of state for FeS2, with bulk modulus K=182.6(74) GPa, pressure derivative K'=3.82(25), and αKT=0.00329(45). Our revised equation of state for pyrite is consistent with a core density deficit satisfied by 9-10 wt.% sulfur. We compare these findings to previously published ab intio equation of state parameters for pyrite under a similar range of pressures [3]. [1] Fischer et al. (2012) EPSL 357-358, 268-276. [2] Merkel et al. (2002) PCM 29, 1-9. [3] Le Page and Rodgers (2005) PCM 32, 564-567.

Pediatric GFR Estimating Equations Applied to Adolescents in the General Population

PubMed Central

Neu, Alicia M.; Schwartz, George J.; Furth, Susan L.

2011-01-01

Summary Background and objectives We examined the distribution of estimated GFR (eGFR) in a healthy cohort of adolescents to inform clinical and research use. Design, setting, participants, & measurements Various creatinine-based (n = 3256) and/or cystatin C–based (n = 811) equations, including the recently developed complete and bedside equations from the Chronic Kidney Disease in Children (CKiD) study, were applied to U.S. adolescents 12 to 17 years of age participating in the 1999–2002 National Health and Nutrition Examination Survey (NHANES). Results The median serum creatinine and cystatin C were 0.7 mg/dl and 0.83 mg/L, respectively. The distribution of eGFR varied widely, with the median GFR ranging from a low of 96.6 ml/min per 1.73 m2 (CKiD) to a high of 140.0 ml/min per 1.73 m2 (original Schwartz). The proportions of participants with eGFRs <75 ml/min per 1.73 m2 are as follows: bedside CKiD 8.9%, Counahan 6.3%, Leger 0.4%, original Schwartz 0%, Filler 1.3%, Grubb 3.1%, Bouvet 2.5%, CKiD 1.8%, and Zappitelli 5.6%. By any equation examined, no group of participants with eGFR ≤10th percentile had an increased prevalence of comorbid conditions consistent with a low measured GFR. Conclusions Most pediatric-specific GFR estimating equations resulted in 25% to 50% of the participants having an eGFR <100 ml/min per 1.73 m2. However, participants with eGFR in the lower ranges did not have an increased prevalence of morbidities associated with chronic kidney disease. Clinical validation of creatinine- or cystatin C–based estimated GFRs in healthy children is needed before it is possible to screen the general population for chronic kidney disease. PMID:21566103

Review of Sample Size for Structural Equation Models in Second Language Testing and Learning Research: A Monte Carlo Approach

ERIC Educational Resources Information Center

In'nami, Yo; Koizumi, Rie

2013-01-01

The importance of sample size, although widely discussed in the literature on structural equation modeling (SEM), has not been widely recognized among applied SEM researchers. To narrow this gap, we focus on second language testing and learning studies and examine the following: (a) Is the sample size sufficient in terms of precision and power of…

Testing different concepts of the equations of motion, describing runout time and distance of slow-moving gravitational slides and flows.

NASA Astrophysics Data System (ADS)

van Asch, Th. W. J.; Daehne, A.; Spickermann, A.; Travelletti, J.; Bégueria-Portuguès, S.

2010-05-01

The kinematics of rapid and slow moving landslides is commonly described by equations of motion, which in case of a viscous component are based on the Navier-Stokes equation. They consist of inertial terms related to the change in velocity in time (local acceleration) and space (convective acceleration) and terms related to respectively the gravity, pressure and viscous forces. These viscous resistance forces in the mass balance can be accompanied or replaced by other rheological (frictional and cohesive) terms depending on the liquid/solid ratio of the moving mass. We designed a 1D and a GIS based 2.5 D model with a numerical implementation for these equations which gave a reasonable simple compromise solution that achieved a desired level of stability, accuracy and controlled diffusion. An explicit finite difference (Eulerian) mesh, i.e. the moving mass was described by variation in the conservative variables at point fixed coordinates (i,j) as a function of time (n). A central difference forward scheme is used for the numerical solutions of the mass and momentum balance equations. A number of case studies of fast debris flows ranging in velocity between 1 and 10 m s-1, carried out in the Faucon torrent French Alps, the Wartschenbach torrent in Austria, near the Turnoff Creek in British Columbia, the Peringalam catchment in SW-India and the Jagüeyes landslide in the Guantánamo province Cuba, showed that the models were able to describe velocity, deposition and run-out reasonable well using different rheological characteristics. Despite the fact that many authors include an inertial term in the equation of motion for slow moving mass movements it appeared that our 1D and GIS based 2.5 D models were not able to simulate properly the velocity of slower moving debris flows or landslides with velocities ranging from 1 to 2 m min-1 until 30 mm y-1.Deletion of the inertial term related to the local acceleration in the equation of motion, thus assuming that there is a permanent equilibrium between gravity, pressure and Coulomb-viscous forces, produced a more flexible tool, able to describe the velocity, deposition and run-out of mass movements with a wide range of values. Examples of successful simulations in 1-D and 2.5-D exist already. In this contribution we will compare 1D simulations with and without a local acceleration term and analyze the results. A slow moving debris flow which developed on the Super-Sauze mudslide and a slow moving landslide in varved clays near Monestier-du-Percy in the French Alps were selected to test the calibration performances of these two options in the equation of motion.

Equations for description of nonlinear standing waves in constant-cross-sectioned resonators.

PubMed

Bednarik, Michal; Cervenka, Milan

2014-03-01

This work is focused on investigation of applicability of two widely used model equations for description of nonlinear standing waves in constant-cross-sectioned resonators. The investigation is based on the comparison of numerical solutions of these model equations with solutions of more accurate model equations whose validity has been verified experimentally in a number of published papers.

Using Regression Equations Built from Summary Data in the Psychological Assessment of the Individual Case: Extension to Multiple Regression

ERIC Educational Resources Information Center

Crawford, John R.; Garthwaite, Paul H.; Denham, Annie K.; Chelune, Gordon J.

2012-01-01

Regression equations have many useful roles in psychological assessment. Moreover, there is a large reservoir of published data that could be used to build regression equations; these equations could then be employed to test a wide variety of hypotheses concerning the functioning of individual cases. This resource is currently underused because…

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

NASA Astrophysics Data System (ADS)

Mae, H.

2006-08-01

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

Need for optimal body composition data analysis using air-displacement plethysmography in children and adolescents.

PubMed

Bosy-Westphal, Anja; Danielzik, Sandra; Becker, Christine; Geisler, Corinna; Onur, Simone; Korth, Oliver; Bührens, Frederike; Müller, Manfred J

2005-09-01

Air-displacement plethysmography (ADP) is now widely used for body composition measurement in pediatric populations. However, the manufacturer's software developed for adults leaves a potential bias for application in children and adolescents, and recent publications do not consistently use child-specific corrections. Therefore we analyzed child-specific ADP corrections with respect to quantity and etiology of bias compared with adult formulas. An optimal correction protocol is provided giving step-by-step instructions for calculations. In this study, 258 children and adolescents (143 girls and 115 boys ranging from 5 to 18 y) with a high prevalence of overweight or obesity (28.0% in girls and 22.6% in boys) were examined by ADP applying the manufacturer's software as well as published equations for child-specific corrections for surface area artifact (SAA), thoracic gas volume (TGV), and density of fat-free mass (FFM). Compared with child-specific equations for SAA, TGV, and density of FFM, the mean overestimation of the percentage of fat mass using the manufacturer's software was 10% in children and adolescents. Half of the bias derived from the use of Siri's equation not corrected for age-dependent differences in FFM density. An additional 3 and 2% of bias resulted from the application of adult equations for prediction of SAA and TGV, respectively. Different child-specific equations used to predict TGV did not differ in the percentage of fat mass. We conclude that there is a need for child-specific equations in ADP raw data analysis considering SAA, TGV, and density of FFM.

Mesoscale magnetism

DOE PAGES

Hoffmann, Axel; Schultheiß, Helmut

2014-12-17

Magnetic interactions give rise to a surprising amount of complexity due to the fact that both static and dynamic magnetic properties are governed by competing short-range exchange interactions and long-range dipolar coupling. Even though the underlying dynamical equations are well established, the connection of magnetization dynamics to other degrees of freedom, such as optical excitations, charge and heat flow, or mechanical motion, make magnetism a mesoscale research problem that is still wide open for exploration. Synthesizing magnetic materials and heterostructures with tailored properties will allow to take advantage of magnetic interactions spanning many length-scales, which can be probed with advancedmore » spectroscopy and microscopy and modeled with multi-scale simulations. Finally, this paper highlights some of the current basic research topics in mesoscale magnetism, which beyond their fundamental science impact are also expected to influence applications ranging from information technologies to magnetism based energy conversion.« less

Theory connecting nonlocal sediment transport, earth surface roughness, and the Sadler effect

NASA Astrophysics Data System (ADS)

Schumer, Rina; Taloni, Alessandro; Furbish, David Jon

2017-03-01

Earth surface evolution, like many natural phenomena typified by fluctuations on a wide range of scales and deterministic smoothing, results in a statistically rough surface. We present theory demonstrating that scaling exponents of topographic and stratigraphic statistics arise from long-time averaging of noisy surface evolution rather than specific landscape evolution processes. This is demonstrated through use of "elastic" Langevin equations that generically describe disturbance from a flat earth surface using a noise term that is smoothed deterministically via sediment transport. When smoothing due to transport is a local process, the geologic record self organizes such that a specific Sadler effect and topographic power spectral density (PSD) emerge. Variations in PSD slope reflect the presence or absence and character of nonlocality of sediment transport. The range of observed stratigraphic Sadler slopes captures the same smoothing feature combined with the presence of long-range spatial correlation in topographic disturbance.

Cloud-System Resolving Models: Status and Prospects

NASA Technical Reports Server (NTRS)

Tao, Wei-Kuo; Moncreiff, Mitch

2008-01-01

Cloud-system resolving models (CRM), which are based on the nonhydrostatic equations of motion and typically have a grid-spacing of about a kilometer, originated as cloud-process models in the 1970s. This paper reviews the status and prospects of CRMs across a wide range of issues, such as microphysics and precipitation; interaction between clouds and radiation; and the effects of boundary-layer and surface-processes on cloud systems. Since CRMs resolve organized convection, tropical waves and the large-scale circulation, there is the prospect for several advances in both basic knowledge of scale-interaction requisite to parameterizing mesoscale processes in climate models. In superparameterization, CRMs represent convection, explicitly replacing many of the assumptions necessary in contemporary parameterization. Global CRMs have been run on an experimental basis, giving prospect to a new generation of climate weather prediction in a decade, and climate models due course. CRMs play a major role in the retrieval of surface-rain and latent heating from satellite measurements. Finally, enormous wide dynamic ranges of CRM simulations present new challenges for model validation against observations.

Electron-helium S-wave model benchmark calculations. I. Single ionization and single excitation

NASA Astrophysics Data System (ADS)

Bartlett, Philip L.; Stelbovics, Andris T.

2010-02-01

A full four-body implementation of the propagating exterior complex scaling (PECS) method [J. Phys. B 37, L69 (2004)] is developed and applied to the electron-impact of helium in an S-wave model. Time-independent solutions to the Schrödinger equation are found numerically in coordinate space over a wide range of energies and used to evaluate total and differential cross sections for a complete set of three- and four-body processes with benchmark precision. With this model we demonstrate the suitability of the PECS method for the complete solution of the full electron-helium system. Here we detail the theoretical and computational development of the four-body PECS method and present results for three-body channels: single excitation and single ionization. Four-body cross sections are presented in the sequel to this article [Phys. Rev. A 81, 022716 (2010)]. The calculations reveal structure in the total and energy-differential single-ionization cross sections for excited-state targets that is due to interference from autoionization channels and is evident over a wide range of incident electron energies.

Viscous friction of hydrogen-bonded matter

NASA Astrophysics Data System (ADS)

Erbas, Aykut; Horinek, Dominik; Netz, Roland R.

2012-02-01

Amontons' law successfully describes friction between macroscopic solid bodies for a wide range of velocities and normal forces. For the diffusion and forced sliding of adhering or entangled macromolecules, proteins and biological complexes, temperature effects are invariably important and a similarly successful friction law at biological length and velocity scales is missing. Hydrogen bonds are key to the specific binding of bio-matter. Here we show that friction between hydrogen-bonded matter obeys in the biologically relevant low-velocity viscous regime a simple equations: the friction force is proportional to the number of hydrogen bonds, the sliding velocity, and a friction coefficient γHB. This law is deduced from atomistic molecular dynamics simulations for short peptide chains that are laterally pulled over hydroxylated substrates in the presence of water and holds for widely different peptides, surface polarities and applied normal forces. The value of γHB is extrapolated from simulations at sliding velocities in the range from v=10-2 m/s to 100 m/s by mapping on a simple stochastic model and turns out to be of the order of γHB˜10-8 kg/s. 3 hydrogen bonds act collectively.

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

DOE PAGES

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

2018-02-14

The potential for density functional calculations to predict the properties of matter under extreme conditions depends crucially upon having a non-empirical approximate free energy functional valid over a wide range of state conditions. Unlike the ground-state case, no such free-energy exchange- correlation (XC) functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Application in Kohn-Sham calculations for hot electrons inmore » a static fcc Aluminum lattice demon- strates the combined magnitude of thermal and gradient effects handled by this functional. Its accuracy in the increasingly important warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated temperatures and by low density Al calculations over a wide T range.« less

Nonempirical Semilocal Free-Energy Density Functional for Matter under Extreme Conditions

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

Karasiev, Valentin V.; Dufty, James W.; Trickey, S. B.

The potential for density functional calculations to predict the properties of matter under extreme conditions depends crucially upon having a non-empirical approximate free energy functional valid over a wide range of state conditions. Unlike the ground-state case, no such free-energy exchange- correlation (XC) functional exists. We remedy that with systematic construction of a generalized gradient approximation XC free-energy functional based on rigorous constraints, including the free energy gradient expansion. The new functional provides the correct temperature dependence in the slowly varying regime and the correct zero-T, high-T, and homogeneous electron gas limits. Application in Kohn-Sham calculations for hot electrons inmore » a static fcc Aluminum lattice demon- strates the combined magnitude of thermal and gradient effects handled by this functional. Its accuracy in the increasingly important warm dense matter regime is attested by excellent agreement of the calculated deuterium equation of state with reference path integral Monte Carlo results at intermediate and elevated temperatures and by low density Al calculations over a wide T range.« less

Thermofluid Analysis of Magnetocaloric Refrigeration

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

Abdelaziz, Omar; Gluesenkamp, Kyle R; Vineyard, Edward Allan

While there have been extensive studies on thermofluid characteristics of different magnetocaloric refrigeration systems, a conclusive optimization study using non-dimensional parameters which can be applied to a generic system has not been reported yet. In this study, a numerical model has been developed for optimization of active magnetic refrigerator (AMR). This model is computationally efficient and robust, making it appropriate for running the thousands of simulations required for parametric study and optimization. The governing equations have been non-dimensionalized and numerically solved using finite difference method. A parametric study on a wide range of non-dimensional numbers has been performed. While themore » goal of AMR systems is to improve the performance of competitive parameters including COP, cooling capacity and temperature span, new parameters called AMR performance index-1 have been introduced in order to perform multi objective optimization and simultaneously exploit all these parameters. The multi-objective optimization is carried out for a wide range of the non-dimensional parameters. The results of this study will provide general guidelines for designing high performance AMR systems.« less

Poiseuille, thermal transpiration and Couette flows of a rarefied gas between plane parallel walls with nonuniform surface properties in the transverse direction and their reciprocity relations

NASA Astrophysics Data System (ADS)

Doi, Toshiyuki

2018-04-01

Slow flows of a rarefied gas between two plane parallel walls with nonuniform surface properties are studied based on kinetic theory. It is assumed that one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary whose accommodation coefficient varies periodically in the direction perpendicular to the flow. The time-independent Poiseuille, thermal transpiration and Couette flows are considered. The flow behavior is numerically studied based on the linearized Bhatnagar-Gross-Krook-Welander model of the Boltzmann equation. The flow field, the mass and heat flow rates in the gas, and the tangential force acting on the wall surface are studied over a wide range of the gas rarefaction degree and the parameters characterizing the distribution of the accommodation coefficient. The locally convex velocity distribution is observed in Couette flow of a highly rarefied gas, similarly to Poiseuille flow and thermal transpiration. The reciprocity relations are numerically confirmed over a wide range of the flow parameters.

How to derive biological information from the value of the normalization constant in allometric equations.

PubMed

Kaitaniemi, Pekka

2008-04-09

Allometric equations are widely used in many branches of biological science. The potential information content of the normalization constant b in allometric equations of the form Y = bX(a) has, however, remained largely neglected. To demonstrate the potential for utilizing this information, I generated a large number of artificial datasets that resembled those that are frequently encountered in biological studies, i.e., relatively small samples including measurement error or uncontrolled variation. The value of X was allowed to vary randomly within the limits describing different data ranges, and a was set to a fixed theoretical value. The constant b was set to a range of values describing the effect of a continuous environmental variable. In addition, a normally distributed random error was added to the values of both X and Y. Two different approaches were then used to model the data. The traditional approach estimated both a and b using a regression model, whereas an alternative approach set the exponent a at its theoretical value and only estimated the value of b. Both approaches produced virtually the same model fit with less than 0.3% difference in the coefficient of determination. Only the alternative approach was able to precisely reproduce the effect of the environmental variable, which was largely lost among noise variation when using the traditional approach. The results show how the value of b can be used as a source of valuable biological information if an appropriate regression model is selected.

Equation of state and shock compression of warm dense sodium—A first-principles study

DOE PAGES

Zhang, Shuai; Driver, Kevin P.; Soubiran, Francois; ...

2017-02-21

As one of the simple alkali metals, sodium has been of fundamental interest for shock physics experiments, but knowledge of its equation of state (EOS) in hot, dense regimes is not well known. By combining path integral Monte Carlo (PIMC) results for partially ionized states at high temperatures and density functional theory molecular dynamics (DFT-MD) results at lower temperatures, we have constructed a coherent equation of state for sodium over a wide density-temperature range of 1.93-11.60 g/cm 3 and 10 3–1.29×10 8 K. We find that a localized, Hartree-Fock nodal structure in PIMC yields pressures and internal energies that aremore » consistent with DFT-MD at intermediate temperatures of 2×10 6 K. Since PIMC and DFT-MD provide a first-principles treatment of electron shell and excitation effects, we are able to identify two compression maxima in the shock Hugoniot curve corresponding to K-shell and L-shell ionization. Our Hugoniot curves provide a benchmark for widely used EOS models: SESAME, LEOS, and Purgatorio. Due to the low ambient density, sodium has an unusually high first compression maximum along the shock Hugoniot curve. At beyond 10 7 K, we show that the radiation effect leads to very high compression along the Hugoniot curve, surpassing relativistic corrections, and observe an increasing deviation of the shock and particle velocities from a linear relation. Here, we also compute the temperature-density dependence of thermal and pressure ionization processes.« less

Calcic amphiboles in calc-alkaline and alkaline magmas: thermobarometric and chemometric empirical equations valid up to 1,130°C and 2.2 GPa

NASA Astrophysics Data System (ADS)

Ridolfi, Filippo; Renzulli, Alberto

2012-05-01

The following article presents constraints of the stability of Mg-rich (Mg/(Mg + Fe2+) > 0.5) calcic amphibole in both calc-alkaline and alkaline magmas, testing of previous thermobarometers, and formulation of new empirical equations that take into consideration a large amount of literature data (e.g. more than one thousand amphibole compositions among experimental and natural crystals). Particular care has been taken in choosing a large number of natural amphiboles and selecting quality experimental data from literature. The final database of experimental data, composed of 61 amphiboles synthesized in the ranges of 800-1,130°C and 130-2,200 MPa, indicates that amphibole crystallization occurs in a horn-like P- T stability field limited by two increasing curves (i.e. the thermal stability and an upper limit), which should start to bend back to higher pressures. Among calcic amphiboles, magnesiohornblendes and tschermakitic pargasites are only found in equilibrium with calc-alkaline melts and crystallize at relatively shallow conditions ( P up to ~1 GPa). Kaersutite and pargasite are species almost exclusively found in alkaline igneous products, while magnesiohastingsite is equally distributed in calc-alkaline and alkaline rocks. The reliability of previous amphibole applications was checked using the selected experimental database. The results of this testing indicate that none of the previous thermobarometers can be successfully used to estimate the P, T and fO2 in a wide range of amphibole crystallization conditions. Multivariate least-square analyses of experimental amphibole compositions and physico-chemical parameters allowed us to achieve a new thermobarometric model that gives reasonably low uncertainties ( T ± 23.5°C, P ± 11.5%, H2Omelt ± 0.78wt%) for calc-alkaline and alkaline magmas in a wide range of P- T conditions (up to 1,130°C and 2,200 MPa) and ΔNNO values (±0.37 log units) up to 500 MPa. The AK-[4]Al relation in amphibole can be readily used to distinguish crystals of calc-alkaline liquids from those of alkaline magmas. In addition, several chemometric equations allowing to estimate the anhydrous composition of the melts in equilibrium with amphiboles of calc-alkaline magmas were derived.

The element level time domain (ELTD) method for the analysis of nano-optical systems: I. Nondispersive media

NASA Astrophysics Data System (ADS)

Fallahi, Arya; Oswald, Benedikt; Leidenberger, Patrick

2012-04-01

We study a 3-dimensional, dual-field, fully explicit method for the solution of Maxwell's equations in the time domain on unstructured, tetrahedral grids. The algorithm uses the element level time domain (ELTD) discretization of the electric and magnetic vector wave equations. In particular, the suitability of the method for the numerical analysis of nanometer structured systems in the optical region of the electromagnetic spectrum is investigated. The details of the theory and its implementation as a computer code are introduced and its convergence behavior as well as conditions for stable time domain integration is examined. Here, we restrict ourselves to non-dispersive dielectric material properties since dielectric dispersion will be treated in a subsequent paper. Analytically solvable problems are analyzed in order to benchmark the method. Eventually, a dielectric microlens is considered to demonstrate the potential of the method. A flexible method of 2nd order accuracy is obtained that is applicable to a wide range of nano-optical configurations and can be a serious competitor to more conventional finite difference time domain schemes which operate only on hexahedral grids. The ELTD scheme can resolve geometries with a wide span of characteristic length scales and with the appropriate level of detail, using small tetrahedra where delicate, physically relevant details must be modeled.

AB INITIO EQUATIONS OF STATE FOR HYDROGEN (H-REOS.3) AND HELIUM (He-REOS.3) AND THEIR IMPLICATIONS FOR THE INTERIOR OF BROWN DWARFS

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

Becker, Andreas; Lorenzen, Winfried; Schöttler, Manuel

2015-01-01

We present new equations of state (EOSs) for hydrogen and helium covering a wide range of temperatures from 60 K to 10{sup 7} K and densities from 10{sup –10} g cm{sup –3} to 10{sup 3} g cm{sup –3}. They include an extended set of ab initio EOS data for the strongly correlated quantum regime with an accurate connection to data derived from other approaches for the neighboring regions. We compare linear mixing isotherms based on our EOS tables with available real mixture data. A first important astrophysical application of this new EOS data is the calculation of interior models formore » Jupiter and comparison with recent results. Second, mass-radius relations are calculated for Brown Dwarfs (BDs) which we compare with predictions derived from the widely used EOS of Saumon, Chabrier, and van Horn. Furthermore, we calculate interior models for typical BDs with different masses, namely, Corot-3b, Gliese-229b, and Corot-15b, and the giant planet KOI-889b. The predictions for the central pressures and densities differ by up to 10% dependent on the EOS used. Our EOS tables are made available in the supplemental material of this paper.« less

Normalization and extension of single-collector efficiency correlation equation

NASA Astrophysics Data System (ADS)

Messina, Francesca; Marchisio, Daniele; Sethi, Rajandrea

2015-04-01

The colloidal transport and deposition are important phenomena involved in many engineering problems. In the environmental engineering field the use of micro- and nano-scale zerovalent iron (M-NZVI) is one of the most promising technologies for groundwater remediation. Colloid deposition is normally studied from a micro scale point of view and the results are then implemented in macro scale models that are used to design field-scale applications. The single collector efficiency concept predicts particles deposition onto a single grain of a complex porous medium in terms of probability that an approaching particle would be retained on the solid grain. In literature, many different approaches and equations exist to predict it, but most of them fail under specific conditions (e.g. very small or very big particle size and very low fluid velocity) because they predict efficiency values exceeding unity. By analysing particle fluxes and deposition mechanisms and performing a mass balance on the entire domain, the traditional definition of efficiency was reformulated and a novel total flux normalized correlation equation is proposed for predicting single-collector efficiency under a broad range of parameters. It has been formulated starting from a combination of Eulerian and Lagrangian numerical simulations, performed under Smoluchowski-Levich conditions, in a geometry which consists of a sphere enveloped by a control volume. In order to guarantee the independence of each term, the correlation equation is derived through a rigorous hierarchical parameter estimation process, accounting for single and mutual interacting transport mechanisms. The correlation equation provides efficiency values lower than one over a wide range of parameters and is valid both for point and finite-size particles. A reduced form is also proposed by elimination of the less relevant terms. References 1. Yao, K. M.; Habibian, M. M.; Omelia, C. R., Water and Waste Water Filtration - Concepts and Applications. Environ Sci Technol 1971, 5, (11), 1105-&. 2. Tufenkji, N., and M. Elimelech, Correlation equation for predicting single-collector efficiency in physicochemical filtration in saturated porous media. Environmental Science & Technology 2004 38(2):529-536. 3. Boccardo, G.; Marchisio, D. L.; Sethi, R., Microscale simulation of particle deposition in porous media. J Colloid Interface Sci 2014, 417, 227-37

Kinetic modeling of non-ideal explosives with CHEETAH

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

Fried, L E; Howard, W M; Souers, P C

1998-08-06

We report an implementation of the Wood-Kirkwood kinetic detonation model based on multi-species equations of state and multiple reaction rate laws. Finite rate laws are used for the slowest chemical reactions. Other reactions are given infinite rates and are kept in constant thermodynamic equilibrium. We model a wide range of ideal and non-ideal composite energetic materials. We find that we can replicate experimental detonation velocities to within a few per cent, while obtaining good agreement with estimated reaction zone lengths. The detonation velocity as a function of charge radius is also correctly reproduced.

Arrayed waveguide Sagnac interferometer.

PubMed

Capmany, José; Muñoz, Pascual; Sales, Salvador; Pastor, Daniel; Ortega, Beatriz; Martinez, Alfonso

2003-02-01

We present a novel device, an arrayed waveguide Sagnac interferometer, that combines the flexibility of arrayed waveguides and the wide application range of fiber or integrated optics Sagnac loops. We form the device by closing an array of wavelength-selective light paths provided by two arrayed waveguides with a single 2 x 2 coupler in a Sagnac configuration. The equations that describe the device's operation in general conditions are derived. A preliminary experimental demonstration is provided of a fiber prototype in passive operation that shows good agreement with the expected theoretical performance. Potential applications of the device in nonlinear operation are outlined and discussed.

Method for Evaluating the Corrosion Resistance of Aluminum Metallization of Integrated Circuits under Multifactorial Influence

NASA Astrophysics Data System (ADS)

Kolomiets, V. I.

2018-03-01

The influence of complex influence of climatic factors (temperature, humidity) and electric mode (supply voltage) on the corrosion resistance of metallization of integrated circuits has been considered. The regression dependence of the average time of trouble-free operation t on the mentioned factors has been established in the form of a modified Arrhenius equation that is adequate in a wide range of factor values and is suitable for selecting accelerated test modes. A technique for evaluating the corrosion resistance of aluminum metallization of depressurized CMOS integrated circuits has been proposed.

Piecewise uniform conduction-like flow channels and method therefor

DOEpatents

Cummings, Eric B [Livermore, CA; Fiechtner, Gregory J [Livermore, CA

2006-02-28

A low-dispersion methodology for designing microfabricated conduction channels for on-chip electrokinetic-based systems is presented. The technique relies on trigonometric relations that apply for ideal electrokinetic flows, allowing faceted channels to be designed on chips using common drafting software and a hand calculator. Flows are rotated and stretched along the abrupt interface between adjacent regions with differing permeability. Regions bounded by interfaces form flow "prisms" that can be combined with other designed prisms to obtain a wide range of turning angles and expansion ratios while minimizing dispersion. Designs are demonstrated using two-dimensional numerical solutions of the Laplace equation.

High-pressure melting of molybdenum.

PubMed

Belonoshko, A B; Simak, S I; Kochetov, A E; Johansson, B; Burakovsky, L; Preston, D L

2004-05-14

The melting curve of the body-centered cubic (bcc) phase of Mo has been determined for a wide pressure range using both direct ab initio molecular dynamics simulations of melting as well as a phenomenological theory of melting. These two methods show very good agreement. The simulations are based on density functional theory within the generalized gradient approximation. Our calculated equation of state of bcc Mo is in excellent agreement with experimental data. However, our melting curve is substantially higher than the one determined in diamond anvil cell experiments up to a pressure of 100 GPa. An explanation is suggested for this discrepancy.

Theoretical and experimental investigation of the destruction of graphites in a flow of dissociated air

NASA Technical Reports Server (NTRS)

Bovina, T. A.; Zviagin, Y. V.; Markelov, N. V.; Chudetskiy, Y. V.

1986-01-01

A method is presented for calculating the heating and erosion of blunt bodies made of graphite in a high-enthalpy flow of dissociated air, assuming chemical equilibrium on the surface and taking account of the thermal effects of combustion and sublimation of graphite. The analysis involves the use of a finite difference scheme to solve an equation of unsteady heat conduction. Attention is given to the equilibrium vaporization of C, C2 and C3 molecules. The calculations agree well with experimental data for a wide range of temperatures and stagnation pressures.

Diversification of the rare-earth business in the existing enterprises

NASA Astrophysics Data System (ADS)

Bogdanov, S. V.; Grishaev, S. I.; Yazev, V. A.

2013-12-01

The development of the modern rare-earth business is analyzed, and the possibilities of using a mathematical description of the prospects of this business on the basis of nonlinear evolution equations are estimated. The well-known methods of describing the life cycle of the economic activity of a commercial company in the closed multisector model of market economics is used to determine the boundaries of changing the average labor productivity during the diversification of business on operating Russian enterprises that produce a wide range of products and are intended to manufacture new types of high-technology rare-earth metal products.

Two-Dimensional Thermal Boundary Layer Corrections for Convective Heat Flux Gauges

NASA Technical Reports Server (NTRS)

Kandula, Max; Haddad, George

2007-01-01

This work presents a CFD (Computational Fluid Dynamics) study of two-dimensional thermal boundary layer correction factors for convective heat flux gauges mounted in flat plate subjected to a surface temperature discontinuity with variable properties taken into account. A two-equation k - omega turbulence model is considered. Results are obtained for a wide range of Mach numbers (1 to 5), gauge radius ratio, and wall temperature discontinuity. Comparisons are made for correction factors with constant properties and variable properties. It is shown that the variable-property effects on the heat flux correction factors become significant

Fiber-optics implementation of an asymmetric phase-covariant quantum cloner.

PubMed

Bartůsková, Lucie; Dusek, Miloslav; Cernoch, Antonín; Soubusta, Jan; Fiurásek, Jaromír

2007-09-21

We present the experimental realization of optimal symmetric and asymmetric phase-covariant 1-->2 cloning of qubit states using fiber optics. The state of each qubit is encoded into a single photon which can propagate through two optical fibers. The operation of our device is based on one- and two-photon interference. We have demonstrated the creation of two copies for a wide range of qubit states from the equator of the Bloch sphere. The measured fidelities of both copies are close to the theoretical values and they surpass the theoretical maximum obtainable with the universal cloner.

Micro and Macro Mechanics of Fracture in Ceramics.

DTIC Science & Technology

1982-10-30

XrP /Kc)21 (2.2) The validity of Eq. (2.2) has been tested with Vickers indentation in a wide range of ceramic materials (Anstis et al. 1981). J6...basis that the replacement of Kr in Eq. (2.1) with any function of the form Kr - XrP /cn (n > 0) yields a set of equations of the same form as (2.2) to...superposition of two components, one due to the residual stress (Eqn. 8) and the other due to the applied load (Eqn. 2) -272- K XrP /C 3/2 + G(7SIc)1/2

Validity of the BodyGem calorimeter and prediction equations for the assessment of resting energy expenditure in overweight and obese Saudi males.

PubMed

Almajwal, Ali M; Williams, Peter G; Batterham, Marijka J

2011-07-01

To assess the accuracy of resting energy expenditure (REE) measurement in a sample of overweight and obese Saudi males, using the BodyGem device (BG) with whole room calorimetry (WRC) as a reference, and to evaluate the accuracy of predictive equations. Thirty-eight subjects (mean +/- SD, age 26.8+/- 3.7 years, body mass index 31.0+/- 4.8) were recruited during the period from 5 February 2007 to 28 March 2008. Resting energy expenditure was measured using a WRC and BG device, and also calculated using 7 prediction equations. Mean differences, bias, percent of bias (%bias), accurate estimation, underestimation and overestimation were calculated. Repeated measures with the BG were not significantly different (accurate prediction: 81.6%; %bias 1.1+/- 6.3, p>0.24) with limits of agreement ranging from +242 to -200 kcal. Resting energy expenditure measured by BG was significantly less than WRC values (accurate prediction: 47.4%; %bias: 11.0+/- 14.6, p = 0.0001) with unacceptably wide limits of agreement. Harris-Benedict, Schofield and World Health Organization equations were the most accurate, estimating REE within 10% of measured REE, but none seem appropriate to predict the REE of individuals. There was a poor agreement between the REE measured by WRC compared to BG or predictive equations. The BG assessed REE accurately in 47.4% of the subjects on an individual level.

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

NASA Technical Reports Server (NTRS)

Cross, M. F.

2011-01-01

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

A B-spline Galerkin method for the Dirac equation

NASA Astrophysics Data System (ADS)

Froese Fischer, Charlotte; Zatsarinny, Oleg

2009-06-01

The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y=-λy, that can also be written as a pair of first-order equations y=λz, z=-λy. Expanding both y(r) and z(r) in the B basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the B basis and z(r) in the dB/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method ( B,B) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.

The Search for Carbonates on Mars

NASA Technical Reports Server (NTRS)

Farmer, Jack D.; DesMarais, David J.; Morrison, David (Technical Monitor)

1994-01-01

Liquid water is presently unstable at the Martian surface, where the mean atmospheric pressure is 6 mbar (due to CO2) and the winter diurnal temperature ranges from 150 K at the pole to 220 K at the equator. Liquid water is widely regarded as a basic requirement for living systems, suggesting that life as we know it is not possible in present surface environments on Mars. However, life may survive within "oases" where liquid water is present. Potential oases on Mars include subsurface hydrothermal systems or deeply buried aquifers where chemoautolithotrophic microorganisms may exist. Potential metabolic strategies for primary production in such environments on Mars (and for the microbial mediation of geologic processes!) encompass the full range presently known for subsurface environments on the Earth (e.g. sulphate reduction, methanogenesis, acetogenesis, etc).

A dynamic growth model of vegetative soya bean plants: model structure and behaviour under varying root temperature and nitrogen concentration

NASA Technical Reports Server (NTRS)

Lim, J. T.; Wilkerson, G. G.; Raper, C. D. Jr; Gold, H. J.

1990-01-01

A differential equation model of vegetative growth of the soya bean plant (Glycine max (L.) Merrill cv. Ransom') was developed to account for plant growth in a phytotron system under variation of root temperature and nitrogen concentration in nutrient solution. The model was tested by comparing model outputs with data from four different experiments. Model predictions agreed fairly well with measured plant performance over a wide range of root temperatures and over a range of nitrogen concentrations in nutrient solution between 0.5 and 10.0 mmol NO3- in the phytotron environment. Sensitivity analyses revealed that the model was most sensitive to changes in parameters relating to carbohydrate concentration in the plant and nitrogen uptake rate.

Improving North American forest biomass estimates from literature synthesis and meta-analysis of existing biomass equations

Treesearch

David C. Chojnacky; Jennifer C. Jenkins; Amanda K. Holland

2009-01-01

Thousands of published equations purport to estimate biomass of individual trees. These equations are often based on very small samples, however, and can provide widely different estimates for trees of the same species. We addressed this issue in a previous study by devising 10 new equations that estimated total aboveground biomass for all species in North America (...

Quantitative modeling of multiscale neural activity

NASA Astrophysics Data System (ADS)

Robinson, Peter A.; Rennie, Christopher J.

2007-01-01

The electrical activity of the brain has been observed for over a century and is widely used to probe brain function and disorders, chiefly through the electroencephalogram (EEG) recorded by electrodes on the scalp. However, the connections between physiology and EEGs have been chiefly qualitative until recently, and most uses of the EEG have been based on phenomenological correlations. A quantitative mean-field model of brain electrical activity is described that spans the range of physiological and anatomical scales from microscopic synapses to the whole brain. Its parameters measure quantities such as synaptic strengths, signal delays, cellular time constants, and neural ranges, and are all constrained by independent physiological measurements. Application of standard techniques from wave physics allows successful predictions to be made of a wide range of EEG phenomena, including time series and spectra, evoked responses to stimuli, dependence on arousal state, seizure dynamics, and relationships to functional magnetic resonance imaging (fMRI). Fitting to experimental data also enables physiological parameters to be infered, giving a new noninvasive window into brain function, especially when referenced to a standardized database of subjects. Modifications of the core model to treat mm-scale patchy interconnections in the visual cortex are also described, and it is shown that resulting waves obey the Schroedinger equation. This opens the possibility of classical cortical analogs of quantum phenomena.

A volume-filtered formulation to capture particle-shock interactions in multiphase compressible flows

NASA Astrophysics Data System (ADS)

Shallcross, Gregory; Capecelatro, Jesse

2017-11-01

Compressible particle-laden flows are common in engineering systems. Applications include but are not limited to water injection in high-speed jet flows for noise suppression, rocket-plume surface interactions during planetary landing, and explosions during coal mining operations. Numerically, it is challenging to capture these interactions due to the wide range of length and time scales. Additionally, there are many forms of the multiphase compressible flow equations with volume fraction effects, some of which are conflicting in nature. The purpose of this presentation is to develop the capability to accurately capture particle-shock interactions in systems with a large number of particles from dense to dilute regimes. A thorough derivation of the volume filtered equations is presented. The volume filtered equations are then implemented in a high-order, energy-stable Eulerian-Lagrangian framework. We show this framework is capable of decoupling the fluid mesh from the particle size, enabling arbitrary particle size distributions in the presence of shocks. The proposed method is then assessed against particle-laden shock tube data. Quantities of interest include fluid-phase pressure profiles and particle spreading rates. The effect of collisions in 2D and 3D are also evaluated.

Mathematical modeling of influence of ion size effects in an electrolyte in a nanoslit with overlapped EDL

NASA Astrophysics Data System (ADS)

Rajni, Kumar, Prashant

2017-10-01

Many nanofluidic systems are being used in a wide range of applications due to advances in nanotechnology. Due to nanoscale size of the system, the physics involved in the electric double layer and consequently the different phenomena related to it are different than those at microscale. The Poisson-Boltzmann equation governing the electric double layer in the system has many shortcomings such as point sized ions. The inclusion of finite size of ions give rise to various electrokinetic phenomena. Electrocapillarity is one such phenomena where the size effect plays an important role. Theeffect of asymmetric finite ion sizes in nano-confinement in the view of osmotic pressure and electrocapillarity is analyzed. As the confinement width of the system becomes comparable with the Debye length, the overlapped electric double layer (EDL) is influenced and significantly deformed by the steric effects. The osmotic pressure from the modified Poisson-Boltzmann equation in nanoslit is obtained. Due to nonlinear nature of the modified PB equation, the solution is obtained through numerical method. Afterwards, the electrocapillarity due to the steric effect is analyzed under constant surface potential condition at the walls of the nanoslit along with the flat interface assumption.

Numerical Modeling of Cavitating Venturi: A Flow Control Element of Propulsion System

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Saxon, Jeff (Technical Monitor)

2002-01-01

In a propulsion system, the propellant flow and mixture ratio could be controlled either by variable area flow control valves or by passive flow control elements such as cavitating venturies. Cavitating venturies maintain constant propellant flowrate for fixed inlet conditions (pressure and temperature) and wide range of outlet pressures, thereby maintain constant, engine thrust and mixture ratio. The flowrate through the venturi reaches a constant value and becomes independent of outlet pressure when the pressure at throat becomes equal to vapor pressure. In order to develop a numerical model of propulsion system, it is necessary to model cavitating venturies in propellant feed systems. This paper presents a finite volume model of flow network of a cavitating venturi. The venturi was discretized into a number of control volumes and mass, momentum and energy conservation equations in each control volume are simultaneously solved to calculate one-dimensional pressure, density, and flowrate and temperature distribution. The numerical model predicts cavitations at the throat when outlet pressure was gradually reduced. Once cavitation starts, with further reduction of downstream pressure, no change in flowrate is found. The numerical predictions have been compared with test data and empirical equation based on Bernoulli's equation.

Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yurkin, Maxim A.

2018-07-01

Although free space cannot generate electromagnetic waves, the majority of existing accounts of frequency-domain electromagnetic scattering by particles and particle groups are based on the postulate of existence of an impressed incident field, usually in the form of a plane wave. In this tutorial we discuss how to account for the actual existence of impressed source currents rather than impressed incident fields. Specifically, we outline a self-consistent theoretical formalism describing electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents, some of which can be far removed from the object and some can reside in its vicinity, including inside the object. To make the resulting formalism applicable to a wide range of scattering-object morphologies, we use the framework of the volume integral equation formulation of electromagnetic scattering, couple it with the notion of the transition operator, and exploit the fundamental symmetry property of this operator. Among novel results, this tutorial includes a streamlined proof of fundamental symmetry (reciprocity) relations, a simplified derivation of the Foldy equations, and an explicit analytical expression for the transition operator of a multi-component scattering object.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Resonant-Triad Interaction

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.

One-dimensional Lagrangian implicit hydrodynamic algorithm for Inertial Confinement Fusion applications

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

Ramis, Rafael, E-mail: rafael.ramis@upm.es

A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative Lagrangian formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted tomore » optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.« less

Tensile properties and flow behavior analysis of modified 9Cr-1Mo steel clad tube material

NASA Astrophysics Data System (ADS)

Singh, Kanwarjeet; Latha, S.; Nandagopal, M.; Mathew, M. D.; Laha, K.; Jayakumar, T.

2014-11-01

The tensile properties and flow behavior of modified 9Cr-1Mo steel clad tube have been investigated in the framework of various constitutive equations for a wide range of temperatures (300-923 K) and strain rates (3 × 10-3 s-1, 3 × 10-4 s-1 and 3 × 10-5 s-1). The tensile flow behavior of modified 9Cr-1Mo steel clad tube was most accurately described by Voce equation. The variation of instantaneous work hardening rate (θ = dσ/dε) and σθ with stress (σ) indicated two stage behavior characterized by rapid decrease at low stresses (transient stage) followed by a gradual decrease in high stresses (Stage III). The variation of work hardening parameters and work hardening rate in terms of θ vs. σ and σθ vs. σ with temperature exhibited three distinct regimes. Rapid decrease in flow stress and work hardening parameters and rapid shift of θ vs. σ and σθ vs. σ towards low stresses with increase in temperature indicated dynamic recovery at high temperatures. Tensile properties of the material have been best predicted from Voce equation.

Comparisons of volcanic eruptions from linear and central vents on Earth, Venus, and Mars (Invited)

NASA Astrophysics Data System (ADS)

Glaze, L. S.; Baloga, S. M.

2010-12-01

Vent geometry (linear versus central) plays a significant role in the ability of an explosive eruption to sustain a buoyant, convective plume. This has important implications for the injection and dispersal of particulates into planetary atmospheres and the ability to interpret the geologic record of planetary volcanism. The approach to modeling linear volcanic vents builds on the original work by Stothers [1], and takes advantage of substantial improvements that have been made in volcanic plume modeling over the last 20 years [e.g., 2,3]. A complete system of equations describing buoyant plume rise requires at least a half dozen differential equations and another half dozen equations for the parameters and constraints within the plume and ambient atmosphere. For the cylindrically axisymmetric system of differential equations given in [2], the control volume is defined as V = πr2dz. The area through which ambient atmosphere is entrained is Ae = 2πr dz, where r is the plume radius and z is vertical distance. The analogous linear vent system has a corresponding control volume, V = 2bLdz and entrainment area, Ae ≈ 2Ldz, where L is the length of the linear plume, 2b is the width of the linear plume, and it is assumed that L >> b. For typical terrestrial boundary conditions (temperature, velocity, gas mass fraction), buoyant plumes from circular vents can be maintained with substantial maximum heights over a wide range of vent sizes. However, linear vent plumes are much more sensitive to vent size, and can maintain a convective plume only over a much more narrow range of half widths. As L increases, linear plumes become more capable of establishing a convective regime over a broad range of bo, similar to the circular vents. This is primarily because as L increases, the entrainment area of the linear plumes increases, relative to the control volume. The ability of a plume to become buoyant is driven by whether or not sufficient air can be entrained (and warmed) to reduce the bulk plume density before upward momentum is exhausted. From mass conservation, linear plumes surpass circular vents in entrainment efficiency approximately when Lo ≥ 3ro. Consistent with other work [3,4], the range of conditions for maintaining a buoyant plume from a circular vent on Venus is very narrow, and the range of linear vent widths is more limited still. Unlike the terrestrial case, linear vents on Venus appear capable of driving a plume to somewhat higher maximum altitudes, with all other things remaining equal. Similar analyses were conducted for current atmospheric conditions on Mars. Results indicate a preference for the formation of pyroclastic flows on Mars from both circular and linear vents, as opposed to widely dispersed airfall deposits. Only the Earth, with its thick wet atmosphere, favors explosive eruptions that can maintain convective plumes reaching 10s of km in altitude over a broad range of eruptive conditions. References: [1] Stothers, R.B. (1989) J Atmos Sci, 46, 2662-2670. [2] Glaze. L.S., Baloga, S. M., and Wilson, L. (1997) JGR, 102, 6099-6108. [3] Glaze, L.S. (1999) JGR, 104, 18,899-18,906. [4] Thornhill, G.D. (1993) JGR, 98, 9107-9111.

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

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

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

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

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

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

Algorithm development

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Lomax, Harvard

1987-01-01

The past decade has seen considerable activity in algorithm development for the Navier-Stokes equations. This has resulted in a wide variety of useful new techniques. Some examples for the numerical solution of the Navier-Stokes equations are presented, divided into two parts. One is devoted to the incompressible Navier-Stokes equations, and the other to the compressible form.

Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations.

PubMed

Kilic, Mustafa Sabri; Bazant, Martin Z; Ajdari, Armand

2007-02-01

In situations involving large potentials or surface charges, the Poisson-Boltzman (PB) equation has shortcomings because it neglects ion-ion interactions and steric effects. This has been widely recognized by the electrochemistry community, leading to the development of various alternative models resulting in different sets "modified PB equations," which have had at least qualitative success in predicting equilibrium ion distributions. On the other hand, the literature is scarce in terms of descriptions of concentration dynamics in these regimes. Here, adapting strategies developed to modify the PB equation, we propose a simple modification of the widely used Poisson-Nernst-Planck (PNP) equations for ionic transport, which at least qualitatively accounts for steric effects. We analyze numerical solutions of these modified PNP equations on the model problem of the charging of a simple electrolyte cell, and compare the outcome to that of the standard PNP equations. Finally, we repeat the asymptotic analysis of Bazant, Thornton, and Ajdari [Phys. Rev. E 70, 021506 (2004)] for this new system of equations to further document the interest and limits of validity of the simpler equivalent electrical circuit models introduced in Part I [Kilic, Bazant, and Ajdari, Phys. Rev. E 75, 021502 (2007)] for such problems.

Why does shear banding behave like first-order phase transitions? Derivation of a potential from a mechanical constitutive model.

PubMed

Sato, K; Yuan, X-F; Kawakatsu, T

2010-02-01

Numerous numerical and experimental evidence suggest that shear banding behavior looks like first-order phase transitions. In this paper, we demonstrate that this correspondence is actually established in the so-called non-local diffusive Johnson-Segalman model (the DJS model), a typical mechanical constitutive model that has been widely used for describing shear banding phenomena. In the neighborhood of the critical point, we apply the reduction procedure based on the center manifold theory to the governing equations of the DJS model. As a result, we obtain a time evolution equation of the flow field that is equivalent to the time-dependent Ginzburg-Landau (TDGL) equations for modeling thermodynamic first-order phase transitions. This result, for the first time, provides a mathematical proof that there is an analogy between the mechanical instability and thermodynamic phase transition at least in the vicinity of the critical point of the shear banding of DJS model. Within this framework, we can clearly distinguish the metastable branch in the stress-strain rate curve around the shear banding region from the globally stable branch. A simple extension of this analysis to a class of more general constitutive models is also discussed. Numerical simulations for the original DJS model and the reduced TDGL equation is performed to confirm the range of validity of our reduction theory.

A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh

NASA Astrophysics Data System (ADS)

Sun, Wenjun; Jiang, Song; Xu, Kun

2017-12-01

In order to extend the unified gas kinetic scheme (UGKS) to solve radiative transfer equations in a complex geometry, a multidimensional asymptotic preserving implicit method on unstructured mesh is constructed in this paper. With an implicit formulation, the CFL condition for the determination of the time step in UGKS can be much relaxed, and a large time step is used in simulations. Differently from previous direction-by-direction UGKS on orthogonal structured mesh, on unstructured mesh the interface flux transport takes into account multi-dimensional effect, where gradients of radiation intensity and material temperature in both normal and tangential directions of a cell interface are included in the flux evaluation. The multiple scale nature makes the UGKS be able to capture the solutions in both optically thin and thick regions seamlessly. In the optically thick region the condition of cell size being less than photon's mean free path is fully removed, and the UGKS recovers a solver for diffusion equation in such a limit on unstructured mesh. For a distorted quadrilateral mesh, the UGKS goes to a nine-point scheme for the diffusion equation, and it naturally reduces to the standard five-point scheme for a orthogonal quadrilateral mesh. Numerical computations covering a wide range of transport regimes on unstructured and distorted quadrilateral meshes will be presented to validate the current approach.

The rate of bubble growth in a superheated liquid in pool boiling

NASA Astrophysics Data System (ADS)

Abdollahi, Mohammad Reza; Jafarian, Mehdi; Jamialahmadi, Mohammad

2017-12-01

A semi-empirical model for the estimation of the rate of bubble growth in nucleate pool boiling is presented, considering a new equation to estimate the temperature history of the bubble in the bulk of liquid. The conservation equations of energy, mass and momentum have been firstly derived and solved analytically. The present analytical model of the bubble growth predicts that the radius of the bubble grows as a function of √{t}.{\\operatorname{erf}}( N√{t}) , while so far the bubble growth rate has been mainly correlated to √{t} in the previous studies. In the next step, the analytical solutions were used to develop a new semi-empirical equation. To achieve this, firstly the analytical solution were non-dimensionalised and then the experimental data, available in the literature, were applied to tune the dimensionless coefficients appeared in the dimensionless equation. Finally, the reliability of the proposed semi-empirical model was assessed through comparison of the model predictions with the available experimental data in the literature, which were not applied in the tuning of the dimensionless parameters of the model. The comparison of the model predictions with other proposed models in the literature was also performed. These comparisons show that this model enables more accurate predictions than previously proposed models with a deviation of less than 10% in a wide range of operating conditions.

A Simple "Boxed Molecular Kinetics" Approach To Accelerate Rare Events in the Stochastic Kinetic Master Equation.

PubMed

Shannon, Robin; Glowacki, David R

2018-02-15

The chemical master equation is a powerful theoretical tool for analyzing the kinetics of complex multiwell potential energy surfaces in a wide range of different domains of chemical kinetics spanning combustion, atmospheric chemistry, gas-surface chemistry, solution phase chemistry, and biochemistry. There are two well-established methodologies for solving the chemical master equation: a stochastic "kinetic Monte Carlo" approach and a matrix-based approach. In principle, the results yielded by both approaches are identical; the decision of which approach is better suited to a particular study depends on the details of the specific system under investigation. In this Article, we present a rigorous method for accelerating stochastic approaches by several orders of magnitude, along with a method for unbiasing the accelerated results to recover the "true" value. The approach we take in this paper is inspired by the so-called "boxed molecular dynamics" (BXD) method, which has previously only been applied to accelerate rare events in molecular dynamics simulations. Here we extend BXD to design a simple algorithmic strategy for accelerating rare events in stochastic kinetic simulations. Tests on a number of systems show that the results obtained using the BXD rare event strategy are in good agreement with unbiased results. To carry out these tests, we have implemented a kinetic Monte Carlo approach in MESMER, which is a cross-platform, open-source, and freely available master equation solver.

Alternate corrections for estimating actual wetland evapotranspiration from potential evapotranspiration

USGS Publications Warehouse

Shoemaker, W. Barclay; Sumner, D.M.

2006-01-01

Corrections can be used to estimate actual wetland evapotranspiration (AET) from potential evapotranspiration (PET) as a means to define the hydrology of wetland areas. Many alternate parameterizations for correction coefficients for three PET equations are presented, covering a wide range of possible data-availability scenarios. At nine sites in the wetland Everglades of south Florida, USA, the relatively complex PET Penman equation was corrected to daily total AET with smaller standard errors than the PET simple and Priestley-Taylor equations. The simpler equations, however, required less data (and thus less funding for instrumentation), with the possibility of being corrected to AET with slightly larger, comparable, or even smaller standard errors. Air temperature generally corrected PET simple most effectively to wetland AET, while wetland stage and humidity generally corrected PET Priestley-Taylor and Penman most effectively to wetland AET. Stage was identified for PET Priestley-Taylor and Penman as the data type with the most correction ability at sites that are dry part of each year or dry part of some years. Finally, although surface water generally was readily available at each monitoring site, AET was not occurring at potential rates, as conceptually expected under well-watered conditions. Apparently, factors other than water availability, such as atmospheric and stomata resistances to vapor transport, also were limiting the PET rate. ?? 2006, The Society of Wetland Scientists.

The physics behind Van der Burgh's empirical equation, providing a new predictive equation for salinity intrusion in estuaries

NASA Astrophysics Data System (ADS)

Zhang, Zhilin; Savenije, Hubert H. G.

2017-07-01

The practical value of the surprisingly simple Van der Burgh equation in predicting saline water intrusion in alluvial estuaries is well documented, but the physical foundation of the equation is still weak. In this paper we provide a connection between the empirical equation and the theoretical literature, leading to a theoretical range of Van der Burgh's coefficient of 1/2 < K < 2/3 for density-driven mixing which falls within the feasible range of 0 < K < 1. In addition, we developed a one-dimensional predictive equation for the dispersion of salinity as a function of local hydraulic parameters that can vary along the estuary axis, including mixing due to tide-driven residual circulation. This type of mixing is relevant in the wider part of alluvial estuaries where preferential ebb and flood channels appear. Subsequently, this dispersion equation is combined with the salt balance equation to obtain a new predictive analytical equation for the longitudinal salinity distribution. Finally, the new equation was tested and applied to a large database of observations in alluvial estuaries, whereby the calibrated K values appeared to correspond well to the theoretical range.

Correlation among extinction efficiency and other parameters in an aggregate dust model

NASA Astrophysics Data System (ADS)

Dhar, Tanuj Kumar; Sekhar Das, Himadri

2017-10-01

We study the extinction properties of highly porous Ballistic Cluster-Cluster Aggregate dust aggregates in a wide range of complex refractive indices (1.4≤ n≤ 2.0, 0.001≤ k≤ 1.0) and wavelengths (0.11 {{μ }}{{m}}≤ {{λ }}≤ 3.4 {{μ }} m). An attempt has been made for the first time to investigate the correlation among extinction efficiency ({Q}{ext}), composition of dust aggregates (n,k), wavelength of radiation (λ) and size parameter of the monomers (x). If k is fixed at any value between 0.001 and 1.0, {Q}{ext} increases with increase of n from 1.4 to 2.0. {Q}{ext} and n are correlated via linear regression when the cluster size is small, whereas the correlation is quadratic at moderate and higher sizes of the cluster. This feature is observed at all wavelengths (ultraviolet to optical to infrared). We also find that the variation of {Q}{ext} with n is very small when λ is high. When n is fixed at any value between 1.4 and 2.0, it is observed that {Q}{ext} and k are correlated via a polynomial regression equation (of degree 1, 2, 3 or 4), where the degree of the equation depends on the cluster size, n and λ. The correlation is linear for small size and quadratic/cubic/quartic for moderate and higher sizes. We have also found that {Q}{ext} and x are correlated via a polynomial regression (of degree 3, 4 or 5) for all values of n. The degree of regression is found to be n and k-dependent. The set of relations obtained from our work can be used to model interstellar extinction for dust aggregates in a wide range of wavelengths and complex refractive indices.

Gain in stochastic resonance: Precise numerics versus linear response theory beyond the two-mode approximation

NASA Astrophysics Data System (ADS)

Casado-Pascual, Jesús; Denk, Claus; Gómez-Ordóñez, José; Morillo, Manuel; Hänggi, Peter

2003-03-01

In the context of the phenomenon of stochastic resonance (SR), we study the correlation function, the signal-to-noise ratio (SNR), and the ratio of output over input SNR, i.e., the gain, which is associated to the nonlinear response of a bistable system driven by time-periodic forces and white Gaussian noise. These quantifiers for SR are evaluated using the techniques of linear response theory (LRT) beyond the usually employed two-mode approximation scheme. We analytically demonstrate within such an extended LRT description that the gain can indeed not exceed unity. We implement an efficient algorithm, based on work by Greenside and Helfand (detailed in the Appendix), to integrate the driven Langevin equation over a wide range of parameter values. The predictions of LRT are carefully tested against the results obtained from numerical solutions of the corresponding Langevin equation over a wide range of parameter values. We further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the SNR and the gain. As a main result we show for subthreshold driving that both the correlation function and the SNR can deviate substantially from the predictions of LRT and yet the gain can be either larger or smaller than unity. In particular, we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle. This latter result is in agreement with recent analog simulation results by Gingl et al. [ICNF 2001, edited by G. Bosman (World Scientific, Singapore, 2002), pp. 545 548; Fluct. Noise Lett. 1, L181 (2001)].

Nucleophilicities of Lewis Bases B and Electrophilicities of Lewis Acids A Determined from the Dissociation Energies of Complexes B⋯A Involving Hydrogen Bonds, Tetrel Bonds, Pnictogen Bonds, Chalcogen Bonds and Halogen Bonds.

PubMed

Alkorta, Ibon; Legon, Anthony C

2017-10-23

It is shown that the dissociation energy D e for the process B⋯A = B + A for 250 complexes B⋯A composed of 11 Lewis bases B (N₂, CO, HC≡CH, CH₂=CH₂, C₃H₆, PH₃, H₂S, HCN, H₂O, H₂CO and NH₃) and 23 Lewis acids (HF, HCl, HBr, HC≡CH, HCN, H₂O, F₂, Cl₂, Br₂, ClF, BrCl, H₃SiF, H₃GeF, F₂CO, CO₂, N₂O, NO₂F, PH₂F, AsH₂F, SO₂, SeO₂, SF₂, and SeF₂) can be represented to good approximation by means of the equation D e = c ' N B E A , in which N B is a numerical nucleophilicity assigned to B, E A is a numerical electrophilicity assigned to A, and c ' is a constant, conveniently chosen to have the value 1.00 kJ mol -1 here. The 250 complexes were chosen to cover a wide range of non-covalent interaction types, namely: (1) the hydrogen bond; (2) the halogen bond; (3) the tetrel bond; (4) the pnictogen bond; and (5) the chalcogen bond. Since there is no evidence that one group of non-covalent interaction was fitted any better than the others, it appears the equation is equally valid for all the interactions considered and that the values of N B and E A so determined define properties of the individual molecules. The values of N B and E A can be used to predict the dissociation energies of a wide range of binary complexes B⋯A with reasonable accuracy.

Aerosol hygroscopic growth parameterization based on a solute specific coefficient

NASA Astrophysics Data System (ADS)

Metzger, S.; Steil, B.; Xu, L.; Penner, J. E.; Lelieveld, J.

2011-09-01

Water is a main component of atmospheric aerosols and its amount depends on the particle chemical composition. We introduce a new parameterization for the aerosol hygroscopic growth factor (HGF), based on an empirical relation between water activity (aw) and solute molality (μs) through a single solute specific coefficient νi. Three main advantages are: (1) wide applicability, (2) simplicity and (3) analytical nature. (1) Our approach considers the Kelvin effect and covers ideal solutions at large relative humidity (RH), including CCN activation, as well as concentrated solutions with high ionic strength at low RH such as the relative humidity of deliquescence (RHD). (2) A single νi coefficient suffices to parameterize the HGF for a wide range of particle sizes, from nanometer nucleation mode to micrometer coarse mode particles. (3) In contrast to previous methods, our analytical aw parameterization depends not only on a linear correction factor for the solute molality, instead νi also appears in the exponent in form x · ax. According to our findings, νi can be assumed constant for the entire aw range (0-1). Thus, the νi based method is computationally efficient. In this work we focus on single solute solutions, where νi is pre-determined with the bisection method from our analytical equations using RHD measurements and the saturation molality μssat. The computed aerosol HGF and supersaturation (Köhler-theory) compare well with the results of the thermodynamic reference model E-AIM for the key compounds NaCl and (NH4)2SO4 relevant for CCN modeling and calibration studies. The equations introduced here provide the basis of our revised gas-liquid-solid partitioning model, i.e. version 4 of the EQuilibrium Simplified Aerosol Model (EQSAM4), described in a companion paper.

Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales

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

Schwerdtfeger, Christine A.; Soudackov, Alexander V.; Hammes-Schiffer, Sharon, E-mail: shs3@illinois.edu

2014-01-21

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents formore » a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.« less

Refraction corrections for surveying

NASA Technical Reports Server (NTRS)

Lear, W. M.

1979-01-01

Optical measurements of range and elevation angle are distorted by the earth's atmosphere. High precision refraction correction equations are presented which are ideally suited for surveying because their inputs are optically measured range and optically measured elevation angle. The outputs are true straight line range and true geometric elevation angle. The 'short distances' used in surveying allow the calculations of true range and true elevation angle to be quickly made using a programmable pocket calculator. Topics covered include the spherical form of Snell's Law; ray path equations; and integrating the equations. Short-, medium-, and long-range refraction corrections are presented in tables.

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women.

PubMed

Kulkarni, Bharati; Kuper, Hannah; Taylor, Amy; Wells, Jonathan C; Radhakrishna, K V; Kinra, Sanjay; Ben-Shlomo, Yoav; Smith, George Davey; Ebrahim, Shah; Byrne, Nuala M; Hills, Andrew P

2013-10-15

Lean body mass (LBM) and muscle mass remain difficult to quantify in large epidemiological studies due to the unavailability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual-energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n = 2,220; 36% women; age 18-79 yr), representing a wide range of body mass index (14-44 kg/m(2)), participated in this study. Their LBM, including ALST, was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA-measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height, and weight explained >90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of skinfold thicknesses) increased the explained variation by 5-8% in the fully adjusted models predicting LBM and ALST. More complex equations using all of the above anthropometric variables could predict the DXA-measured LBM and ALST accurately, as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively), as well as good agreement by Bland-Altman analyses (Bland JM, Altman D. Lancet 1: 307-310, 1986). These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition.

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women

PubMed Central

Kuper, Hannah; Taylor, Amy; Wells, Jonathan C.; Radhakrishna, K. V.; Kinra, Sanjay; Ben-Shlomo, Yoav; Smith, George Davey; Ebrahim, Shah; Byrne, Nuala M.; Hills, Andrew P.

2013-01-01

Lean body mass (LBM) and muscle mass remain difficult to quantify in large epidemiological studies due to the unavailability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual-energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n = 2,220; 36% women; age 18-79 yr), representing a wide range of body mass index (14–44 kg/m2), participated in this study. Their LBM, including ALST, was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA-measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height, and weight explained >90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of skinfold thicknesses) increased the explained variation by 5–8% in the fully adjusted models predicting LBM and ALST. More complex equations using all of the above anthropometric variables could predict the DXA-measured LBM and ALST accurately, as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively), as well as good agreement by Bland-Altman analyses (Bland JM, Altman D. Lancet 1: 307–310, 1986). These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition. PMID:23950165

Truly self-consistent solution of Kohn-Sham equations for extended systems with inhomogeneous electron gas

NASA Astrophysics Data System (ADS)

Shul'man, A. Ya; Posvyanskii, D. V.

2014-05-01

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistent solution method for infinite systems involves iterations with alternate solutions of the Poisson and Schrödinger equations. One of problems with such an approach is that the charge distribution, updated by solving the Schrodinger equation, may be incompatible with the boundary conditions of the Poisson equation for Coulomb potential. The resulting instability or divergence manifests itself most appreciably in the case of infinitely extended systems because the corresponding boundary-value problem becomes singular. In this work the stable iterative scheme for solving the Kohn-Sham equations for infinite systems with inhomogeneous electron gas is described based on eliminating the long-range character of the Coulomb interaction, which causes the tight coupling of the charge distribution with the boundary conditions. This algorithm has been previously successfully implemented in the calculation of work function and surface energy of simple metals in the jellium model. Here it is used to calculate the energy spectrum of quasi-two-dimensional electron gas in the accumulation layer at the semiconductor surface n-InAs. The electrons in such a structure occupy states that belong to both discrete and continuous parts of the energy spectrum. This causes the problems of convergence in the usually used approaches, which do not exist in our case. Because of the narrow bandgap of InAs, it is necessary to take the nonparabolicity of the conduction band into account; this is done by means of a new effective mass method. The calculated quasi-two-dimensional energy bands correspond well to experimental data measured by the angle resolved photoelectron spectroscopy technique.

A Maximum Likelihood Approach for Multisample Nonlinear Structural Equation Models with Missing Continuous and Dichotomous Data

ERIC Educational Resources Information Center

Song, Xin-Yuan; Lee, Sik-Yum

2006-01-01

Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation.…

Nonstandard Topics for Student Presentations in Differential Equations

ERIC Educational Resources Information Center

LeMasurier, Michelle

2006-01-01

An interesting and effective way to showcase the wide variety of fields to which differential equations can be applied is to have students give short oral presentations on a specific application. These talks, which have been presented by 30-40 students per year in our differential equations classes, provide exposure to a diverse array of topics…

An iterative method for the Helmholtz equation

NASA Technical Reports Server (NTRS)

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

1983-01-01

An iterative algorithm for the solution of the Helmholtz equation is developed. The algorithm is based on a preconditioned conjugate gradient iteration for the normal equations. The preconditioning is based on an SSOR sweep for the discrete Laplacian. Numerical results are presented for a wide variety of problems of physical interest and demonstrate the effectiveness of the algorithm.

Investigation of Damping Physics and CFD Tool Validation for Simulation of Baffled Tanks at Variable Slosh Amplitude

NASA Technical Reports Server (NTRS)

Yang, H. Q.; West, Jeffrey

2016-01-01

To meet the flight control damping requirement, baffles of various configurations have been devised to increase the natural viscous damping and decrease the magnitude of the slosh forces and torques. In the design of slosh baffles, the most widely used damping equation is the one derived by Miles, which is based on the experiments of Keulegan and Carpenter. This equation has been used in predicting damping of the baffled tanks in different diameters ranging from 12 to 112 inches. The analytical expression of Miles equation is easy to use, especially in the design of complex baffle system. Previous investigations revealed that some experiments had shown good agreements with the prediction method of Miles, whereas other experiments have shown significant deviations. For example, damping from Miles equation differs from experimental measurements by as much as 100 percent over a range of tank diameters from 12 to 112 inches, oscillation amplitudes from 0.1 to 1.5 baffle widths, and baffle depths of 0.3 to 0.5 tank radius. Previously, much of this difference has been attributed to experimental scatter. A systematical study is needed to understand the damping physics of baffled tanks, to identify the difference between Miles equation and experimental measurement, and to develop new semi-empirical relations to better represent the real damping physics. The approach of this study is to use CFD technology to shed light on the damping mechanisms of a baffled tank. First, a 1-D Navier-Stokes equation representing different length scales and time scales in the baffle damping physics is developed and analyzed. A well validated CFD solver, developed at NASA MSFC, Loci-STREAM-VOF, is applied to study vorticity field around the baffle and around the fluid interface to highlight the dissipation mechanisms at different slosh amplitudes. Previous measurement data are then used to validate the CFD damping results. The study found several critical parameters controlling fluid damping from a baffle: local slosh amplitude to baffle thickness (A/t), surface liquid depth to tank radius (h/R), local slosh amplitude to baffle width (A/W); and non-dimensional slosh frequency. The simulation highlights three significant damping regimes where different mechanisms dominate. The study proves that the previously found discrepancies between Miles equation and experimental measurement are not due to the measurement scatter, but rather due to different damping mechanisms at various slosh amplitudes. The limitations on the use of Miles equation are discussed based on the flow regime.

Combining Cystatin C and Creatinine Yields a Reliable Glomerular Filtration Rate Estimation in Older Adults in Contrast to β-Trace Protein and β2-Microglobulin.

PubMed

Werner, Karin; Pihlsgård, Mats; Elmståhl, Sölve; Legrand, Helen; Nyman, Ulf; Christensson, Anders

2017-01-01

The glomerular filtration rate (GFR) is the most important measure of kidney function and chronic kidney disease (CKD). This study aims to validate commonly used equations for estimated GFR (eGFR) based on creatinine (cr), cystatin C (cys), β-trace protein (BTP), and β2-microglobulin (B2M) in older adults. We conducted a validation study with 126 participants aged between 72 and 98 with a mean measured GFR (mGFR) by iohexol clearance of 54 mL/min/1.73 m2. The eGFR equations (CKD-Epidemiology collaboration [CKD-EPI], Berlin Initiative Study [BIS], Full Age Spectrum [FAS], Modification of Diet in Renal Disease [MDRD]cr, Caucasian-Asian-Pediatric-Adult [CAPA]cys, Lund-Malmö Revised [LM-REV]cr, and MEAN-LM-CAPAcr-cys), were assessed in terms of bias (median difference: eGFR-mGFR), precision (interquartile range of the differences), and accuracy (P30: percentage of estimates ±30% of mGFR). The equations were compared to a benchmark equation: CKD-EPIcr-cys. All cystatin C-based equations underestimated the GFR compared to mGFR, whereas bias was mixed for the equations based only on creatinine. Accuracy was the highest for CKD-EPIcr-cys (98%) and lowest for MDRD (82%). Below mGFR 45 mL/min/1.73 m2 only equations incorporating cystatin C reached P30 accuracy >90%. CKD-EPIcr-cys was not significantly more accurate than the other cystatin C-based equations. In contrast, CKD-EPIcr-cys was significantly more accurate than all creatinine-based equations except LM-REVcr. This study confirms that it is reasonable to use equations incorporating cystatin C and creatinine in older patients across a wide spectrum of GFR. However, the results call into question the use of creatinine alone below mGFR 45 mL/min/1.73 m2. B2M and BTP do not demonstrate additional value in eGFR determination in older adults. © 2017 S. Karger AG, Basel.

Computational tools for fitting the Hill equation to dose-response curves.

PubMed

Gadagkar, Sudhindra R; Call, Gerald B

2015-01-01

Many biological response curves commonly assume a sigmoidal shape that can be approximated well by means of the 4-parameter nonlinear logistic equation, also called the Hill equation. However, estimation of the Hill equation parameters requires access to commercial software or the ability to write computer code. Here we present two user-friendly and freely available computer programs to fit the Hill equation - a Solver-based Microsoft Excel template and a stand-alone GUI-based "point and click" program, called HEPB. Both computer programs use the iterative method to estimate two of the Hill equation parameters (EC50 and the Hill slope), while constraining the values of the other two parameters (the minimum and maximum asymptotes of the response variable) to fit the Hill equation to the data. In addition, HEPB draws the prediction band at a user-defined confidence level, and determines the EC50 value for each of the limits of this band to give boundary values that help objectively delineate sensitive, normal and resistant responses to the drug being tested. Both programs were tested by analyzing twelve datasets that varied widely in data values, sample size and slope, and were found to yield estimates of the Hill equation parameters that were essentially identical to those provided by commercial software such as GraphPad Prism and nls, the statistical package in the programming language R. The Excel template provides a means to estimate the parameters of the Hill equation and plot the regression line in a familiar Microsoft Office environment. HEPB, in addition to providing the above results, also computes the prediction band for the data at a user-defined level of confidence, and determines objective cut-off values to distinguish among response types (sensitive, normal and resistant). Both programs are found to yield estimated values that are essentially the same as those from standard software such as GraphPad Prism and the R-based nls. Furthermore, HEPB also has the option to simulate 500 response values based on the range of values of the dose variable in the original data and the fit of the Hill equation to that data. Copyright © 2014. Published by Elsevier Inc.

Use of Longitudinal Data in Genetic Studies in the Genome-wide Association Studies Era: Summary of Group 14

PubMed Central

Kerner, Berit; North, Kari E; Fallin, M Daniele

2010-01-01

Participants analyzed actual and simulated longitudinal data from the Framingham Heart Study for various metabolic and cardiovascular traits. The genetic information incorporated into these investigations ranged from selected single-nucleotide polymorphisms to genome-wide association arrays. Genotypes were incorporated using a broad range of methodological approaches including conditional logistic regression, linear mixed models, generalized estimating equations, linear growth curve estimation, growth modeling, growth mixture modeling, population attributable risk fraction based on survival functions under the proportional hazards models, and multivariate adaptive splines for the analysis of longitudinal data. The specific scientific questions addressed by these different approaches also varied, ranging from a more precise definition of the phenotype, bias reduction in control selection, estimation of effect sizes and genotype associated risk, to direct incorporation of genetic data into longitudinal modeling approaches and the exploration of population heterogeneity with regard to longitudinal trajectories. The group reached several overall conclusions: 1) The additional information provided by longitudinal data may be useful in genetic analyses. 2) The precision of the phenotype definition as well as control selection in nested designs may be improved, especially if traits demonstrate a trend over time or have strong age-of-onset effects. 3) Analyzing genetic data stratified for high-risk subgroups defined by a unique development over time could be useful for the detection of rare mutations in common multi-factorial diseases. 4) Estimation of the population impact of genomic risk variants could be more precise. The challenges and computational complexity demanded by genome-wide single-nucleotide polymorphism data were also discussed. PMID:19924713

Modeling oil generation with time-temperature index graphs based on the Arrhenius equation

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

Hunt, J.M.; Lewan, M.D.; Hennet, R.J.C.

1991-04-01

The time and depth of oil generation from petroleum source rocks containing type II kerogens can be determined using time-temperature index (TTI) graphs based on the Arrhenius equation. Activation energies (E) and frequency factors (A) used in the Arrhenius equation were obtained from hydrous pyrolysis experiments on rock samples in which the kerogens represent the range of type II kerogen compositions encountered in most petroleum basins. The E and A values obtained were used to construct graphs that define the beginning and end of oil generation for most type II kerogens having chemical compositions in the range of these standards.more » Activation energies of these standard kerogens vary inversely with their sulfur content. The kerogen with the highest sulfur content had the lowest E value and was the fastest in generating oil, whereas the kerogen with the lowest sulfur content had the highest E value and was the slowest in generating oil. These standard kerogens were designated as types IIA, B, C, and D on the basis of decreasing sulfur content and corresponding increasing time-temperature requirements for generating oil. The {Sigma}TTI{sub ARR} values determined graphically with these type II kerogen standards in two basin models were compared with a computer calculation using 2,000 increments. The graphical method came within {plus minus} 3% of the computer calculation. As type II kerogens are the major oil generators in the world, these graphs should have wide application in making preliminary evaluations of the depth of the oil window in exploration areas.« less

Accurate experimental determination of the isotope effects on the triple point temperature of water. II. Combined dependence on the 18O and 17O abundances

NASA Astrophysics Data System (ADS)

Faghihi, V.; Kozicki, M.; Aerts-Bijma, A. T.; Jansen, H. G.; Spriensma, J. J.; Peruzzi, A.; Meijer, H. A. J.

2015-12-01

This paper is the second of two articles on the quantification of isotope effects on the triple point temperature of water. In this second article, we address the combined effects of 18O and 17O isotopes. We manufactured five triple point cells with waters with 18O and 17O abundances exceeding widely the natural abundance range while maintaining their natural 18O/17O relationship. The 2H isotopic abundance was kept close to that of VSMOW (Vienna Standard Mean Ocean Water). These cells realized triple point temperatures ranging between  -220 μK to 1420 μK with respect to the temperature realized by a triple point cell filled with VSMOW. Our experiment allowed us to determine an accurate and reliable value for the newly defined combined 18, 17O correction parameter of AO  =  630 μK with a combined uncertainty of 10 μK. To apply this correction, only the 18O abundance of the TPW needs to be known (and the water needs to be of natural origin). Using the results of our two articles, we recommend a correction equation along with the coefficient values for isotopic compositions differing from that of VSMOW and compare the effect of this new equation on a number of triple point cells from the literature and from our own institute. Using our correction equation, the uncertainty in the isotope correction for triple point cell waters used around the world will be  <1 μK.

Robotic fish tracking method based on suboptimal interval Kalman filter

NASA Astrophysics Data System (ADS)

Tong, Xiaohong; Tang, Chao

2017-11-01

Autonomous Underwater Vehicle (AUV) research focused on tracking and positioning, precise guidance and return to dock and other fields. The robotic fish of AUV has become a hot application in intelligent education, civil and military etc. In nonlinear tracking analysis of robotic fish, which was found that the interval Kalman filter algorithm contains all possible filter results, but the range is wide, relatively conservative, and the interval data vector is uncertain before implementation. This paper proposes a ptimization algorithm of suboptimal interval Kalman filter. Suboptimal interval Kalman filter scheme used the interval inverse matrix with its worst inverse instead, is more approximate nonlinear state equation and measurement equation than the standard interval Kalman filter, increases the accuracy of the nominal dynamic system model, improves the speed and precision of tracking system. Monte-Carlo simulation results show that the optimal trajectory of sub optimal interval Kalman filter algorithm is better than that of the interval Kalman filter method and the standard method of the filter.

First-principles studies on the equation-of-state, thermal-conductivity, and opacity of deuterium-tritium and polystyrene (CH) for inertial confinement fusion applications

DOE PAGES

Hu, Suxing; Collins, Lee A.; Goncharov, V. N.; ...

2016-05-26

Using first-principles (FP) methods, we have performed ab initio compute for the equation of state (EOS), thermal conductivity, and opacity of deuterium-tritium (DT) in a wide range of densities and temperatures for inertial confinement fusion (ICF) applications. These systematic investigations have recently been expanded to accurately compute the plasma properties of CH ablators under extreme conditions. In particular, the first-principles EOS and thermal-conductivity tables of CH are self-consistently built from such FP calculations, which are benchmarked by experimental measurements. When compared with the traditional models used for these plasma properties in hydrocodes, significant differences have been identified in the warmmore » dense plasma regime. When these FP-calculated properties of DT and CH were used in our hydrodynamic simulations of ICF implosions, we found that the target performance in terms of neutron yield and energy gain can vary by a factor of 2 to 3, relative to traditional model simulations.« less

A Generalized Hydrodynamic-Impact Theory for the Loads and Motions of Deeply Immersed Prismatic Bodies

NASA Technical Reports Server (NTRS)

Markey, Melvin F.

1959-01-01

A theory is derived for determining the loads and motions of a deeply immersed prismatic body. The method makes use of a two-dimensional water-mass variation and an aspect-ratio correction for three-dimensional flow. The equations of motion are generalized by using a mean value of the aspect-ratio correction and by assuming a variation of the two-dimensional water mass for the deeply immersed body. These equations lead to impact coefficients that depend on an approach parameter which, in turn, depends upon the initial trim and flight-path angles. Comparison of experiment with theory is shown at maximum load and maximum penetration for the flat-bottom (0 deg dead-rise angle) model with bean-loading coefficients from 36.5 to 133.7 over a wide range of initial conditions. A dead-rise angle correction is applied and maximum-load data are compared with theory for the case of a model with 300 dead-rise angle and beam-loading coefficients from 208 to 530.

On the energy integral for first post-Newtonian approximation

NASA Astrophysics Data System (ADS)

O'Leary, Joseph; Hill, James M.; Bennett, James C.

2018-07-01

The post-Newtonian approximation for general relativity is widely adopted by the geodesy and astronomy communities. It has been successfully exploited for the inclusion of relativistic effects in practically all geodetic applications and techniques such as satellite/lunar laser ranging and very long baseline interferometry. Presently, the levels of accuracy required in geodetic techniques require that reference frames, planetary and satellite orbits and signal propagation be treated within the post-Newtonian regime. For arbitrary scalar W and vector gravitational potentials W^j (j=1,2,3), we present a novel derivation of the energy associated with a test particle in the post-Newtonian regime. The integral so obtained appears not to have been given previously in the literature and is deduced through algebraic manipulation on seeking a Jacobi-like integral associated with the standard post-Newtonian equations of motion. The new integral is independently verified through a variational formulation using the post-Newtonian metric components and is subsequently verified by numerical integration of the post-Newtonian equations of motion.

Rogue-pair and dark-bright-rogue waves of the coupled nonlinear Schrödinger equations from inhomogeneous femtosecond optical fibers.

PubMed

Yomba, Emmanuel; Zakeri, Gholam-Ali

2016-08-01

The coupled inhomogeneous Schrödinger equations with a wide range of applications describing a field of pluses with the right and the left polarizations that take into account cross-phase modulations, stimulated Ramani scattering, and absorption effects are investigated. A combination of several different approaches is used in a novel way to obtain the explicit expressions for the rogue-pair and dark-bright-rogue waves. We study the dynamics of these structurally stable rogues and analyze the effects of a parameter that controls the region of stability that intrinsically connects the cross-phase modulation and other Kerr nonlinearity factors. The effects of the right and left polarizations on the shape of the rogue-pair and other solitary rogue waves are graphically analyzed. These rogue-pair waves are studied on periodic and non-periodic settings. We observe that rogue-pair wave from the right and left polarizations has a similar structure while the dark-bright-rogue waves have quite different intensity profiles.

Long-time stability effects of quadrature and artificial viscosity on nodal discontinuous Galerkin methods for gas dynamics

NASA Astrophysics Data System (ADS)

Durant, Bradford; Hackl, Jason; Balachandar, Sivaramakrishnan

2017-11-01

Nodal discontinuous Galerkin schemes present an attractive approach to robust high-order solution of the equations of fluid mechanics, but remain accompanied by subtle challenges in their consistent stabilization. The effect of quadrature choices (full mass matrix vs spectral elements), over-integration to manage aliasing errors, and explicit artificial viscosity on the numerical solution of a steady homentropic vortex are assessed over a wide range of resolutions and polynomial orders using quadrilateral elements. In both stagnant and advected vortices in periodic and non-periodic domains the need arises for explicit stabilization beyond the numerical surface fluxes of discontinuous Galerkin spectral elements. Artificial viscosity via the entropy viscosity method is assessed as a stabilizing mechanism. It is shown that the regularity of the artificial viscosity field is essential to its use for long-time stabilization of small-scale features in nodal discontinuous Galerkin solutions of the Euler equations of gas dynamics. Supported by the Department of Energy Predictive Science Academic Alliance Program Contract DE-NA0002378.

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

PubMed Central

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

2014-01-01

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

Dirac electron in a chiral space-time crystal created by counterpropagating circularly polarized plane electromagnetic waves

NASA Astrophysics Data System (ADS)

Borzdov, G. N.

2017-10-01

The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero quasimomentum, the dispersion equation has two solutions which specify bispinor wave functions describing electron states with different energies and mean values of momentum and spin operators. The inversion of the quasimomentum results in two other linearly independent solutions. These four basic wave functions are uniquely defined by eight complex scalar functions (structural functions), which serve as convenient building blocks of the relations describing the electron properties. These properties are illustrated in graphical form over a wide range of quasimomenta. The superpositions of two basic wave functions describing different spin states and corresponding to (i) the same quasimomentum (unidirectional electron states with the spin precession) and (ii) the two equal-in-magnitude but oppositely directed quasimomenta (bidirectional electron states) are also treated.

Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior

NASA Astrophysics Data System (ADS)

Huang, Qingdao; Qian, Hong

2009-09-01

We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells.

Absolute calibration of the OMEGA streaked optical pyrometer for temperature measurements of compressed materials

DOE PAGES

Gregor, M. C.; Boni, R.; Sorce, A.; ...

2016-11-29

Experiments in high-energy-density physics often use optical pyrometry to determine temperatures of dynamically compressed materials. In combination with simultaneous shock-velocity and optical-reflectivity measurements using velocity interferometry, these experiments provide accurate equation-of-state data at extreme pressures (P > 1 Mbar) and temperatures (T > 0.5 eV). This paper reports on the absolute calibration of the streaked optical pyrometer (SOP) at the Omega Laser Facility. The wavelength-dependent system response was determined by measuring the optical emission from a National Institute of Standards and Technology–traceable tungsten-filament lamp through various narrowband (40 nm-wide) filters. The integrated signal over the SOP’s ~250-nm operating range ismore » then related to that of a blackbody radiator using the calibrated response. We present a simple closed-form equation for the brightness temperature as a function of streak-camera signal derived from this calibration. As a result, error estimates indicate that brightness temperature can be inferred to a precision of <5%.« less

Performance of a cavity-method-based algorithm for the prize-collecting Steiner tree problem on graphs

NASA Astrophysics Data System (ADS)

Biazzo, Indaco; Braunstein, Alfredo; Zecchina, Riccardo

2012-08-01

We study the behavior of an algorithm derived from the cavity method for the prize-collecting steiner tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks, networks, and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the dhea solver, a branch and cut integer linear programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two postprocessing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases.

BLSTA: A boundary layer code for stability analysis

NASA Technical Reports Server (NTRS)

Wie, Yong-Sun

1992-01-01

A computer program is developed to solve the compressible, laminar boundary-layer equations for two-dimensional flow, axisymmetric flow, and quasi-three-dimensional flows including the flow along the plane of symmetry, flow along the leading-edge attachment line, and swept-wing flows with a conical flow approximation. The finite-difference numerical procedure used to solve the governing equations is second-order accurate. The flow over a wide range of speed, from subsonic to hypersonic speed with perfect gas assumption, can be calculated. Various wall boundary conditions, such as wall suction or blowing and hot or cold walls, can be applied. The results indicate that this boundary-layer code gives velocity and temperature profiles which are accurate, smooth, and continuous through the first and second normal derivatives. The code presented herein can be coupled with a stability analysis code and used to predict the onset of the boundary-layer transition which enables the assessment of the laminar flow control techniques. A user's manual is also included.

Properties of a soft-core model of methanol: An integral equation theory and computer simulation study

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

Huš, Matej; Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si; Munaò, Gianmarco

Thermodynamic and structural properties of a coarse-grained model of methanol are examined by Monte Carlo simulations and reference interaction site model (RISM) integral equation theory. Methanol particles are described as dimers formed from an apolar Lennard-Jones sphere, mimicking the methyl group, and a sphere with a core-softened potential as the hydroxyl group. Different closure approximations of the RISM theory are compared and discussed. The liquid structure of methanol is investigated by calculating site-site radial distribution functions and static structure factors for a wide range of temperatures and densities. Results obtained show a good agreement between RISM and Monte Carlo simulations.more » The phase behavior of methanol is investigated by employing different thermodynamic routes for the calculation of the RISM free energy, drawing gas-liquid coexistence curves that match the simulation data. Preliminary indications for a putative second critical point between two different liquid phases of methanol are also discussed.« less

Absolute calibration of the OMEGA streaked optical pyrometer for temperature measurements of compressed materials

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

Gregor, M. C.; Boni, R.; Sorce, A.

Experiments in high-energy-density physics often use optical pyrometry to determine temperatures of dynamically compressed materials. In combination with simultaneous shock-velocity and optical-reflectivity measurements using velocity interferometry, these experiments provide accurate equation-of-state data at extreme pressures (P > 1 Mbar) and temperatures (T > 0.5 eV). This paper reports on the absolute calibration of the streaked optical pyrometer (SOP) at the Omega Laser Facility. The wavelength-dependent system response was determined by measuring the optical emission from a National Institute of Standards and Technology–traceable tungsten-filament lamp through various narrowband (40 nm-wide) filters. The integrated signal over the SOP’s ~250-nm operating range ismore » then related to that of a blackbody radiator using the calibrated response. We present a simple closed-form equation for the brightness temperature as a function of streak-camera signal derived from this calibration. As a result, error estimates indicate that brightness temperature can be inferred to a precision of <5%.« less

Calibration of the 7—Equation Transition Model for High Reynolds Flows at Low Mach

NASA Astrophysics Data System (ADS)

Colonia, S.; Leble, V.; Steijl, R.; Barakos, G.

2016-09-01

The numerical simulation of flows over large-scale wind turbine blades without considering the transition from laminar to fully turbulent flow may result in incorrect estimates of the blade loads and performance. Thanks to its relative simplicity and promising results, the Local-Correlation based Transition Modelling concept represents a valid way to include transitional effects into practical CFD simulations. However, the model involves coefficients that need tuning. In this paper, the γ—equation transition model is assessed and calibrated, for a wide range of Reynolds numbers at low Mach, as needed for wind turbine applications. An aerofoil is used to evaluate the original model and calibrate it; while a large scale wind turbine blade is employed to show that the calibrated model can lead to reliable solutions for complex three-dimensional flows. The calibrated model shows promising results for both two-dimensional and three-dimensional flows, even if cross-flow instabilities are neglected.

A new Hysteretic Nonlinear Energy Sink (HNES)

NASA Astrophysics Data System (ADS)

Tsiatas, George C.; Charalampakis, Aristotelis E.

2018-07-01

The behavior of a new Hysteretic Nonlinear Energy Sink (HNES) coupled to a linear primary oscillator is investigated in shock mitigation. Apart from a small mass and a nonlinear elastic spring of the Duffing oscillator, the HNES is also comprised of a purely hysteretic and a linear elastic spring of potentially negative stiffness, connected in parallel. The Bouc-Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. Coupling the primary oscillator with the HNES, three nonlinear equations of motion are derived in terms of the two displacements and the dimensionless hysteretic variable, which are integrated numerically using the analog equation method. The performance of the HNES is examined by quantifying the percentage of the initially induced energy in the primary system that is passively transferred and dissipated by the HNES. Remarkable results are achieved for a wide range of initial input energies. The great performance of the HNES is mostly evidenced when the linear spring stiffness takes on negative values.

Computation of multi-dimensional viscous supersonic flow

NASA Technical Reports Server (NTRS)

Buggeln, R. C.; Kim, Y. N.; Mcdonald, H.

1986-01-01

A method has been developed for two- and three-dimensional computations of viscous supersonic jet flows interacting with an external flow. The approach employs a reduced form of the Navier-Stokes equations which allows solution as an initial-boundary value problem in space, using an efficient noniterative forward marching algorithm. Numerical instability associated with forward marching algorithms for flows with embedded subsonic regions is avoided by approximation of the reduced form of the Navier-Stokes equations in the subsonic regions of the boundary layers. Supersonic and subsonic portions of the flow field are simultaneously calculated by a consistently split linearized block implicit computational algorithm. The results of computations for a series of test cases associated with supersonic jet flow is presented and compared with other calculations for axisymmetric cases. Demonstration calculations indicate that the computational technique has great promise as a tool for calculating a wide range of supersonic flow problems including jet flow. Finally, a User's Manual is presented for the computer code used to perform the calculations.

Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials

NASA Astrophysics Data System (ADS)

Yang, Jianke; Nixon, Sean

2016-11-01

Stability of soliton families in one-dimensional nonlinear Schrödinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets (λ , - λ ,λ* , -λ*), similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non- PT-symmetric systems, and it has far-reaching consequences on the stability behaviors of solitons.

The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Sabin, Julien

2015-02-01

We show local and global well-posedness results for the Hartree equation where γ is a bounded self-adjoint operator on , ρ γ ( x) = γ( x, x) and w is a smooth short-range interaction potential. The initial datum γ(0) is assumed to be a perturbation of a translation-invariant state γ f = f(-Δ) which describes a quantum system with an infinite number of particles, such as the Fermi sea at zero temperature, or the Fermi-Dirac and Bose-Einstein gases at positive temperature. Global well-posedness follows from the conservation of the relative (free) energy of the state γ( t), counted relatively to the stationary state γ f . We indeed use a general notion of relative entropy, which allows us to treat a wide class of stationary states f(-Δ). Our results are based on a Lieb-Thirring inequality at positive density and on a recent Strichartz inequality for orthonormal functions, which are both due to Frank, Lieb, Seiringer and the first author of this article.

A multiblock multigrid three-dimensional Euler equation solver

NASA Technical Reports Server (NTRS)

Cannizzaro, Frank E.; Elmiligui, Alaa; Melson, N. Duane; Vonlavante, E.

1990-01-01

Current aerodynamic designs are often quite complex (geometrically). Flexible computational tools are needed for the analysis of a wide range of configurations with both internal and external flows. In the past, geometrically dissimilar configurations required different analysis codes with different grid topologies in each. The duplicity of codes can be avoided with the use of a general multiblock formulation which can handle any grid topology. Rather than hard wiring the grid topology into the program, it is instead dictated by input to the program. In this work, the compressible Euler equations, written in a body-fitted finite-volume formulation, are solved using a pseudo-time-marching approach. Two upwind methods (van Leer's flux-vector-splitting and Roe's flux-differencing) were investigated. Two types of explicit solvers (a two-step predictor-corrector and a modified multistage Runge-Kutta) were used with multigrid acceleration to enhance convergence. A multiblock strategy is used to allow greater geometric flexibility. A report on simple explicit upwind schemes for solving compressible flows is included.

THE ECONOMICS OF REPROCESSING vs DIRECT DISPOSAL OF SPENT NUCLEAR FUEL

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

Matthew Bunn; Steve Fetter; John P. Holdren

This report assesses the economics of reprocessing versus direct disposal of spent nuclear fuel. The breakeven uranium price at which reprocessing spent nuclear fuel from existing light-water reactors (LWRs) and recycling the resulting plutonium and uranium in LWRs would become economic is assessed, using central estimates of the costs of different elements of the nuclear fuel cycle (and other fuel cycle input parameters), for a wide range of range of potential reprocessing prices. Sensitivity analysis is performed, showing that the conclusions reached are robust across a wide range of input parameters. The contribution of direct disposal or reprocessing and recyclingmore » to electricity cost is also assessed. The choice of particular central estimates and ranges for the input parameters of the fuel cycle model is justified through a review of the relevant literature. The impact of different fuel cycle approaches on the volume needed for geologic repositories is briefly discussed, as are the issues surrounding the possibility of performing separations and transmutation on spent nuclear fuel to reduce the need for additional repositories. A similar analysis is then performed of the breakeven uranium price at which deploying fast neutron breeder reactors would become competitive compared with a once-through fuel cycle in LWRs, for a range of possible differences in capital cost between LWRs and fast neutron reactors. Sensitivity analysis is again provided, as are an analysis of the contribution to electricity cost, and a justification of the choices of central estimates and ranges for the input parameters. The equations used in the economic model are derived and explained in an appendix. Another appendix assesses the quantities of uranium likely to be recoverable worldwide in the future at a range of different possible future prices.« less

Numerical simulation of jet aerodynamics using the three-dimensional Navier-Stokes code PAB3D

NASA Technical Reports Server (NTRS)

Pao, S. Paul; Abdol-Hamid, Khaled S.

1996-01-01

This report presents a unified method for subsonic and supersonic jet analysis using the three-dimensional Navier-Stokes code PAB3D. The Navier-Stokes code was used to obtain solutions for axisymmetric jets with on-design operating conditions at Mach numbers ranging from 0.6 to 3.0, supersonic jets containing weak shocks and Mach disks, and supersonic jets with nonaxisymmetric nozzle exit geometries. This report discusses computational methods, code implementation, computed results, and comparisons with available experimental data. Very good agreement is shown between the numerical solutions and available experimental data over a wide range of operating conditions. The Navier-Stokes method using the standard Jones-Launder two-equation kappa-epsilon turbulence model can accurately predict jet flow, and such predictions are made without any modification to the published constants for the turbulence model.

Glassy dynamics of landscape evolution

PubMed Central

Ortiz, Carlos P.; Jerolmack, Douglas J.

2018-01-01

Soil creeps imperceptibly downhill, but also fails catastrophically to create landslides. Despite the importance of these processes as hazards and in sculpting landscapes, there is no agreed-upon model that captures the full range of behavior. Here we examine the granular origins of hillslope soil transport by discrete element method simulations and reanalysis of measurements in natural landscapes. We find creep for slopes below a critical gradient, where average particle velocity (sediment flux) increases exponentially with friction coefficient (gradient). At critical gradient there is a continuous transition to a dense-granular flow rheology. Slow earthflows and landslides thus exhibit glassy dynamics characteristic of a wide range of disordered materials; they are described by a two-phase flux equation that emerges from grain-scale friction alone. This glassy model reproduces topographic profiles of natural hillslopes, showing its promise for predicting hillslope evolution over geologic timescales. PMID:29686102

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

Remming, Ian S.; Khokhlov, Alexei M.

We present general equations for non-ideal, reactive flow magnetohydrodynamics (RFMHD) in the form best suited for describing thermonuclear combustion in high-density degenerate matter of SNe Ia. The relative importance of various non-ideal effects is analyzed as a function of characteristic spatial and temporal scales of the problem. From the general RFMHD equations, we derive the one-dimensional ordinary differential equations describing the steady-state propagation of a planar thermonuclear flame front in a magnetic field. The physics of the flame is first studied qualitatively using a simple case of one-step Arrhenius kinetics, a perfect gas equation of state (EOS), and constant thermalmore » conductivity coefficients. After that, the equations are solved, the internal flame front structure is calculated, and the flame velocity, S {sub l} , and flame thickness, δ {sub l} , are found for carbon–oxygen degenerate material of supernovae using a realistic EOS, transport properties, and detailed nuclear kinetics. The magnetic field changes the flame behavior significantly, both qualitatively and quantitatively, as compared to the non-magnetic case of classical combustion. (1) The magnetic field influences the evolutionarity of a flame front and makes it impossible for a flame to propagate steadily in a wide range of magnetic field strengths and orientations relative to the front. (2) When the flame moves steadily, it can propagate in several distinct modes, the most important being the slow C {sub S} and super-Alfvénic C {sub sup} modes. (3) The speed of the flame can be diminished or enhanced by up to several factors relative to the non-magnetic laminar flame speed.« less

Upscaling of nanoparticle transport in porous media under unfavorable conditions: Pore scale to Darcy scale

NASA Astrophysics Data System (ADS)

Seetha, N.; Raoof, Amir; Mohan Kumar, M. S.; Majid Hassanizadeh, S.

2017-05-01

Transport and deposition of nanoparticles in porous media is a multi-scale problem governed by several pore-scale processes, and hence, it is critical to link the processes at pore scale to the Darcy-scale behavior. In this study, using pore network modeling, we develop correlation equations for deposition rate coefficients for nanoparticle transport under unfavorable conditions at the Darcy scale based on pore-scale mechanisms. The upscaling tool is a multi-directional pore-network model consisting of an interconnected network of pores with variable connectivities. Correlation equations describing the pore-averaged deposition rate coefficients under unfavorable conditions in a cylindrical pore, developed in our earlier studies, are employed for each pore element. Pore-network simulations are performed for a wide range of parameter values to obtain the breakthrough curves of nanoparticle concentration. The latter is fitted with macroscopic 1-D advection-dispersion equation with a two-site linear reversible deposition accounting for both equilibrium and kinetic sorption. This leads to the estimation of three Darcy-scale deposition coefficients: distribution coefficient, kinetic rate constant, and the fraction of equilibrium sites. The correlation equations for the Darcy-scale deposition coefficients, under unfavorable conditions, are provided as a function of measurable Darcy-scale parameters, including: porosity, mean pore throat radius, mean pore water velocity, nanoparticle radius, ionic strength, dielectric constant, viscosity, temperature, and surface potentials of the particle and grain surfaces. The correlation equations are found to be consistent with the available experimental results, and in qualitative agreement with Colloid Filtration Theory for all parameters, except for the mean pore water velocity and nanoparticle radius.

Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution.

PubMed

Sicuro, Gabriele; Rapčan, Peter; Tsallis, Constantino

2016-12-01

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer-Viscous-Liquid-Layer System

NASA Astrophysics Data System (ADS)

Guz, A. N.; Bagno, A. M.

2017-07-01

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier -Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.

Comparison of electrical conductivity calculation methods for natural waters

USGS Publications Warehouse

McCleskey, R. Blaine; Nordstrom, D. Kirk; Ryan, Joseph N.

2012-01-01

The capability of eleven methods to calculate the electrical conductivity of a wide range of natural waters from their chemical composition was investigated. A brief summary of each method is presented including equations to calculate the conductivities of individual ions, the ions incorporated, and the method's limitations. The ability of each method to reliably predict the conductivity depends on the ions included, effective accounting of ion pairing, and the accuracy of the equation used to estimate the ionic conductivities. The performances of the methods were evaluated by calculating the conductivity of 33 environmentally important electrolyte solutions, 41 U.S. Geological Survey standard reference water samples, and 1593 natural water samples. The natural waters tested include acid mine waters, geothermal waters, seawater, dilute mountain waters, and river water impacted by municipal waste water. The three most recent conductivity methods predict the conductivity of natural waters better than other methods. Two of the recent methods can be used to reliably calculate the conductivity for samples with pH values greater than about 3 and temperatures between 0 and 40°C. One method is applicable to a variety of natural water types with a range of pH from 1 to 10, temperature from 0 to 95°C, and ionic strength up to 1 m.

Cylindrical Couette flow of a rarefied gas: Effect of a boundary condition on the inverted velocity profile.

PubMed

Kosuge, Shingo

2015-07-01

The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated under the following two kinds of kinetic boundary conditions. One is the modified Maxwell-type boundary condition proposed by Dadzie and Méolans [J. Math. Phys. 45, 1804 (2004)] and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. An asymptotic analysis of the Boltzmann equation for small Knudsen numbers and a numerical analysis of the Bhatnagar-Gross-Krook model equation for a wide range of the Knudsen number are performed to clarify the effect of each accommodation coefficient as well as of the boundary condition itself on the behavior of the gas, especially on the flow-velocity profile. As a result, the velocity-slip and temperature-jump conditions corresponding to the above kinetic boundary conditions are derived, which are necessary for the fluid-dynamic description of the problem for small Knudsen numbers. The parameter range for the onset of the velocity inversion phenomenon, which is related mainly to the decrease in the tangential momentum accommodation, is also obtained.

Decoherence and spin echo in biological systems.

PubMed

Nesterov, Alexander I; Berman, Gennady P

2015-05-01

The spin-echo approach is extended to include biocomplexes for which the interaction with dynamical noise, produced by the protein environment, is strong. Significant restoration of the free induction decay signal due to homogeneous (decoherence) and inhomogeneous (dephasing) broadening is demonstrated analytically and numerically for both an individual dimer of interacting chlorophylls and for an ensemble of dimers. Our approach does not require the use of small interaction constants between the electron states and the protein fluctuations. It is based on an exact and closed system of ordinary differential equations that can be easily solved for a wide range of parameters that are relevant for bioapplications.

Thermodynamic model of a solid with RKKY interaction and magnetoelastic coupling

NASA Astrophysics Data System (ADS)

Balcerzak, T.; Szałowski, K.; Jaščur, M.

2018-04-01

Thermodynamic description of a model system with magnetoelastic coupling is presented. The elastic, vibrational, electronic and magnetic energy contributions are taken into account. The long-range RKKY interaction is considered together with the nearest-neighbour direct exchange. The generalized Gibbs potential and the set of equations of state are derived, from which all thermodynamic functions are self-consistently obtained. Thermodynamic properties are calculated numerically for FCC structure for arbitrary external pressure, magnetic field and temperature, and widely discussed. In particular, for some parameters of interaction potential and electron concentration corresponding to antiferromagnetic phase, the existence of negative thermal expansion coefficient is predicted.