The area-time-integral technique to estimate convective rain volumes over areas applied to satellite data - A preliminary investigation

NASA Technical Reports Server (NTRS)

Doneaud, Andre A.; Miller, James R., Jr.; Johnson, L. Ronald; Vonder Haar, Thomas H.; Laybe, Patrick

1987-01-01

The use of the area-time-integral (ATI) technique, based only on satellite data, to estimate convective rain volume over a moving target is examined. The technique is based on the correlation between the radar echo area coverage integrated over the lifetime of the storm and the radar estimated rain volume. The processing of the GOES and radar data collected in 1981 is described. The radar and satellite parameters for six convective clusters from storm events occurring on June 12 and July 2, 1981 are analyzed and compared in terms of time steps and cluster lifetimes. Rain volume is calculated by first using the regression analysis to generate the regression equation used to obtain the ATI; the ATI versus rain volume relation is then employed to compute rain volume. The data reveal that the ATI technique using satellite data is applicable to the calculation of rain volume.

Useful integral function and its application in thermal radiation calculations

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

Chang, S.L.; Rhee, K.T.

1983-07-01

In applying the Planck formula for computing the energy radiated from an isothermal source, the emissivity of the source must be found. This emissivity is expressed in terms of its spectral emissivity. This spectral emissivity of an isothermal volume with a given optical length containing radiating gases and/or soot, is computed through a relation (Sparrow and Cess, 1978) that contains the optical length and the spectral volume absorption coefficient. An exact solution is then offered to the equation that results from introducing the equation for the spectral emissivity into the equation for the emissivity. The function obtained is shown tomore » be useful in computing the spectral emissivity of an isothermal volume containing either soot or gaseous species, or both. Examples are presented.« less

Control volume based hydrocephalus research; analysis of human data

NASA Astrophysics Data System (ADS)

Cohen, Benjamin; Wei, Timothy; Voorhees, Abram; Madsen, Joseph; Anor, Tomer

2010-11-01

Hydrocephalus is a neuropathophysiological disorder primarily diagnosed by increased cerebrospinal fluid volume and pressure within the brain. To date, utilization of clinical measurements have been limited to understanding of the relative amplitude and timing of flow, volume and pressure waveforms; qualitative approaches without a clear framework for meaningful quantitative comparison. Pressure volume models and electric circuit analogs enforce volume conservation principles in terms of pressure. Control volume analysis, through the integral mass and momentum conservation equations, ensures that pressure and volume are accounted for using first principles fluid physics. This approach is able to directly incorporate the diverse measurements obtained by clinicians into a simple, direct and robust mechanics based framework. Clinical data obtained for analysis are discussed along with data processing techniques used to extract terms in the conservation equation. Control volume analysis provides a non-invasive, physics-based approach to extracting pressure information from magnetic resonance velocity data that cannot be measured directly by pressure instrumentation.

External validation of a forest inventory and analysis volume equation and comparisons with estimates from multiple stem-profile models

Treesearch

Christopher M. Oswalt; Adam M. Saunders

2009-01-01

Sound estimation procedures are desideratum for generating credible population estimates to evaluate the status and trends in resource conditions. As such, volume estimation is an integral component of the U.S. Department of Agriculture, Forest Service, Forest Inventory and Analysis (FIA) program's reporting. In effect, reliable volume estimation procedures are...

Applied Mathematical Methods in Theoretical Physics

NASA Astrophysics Data System (ADS)

Masujima, Michio

2005-04-01

All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.

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

NASA Technical Reports Server (NTRS)

Morrison, Joseph H.

1992-01-01

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

Incorporation of an Energy Equation into a Pulsed Inductive Thruster Performance Model

NASA Technical Reports Server (NTRS)

Polzin, Kurt A.; Reneau, Jarred P.; Sankaran, Kameshwaran

2011-01-01

A model for pulsed inductive plasma acceleration containing an energy equation to account for the various sources and sinks in such devices is presented. The model consists of a set of circuit equations coupled to an equation of motion and energy equation for the plasma. The latter two equations are obtained for the plasma current sheet by treating it as a one-element finite volume, integrating the equations over that volume, and then matching known terms or quantities already calculated in the model to the resulting current sheet-averaged terms in the equations. Calculations showing the time-evolution of the various sources and sinks in the system are presented to demonstrate the efficacy of the model, with two separate resistivity models employed to show an example of how the plasma transport properties can affect the calculation. While neither resistivity model is fully accurate, the demonstration shows that it is possible within this modeling framework to time-accurately update various plasma parameters.

PAN AIR: A Computer Program for Predicting Subsonic or Supersonic Linear Potential Flows About Arbitrary Configurations Using a Higher Order Panel Method. Volume 1; Theory Document (Version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, Alfred E.; Epton, Michael A.

1981-01-01

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the PAN AIR (Panel Aerodynamics) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformations, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments.

A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

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

Ciraolo, Giulio, E-mail: g.ciraolo@math.unipa.it; Gargano, Francesco, E-mail: gargano@math.unipa.it; Sciacca, Vincenzo, E-mail: sciacca@math.unipa.it

2013-08-01

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1992-01-01

A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium

NASA Astrophysics Data System (ADS)

Yurkin, Maxim A.; Mishchenko, Michael I.

2018-04-01

We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a nonmagnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

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

An analytical theory of radio-wave scattering from meteoric ionization - I. Basic equation

NASA Astrophysics Data System (ADS)

Pecina, P.

2016-01-01

We have developed an analytical theory of radio-wave scattering from ionization of meteoric origin. It is based on an integro-differential equation for the polarization vector, P, inside the meteor trail, representing an analytical solution of the set of Maxwell equations, in combination with a generalized radar equation involving an integral of the trail volume electron density, Ne, and P represented by an auxiliary vector, Q, taken over the whole trail volume. During the derivation of the final formulae, the following assumptions were applied: transversal as well as longitudinal dimensions of the meteor trail are small compared with the distances of the relevant trail point to both the transmitter and receiver and the ratio of these distances to the wavelength of the wave emitted by the radar is very large, so that the stationary-phase method can be employed for evaluation of the relevant integrals. Further, it is shown that in the case of sufficiently low electron density, Ne, corresponding to the case of underdense trails, the classical McKinley's radar equation results as a special case of the general theory. The same also applies regarding the Fresnel characteristics. Our approach is also capable of yielding solutions to the problems of the formation of Fresnel characteristics on trails having any electron density, forward scattering and scattering on trails immersed in the magnetic field. However, we have also shown that the geomagnetic field can be removed from consideration, due to its low strength. The full solution of the above integro-differential equation, valid for any electron volume densities, has been left to subsequent works dealing with this particular problem, due to its complexity.

One Solution of the Forward Problem of DC Resistivity Well Logging by the Method of Volume Integral Equations with Allowance for Induced Polarization

NASA Astrophysics Data System (ADS)

Kevorkyants, S. S.

2018-03-01

For theoretically studying the intensity of the influence exerted by the polarization of the rocks on the results of direct current (DC) well logging, a solution is suggested for the direct inner problem of the DC electric logging in the polarizable model of plane-layered medium containing a heterogeneity by the example of the three-layer model of the hosting medium. Initially, the solution is presented in the form of a traditional vector volume-integral equation of the second kind (IE2) for the electric current density vector. The vector IE2 is solved by the modified iteration-dissipation method. By the transformations, the initial IE2 is reduced to the equation with the contraction integral operator for an axisymmetric model of electrical well-logging of the three-layer polarizable medium intersected by an infinitely long circular cylinder. The latter simulates the borehole with a zone of penetration where the sought vector consists of the radial J r and J z axial (relative to the cylinder's axis) components. The decomposition of the obtained vector IE2 into scalar components and the discretization in the coordinates r and z lead to a heterogeneous system of linear algebraic equations with a block matrix of the coefficients representing 2x2 matrices whose elements are the triple integrals of the mixed derivatives of the second-order Green's function with respect to the parameters r, z, r', and z'. With the use of the analytical transformations and standard integrals, the integrals over the areas of the partition cells and azimuthal coordinate are reduced to single integrals (with respect to the variable t = cos ϕ on the interval [-1, 1]) calculated by the Gauss method for numerical integration. For estimating the effective coefficient of polarization of the complex medium, it is suggested to use the Siegel-Komarov formula.

Determination of constant-volume balloon capabilities for aeronautical research. [specifically measurement of atmospheric phenomena

NASA Technical Reports Server (NTRS)

Tatom, F. B.; King, R. L.

1977-01-01

The proper application of constant-volume balloons (CVB) for measurement of atmospheric phenomena was determined. And with the proper interpretation of the resulting data. A literature survey covering 176 references is included. the governing equations describing the three-dimensional motion of a CVB immersed in a flow field are developed. The flowfield model is periodic, three-dimensional, and nonhomogeneous, with mean translational motion. The balloon motion and flow field equations are cast into dimensionless form for greater generality, and certain significant dimensionless groups are identified. An alternate treatment of the balloon motion, based on first-order perturbation analysis, is also presented. A description of the digital computer program, BALLOON, used for numerically integrating the governing equations is provided.

Using high-order polynomial basis in 3-D EM forward modeling based on volume integral equation method

NASA Astrophysics Data System (ADS)

Kruglyakov, Mikhail; Kuvshinov, Alexey

2018-05-01

3-D interpretation of electromagnetic (EM) data of different origin and scale becomes a common practice worldwide. However, 3-D EM numerical simulations (modeling)—a key part of any 3-D EM data analysis—with realistic levels of complexity, accuracy and spatial detail still remains challenging from the computational point of view. We present a novel, efficient 3-D numerical solver based on a volume integral equation (IE) method. The efficiency is achieved by using a high-order polynomial (HOP) basis instead of the zero-order (piecewise constant) basis that is invoked in all routinely used IE-based solvers. We demonstrate that usage of the HOP basis allows us to decrease substantially the number of unknowns (preserving the same accuracy), with corresponding speed increase and memory saving.

Solution of the Average-Passage Equations for the Incompressible Flow through Multiple-Blade-Row Turbomachinery

DTIC Science & Technology

1994-02-01

numerical treatment. An explicit numerical procedure based on Runqe-Kutta time stepping for cell-centered, hexahedral finite volumes is...An explicit numerical procedure based on Runge-Kutta time stepping for cell-centered, hexahedral finite volumes is outlined for the approximate...Discretization 16 3.1 Cell-Centered Finite -Volume Discretization in Space 16 3.2 Artificial Dissipation 17 3.3 Time Integration 21 3.4 Convergence

The evolution of methods for noise prediction of high speed rotors and propellers in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1986-01-01

Linear wave equation models which have been used over the years at NASA Langley for describing noise emissions from high speed rotating blades are summarized. The noise sources are assumed to lie on a moving surface, and analysis of the situation has been based on the Ffowcs Williams-Hawkings (FW-H) equation. Although the equation accounts for two surface and one volume source, the NASA analyses have considered only the surface terms. Several variations on the FW-H model are delineated for various types of applications, noting the computational benefits of removing the frequency dependence of the calculations. Formulations are also provided for compact and noncompact sources, and features of Long's subsonic integral equation and Farassat's high speed integral equation are discussed. The selection of subsonic or high speed models is dependent on the Mach number of the blade surface where the source is located.

A characteristic based volume penalization method for general evolution problems applied to compressible viscous flows

NASA Astrophysics Data System (ADS)

Brown-Dymkoski, Eric; Kasimov, Nurlybek; Vasilyev, Oleg V.

2014-04-01

In order to introduce solid obstacles into flows, several different methods are used, including volume penalization methods which prescribe appropriate boundary conditions by applying local forcing to the constitutive equations. One well known method is Brinkman penalization, which models solid obstacles as porous media. While it has been adapted for compressible, incompressible, viscous and inviscid flows, it is limited in the types of boundary conditions that it imposes, as are most volume penalization methods. Typically, approaches are limited to Dirichlet boundary conditions. In this paper, Brinkman penalization is extended for generalized Neumann and Robin boundary conditions by introducing hyperbolic penalization terms with characteristics pointing inward on solid obstacles. This Characteristic-Based Volume Penalization (CBVP) method is a comprehensive approach to conditions on immersed boundaries, providing for homogeneous and inhomogeneous Dirichlet, Neumann, and Robin boundary conditions on hyperbolic and parabolic equations. This CBVP method can be used to impose boundary conditions for both integrated and non-integrated variables in a systematic manner that parallels the prescription of exact boundary conditions. Furthermore, the method does not depend upon a physical model, as with porous media approach for Brinkman penalization, and is therefore flexible for various physical regimes and general evolutionary equations. Here, the method is applied to scalar diffusion and to direct numerical simulation of compressible, viscous flows. With the Navier-Stokes equations, both homogeneous and inhomogeneous Neumann boundary conditions are demonstrated through external flow around an adiabatic and heated cylinder. Theoretical and numerical examination shows that the error from penalized Neumann and Robin boundary conditions can be rigorously controlled through an a priori penalization parameter η. The error on a transient boundary is found to converge as O(η), which is more favorable than the error convergence of the already established Dirichlet boundary condition.

Scattering from Marine Sediments in a Very Shallow Water Environment

DTIC Science & Technology

2015-12-28

taking into account only large-scale changes of the environment. Keywords: Reciprocity , integral equations, volume and roughness scattering...for Public Release, Distribution Unlimited A. Ivakin: Scattering in range-dependent waveguides 5 II. VOLUME PERTURBATIONS: RECIPROCITY THEOREM...6], i.e. with the same υ , and therefore same Q , which, along with following discussion of reciprocity , explains the choice of this parameter

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1993-01-01

A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

An efficient numerical method for the solution of the problem of elasticity for 3D-homogeneous elastic medium with cracks and inclusions

NASA Astrophysics Data System (ADS)

Kanaun, S.; Markov, A.

2017-06-01

An efficient numerical method for solution of static problems of elasticity for an infinite homogeneous medium containing inhomogeneities (cracks and inclusions) is developed. Finite number of heterogeneous inclusions and planar parallel cracks of arbitrary shapes is considered. The problem is reduced to a system of surface integral equations for crack opening vectors and volume integral equations for stress tensors inside the inclusions. For the numerical solution of these equations, a class of Gaussian approximating functions is used. The method based on these functions is mesh free. For such functions, the elements of the matrix of the discretized system are combinations of explicit analytical functions and five standard 1D-integrals that can be tabulated. Thus, the numerical integration is excluded from the construction of the matrix of the discretized problem. For regular node grids, the matrix of the discretized system has Toeplitz's properties, and Fast Fourier Transform technique can be used for calculation matrix-vector products of such matrices.

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

USGS Publications Warehouse

Faust, Charles R.; Mercer, James W.

1977-01-01

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

Determination of the turbulence integral model parameters for a case of a coolant angular flow in regular rod-bundle

NASA Astrophysics Data System (ADS)

Bayaskhalanov, M. V.; Vlasov, M. N.; Korsun, A. S.; Merinov, I. G.; Philippov, M. Ph

2017-11-01

Research results of “k-ε” turbulence integral model (TIM) parameters dependence on the angle of a coolant flow in regular smooth cylindrical rod-bundle are presented. TIM is intended for the definition of efficient impulse and heat transport coefficients in the averaged equations of a heat and mass transfer in the regular rod structures in an anisotropic porous media approximation. The TIM equations are received by volume-averaging of the “k-ε” turbulence model equations on periodic cell of rod-bundle. The water flow across rod-bundle under angles from 15 to 75 degrees was simulated by means of an ANSYS CFX code. Dependence of the TIM parameters on flow angle was as a result received.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

Development of Improved Surface Integral Methods for Jet Aeroacoustic Predictions

NASA Technical Reports Server (NTRS)

Pilon, Anthony R.; Lyrintzis, Anastasios S.

1997-01-01

The accurate prediction of aerodynamically generated noise has become an important goal over the past decade. Aeroacoustics must now be an integral part of the aircraft design process. The direct calculation of aerodynamically generated noise with CFD-like algorithms is plausible. However, large computer time and memory requirements often make these predictions impractical. It is therefore necessary to separate the aeroacoustics problem into two parts, one in which aerodynamic sound sources are determined, and another in which the propagating sound is calculated. This idea is applied in acoustic analogy methods. However, in the acoustic analogy, the determination of far-field sound requires the solution of a volume integral. This volume integration again leads to impractical computer requirements. An alternative to the volume integrations can be found in the Kirchhoff method. In this method, Green's theorem for the linear wave equation is used to determine sound propagation based on quantities on a surface surrounding the source region. The change from volume to surface integrals represents a tremendous savings in the computer resources required for an accurate prediction. This work is concerned with the development of enhancements of the Kirchhoff method for use in a wide variety of aeroacoustics problems. This enhanced method, the modified Kirchhoff method, is shown to be a Green's function solution of Lighthill's equation. It is also shown rigorously to be identical to the methods of Ffowcs Williams and Hawkings. This allows for development of versatile computer codes which can easily alternate between the different Kirchhoff and Ffowcs Williams-Hawkings formulations, using the most appropriate method for the problem at hand. The modified Kirchhoff method is developed primarily for use in jet aeroacoustics predictions. Applications of the method are shown for two dimensional and three dimensional jet flows. Additionally, the enhancements are generalized so that they may be used in any aeroacoustics problem.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

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

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

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.

Kirkwood-Buff integrals of finite systems: shape effects

NASA Astrophysics Data System (ADS)

Dawass, Noura; Krüger, Peter; Simon, Jean-Marc; Vlugt, Thijs J. H.

2018-06-01

The Kirkwood-Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.

A differential equation for the Generalized Born radii.

PubMed

Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro

2013-06-28

The Generalized Born (GB) model offers a convenient way of representing electrostatics in complex macromolecules like proteins or nucleic acids. The computation of atomic GB radii is currently performed by different non-local approaches involving volume or surface integrals. Here we obtain a non-linear second-order partial differential equation for the Generalized Born radius, which may be solved using local iterative algorithms. The equation is derived under the assumption that the usual GB approximation to the reaction field obeys Laplace's equation. The equation admits as particular solutions the correct GB radii for the sphere and the plane. The tests performed on a set of 55 different proteins show an overall agreement with other reference GB models and "perfect" Poisson-Boltzmann based values.

A study of the use of abstract types for the representation of engineering units in integration and test applications

NASA Technical Reports Server (NTRS)

Johnson, Charles S.

1986-01-01

Physical quantities using various units of measurement can be well represented in Ada by the use of abstract types. Computation involving these quantities (electric potential, mass, volume) can also automatically invoke the computation and checking of some of the implicitly associable attributes of measurements. Quantities can be held internally in SI units, transparently to the user, with automatic conversion. Through dimensional analysis, the type of the derived quantity resulting from a computation is known, thereby allowing dynamic checks of the equations used. The impact of the possible implementation of these techniques in integration and test applications is discussed. The overhead of computing and transporting measurement attributes is weighed against the advantages gained by their use. The construction of a run time interpreter using physical quantities in equations can be aided by the dynamic equation checks provided by dimensional analysis. The effects of high levels of abstraction on the generation and maintenance of software used in integration and test applications are also discussed.

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

NASA Technical Reports Server (NTRS)

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

1983-01-01

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

Self-propulsion of a body with rigid surface and variable coefficient of lift in a perfect fluid

NASA Astrophysics Data System (ADS)

Ramodanov, Sergey M.; Tenenev, Valentin A.; Treschev, Dmitry V.

2012-11-01

We study the system of a 2D rigid body moving in an unbounded volume of incompressible, vortex-free perfect fluid which is at rest at infinity. The body is equipped with a gyrostat and a so-called Flettner rotor. Due to the latter the body is subject to a lifting force (Magnus effect). The rotational velocities of the gyrostat and the rotor are assumed to be known functions of time (control inputs). The equations of motion are presented in the form of the Kirchhoff equations. The integrals of motion are given in the case of piecewise continuous control. Using these integrals we obtain a (reduced) system of first-order differential equations on the configuration space. Then an optimal control problem for several types of the inputs is solved using genetic algorithms.

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each direction on a time step. In each direction, they have tridiagonal structure. They are solved by the sweep method. An important advantage of the discrete-analytical schemes is that the values of derivatives at the boundaries of finite volume are calculated together with the values of the unknown functions. This technique is particularly attractive for problems with dominant convection, as it does not require artificial monotonization and limiters. The same idea of integrating factors is applied in temporal dimension to the stiff systems of equations describing chemical transformation models [2]. The proposed method is applicable for the problems involving convection-diffusion-reaction operators. The work has been partially supported by the Presidium of RAS under Program 43, and by the RFBR grants 14-01-00125 and 14-01-31482. References: 1. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Variational approach and Euler's integrating factors for environmental studies// Computers and Mathematics with Applications, (2014) V.67, Issue 12, P. 2240-2256. 2. V.V.Penenko, E.A.Tsvetova. Variational methods of constructing monotone approximations for atmospheric chemistry models // Numerical analysis and applications, 2013, V. 6, Issue 3, pp 210-220.

SYNTHESIS OF NOVEL ALL-DIELECTRIC GRATING FILTERS USING GENETIC ALGORITHMS

NASA Technical Reports Server (NTRS)

Zuffada, Cinzia; Cwik, Tom; Ditchman, Christopher

1997-01-01

We are concerned with the design of inhomogeneous, all dielectric (lossless) periodic structures which act as filters. Dielectric filters made as stacks of inhomogeneous gratings and layers of materials are being used in optical technology, but are not common at microwave frequencies. The problem is then finding the periodic cell's geometric configuration and permittivity values which correspond to a specified reflectivity/transmittivity response as a function of frequency/illumination angle. This type of design can be thought of as an inverse-source problem, since it entails finding a distribution of sources which produce fields (or quantities derived from them) of given characteristics. Electromagnetic sources (electric and magnetic current densities) in a volume are related to the outside fields by a well known linear integral equation. Additionally, the sources are related to the fields inside the volume by a constitutive equation, involving the material properties. Then, the relationship linking the fields outside the source region to those inside is non-linear, in terms of material properties such as permittivity, permeability and conductivity. The solution of the non-linear inverse problem is cast here as a combination of two linear steps, by explicitly introducing the electromagnetic sources in the computational volume as a set of unknowns in addition to the material unknowns. This allows to solve for material parameters and related electric fields in the source volume which are consistent with Maxwell's equations. Solutions are obtained iteratively by decoupling the two steps. First, we invert for the permittivity only in the minimization of a cost function and second, given the materials, we find the corresponding electric fields through direct solution of the integral equation in the source volume. The sources thus computed are used to generate the far fields and the synthesized triter response. The cost function is obtained by calculating the deviation between the synthesized value of reflectivity/transmittivity and the desired one. Solution geometries for the periodic cell are sought as gratings (ensembles of columns of different heights and widths), or combinations of homogeneous layers of different dielectric materials and gratings. Hence the explicit unknowns of the inversion step are the material permittivities and the relative boundaries separating homogeneous parcels of the periodic cell.

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

A conservative, thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

NASA Astrophysics Data System (ADS)

Nonaka, Andrew; Day, Marcus S.; Bell, John B.

2018-01-01

We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.

Investigation of viscous/inviscid interaction in transonic flow over airfoils with suction

NASA Technical Reports Server (NTRS)

Vemuru, C. S.; Tiwari, S. N.

1988-01-01

The viscous/inviscid interaction over transonic airfoils with and without suction is studied. The streamline angle at the edge of the boundary layer is used to couple the viscous and inviscid flows. The potential flow equations are solved for the inviscid flow field. In the shock region, the Euler equations are solved using the method of integral relations. For this, the potential flow solution is used as the initial and boundary conditions. An integral method is used to solve the laminar boundary-layer equations. Since both methods are integral methods, a continuous interaction is allowed between the outer inviscid flow region and the inner viscous flow region. To avoid the Goldstein singularity near the separation point the laminar boundary-layer equations are derived in an inverse form to obtain solution for the flows with small separations. The displacement thickness distribution is specified instead of the usual pressure distribution to solve the boundry-layer equations. The Euler equations are solved for the inviscid flow using the finite volume technique and the coupling is achieved by a surface transpiration model. A method is developed to apply a minimum amount of suction that is required to have an attached flow on the airfoil. The turbulent boundary layer equations are derived using the bi-logarithmic wall law for mass transfer. The results are found to be in good agreement with available experimental data and with the results of other computational methods.

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

NASA Technical Reports Server (NTRS)

Boretti, A. A.

1990-01-01

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Electromagnetics. Volume 1, Number 4, October-December 1981.

DTIC Science & Technology

1981-01-01

terms. 1.6 Matrix and Operator Theory Integral equations have been cast in approximate numerical form by the moment method (MoM). In this numerical...introduced the eigenmode expansion method to find more properties of the SEM [3.4]. One defines eigenvalues and eigenmodes for the integral operator (kernel...exterior surface of the system. Mechanisms that play a role in the penetration are (1) diffusion through metal skins , (2) field leakage through

Theories of Matter, Space and Time, Volume 2; Quantum theories

NASA Astrophysics Data System (ADS)

Evans, N.; King, S. F.

2018-06-01

This book and its prequel Theories of Matter Space and Time: Classical Theories grew out of courses that we have both taught as part of the undergraduate degree program in Physics at Southampton University, UK. Our goal was to guide the full MPhys undergraduate cohort through some of the trickier areas of theoretical physics that we expect our undergraduates to master. Here we teach the student to understand first quantized relativistic quantum theories. We first quickly review the basics of quantum mechanics which should be familiar to the reader from a prior course. Then we will link the Schrödinger equation to the principle of least action introducing Feynman's path integral methods. Next, we present the relativistic wave equations of Klein, Gordon and Dirac. Finally, we convert Maxwell's equations of electromagnetism to a wave equation for photons and make contact with quantum electrodynamics (QED) at a first quantized level. Between the two volumes we hope to move a student's understanding from their prior courses to a place where they are ready, beyond, to embark on graduate level courses on quantum field theory.

Northeastern forest survey revised cubic-foot volume equations

Treesearch

Charles T. Scott

1981-01-01

Cubic-foot volume equations are presented for the 17 species groups used in the forest survey of the 14 northeastern states. The previous cubic- foot volume equations were simple linear in form; the revised cubic-foot volume equations are nonlinear.

Nonlinear storage models of unconfined flow through a shallow aquifer on an inclined base and their quasi-steady flow application

NASA Astrophysics Data System (ADS)

Varvaris, Ioannis; Gravanis, Elias; Koussis, Antonis; Akylas, Evangelos

2013-04-01

Hillslope processes involving flow through an inclined shallow aquifer range from subsurface stormflow to stream base flow (drought flow, or groundwater recession flow). In the case of recharge, the infiltrating water moves vertically as unsaturated flow until it reaches the saturated groundwater, where the flow is approximately parallel to the base of the aquifer. Boussinesq used the Dupuit-Forchheimer (D-F) hydraulic theory to formulate unconfined groundwater flow through a soil layer resting on an impervious inclined bed, deriving a nonlinear equation for the flow rate that consists of a linear gravity-driven component and a quadratic pressure-gradient component. Inserting that flow rate equation into the differential storage balance equation (volume conservation) Boussinesq obtained a nonlinear second-order partial differential equation for the depth. So far however, only few special solutions have been advanced for that governing equation. The nonlinearity of the equation of Boussinesq is the major obstacle to deriving a general analytical solution for the depth profile of unconfined flow on a sloping base with recharge (from which the discharges could be then determined). Henderson and Wooding (1964) were able to obtain an exact analytical solution for steady unconfined flow on a sloping base, with recharge, and their work deserves special note in the realm of solutions of the nonlinear equation of Boussinesq. However, the absence of a general solution for the transient case, which is of practical interest to hydrologists, has been the motivation for developing approximate solutions of the non-linear equation of Boussinesq. In this work, we derive the aquifer storage function by integrating analytically over the aquifer base the depth profiles resulting from the complete nonlinear Boussinesq equation for steady flow. This storage function consists of a linear and a nonlinear outflow-dependent term. Then, we use this physics-based storage function in the transient storage balance over the hillslope, obtaining analytical solutions of the outflow and the storage, for recharge and drainage, via a quasi-steady flow calculation. The hydraulically derived storage model is thus embedded in a quasi-steady approximation of transient unconfined flow in sloping aquifers. We generalise this hydrologic model of groundwater flow by modifying the storage function to be the weighted sum of the linear and the nonlinear storage terms, determining the weighting factor objectively from a known integral quantity of the flow (either an initial volume of water stored in the aquifer or a drained water volume). We demonstrate the validity of this model through comparisons with experimental data and simulation results.

Towards the development of micromechanics equations for ceramic matrix composites via fiber substructuring

NASA Technical Reports Server (NTRS)

Murthy, P. L. N.; Chamis, C. C.

1992-01-01

A generic unit cell model which includes a unique fiber substructuring concept is proposed for the development of micromechanics equations for continuous fiber reinforcement ceramic composites. The unit cell consists of three constituents: fiber, matrix, and an interphase. In the present approach, the unit cell is further subdivided into several slices and the equations of micromechanics are derived for each slice. These are subsequently integrated to obtain ply level properties. A stand alone computer code containing the micromechanics model as a module is currently being developed specifically for the analysis of ceramic matrix composites. Towards this development, equivalent ply property results for a SiC/Ti-15-3 composite with 0.5 fiber volume ratio are presented and compared with those obtained from customary micromechanics models to illustrate the concept. Also, comparisons with limited experimental data for the ceramic matrix composite, SiC/RBSN (Reaction Bonded Silicon Nitride) with a 0.3 fiber volume ratio are given to validate the concepts.

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Variational approach to the volume viscosity of fluids

NASA Astrophysics Data System (ADS)

Zuckerwar, Allan J.; Ash, Robert L.

2006-04-01

The variational principle of Hamilton is applied to develop an analytical formulation to describe the volume viscosity in fluids. The procedure described here differs from those used in the past in that a dissipative process is represented by the chemical affinity and progress variable (sometimes called "order parameter") of a reacting species. These state variables appear in the variational integral in two places: first, in the expression for the internal energy, and second, in a subsidiary condition accounting for the conservation of the reacting species. As a result of the variational procedure, two dissipative terms appear in the Navier-Stokes equation. The first is the traditional volume viscosity term, proportional to the dilatational component of velocity; the second term is proportional to the material time derivative of the pressure gradient. Values of the respective volume viscosity coefficients are determined by applying the resulting volume-viscous Navier-Stokes equation to the case of acoustical propagation and then comparing expressions for the dispersion and absorption of sound. The formulation includes the special case of equilibration of the translational degrees of freedom. As examples, values are tabulated for dry and humid air, argon, and sea water.

A new approach for electrical properties estimation using a global integral equation and improvements using high permittivity materials.

PubMed

Schmidt, Rita; Webb, Andrew

2016-01-01

Electrical Properties Tomography (EPT) using MRI is a technique that has been developed to provide a new contrast mechanism for in vivo imaging. Currently the most common method relies on the solution of the homogeneous Helmholtz equation, which has limitations in accurate estimation at tissue interfaces. A new method proposed in this work combines a Maxwell's integral equation representation of the problem, and the use of high permittivity materials (HPM) to control the RF field, in order to reconstruct the electrical properties image. The magnetic field is represented by an integral equation considering each point as a contrast source. This equation can be solved in an inverse method. In this study we use a reference simulation or scout scan of a uniform phantom to provide an initial estimate for the inverse solution, which allows the estimation of the complex permittivity within a single iteration. Incorporating two setups with and without the HPM improves the reconstructed result, especially with respect to the very low electric field in the center of the sample. Electromagnetic simulations of the brain were performed at 3T to generate the B1(+) field maps and reconstruct the electric properties images. The standard deviations of the relative permittivity and conductivity were within 14% and 18%, respectively for a volume consisting of white matter, gray matter and cerebellum. Copyright © 2015 Elsevier Inc. All rights reserved.

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution. [rocket nozzle and orbital plume flow fields

NASA Technical Reports Server (NTRS)

Smith, S. D.

1984-01-01

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

Investigation of Volumetric Sources in Airframe Noise Simulations

NASA Technical Reports Server (NTRS)

Casper, Jay H.; Lockard, David P.; Khorrami, Mehdi R.; Streett, Craig L.

2004-01-01

Hybrid methods for the prediction of airframe noise involve a simulation of the near field flow that is used as input to an acoustic propagation formula. The acoustic formulations discussed herein are those based on the Ffowcs Williams and Hawkings equation. Some questions have arisen in the published literature in regard to an apparently significant dependence of radiated noise predictions on the location of the integration surface used in the solution of the Ffowcs Williams and Hawkings equation. These differences in radiated noise levels are most pronounced between solid-body surface integrals and off-body, permeable surface integrals. Such differences suggest that either a non-negligible volumetric source is contributing to the total radiation or the input flow simulation is suspect. The focus of the current work is the issue of internal consistency of the flow calculations that are currently used as input to airframe noise predictions. The case study for this research is a computer simulation for a three-element, high-lift wing profile during landing conditions. The noise radiated from this flow is predicted by a two-dimensional, frequency-domain formulation of the Ffowcs Williams and Hawkings equation. Radiated sound from volumetric sources is assessed by comparison of a permeable surface integration with the sum of a solid-body surface integral and a volume integral. The separate noise predictions are found in good agreement.

Solution of the advection-dispersion equation in two dimensions by a finite-volume Eulerian-Lagrangian localized adjoint method

USGS Publications Warehouse

Healy, R.W.; Russell, T.F.

1998-01-01

We extend the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard finite differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.

PREFACE: Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

2007-10-01

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

PubMed

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Measurement of testicular volume in smaller testes: how accurate is the conventional orchidometer?

PubMed

Lin, Chih-Chieh; Huang, William J S; Chen, Kuang-Kuo

2009-01-01

The aim of this study was to evaluate the accuracy of different methods, including the Seager orchidometer (SO) and ultrasonography (US), for assessing testicular volume of smaller testes (testes volume less than 18 mL). Moreover, the equations used for the calculations--the Hansen formula (length [L] x width [W](2) x 0.52, equation A), the prolate ellipsoid formula (L x W x height [H] x 0.52, equation B), and the Lambert equation (L x W x H x 0.71, equation C)--were also examined and compared with the gold standard testicular volume obtained by water displacement (Archimedes principle). In this study, 30 testes from 15 men, mean age 75.3 (+/-8.3) years, were included. They all had advanced prostate cancer and were admitted for orchiectomy. Before the procedure, all the testes were assessed using SO and US. The dimensions were then input into each equation to obtain the volume estimates. The testicular volume by water displacement was 8.1 +/- 3.5 mL. Correlation coefficients (R(2)) of the 2 different methods (SO, US) to the gold standard were 0.70 and 0.85, respectively. The calculated testicular volumes were 9.2 +/- 3.9 mL (measured by SO, equation A), 11.9 +/- 5.2 mL (measured by SO, equation C), 7.3 +/- 4.2 mL (measured by US, equation A), 6.5 +/- 3.3 mL (measured by US, equation B) and 8.9 +/- 4.5 mL (measured by US, equation C). Only the mean size measured by US and volume calculated with the Hansen equation (equation A) and the mean size measured by US and volume calculated with the Lambert equation (equation C) showed no significant differences when compared with the volumes estimated by water displacement (mean difference 0.81 mL, P = .053, and 0.81 mL, P = .056, respectively). Based on our measurements, we categorized testicular volume by different cutoff values (7.0 mL, 7.5 mL, 8.0 mL, and 8.5 mL) to calculate a new constant for use in the Hansen equation. The new constant was 0.59. We then reexamined the equations using the new 0.59 constant, and found that the equation Volume (V) = L x W(2) x 0.59 was the best for describing testicular volume among our subjects (difference between the new equation and the gold standard of water displacement = 0.19 mL, P = .726). We also found that US was more precise in measuring testicular dimensions. We propose a new formula, V = L x W(2) x 0.59, to assess the volumes of smaller testes.

Unveiling the relationships among the viscosity equations of glass liquids and colloidal suspensions for obtaining universal equations with the generic free volume concept.

PubMed

Hao, Tian

2015-09-14

The underlying relationships among viscosity equations of glass liquids and colloidal suspensions are explored with the aid of free volume concept. Viscosity equations of glass liquids available in literature are focused and found to have a same physical basis but different mathematical expressions for the free volume. The glass transitions induced by temperatures in glass liquids and the percolation transition induced by particle volume fractions in colloidal suspensions essentially are a second order phase transition: both those two transitions could induce the free volume changes, which in turn determines how the viscosities are going to change with temperatures and/or particle volume fractions. Unified correlations of the free volume to both temperatures and particle volume fractions are thus proposed. The resulted viscosity equations are reducible to many popular viscosity equations currently widely used in literature; those equations should be able to cover many different types of materials over a wide temperature range. For demonstration purpose, one of the simplified versions of those newly developed equations is compared with popular viscosity equations and the experimental data: it can well fit the experimental data over a wide temperature range. The current work reveals common physical grounds among various viscosity equations, deepening our understanding on viscosity and unifying the free volume theory across many different systems.

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

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

A Thermo-Optic Propagation Modeling Capability.

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

Schrader, Karl; Akau, Ron

2014-10-01

A new theoretical basis is derived for tracing optical rays within a finite-element (FE) volume. The ray-trajectory equations are cast into the local element coordinate frame and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The FE methodology (FEM) is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The method is implemented in the Matlab(TM) environment and compared to closed- form gradient index models. A software architecture is also developedmore » for implementing the algorithms in the Zemax(TM) commercial ray-trace application. A controlled thermal environment was constructed in the laboratory, and measured data was collected to validate the structural, thermal, and optical modeling methods.« less

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

NASA Technical Reports Server (NTRS)

Slack, David C.; Walters, Robert W.; Lohner, R.

1990-01-01

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

A Comparison of Experimental and Theoretical Results for Labyrinth Gas Seals. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Scharrer, Joseph Kirk

1987-01-01

The basic equations are derived for a two control volume model for compressible flow in a labyrinth seal. The flow is assumed to be completely turbulent and isoenergetic. The wall friction factors are determined using the Blasius formula. Jet flow theory is used for the calculation of the recirculation velocity in the cavity. Linearized zeroth and first order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth order pressure distribution is found by satisfying the leakage equation. The circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variable solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are compared to experimental test results.

The Bethe ansatz

NASA Astrophysics Data System (ADS)

Levkovich-Maslyuk, Fedor

2016-08-01

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross-Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross-Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review

NASA Astrophysics Data System (ADS)

Kahnert, Michael

2016-07-01

Numerical solution methods for electromagnetic scattering by non-spherical particles comprise a variety of different techniques, which can be traced back to different assumptions and solution strategies applied to the macroscopic Maxwell equations. One can distinguish between time- and frequency-domain methods; further, one can divide numerical techniques into finite-difference methods (which are based on approximating the differential operators), separation-of-variables methods (which are based on expanding the solution in a complete set of functions, thus approximating the fields), and volume integral-equation methods (which are usually solved by discretisation of the target volume and invoking the long-wave approximation in each volume cell). While existing reviews of the topic often tend to have a target audience of program developers and expert users, this tutorial review is intended to accommodate the needs of practitioners as well as novices to the field. The required conciseness is achieved by limiting the presentation to a selection of illustrative methods, and by omitting many technical details that are not essential at a first exposure to the subject. On the other hand, the theoretical basis of numerical methods is explained with little compromises in mathematical rigour; the rationale is that a good grasp of numerical light scattering methods is best achieved by understanding their foundation in Maxwell's theory.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 3.0)

NASA Technical Reports Server (NTRS)

Epton, Michael A.; Magnus, Alfred E.

1990-01-01

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the Panel Aerodynamics (PAN AIR) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformation, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments. Principal revisions to version 3.0 are the following: (1) appendices H and K more fully describe the Aerodynamic Influence Coefficient (AIC) construction; (2) appendix L now provides a complete description of the AIC solution process; (3) appendix P is new and discusses the theory for the new FDP module (which calculates streamlines and offbody points); and (4) numerous small corrections and revisions reflecting the MAG module rewrite.

Summer Faculty Systems Design Program. Integrating Wind Tunnels and Computers. Volume 2. Details of Summer Design Study USAF/OSR/ASEE

DTIC Science & Technology

1977-08-01

level is given in the report by El- Ramly and Rainbird of Carleton University in Ontario Canada (Ref. 2.48). This report comments on an investigation of...RefT 3, Äp r i 1 1976. 2.48. El- Ramly , Z. M. and Rainbird, W. J. "Computer-Controlled System for the Investigation of the Flow Behind Wings...detailed studies of "model" equations (such as the Burgers ’ equation) which include all the essential aspects of the actual problem of interest have

High pressure effects on the iron iron oxide and nickel nickel oxide oxygen fugacity buffers

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

Campbell, Andrew J; Danielson, Lisa; Righter, Kevin

The chemical potential of oxygen in natural and experimental samples is commonly reported relative to a specific oxygen fugacity (fO{sub 2}) buffer. These buffers are precisely known at 1 bar, but under high pressures corresponding to the conditions of the deep Earth, oxygen fugacity buffers are poorly calibrated. Reference (1 bar) fO{sub 2} buffers can be integrated to high pressure conditions by integrating the difference in volume between the solid phases, provided that their equations of state are known. In this work, the equations of state and volume difference between the metal-oxide pairs Fe-FeO and Ni-NiO were measured using synchrotronmore » X-ray diffraction in a multi-anvil press and laser heated diamond anvil cells. The results were used to construct high pressure fO{sub 2} buffer curves for these systems. The difference between the Fe-FeO and Ni-NiO buffers is observed to decrease significantly, by several log units, over 80 GPa. The results can be used to improve interpretation of high pressure experiments, specifically Fe-Ni exchange between metallic and oxide phases.« less

Thermodynamics of an ideal generalized gas: I. Thermodynamic laws.

PubMed

Lavenda, B H

2005-11-01

The equations of state for an ideal relativistic, or generalized, gas, like an ideal quantum gas, are expressed in terms of power laws of the temperature. In contrast to an ideal classical gas, the internal energy is a function of volume at constant temperature, implying that the ideal generalized gas will show either attractive or repulsive interactions. This is a necessary condition in order that the third law be obeyed and for matter to have an electromagnetic origin. The transition from an ideal generalized to a classical gas occurs when the two independent solutions of the subsidiary equation to Lagrange's equation coalesce. The equation of state relating the pressure to the internal energy encompasses the full range of cosmological scenarios, from the radiation to the matter dominated universes and finally to the vacuum energy, enabling the coefficient of proportionality, analogous to the Grüeisen ratio, to be interpreted in terms of the degrees of freedom related to the temperature exponents of the internal energy and the absolute temperature expressed in terms of a power of the empirical temperature. The limit where these exponents merge is shown to be the ideal classical gas limit. A corollary to Carnot's theorem is proved, asserting that the ratio of the work done over a cycle to the heat absorbed to increase the temperature at constant volume is the same for all bodies at the same volume. As power means, the energy and entropy are incomparable, and a new adiabatic potential is introduced by showing that the volume raised to a characteristic exponent is also the integrating factor for the quantity of heat so that the second law can be based on the property that power means are monotonically increasing functions of their order. The vanishing of the chemical potential in extensive systems implies that energy cannot be transported without matter and is equivalent to the condition that Clapeyron's equation be satisfied.

Asynchronous discrete event schemes for PDEs

NASA Astrophysics Data System (ADS)

Stone, D.; Geiger, S.; Lord, G. J.

2017-08-01

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method.

PubMed

Guizal, Brahim; Barchiesi, Dominique; Felbacq, Didier

2003-12-01

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Molecular Volumes and the Stokes-Einstein Equation

ERIC Educational Resources Information Center

Edward, John T.

1970-01-01

Examines the limitations of the Stokes-Einstein equation as it applies to small solute molecules. Discusses molecular volume determinations by atomic increments, molecular models, molar volumes of solids and liquids, and molal volumes. Presents an empirical correction factor for the equation which applies to molecular radii as small as 2 angstrom…

A net volume equation for Northeastern Minnesota.

Treesearch

Gerhard K. Raile

1980-01-01

Describes a net volume equation for northeastern Minnesota developed as part of the 1977 Minnesota Forest Inventory. Equation coefficients are presented by species groupings for both cubic foot and board foot volumes for five tree classes.

An analytical approach to obtaining JWL parameters from cylinder tests

NASA Astrophysics Data System (ADS)

Sutton, B. D.; Ferguson, J. W.; Hodgson, A. N.

2017-01-01

An analytical method for determining parameters for the JWL Equation of State from cylinder test data is described. This method is applied to four datasets obtained from two 20.3 mm diameter EDC37 cylinder tests. The calculated pressure-relative volume (p-Vr) curves agree with those produced by hydro-code modelling. The average calculated Chapman-Jouguet (CJ) pressure is 38.6 GPa, compared to the model value of 38.3 GPa; the CJ relative volume is 0.729 for both. The analytical pressure-relative volume curves produced agree with the one used in the model out to the commonly reported expansion of 7 relative volumes, as do the predicted energies generated by integrating under the p-Vr curve. The calculated energy is within 1.6% of that predicted by the model.

Green's function of radial inhomogeneous spheres excited by internal sources.

PubMed

Zouros, Grigorios P; Kokkorakis, Gerassimos C

2011-01-01

Green's function in the interior of penetrable bodies with inhomogeneous compressibility by sources placed inside them is evaluated through a Schwinger-Lippmann volume integral equation. In the case of a radial inhomogeneous sphere, the radial part of the unknown Green's function can be expanded in a double Dini's series, which allows analytical evaluation of the involved cumbersome integrals. The simple case treated here can be extended to more difficult situations involving inhomogeneous density as well as to the corresponding electromagnetic or elastic problem. Finally, numerical results are given for various inhomogeneous compressibility distributions.

A boundary element method for steady incompressible thermoviscous flow

NASA Technical Reports Server (NTRS)

Dargush, G. F.; Banerjee, P. K.

1991-01-01

A boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modeling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.

Kinetic Glomerular Filtration Rate Equation Can Accommodate a Changing Body Volume: Derivation and Usage of the Formula.

PubMed

Chen, Sheldon

2018-05-22

Ascertaining a patient's kidney function is more difficult to do when the serum creatinine is changing than when it is stable. To accomplish the task, various kinetic clearance equations have been developed. To date, however, none of them have allowed for ongoing changes to the creatinine's volume of distribution. These diluting or concentrating effects on the [creatinine] can greatly impact the accuracy of kidney function assessment. Described herein is a model of creatinine kinetics that also accommodates volume changes. The differential equation is solved for the kinetic glomerular filtration rate (GFR), which is helpful information to the physician. Some of the equation's discontinuities, such as from dividing by a volume rate of zero, can be resolved by using limits. Being "volume-capable," the new kinetic equation reveals how a changing volume influences the maximum rate of rise in [creatinine], a parameter that heretofore was chosen empirically. To show the advantages of incorporating volume, the new and old kinetic equations are applied to a clinical case of overzealous fluid resuscitation. Appropriately, when the volume gain's dilution of [creatinine] is taken into account, the creatinine clearance is calculated to be substantially lower. In conclusion, the kinetic GFR equation has been upgraded to handle volume changes simultaneously with [creatinine] changes. Copyright © 2018. Published by Elsevier Inc.

A Volume and Taper Prediction System for Bald Cypress

Treesearch

Bernard R. Parresol; James E. Hotvedt; Quang V. Cao

1987-01-01

A volume and taper prediction system based on d10 and consisting of a total volume equation, two volume ratio equations (one for diameter limits, the other for height limits), and a taper equation was developed for bald cypress using sample tree data collected in Louisiana. Normal diameter (dn), a subjective variable-...

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

A net volume equation for Indiana.

Treesearch

W. Brad Smith; Carol A. Weist

1982-01-01

Describes a Weibull-type volume equation for Indiana developed as part of the ongoing Resource Evaluation research in the Central States. Equation coefficients are presented by species groupings for both cubic foot and board foot volumes for three tree class categories.

Volume-preserving normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a nonzero condition on their quadratic parts are considered. The algebra of all first integrals for any such system has a unique (modulo scalar multiplication) generator. The infinite level volume-preserving parametric normal forms of any nondegenerate perturbation within the Lie algebra of any such system is computed, where it can have rich dynamics. The associated unique generator of the algebra of first integrals are derived. The symmetry group of the infinite level normal forms are also discussed. Some necessary formulas are derived and applied to appropriately modified Rössler and generalized Kuramoto-Sivashinsky equations to demonstrate the applicability of our theoretical results. An approach (introduced by Iooss and Lombardi) is applied to find an optimal truncation for the first level normal forms of these examples with exponentially small remainders. The numerically suggested radius of convergence (for the first integral) associated with a hypernormalization step is discussed for the truncated first level normal forms of the examples. This is achieved by an efficient implementation of the results using Maple.

A new computational method for reacting hypersonic flows

NASA Astrophysics Data System (ADS)

Niculescu, M. L.; Cojocaru, M. G.; Pricop, M. V.; Fadgyas, M. C.; Pepelea, D.; Stoican, M. G.

2017-07-01

Hypersonic gas dynamics computations are challenging due to the difficulties to have reliable and robust chemistry models that are usually added to Navier-Stokes equations. From the numerical point of view, it is very difficult to integrate together Navier-Stokes equations and chemistry model equations because these partial differential equations have different specific time scales. For these reasons, almost all known finite volume methods fail shortly to solve this second order partial differential system. Unfortunately, the heating of Earth reentry vehicles such as space shuttles and capsules is very close linked to endothermic chemical reactions. A better prediction of wall heat flux leads to smaller safety coefficient for thermal shield of space reentry vehicle; therefore, the size of thermal shield decreases and the payload increases. For these reasons, the present paper proposes a new computational method based on chemical equilibrium, which gives accurate prediction of hypersonic heating in order to support the Earth reentry capsule design.

A net volume equation for Michigan's Upper and Lower Peninsulas.

Treesearch

Gerhard K. Raile; W. Brad Smith; Carol A. Weist

1982-01-01

Describes a volume equation for Michigan's Upper and Lower Peninsulas developed as part of the 1981 Michigan Forest Inventory. Equation coefficients are presented by species groupings for both cubic-foot and board-foot volumes for three tree categories.

Space tug economic analysis study. Volume 2: Tug concepts analysis. Part 1: Overall approach and data generation

NASA Technical Reports Server (NTRS)

1972-01-01

An economic analysis of space tug operations is presented. The subjects discussed are: (1) data base for orbit injection stages, (2) data base for reusable space tug, (3) performance equations, (4) data integration and interpretation, (5) tug performance and mission model accomodation, (6) total program cost, (7) payload analysis, (8) computer software, and (9) comparison of tug concepts.

Conference Proceedings: 7th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, California, March 18-22, 1991

DTIC Science & Technology

1991-03-01

34Volume integral Equations and Conjugate Gradient Methods in Electromagnetic Non destructive Evaluation’ by Dr. Harold P.. Sabbagh, Sabbagh Associates...8217 Experimental Demonstrations far teaching Electroamgnetic Folods and Energy’ M. Zathn, J. Mectrer...8217-....................................... . ...................................................... 329 ’PoalarimetrIc Scattering and Control at Radar Crass Section of Chirat Targets at Simple

Functions Character

NASA Astrophysics Data System (ADS)

Dugave, Maxime; Göhmann, Frank; Kozlowski, Karol Kajetan

2014-04-01

We establish several properties of the solutions to the linear integral equations describing the infinite volume properties of the XXZ spin-1/2 chain in the disordered regime. In particular, we obtain lower and upper bounds for the dressed energy, dressed charge and density of Bethe roots. Furthermore, we establish that given a fixed external magnetic field (or a fixed magnetization) there exists a unique value of the boundary of the Fermi zone.

Viscous wing theory development. Volume 2: GRUMWING computer program user's manual

NASA Technical Reports Server (NTRS)

Chow, R. R.; Ogilvie, P. L.

1986-01-01

This report is a user's manual which describes the operation of the computer program, GRUMWING. The program computes the viscous transonic flow over three-dimensional wings using a boundary layer type viscid-inviscid interaction approach. The inviscid solution is obtained by an approximate factorization (AFZ)method for the full potential equation. The boundary layer solution is based on integral entrainment methods.

Statistical Optics

NASA Astrophysics Data System (ADS)

Goodman, Joseph W.

2000-07-01

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

Gas Flux and Density Surrounding a Cylindrical Aperture in the Free Molecular Flow Regime

NASA Technical Reports Server (NTRS)

Soulas, George C.

2011-01-01

The equations for rigorously calculating the particle flux and density surrounding a cylindrical aperture in the free molecular flow regime are developed and presented. The fundamental equations for particle flux and density from a reservoir and a diffusely reflecting surface will initially be developed. Assumptions will include a Maxwell-Boltzmann speed distribution, equal particle and wall temperatures, and a linear flux distribution along the cylindrical aperture walls. With this information, the equations for axial flux and density surrounding a cylindrical aperture will be developed. The cylindrical aperture will be divided into multiple volumes and regions to rigorously determine the surrounding axial flux and density, and appropriate limits of integration will be determined. The results of these equations will then be evaluated. The linear wall flux distribution assumption will be assessed. The axial flux and density surrounding a cylindrical aperture with a thickness-to-radius ratio of 1.25 will be presented. Finally, the equations determined in this study will be verified using multiple methods.

An exact solution for ideal dam-break floods on steep slopes

USGS Publications Warehouse

Ancey, C.; Iverson, R.M.; Rentschler, M.; Denlinger, R.P.

2008-01-01

The shallow-water equations are used to model the flow resulting from the sudden release of a finite volume of frictionless, incompressible fluid down a uniform slope of arbitrary inclination. The hodograph transformation and Riemann's method make it possible to transform the governing equations into a linear system and then deduce an exact analytical solution expressed in terms of readily evaluated integrals. Although the solution treats an idealized case never strictly realized in nature, it is uniquely well-suited for testing the robustness and accuracy of numerical models used to model shallow-water flows on steep slopes. Copyright 2008 by the American Geophysical Union.

A critical review and database of biomass and volume allometric equation for trees and shrubs of Bangladesh

NASA Astrophysics Data System (ADS)

Mahmood, H.; Siddique, M. R. H.; Akhter, M.

2016-08-01

Estimations of biomass, volume and carbon stock are important in the decision making process for the sustainable management of a forest. These estimations can be conducted by using available allometric equations of biomass and volume. Present study aims to: i. develop a compilation with verified allometric equations of biomass, volume, and carbon for trees and shrubs of Bangladesh, ii. find out the gaps and scope for further development of allometric equations for different trees and shrubs of Bangladesh. Key stakeholders (government departments, research organizations, academic institutions, and potential individual researchers) were identified considering their involvement in use and development of allometric equations. A list of documents containing allometric equations was prepared from secondary sources. The documents were collected, examined, and sorted to avoid repetition, yielding 50 documents. These equations were tested through a quality control scheme involving operational verification, conceptual verification, applicability, and statistical credibility. A total of 517 allometric equations for 80 species of trees, shrubs, palm, and bamboo were recorded. In addition, 222 allometric equations for 39 species were validated through the quality control scheme. Among the verified equations, 20%, 12% and 62% of equations were for green-biomass, oven-dried biomass, and volume respectively and 4 tree species contributed 37% of the total verified equations. Five gaps have been pinpointed for the existing allometric equations of Bangladesh: a. little work on allometric equation of common tree and shrub species, b. most of the works were concentrated on certain species, c. very little proportion of allometric equations for biomass estimation, d. no allometric equation for belowground biomass and carbon estimation, and d. lower proportion of valid allometric equations. It is recommended that site and species specific allometric equations should be developed and consistency in field sampling, sample processing, data recording and selection of allometric equations should be maintained to ensure accuracy in estimation of biomass, volume, and carbon stock in different forest types of Bangladesh.

Electromagnetic scattering of large structures in layered earths using integral equations

NASA Astrophysics Data System (ADS)

Xiong, Zonghou; Tripp, Alan C.

1995-07-01

An electromagnetic scattering algorithm for large conductivity structures in stratified media has been developed and is based on the method of system iteration and spatial symmetry reduction using volume electric integral equations. The method of system iteration divides a structure into many substructures and solves the resulting matrix equation using a block iterative method. The block submatrices usually need to be stored on disk in order to save computer core memory. However, this requires a large disk for large structures. If the body is discretized into equal-size cells it is possible to use the spatial symmetry relations of the Green's functions to regenerate the scattering impedance matrix in each iteration, thus avoiding expensive disk storage. Numerical tests show that the system iteration converges much faster than the conventional point-wise Gauss-Seidel iterative method. The numbers of cells do not significantly affect the rate of convergency. Thus the algorithm effectively reduces the solution of the scattering problem to an order of O(N2), instead of O(N3) as with direct solvers.

Validation of equations for pleural effusion volume estimation by ultrasonography.

PubMed

Hassan, Maged; Rizk, Rana; Essam, Hatem; Abouelnour, Ahmed

2017-12-01

To validate the accuracy of previously published equations that estimate pleural effusion volume using ultrasonography. Only equations using simple measurements were tested. Three measurements were taken at the posterior axillary line for each case with effusion: lateral height of effusion ( H ), distance between collapsed lung and chest wall ( C ) and distance between lung and diaphragm ( D ). Cases whose effusion was aspirated to dryness were included and drained volume was recorded. Intra-class correlation coefficient (ICC) was used to determine the predictive accuracy of five equations against the actual volume of aspirated effusion. 46 cases with effusion were included. The most accurate equation in predicting effusion volume was ( H  +  D ) × 70 (ICC 0.83). The simplest and yet accurate equation was H  × 100 (ICC 0.79). Pleural effusion height measured by ultrasonography gives a reasonable estimate of effusion volume. Incorporating distance between lung base and diaphragm into estimation improves accuracy from 79% with the first method to 83% with the latter.

An Analytical Approach to Obtaining JWL Parameters from Cylinder Tests

NASA Astrophysics Data System (ADS)

Sutton, Ben; Ferguson, James

2015-06-01

An analytical method for determining parameters for the JWL equation of state (EoS) from cylinder test data is described. This method is applied to four datasets obtained from two 20.3 mm diameter EDC37 cylinder tests. The calculated parameters and pressure-volume (p-V) curves agree with those produced by hydro-code modelling. The calculated Chapman-Jouguet (CJ) pressure is 38.6 GPa, compared to the model value of 38.3 GPa; the CJ relative volume is 0.729 for both. The analytical pressure-volume curves produced agree with the one used in the model out to the commonly reported expansion of 7 relative volumes, as do the predicted energies generated by integrating under the p-V curve. The calculated and model energies are 8.64 GPa and 8.76 GPa respectively.

PIV-based estimation of unsteady loads on a flat plate at high angle of attack using momentum equation approaches

NASA Astrophysics Data System (ADS)

Guissart, Amandine; Bernal, Luis; Dimitriadis, Gregorios; Terrapon, Vincent

2015-11-01

The direct measurement of loads with force balance can become challenging when the forces are small or when the body is moving. An alternative is the use of Particle Image Velocimetry (PIV) velocity fields to indirectly obtain the aerodynamic coefficients. This can be done by the use of control volume approaches which lead to the integration of velocities, and other fields deriving from them, on a contour surrounding the studied body and its supporting surface. This work exposes and discusses results obtained with two different methods: the direct use of the integral formulation of the Navier-Stokes equations and the so-called Noca's method. The latter is a reformulation of the integral Navier-Stokes equations in order to get rid of the pressure. Results obtained using the two methods are compared and the influence of different parameters is discussed. The methods are applied to PIV data obtained from water channel testing for the flow around a 16:1 plate. Two cases are considered: a static plate at high angle of attack and a large amplitude imposed pitching motion. Two-dimensional PIV velocity fields are used to compute the aerodynamic forces. Direct measurements of dynamic loads are also carried out in order to assess the quality of the indirectly calculated coefficients.

BHR equations re-derived with immiscible particle effects

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

Schwarzkopf, John Dennis; Horwitz, Jeremy A.

2015-05-01

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

Study of scattering cross section of a plasma column using Green's function volume integral equation method

NASA Astrophysics Data System (ADS)

Soltanmoradi, Elmira; Shokri, Babak

2017-05-01

In this article, the electromagnetic wave scattering from plasma columns with inhomogeneous electron density distribution is studied by the Green's function volume integral equation method. Due to the ready production of such plasmas in the laboratories and their practical application in various technological fields, this study tries to find the effects of plasma parameters such as the electron density, radius, and pressure on the scattering cross-section of a plasma column. Moreover, the incident wave frequency influence of the scattering pattern is demonstrated. Furthermore, the scattering cross-section of a plasma column with an inhomogeneous collision frequency profile is calculated and the effect of this inhomogeneity is discussed first in this article. These results are especially used to determine the appropriate conditions for radar cross-section reduction purposes. It is shown that the radar cross-section of a plasma column reduces more for a larger collision frequency, for a relatively lower plasma frequency, and also for a smaller radius. Furthermore, it is found that the effect of the electron density on the scattering cross-section is more obvious in comparison with the effect of other plasma parameters. Also, the plasma column with homogenous collision frequency can be used as a better shielding in contrast to its inhomogeneous counterpart.

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

DOE PAGES

Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...

2015-02-24

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

Pozsgay, B.; Szécsényi, I. M.; Takács, G.

2015-04-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Weight and volume equations and tables for red maple in the Lake States.

Treesearch

Thomas R. Crow; G.G. Erdmann

1983-01-01

Weight and volume information based on regional sampling are provided for red maple in the Lake States. Both green weight and dry weight values are presented for biomass. Volume equations predict total stem volume, volume to 8-inch top, and volume to 4-inch top, inside and outside bark.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Compatible taper algorithms for California hardwoods

Treesearch

James W. Flewelling

2007-01-01

For 13 species of California hardwoods, cubic volume equations to three merchantability standards had been developed earlier. The equations predict cubic volume from the primary bole, forks, and branches, but do not differentiate between the sources of the wood. The Forest Inventory and Analysis (FIA) program needed taper equations that are compatible with the volume...

A calculation procedure for viscous flow in turbomachines, volume 3. [computer programs

NASA Technical Reports Server (NTRS)

Khalil, I.; Sheoran, Y.; Tabakoff, W.

1980-01-01

A method for analyzing the nonadiabatic viscous flow through turbomachine blade passages was developed. The field analysis is based upon the numerical integration of the full incompressible Navier-Stokes equations, together with the energy equation on the blade-to-blade surface. A FORTRAN IV computer program was written based on this method. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system. The flow may be axial, radial or mixed and there may be a change in stream channel thickness in the through-flow direction. The inputs required for two FORTRAN IV programs are presented. The first program considers laminar flows and the second can handle turbulent flows. Numerical examples are included to illustrate the use of the program, and to show the results that are obtained.

Unimodular Einstein-Cartan gravity: Dynamics and conservation laws

NASA Astrophysics Data System (ADS)

Bonder, Yuri; Corral, Cristóbal

2018-04-01

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

Structural characterization and numerical simulations of flow properties of standard and reservoir carbonate rocks using micro-tomography

NASA Astrophysics Data System (ADS)

Islam, Amina; Chevalier, Sylvie; Sassi, Mohamed

2018-04-01

With advances in imaging techniques and computational power, Digital Rock Physics (DRP) is becoming an increasingly popular tool to characterize reservoir samples and determine their internal structure and flow properties. In this work, we present the details for imaging, segmentation, as well as numerical simulation of single-phase flow through a standard homogenous Silurian dolomite core plug sample as well as a heterogeneous sample from a carbonate reservoir. We develop a procedure that integrates experimental results into the segmentation step to calibrate the porosity. We also look into using two different numerical tools for the simulation; namely Avizo Fire Xlab Hydro that solves the Stokes' equations via the finite volume method and Palabos that solves the same equations using the Lattice Boltzmann Method. Representative Elementary Volume (REV) and isotropy studies are conducted on the two samples and we show how DRP can be a useful tool to characterize rock properties that are time consuming and costly to obtain experimentally.

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Towards a universal method for calculating hydration free energies: a 3D reference interaction site model with partial molar volume correction.

PubMed

Palmer, David S; Frolov, Andrey I; Ratkova, Ekaterina L; Fedorov, Maxim V

2010-12-15

We report a simple universal method to systematically improve the accuracy of hydration free energies calculated using an integral equation theory of molecular liquids, the 3D reference interaction site model. A strong linear correlation is observed between the difference of the experimental and (uncorrected) calculated hydration free energies and the calculated partial molar volume for a data set of 185 neutral organic molecules from different chemical classes. By using the partial molar volume as a linear empirical correction to the calculated hydration free energy, we obtain predictions of hydration free energies in excellent agreement with experiment (R = 0.94, σ = 0.99 kcal mol (- 1) for a test set of 120 organic molecules).

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Exact finite volume expectation values of \\overline{Ψ}Ψ in the massive Thirring model from light-cone lattice correlators

NASA Astrophysics Data System (ADS)

Hegedűs, Árpád

2018-03-01

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator \\overline{Ψ}Ψ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator \\overline{Ψ}Ψ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

HYDRODYNAMIC SIMULATION OF THE UPPER POTOMAC ESTUARY.

USGS Publications Warehouse

Schaffranck, Raymond W.

1986-01-01

Hydrodynamics of the upper extent of the Potomac Estuary between Indian Head and Morgantown, Md. , are simulated using a two-dimensional model. The model computes water-surface elevations and depth-averaged velocities by numerically integrating finite-difference forms of the equations of mass and momentum conservation using the alternating direction implicit method. The fundamental, non-linear, unsteady-flow equations, upon which the model is formulated, include additional terms to account for Coriolis acceleration and meteorological influences. Preliminary model/prototype data comparisons show agreement to within 9% for tidal flow volumes and phase differences within the measured-data-recording interval. Use of the model to investigate the hydrodynamics and certain aspects of transport within this Potomac Estuary reach is demonstrated. Refs.

Measurements and Modeling of Soot Formation and Radiation in Microgravity Jet Diffusion Flames. Volume 4

NASA Technical Reports Server (NTRS)

Ku, Jerry C.; Tong, Li; Greenberg, Paul S.

1996-01-01

This is a computational and experimental study for soot formation and radiative heat transfer in jet diffusion flames under normal gravity (1-g) and microgravity (0-g) conditions. Instantaneous soot volume fraction maps are measured using a full-field imaging absorption technique developed by the authors. A compact, self-contained drop rig is used for microgravity experiments in the 2.2-second drop tower facility at NASA Lewis Research Center. On modeling, we have coupled flame structure and soot formation models with detailed radiation transfer calculations. Favre-averaged boundary layer equations with a k-e-g turbulence model are used to predict the flow field, and a conserved scalar approach with an assumed Beta-pdf are used to predict gaseous species mole fraction. Scalar transport equations are used to describe soot volume fraction and number density distributions, with formation and oxidation terms modeled by one-step rate equations and thermophoretic effects included. An energy equation is included to couple flame structure and radiation analyses through iterations, neglecting turbulence-radiation interactions. The YIX solution for a finite cylindrical enclosure is used for radiative heat transfer calculations. The spectral absorption coefficient for soot aggregates is calculated from the Rayleigh solution using complex refractive index data from a Drude- Lorentz model. The exponential-wide-band model is used to calculate the spectral absorption coefficient for H20 and C02. It is shown that when compared to results from true spectral integration, the Rosseland mean absorption coefficient can provide reasonably accurate predictions for the type of flames studied. The soot formation model proposed by Moss, Syed, and Stewart seems to produce better fits to experimental data and more physically sound than the simpler model by Khan et al. Predicted soot volume fraction and temperature results agree well with published data for a normal gravity co-flow laminar flames and turbulent jet flames. Predicted soot volume fraction results also agree with our data for 1-g and 0-g laminar jet names as well as 1-g turbulent jet flames.

A Local Net Volume Equation for Iowa

Treesearch

Jerold T. Hahn

1976-01-01

As a part of the 1974 Forest Survey of Iowa, the Station''s Forst Resources Evaluatioin Research Staff developed a merchantable tree volume equation and tables of coefficients for Iowa. They were developed for both board-foot (International ?-inch rule) and cubic foot volumes, for several species and species groups of growing-stock trees. The equation and...

On adiabatic pair potentials of highly charged colloid particles

NASA Astrophysics Data System (ADS)

Sogami, Ikuo S.

2018-03-01

Generalizing the Debye-Hückel formalism, we develop a new mean field theory for adiabatic pair potentials of highly charged particles in colloid dispersions. The unoccupied volume and the osmotic pressure are the key concepts to describe the chemical and thermodynamical equilibrium of the gas of small ions in the outside region of all of the colloid particles. To define the proper thermodynamic quantities, it is postulated to take an ensemble averaging with respect to the particle configurations in the integrals for their densities consisting of the electric potential satisfying a set of equations that are derived by linearizing the Poisson-Boltzmann equation. With the Fourier integral representation of the electric potential, we calculate first the internal electric energy of the system from which the Helmholtz free energy is obtained through the Legendre transformation. Then, the Gibbs free energy is calculated using both ways of the Legendre transformation with respect to the unoccupied volume and the summation of chemical potentials. The thermodynamic functions provide three types of pair potentials, all of which are inversely proportional to the fraction of the unoccupied volume. At the limit when the fraction factor reduces to unity, the Helmholtz pair potential turns exactly into the well known Derjaguin-Landau-Verwey-Overbeek repulsive potential. The Gibbs pair potential possessing a medium-range strong repulsive part and a long-range weak attractive tail can explain the Schulze-Hardy rule for coagulation in combination with the van der Waals-London potential and describes a rich variety of phenomena of phase transitions observed in the dilute dispersions of highly charged particles.

Effects of Turbulence Model on Prediction of Hot-Gas Lateral Jet Interaction in a Supersonic Crossflow

DTIC Science & Technology

2015-07-01

performance computing time from the US Department of Defense (DOD) High Performance Computing Modernization program at the US Army Research Laboratory...Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time ...dimensional, compressible, Reynolds-averaged Navier-Stokes (RANS) equations are solved using a finite volume method. A point-implicit time - integration

Calibration of volume and component biomass equations for Douglas-fir and lodgepole pine in Western Oregon forests

Treesearch

Krishna P. Poudel; Temesgen Hailemariam

2016-01-01

Using data from destructively sampled Douglas-fir and lodgepole pine trees, we evaluated the performance of regional volume and component biomass equations in terms of bias and RMSE. The volume and component biomass equations were calibrated using three different adjustment methods that used: (a) a correction factor based on ordinary least square regression through...

Tree volume and biomass equations for the Lake States.

Treesearch

Jerold T. Hahn

1984-01-01

Presents species specific equations and methods for computing tree height, cubic foot, and board foot volume, and biomass for the Lake States (Michigan, Minnesota, and Wisconsin). Height equations compute either total or merchantable height to a variable top d.o.b. from d.b.h., site index, and basal area. Volumes and biomass are computed from d.b.h. and height.

On the Divergence of the Velocity Vector in Real-Gas Flow

NASA Technical Reports Server (NTRS)

Bellan, Josette

2009-01-01

A theoretical study was performed addressing the degree of applicability or inapplicability, to a real gas, of the occasionally stated belief that for an ideal gas, incompressibility is synonymous with a zero or very low Mach number. The measure of compressibility used in this study is the magnitude of the divergence of the flow velocity vector [V(bar) (raised dot) u (where u is the flow velocity)]. The study involves a mathematical derivation that begins with the governing equations of flow and involves consideration of equations of state, thermodynamics, and fluxes of heat, mass, and the affected molecular species. The derivation leads to an equation for the volume integral of (V(bar) (raised dot) u)(sup 2) that indicates contributions of several thermodynamic, hydrodynamic, and species-flux effects to compressibility and reveals differences between real and ideal gases. An analysis of the equation leads to the conclusion that for a real gas, incompressibility is not synonymous with zero or very small Mach number. Therefore, it is further concluded, the contributions to compressibility revealed by the derived equation should be taken into account in simulations of real-gas flows.

Estimating value and volume of ponderosa pine trees by equations.

Treesearch

Martin E. Plank

1981-01-01

Equations for estimating the selling value and tally volume for ponderosa pine lumber from the standing trees are described. Only five characteristics are required for the equations. Development and application of the system are described.

Computation of nonlinear ultrasound fields using a linearized contrast source method.

PubMed

Verweij, Martin D; Demi, Libertario; van Dongen, Koen W A

2013-08-01

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

A Comparison of Height-Accumulation and Volume-Equation Methods for Estimating Tree and Stand Volumes

Treesearch

R.B. Ferguson; V. Clark Baldwin

1995-01-01

Estimating tree and stand volume in mature plantations is time consuming, involving much manpower and equipment; however, several sampling and volume-prediction techniques are available. This study showed that a well-constructed, volume-equation method yields estimates comparable to those of the often more time-consuming, height-accumulation method, even though the...

Growth and yield of quaking aspen in North-central Minnesota.

Treesearch

Bryce E. Schlaegel

1971-01-01

Summaries of total and merchantable stand data from 34 permanent sample plots were used to derive equations for predicting present and future stand volumes. Equations are presented for predicting total cubic-foot volume, ratio of merchantable volume to total volume, and future stand diameter, heights, and basal area. Yield tables are given for total stand volume and...

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

Homogeneous quantum electrodynamic turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1992-01-01

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Diffusion length measurements in bulk and epitaxially grown 3-5 semiconductors using charge collection microscopy

NASA Technical Reports Server (NTRS)

Leon, R. P.

1987-01-01

Diffusion lengths and surface recombination velocities were measured in GaAs diodes and InP finished solar cells. The basic techniques used was charge collection microscopy also known as electron beam induced current (EBIC). The normalized currents and distances from the pn junction were read directly from the calibrated curves obtained while using the line scan mode in an SEM. These values were then equated to integral and infinite series expressions resulting from the solution of the diffusion equation with both extended generation and point generation functions. This expands previous work by examining both thin and thick samples. The surface recombination velocity was either treated as an unknown in a system of two equations, or measured directly using low e(-) beam accelerating voltages. These techniques give accurate results by accounting for the effects of surface recombination and the finite size of the generation volume.

The terminal area simulation system. Volume 1: Theoretical formulation

NASA Technical Reports Server (NTRS)

Proctor, F. H.

1987-01-01

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Validation the use of refractometer and mathematic equations to measure dietary formula contents for clinical application.

PubMed

Chang, W-K; Chao, Y-C; Mcclave, S-A; Yeh, M-K

2005-10-01

Gastric residual volumes are widely used to evaluate gastric emptying for patients receiving enteral feeding, but controversy exists about what constitutes gastric residual volume. We have developed a method by using refractometer and derived mathematical equations to calculate the formula concentration, total residual volume (TRV), and formula volume. In this study, we like to validate these mathematical equations before they can be implemented for clinical patient care. Four dietary formulas were evaluated in two consecutive validation experiments. Firstly, dietary formula volume of 50, 100, 200, and 400 ml were diluted with 50 ml water, and then the Brix value (BV) was measured by the refractometer. Secondly, 50 ml of water, then 100 ml of dietary formula were infused into a beaker, and followed by the BV measurement. After this, 50 ml of water was infused and followed by the second BV measurement. The entire procedure of infusing of dietary formula (100 ml) and waster (50 ml) was repeated twice and followed by the BV measurement. The formula contents (formula concentration, TRV, and formula volume) were calculated by mathematical equations. The calculated formula concentrations, TRVs, and formula volumes measured from mathematic equations were strongly close to the true values in the first and second validation experiments (R2>0.98, P<0.001). Refractometer and the derived mathematical equations may be used to accurately measure the formula concentration, TRV, and formula volume and served as a tool to monitor gastric emptying for patients receiving enteral feeding.

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

NASA Astrophysics Data System (ADS)

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon

2010-11-01

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.

Numerical Simulations for Landing Gear Noise Generation and Radiation

NASA Technical Reports Server (NTRS)

Morris, Philip J.; Long, Lyle N.

2002-01-01

Aerodynamic noise from a landing gear in a uniform flow is computed using the Ffowcs Williams -Hawkings (FW-H) equation. The time accurate flow data on the surface is obtained using a finite volume flow solver on an unstructured and. The Ffowcs Williams-Hawkings equation is solved using surface integrals over the landing gear surface and over a permeable surface away from the landing gear. Two geometric configurations are tested in order to assess the impact of two lateral struts on the sound level and directivity in the far-field. Predictions from the Ffowcs Williams-Hawkings code are compared with direct calculations by the flow solver at several observer locations inside the computational domain. The permeable Ffowcs Williams-Hawkings surface predictions match those of the flow solver in the near-field. Far-field noise calculations coincide for both integration surfaces. The increase in drag observed between the two landing gear configurations is reflected in the sound pressure level and directivity mainly in the streamwise direction.

LS-DYNA Simulation of Hemispherical-punch Stamping Process Using an Efficient Algorithm for Continuum Damage Based Elastoplastic Constitutive Equation

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

Salajegheh, Nima; Abedrabbo, Nader; Pourboghrat, Farhang

An efficient integration algorithm for continuum damage based elastoplastic constitutive equations is implemented in LS-DYNA. The isotropic damage parameter is defined as the ratio of the damaged surface area over the total cross section area of the representative volume element. This parameter is incorporated into the integration algorithm as an internal variable. The developed damage model is then implemented in the FEM code LS-DYNA as user material subroutine (UMAT). Pure stretch experiments of a hemispherical punch are carried out for copper sheets and the results are compared against the predictions of the implemented damage model. Evaluation of damage parameters ismore » carried out and the optimized values that correctly predicted the failure in the sheet are reported. Prediction of failure in the numerical analysis is performed through element deletion using the critical damage value. The set of failure parameters which accurately predict the failure behavior in copper sheets compared to experimental data is reported as well.« less

Relation Between the Cell Volume and the Cell Cycle Dynamics in Mammalian cell

NASA Astrophysics Data System (ADS)

Magno, A. C. G.; Oliveira, I. L.; Hauck, J. V. S.

2016-08-01

The main goal of this work is to add and analyze an equation that represents the volume in a dynamical model of the mammalian cell cycle proposed by Gérard and Goldbeter (2011) [1]. The cell division occurs when the cyclinB/Cdkl complex is totally degraded (Tyson and Novak, 2011)[2] and it reaches a minimum value. At this point, the cell is divided into two newborn daughter cells and each one will contain the half of the cytoplasmic content of the mother cell. The equations of our base model are only valid if the cell volume, where the reactions occur, is constant. Whether the cell volume is not constant, that is, the rate of change of its volume with respect to time is explicitly taken into account in the mathematical model, then the equations of the original model are no longer valid. Therefore, every equations were modified from the mass conservation principle for considering a volume that changes with time. Through this approach, the cell volume affects all model variables. Two different dynamic simulation methods were accomplished: deterministic and stochastic. In the stochastic simulation, the volume affects every model's parameters which have molar unit, whereas in the deterministic one, it is incorporated into the differential equations. In deterministic simulation, the biochemical species may be in concentration units, while in stochastic simulation such species must be converted to number of molecules which are directly proportional to the cell volume. In an effort to understand the influence of the new equation a stability analysis was performed. This elucidates how the growth factor impacts the stability of the model's limit cycles. In conclusion, a more precise model, in comparison to the base model, was created for the cell cycle as it now takes into consideration the cell volume variation

A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries

NASA Astrophysics Data System (ADS)

Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.

2013-03-01

A finite volume cell-centered Lagrangian formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative Eulerian and Lagrangian hydrocodes in addition to analytical and experimental results are made to validate the current approach.

A robust, efficient equidistribution 2D grid generation method

NASA Astrophysics Data System (ADS)

Chacon, Luis; Delzanno, Gian Luca; Finn, John; Chung, Jeojin; Lapenta, Giovanni

2007-11-01

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).

Modeling erosion and sedimentation coupled with hydrological and overland flow processes at the watershed scale

NASA Astrophysics Data System (ADS)

Kim, Jongho; Ivanov, Valeriy Y.; Katopodes, Nikolaos D.

2013-09-01

A novel two-dimensional, physically based model of soil erosion and sediment transport coupled to models of hydrological and overland flow processes has been developed. The Hairsine-Rose formulation of erosion and deposition processes is used to account for size-selective sediment transport and differentiate bed material into original and deposited soil layers. The formulation is integrated within the framework of the hydrologic and hydrodynamic model tRIBS-OFM, Triangulated irregular network-based, Real-time Integrated Basin Simulator-Overland Flow Model. The integrated model explicitly couples the hydrodynamic formulation with the advection-dominated transport equations for sediment of multiple particle sizes. To solve the system of equations including both the Saint-Venant and the Hairsine-Rose equations, the finite volume method is employed based on Roe's approximate Riemann solver on an unstructured grid. The formulation yields space-time dynamics of flow, erosion, and sediment transport at fine scale. The integrated model has been successfully verified with analytical solutions and empirical data for two benchmark cases. Sensitivity tests to grid resolution and the number of used particle sizes have been carried out. The model has been validated at the catchment scale for the Lucky Hills watershed located in southeastern Arizona, USA, using 10 events for which catchment-scale streamflow and sediment yield data were available. Since the model is based on physical laws and explicitly uses multiple types of watershed information, satisfactory results were obtained. The spatial output has been analyzed and the driving role of topography in erosion processes has been discussed. It is expected that the integrated formulation of the model has the promise to reduce uncertainties associated with typical parameterizations of flow and erosion processes. A potential for more credible modeling of earth-surface processes is thus anticipated.

Volume and biomass for curlleaf cercocarpus in Nevada

Treesearch

David C. Chojnacky

1984-01-01

Volume and biomass equations were developed for curlleaf cercocarpus (Cercocarpus ledifolius Nutt.) in the Egan and Schell Mountains near Ely, NV. The equations predict cubic foot volume of wood and bark for variable minimum branch diameters. Wood density factors are given to convert volume predictions to pounds of fiber biomass. The reliability of...

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...

Gaussian model for emission rate measurement of heated plumes using hyperspectral data

NASA Astrophysics Data System (ADS)

Grauer, Samuel J.; Conrad, Bradley M.; Miguel, Rodrigo B.; Daun, Kyle J.

2018-02-01

This paper presents a novel model for measuring the emission rate of a heated gas plume using hyperspectral data from an FTIR imaging spectrometer. The radiative transfer equation (RTE) is used to relate the spectral intensity of a pixel to presumed Gaussian distributions of volume fraction and temperature within the plume, along a line-of-sight that corresponds to the pixel, whereas previous techniques exclusively presume uniform distributions for these parameters. Estimates of volume fraction and temperature are converted to a column density by integrating the local molecular density along each path. Image correlation velocimetry is then employed on raw spectral intensity images to estimate the volume-weighted normal velocity at each pixel. Finally, integrating the product of velocity and column density along a control surface yields an estimate of the instantaneous emission rate. For validation, emission rate estimates were derived from synthetic hyperspectral images of a heated methane plume, generated using data from a large-eddy simulation. Calculating the RTE with Gaussian distributions of volume fraction and temperature, instead of uniform distributions, improved the accuracy of column density measurement by 14%. Moreover, the mean methane emission rate measured using our approach was within 4% of the ground truth. These results support the use of Gaussian distributions of thermodynamic properties in calculation of the RTE for optical gas diagnostics.

Multilayer integral method for simulation of eddy currents in thin volumes of arbitrary geometry produced by MRI gradient coils.

PubMed

Sanchez Lopez, Hector; Freschi, Fabio; Trakic, Adnan; Smith, Elliot; Herbert, Jeremy; Fuentes, Miguel; Wilson, Stephen; Liu, Limei; Repetto, Maurizio; Crozier, Stuart

2014-05-01

This article aims to present a fast, efficient and accurate multi-layer integral method (MIM) for the evaluation of complex spatiotemporal eddy currents in nonmagnetic and thin volumes of irregular geometries induced by arbitrary arrangements of gradient coils. The volume of interest is divided into a number of layers, wherein the thickness of each layer is assumed to be smaller than the skin depth and where one of the linear dimensions is much smaller than the remaining two dimensions. The diffusion equation of the current density is solved both in time-harmonic and transient domain. The experimentally measured magnetic fields produced by the coil and the induced eddy currents as well as the corresponding time-decay constants were in close agreement with the results produced by the MIM. Relevant parameters such as power loss and force induced by the eddy currents in a split cryostat were simulated using the MIM. The proposed method is capable of accurately simulating the current diffusion process inside thin volumes, such as the magnet cryostat. The method permits the priori-calculation of optimal pre-emphasis parameters. The MIM enables unified designs of gradient coil-magnet structures for an optimal mitigation of deleterious eddy current effects. Copyright © 2013 Wiley Periodicals, Inc.

Programmable calculator programs to solve softwood volume and value equations.

Treesearch

Janet K. Ayer Sachet

1982-01-01

This paper presents product value and product volume equations as programs for handheld calculators. These tree equations are for inland Douglas-fir, young-growth Douglas-fir, western white pine, ponderosa pine, and western larch. Operating instructions and an example are included.

40 CFR 60.393 - Performance test and compliance provisions.

Code of Federal Regulations, 2011 CFR

2011-07-01

... volume of applied solids emitted after the control device, by the following equation: N=G[1-FE] (A... month by the following equation: EC16NO91.031 (v) If the volume weighted average mass of VOC per volume...

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.

Volume tables for important second-growth northern hardwood forests in northeastern Wisconsin

Treesearch

Gayne G. Erdmann; Thomas R. Crow; Robert R. Oberg

1982-01-01

Cubic-foot volume equations are presented for sugar maple, basswood, yellow birch, and white ash. Conversion factors for board-foot and cordwood volumes are also provided. The equations are useful for even-aged, second-growth hardwoods in northeastern Wisconsin.

Cubic-foot tree volume equations and tables for western juniper.

Treesearch

Judith M. Chittester; Colin D. MacLean

1984-01-01

This note presents cubic-foot volume equations and tables for western juniper (Juniperus occidentalis Hook. ). Total cubicfoot volume (ground to tip, excluding all branches (CVTS)) is expressed as a function of diameter at breast height (DBH) and total height. Utilizable cubic-foot volume (top of 12-inch stump to a 4-inch top, excluding all...

A finite-volume module for all-scale Earth-system modelling at ECMWF

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Malardel, Sylvie; Smolarkiewicz, Piotr

2017-04-01

We highlight recent advancements in the development of the finite-volume module (FVM) (Smolarkiewicz et al., 2016) for the IFS at ECMWF. FVM represents an alternative dynamical core that complements the operational spectral dynamical core of the IFS with new capabilities. Most notably, these include a compact-stencil finite-volume discretisation, flexible meshes, conservative non-oscillatory transport and all-scale governing equations. As a default, FVM solves the compressible Euler equations in a geospherical framework (Szmelter and Smolarkiewicz, 2010). The formulation incorporates a generalised terrain-following vertical coordinate. A hybrid computational mesh, fully unstructured in the horizontal and structured in the vertical, enables efficient global atmospheric modelling. Moreover, a centred two-time-level semi-implicit integration scheme is employed with 3D implicit treatment of acoustic, buoyant, and rotational modes. The associated 3D elliptic Helmholtz problem is solved using a preconditioned Generalised Conjugate Residual approach. The solution procedure employs the non-oscillatory finite-volume MPDATA advection scheme that is bespoke for the compressible dynamics on the hybrid mesh (Kühnlein and Smolarkiewicz, 2017). The recent progress of FVM is illustrated with results of benchmark simulations of intermediate complexity, and comparison to the operational spectral dynamical core of the IFS. C. Kühnlein, P.K. Smolarkiewicz: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics, J. Comput. Phys. (2017), in press. P.K. Smolarkiewicz, W. Deconinck, M. Hamrud, C. Kühnlein, G. Mozdzynski, J. Szmelter, N.P. Wedi: A finite-volume module for simulating global all-scale atmospheric flows, J. Comput. Phys. 314 (2016) 287-304. J. Szmelter, P.K. Smolarkiewicz: An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys. 229 (2010) 4980-4995.

Comparison of cell centered and cell vertex scheme in the calculation of high speed compressible flows

NASA Astrophysics Data System (ADS)

Rahman, Syazila; Yusoff, Mohd. Zamri; Hasini, Hasril

2012-06-01

This paper describes the comparison between the cell centered scheme and cell vertex scheme in the calculation of high speed compressible flow properties. The calculation is carried out using Computational Fluid Dynamic (CFD) in which the mass, momentum and energy equations are solved simultaneously over the flow domain. The geometry under investigation consists of a Binnie and Green convergent-divergent nozzle and structured mesh scheme is implemented throughout the flow domain. The finite volume CFD solver employs second-order accurate central differencing scheme for spatial discretization. In addition, the second-order accurate cell-vertex finite volume spatial discretization is also introduced in this case for comparison. The multi-stage Runge-Kutta time integration is implemented for solving a set of non-linear governing equations with variables stored at the vertices. Artificial dissipations used second and fourth order terms with pressure switch to detect changes in pressure gradient. This is important to control the solution stability and capture shock discontinuity. The result is compared with experimental measurement and good agreement is obtained for both cases.

Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field

NASA Astrophysics Data System (ADS)

Ashorynejad, H. R.; Sheikholeslami, M.; Pop, I.; Ganji, D. D.

2013-03-01

In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge-Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al2O3) and titanium oxide (TiO2) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.

Material point method modeling in oil and gas reservoirs

DOEpatents

Vanderheyden, William Brian; Zhang, Duan

2016-06-28

A computer system and method of simulating the behavior of an oil and gas reservoir including changes in the margins of frangible solids. A system of equations including state equations such as momentum, and conservation laws such as mass conservation and volume fraction continuity, are defined and discretized for at least two phases in a modeled volume, one of which corresponds to frangible material. A material point model technique for numerically solving the system of discretized equations, to derive fluid flow at each of a plurality of mesh nodes in the modeled volume, and the velocity of at each of a plurality of particles representing the frangible material in the modeled volume. A time-splitting technique improves the computational efficiency of the simulation while maintaining accuracy on the deformation scale. The method can be applied to derive accurate upscaled model equations for larger volume scale simulations.

Perturbation Solutions for Variable Energy Blast Waves.

DTIC Science & Technology

1976-08-01

SUPPLEMENTARY NOTES The findings in this report are not to be construed as an official Department of the Army position, unless so designated by other...over that of the same volume of undisturbed gas is Converting to non-dimensional form, using Equation (2.12) and letting a prime designate D/3m... designating the integral J after Sakurai1 this becomes Ea J . — - b p0R a+l y (2.20) If the total energy behind the shock varies as a

Characterizing functional lung heterogeneity in COPD using reference equations for CT scan-measured lobar volumes.

PubMed

Come, Carolyn E; Diaz, Alejandro A; Curran-Everett, Douglas; Muralidhar, Nivedita; Hersh, Craig P; Zach, Jordan A; Schroeder, Joyce; Lynch, David A; Celli, Bartolome; Washko, George R

2013-06-01

CT scanning is increasingly used to characterize COPD. Although it is possible to obtain CT scan-measured lung lobe volumes, normal ranges remain unknown. Using COPDGene data, we developed reference equations for lobar volumes at maximal inflation (total lung capacity [TLC]) and relaxed exhalation (approximating functional residual capacity [FRC]). Linear regression was used to develop race-specific (non-Hispanic white [NHW], African American) reference equations for lobar volumes. Covariates included height and sex. Models were developed in a derivation cohort of 469 subjects with normal pulmonary function and validated in 546 similar subjects. These cohorts were combined to produce final prediction equations, which were applied to 2,191 subjects with old GOLD (Global Initiative for Chronic Obstructive Lung Disease) stage II to IV COPD. In the derivation cohort, women had smaller lobar volumes than men. Height positively correlated with lobar volumes. Adjusting for height, NHWs had larger total lung and lobar volumes at TLC than African Americans; at FRC, NHWs only had larger lower lobes. Age and weight had no effect on lobar volumes at TLC but had small effects at FRC. In subjects with COPD at TLC, upper lobes exceeded 100% of predicted values in GOLD II disease; lower lobes were only inflated to this degree in subjects with GOLD IV disease. At FRC, gas trapping was severe irrespective of disease severity and appeared uniform across the lobes. Reference equations for lobar volumes may be useful in assessing regional lung dysfunction and how it changes in response to pharmacologic therapies and surgical or endoscopic lung volume reduction.

On the Geometry of the Hamilton-Jacobi Equation and Generating Functions

NASA Astrophysics Data System (ADS)

Ferraro, Sebastián; de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David; Vaquero, Miguel

2017-10-01

In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results about symplectic groupoids, in particular cotangent groupoids, as a keystone for the construction of our framework. Our methodology follows the ambitious program proposed by Weinstein (In Mechanics day (Waterloo, ON, 1992), volume 7 of fields institute communications, American Mathematical Society, Providence, 1996) in order to develop geometric formulations of the dynamical behavior of Lagrangian and Hamiltonian systems on Lie algebroids and Lie groupoids. This procedure allows us to take symmetries into account, and, as a by-product, we recover results from Channell and Scovel (Phys D 50(1):80-88, 1991), Ge (Indiana Univ. Math. J. 39(3):859-876, 1990), Ge and Marsden (Phys Lett A 133(3):134-139, 1988), but even in these situations our approach is new. A theory of generating functions for the Poisson structures considered here is also developed following the same pattern, solving a longstanding problem of the area: how to obtain a generating function for the identity transformation and the nearby Poisson automorphisms of Poisson manifolds. A direct application of our results gives the construction of a family of Poisson integrators, that is, integrators that conserve the underlying Poisson geometry. These integrators are implemented in the paper in benchmark problems. Some conclusions, current and future directions of research are shown at the end of the paper.

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

Two Optical Atmospheric Remote Sensing Techniques and AN Associated Analytic Solution to a Class of Integral Equations

NASA Astrophysics Data System (ADS)

Manning, Robert Michael

This work concerns itself with the analysis of two optical remote sensing methods to be used to obtain parameters of the turbulent atmosphere pertinent to stochastic electromagnetic wave propagation studies, and the well -posed solution to a class of integral equations that are central to the development of these remote sensing methods. A remote sensing technique is theoretically developed whereby the temporal frequency spectrum of the scintillations of a stellar source or a point source within the atmosphere, observed through a variable radius aperture, is related to the space-time spectrum of atmospheric scintillation. The key to this spectral remote sensing method is the spatial filtering performed by a finite aperture. The entire method is developed without resorting to a priori information such as results from stochastic wave propagation theory. Once the space-time spectrum of the scintillations is obtained, an application of known results of atmospheric wave propagation theory and simple geometric considerations are shown to yield such important information such as the spectrum of atmospheric turbulence, the cross-wind velocity, and the path profile of the atmospheric refractive index structure parameter. A method is also developed to independently verify the Taylor frozen flow hypothesis. The success of the spectral remote sensing method relies on the solution to a Fredholm integral equation of the first kind. An entire class of such equations, that are peculiar to inverse diffraction problems, is studied and a well-posed solution (in the sense of Hadamard) is obtained and probed. Conditions of applicability are derived and shown not to limit the useful operating range of the spectral remote sensing method. The general integral equation solution obtained is then applied to another remote sensing problem having to do with the characterization of the particle size distribution to atmospheric aerosols and hydrometeors. By measuring the diffraction pattern in the focal plane of a lens created by the passage of a laser beam through a distribution of particles, it is shown that the particle-size distribution of the particles can be obtained. An intermediate result of the analysis also gives the total volume concentration of the particles.

Numerical computation of viscous flow about unconventional airfoil shapes

NASA Technical Reports Server (NTRS)

Ahmed, S.; Tannehill, J. C.

1990-01-01

A new two-dimensional computer code was developed to analyze the viscous flow around unconventional airfoils at various Mach numbers and angles of attack. The Navier-Stokes equations are solved using an implicit, upwind, finite-volume scheme. Both laminar and turbulent flows can be computed. A new nonequilibrium turbulence closure model was developed for computing turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present code was evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the present code in conjunction with the new nonequilibrium turbulence model gives excellent results.

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2002-01-01

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

Converting wood volume to biomass for pinyon and juniper. Forest Service research note

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

Chojnacky, D.C.; Moisen, G.G.

1993-03-01

A technique was developed to convert pinyon-juniper volume equation predictions to weights. The method uses specific gravity and biomass conversion equations to obtain foliage weight and total wood weight of all stems, branches, and bark. Specific gravity data are given for several Arizona pinyon-juniper species. Biomass conversion equations are constructed from pinyon-juniper data collected in Nevada. Results provide an interim means of estimating pinyon-juniper aboveground biomass from available volume inventory data.

HYDRA-II: A hydrothermal analysis computer code: Volume 2, User's manual

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

McCann, R.A.; Lowery, P.S.; Lessor, D.L.

1987-09-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite-difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equations formore » conservation of momentum incorporate directional porosities and permeabilities that are available to model solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated methods are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume 1 - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. This volume, Volume 2 - User's Manual, contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a sample problem. The final volume, Volume 3 - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. 6 refs.« less

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

Dimension reduction method for SPH equations

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

Tartakovsky, Alexandre M.; Scheibe, Timothy D.

2011-08-26

Smoothed Particle Hydrodynamics model of a complex multiscale processe often results in a system of ODEs with an enormous number of unknowns. Furthermore, a time integration of the SPH equations usually requires time steps that are smaller than the observation time by many orders of magnitude. A direct solution of these ODEs can be extremely expensive. Here we propose a novel dimension reduction method that gives an approximate solution of the SPH ODEs and provides an accurate prediction of the average behavior of the modeled system. The method consists of two main elements. First, effective equationss for evolution of averagemore » variables (e.g. average velocity, concentration and mass of a mineral precipitate) are obtained by averaging the SPH ODEs over the entire computational domain. These effective ODEs contain non-local terms in the form of volume integrals of functions of the SPH variables. Second, a computational closure is used to close the system of the effective equations. The computational closure is achieved via short bursts of the SPH model. The dimension reduction model is used to simulate flow and transport with mixing controlled reactions and mineral precipitation. An SPH model is used model transport at the porescale. Good agreement between direct solutions of the SPH equations and solutions obtained with the dimension reduction method for different boundary conditions confirms the accuracy and computational efficiency of the dimension reduction model. The method significantly accelerates SPH simulations, while providing accurate approximation of the solution and accurate prediction of the average behavior of the system.« less

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

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

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

Study of electromagnetic wave scattering from an inhomogeneous plasma layer using Green's function volume integral equation method

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

Soltanmoradi, Elmira; Shokri, Babak, E-mail: b-shokri@sbu.ac.ir; Laser and Plasma Research Institute, Shahid Beheshti University, G. C., Evin, Tehran 19839-63113

Gigahertz electromagnetic wave scattering from an inhomogeneous collisional plasma layer with bell-like and Epstein electron density distributions is studied by the Green's function volume integral equation method to find the reflectance, transmittance, and absorbance coefficients of this inhomogeneous plasma. Also, the effects of the frequency of the electromagnetic wave, plasma parameters, such as collision frequency, electron density, and plasma thickness, and the effects of the profile of the electron density on the electromagnetic wave scattering from this plasma slab are investigated. According to the results, when the electron density, collision frequency, and plasma thickness are increased, collisional absorbance is enhanced,more » and as a result, the absorbance bandwidth of plasma is broadened. Moreover, this broadening is more evident for plasma with bell-like electron density profile. Also, the bandwidth of the frequency and the range of pressure in which plasma behaves as a good reflector are determined in this article. According to the results, the bandwidth of the frequency is decreased for thicker plasma with bell-like profile, while it does not vary for a different plasma thickness with Epstein profile. Moreover, the range of the pressure is decreased for bell-like profile in comparison with Epstein profile. Furthermore, due to the sharp inhomogeneity of the Epstein profile, the coefficients of plasma that are uniform for plasma with bell-like profile are changed for plasma with Epstein profile, and some perturbations are seen.« less

A Comparison of Regional and SiteSpecific Volume Estimation Equations

Treesearch

Joe P. McClure; Jana Anderson; Hans T. Schreuder

1987-01-01

Regression equations for volume by region and site class were examined for lobiolly pine. The regressions for the Coastal Plain and Piedmont regions had significantly different slopes. The results shared important practical differences in percentage of confidence intervals containing the true total volume and in percentage of estimates within a specific proportion of...

Thermal radiation from large bolides and impact plumes

NASA Astrophysics Data System (ADS)

Svetsov, V.; Shuvalov, V.

2017-09-01

Numerical simulations of the impacts of asteroids and comets from 20 m to 3 km in diameter have been carried out and thermal radiation fluxes on the ground and luminous efficiencies of the impacts have been calculated. It was assumed that the cosmic objects have no strength, deform, fragment, and vaporize in the atmosphere. After the impact on the ground, formation of craters and plumes was simulated taking into account internal friction of destroyed rocks and a wake formed in the atmosphere. The equations of radiative transfer, added to the equations of gas dynamics, were used in the approximation of radiative heat diffusion or, if the Rosseland optical depth of a radiating volume of gas and vapor was less than unity, in the approximation of volume emission. Radiation fluxes on the Earth's surface were calculated by integrating the equation of radiative transfer along rays passing through a luminous area. Direct thermal radiation from fireballs and impact plumes produced by asteroids and comets larger than 50 m in diameter is dangerous for people, animals, plants, economic objects. Forest fires can be ignited on the ground within a radius of roughly 1000 times the body's diameter (for diameters of the order or smaller than 1 km), 50-m-diameter bodies can ignite forest fires within a radius of up to 40 km and 3-km asteroids - within 1700 km.

Nonlinear mesomechanics of composites with periodic microstructure

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Jordan, Eric H.; Freed, Alan D.

1989-01-01

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

Development of advanced Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan

1994-01-01

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

Identification of Spurious Signals from Permeable Ffowcs Williams and Hawkings Surfaces

NASA Technical Reports Server (NTRS)

Lopes, Leonard V.; Boyd, David D., Jr.; Nark, Douglas M.; Wiedemann, Karl E.

2017-01-01

Integral forms of the permeable surface formulation of the Ffowcs Williams and Hawkings (FW-H) equation often require an input in the form of a near field Computational Fluid Dynamics (CFD) solution to predict noise in the near or far field from various types of geometries. The FW-H equation involves three source terms; two surface terms (monopole and dipole) and a volume term (quadrupole). Many solutions to the FW-H equation, such as several of Farassat's formulations, neglect the quadrupole term. Neglecting the quadrupole term in permeable surface formulations leads to inaccuracies called spurious signals. This paper explores the concept of spurious signals, explains how they are generated by specifying the acoustic and hydrodynamic surface properties individually, and provides methods to determine their presence, regardless of whether a correction algorithm is employed. A potential approach based on the equivalent sources method (ESM) and the sensitivity of Formulation 1A (Formulation S1A) is also discussed for the removal of spurious signals.

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Reference Equations for Static Lung Volumes and TLCO from a Population Sample in Northern Greece.

PubMed

Michailopoulos, Pavlos; Kontakiotis, Theodoros; Spyratos, Dionisios; Argyropoulou-Pataka, Paraskevi; Sichletidis, Lazaros

2015-02-14

Background: The most commonly used reference equations for the measurement of static lung volumes/capacities and transfer factor of the lung for CO (TL CO ) are based on studies around 30-40 years old with significant limitations. Objectives: Our aim was to (1) develop reference equations for static lung volumes and TL CO using the current American Thoracic Society/European Respiratory Society guidelines, and (2) compare the equations derived with those most commonly used. Methods: Healthy Caucasian subjects (234 males and 233 females) aged 18-91 years were recruited. All of them were healthy never smokers with a normal chest X-ray. Static lung volumes and TL CO were measured with a single-breath technique according to the latest guidelines. Results: Curvilinear regression prediction equations derived from the present study were compared with those that are most commonly used. Our reference equations in accordance with the latest studies show lower values for all static lung volume parameters and TL CO as well as a different way of deviation of those parameters (i.e. declining with age total lung capacity, TL CO age decline in both sex and functional residual capacity age rise in males). Conclusions: We suggest that old reference values of static lung volumes and TL CO should be updated, and our perception of deviation of some spirometric parameters should be revised. Our new reference curvilinear equations derived according to the latest guidelines could contribute to the updating by respiratory societies of old existing reference values and result in a better estimation of the lung function of contemporary populations with similar Caucasian characteristics. © 2015 S. Karger AG, Basel.

Toroidal regularization of the guiding center Lagrangian

DOE PAGES

Burby, J. W.; Ellison, C. L.

2017-11-22

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.

1984-01-01

This paper describes DIGTEM (digital turbofan engine model), a computer program that simulates two spool, two stream (turbofan) engines. DIGTEM was developed to support the development of a real time multiprocessor based engine simulator being designed at the Lewis Research Center. The turbofan engine model in DIGTEM contains steady state performance maps for all the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. DIGTEM features an implicit integration scheme for integrating stiff systems and trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off design points and iterates to a balanced engine condition. Transients are generated by defining the engine inputs as functions of time in a user written subroutine (TMRSP). Closed loop controls can also be simulated. DIGTEM is generalized in the aerothermodynamic treatment of components. This feature, along with DIGTEM's trimming at a design point, make it a very useful tool for developing a model of a specific turbofan engine.

A generalized computer code for developing dynamic gas turbine engine models (DIGTEM)

NASA Technical Reports Server (NTRS)

Daniele, C. J.

1983-01-01

This paper describes DIGTEM (digital turbofan engine model), a computer program that simulates two spool, two stream (turbofan) engines. DIGTEM was developed to support the development of a real time multiprocessor based engine simulator being designed at the Lewis Research Center. The turbofan engine model in DIGTEM contains steady state performance maps for all the components and has control volumes where continuity and energy balances are maintained. Rotor dynamics and duct momentum dynamics are also included. DIGTEM features an implicit integration scheme for integrating stiff systems and trims the model equations to match a prescribed design point by calculating correction coefficients that balance out the dynamic equations. It uses the same coefficients at off design points and iterates to a balanced engine condition. Transients are generated by defining the engine inputs as functions of time in a user written subroutine (TMRSP). Closed loop controls can also be simulated. DIGTEM is generalized in the aerothermodynamic treatment of components. This feature, along with DIGTEM's trimming at a design point, make it a very useful tool for developing a model of a specific turbofan engine.

Toroidal regularization of the guiding center Lagrangian

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

Burby, J. W.; Ellison, C. L.

In the Lagrangian theory of guiding center motion, an effective magnetic field B* = B+ (m/e)v ∥∇ x b appears prominently in the equations of motion. Because the parallel component of this field can vanish, there is a range of parallel velocities where the Lagrangian guiding center equations of motion are either ill-defined or very badly behaved. Moreover, the velocity dependence of B* greatly complicates the identification of canonical variables and therefore the formulation of symplectic integrators for guiding center dynamics. Here, this letter introduces a simple coordinate transformation that alleviates both these problems simultaneously. In the new coordinates, themore » Liouville volume element is equal to the toroidal contravariant component of the magnetic field. Consequently, the large-velocity singularity is completely eliminated. Moreover, passing from the new coordinate system to canonical coordinates is extremely simple, even if the magnetic field is devoid of flux surfaces. We demonstrate the utility of this approach in regularizing the guiding center Lagrangian by presenting a new and stable one-step variational integrator for guiding centers moving in arbitrary time-dependent electromagnetic fields.« less

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

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

1979-01-01

Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

NASA Technical Reports Server (NTRS)

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

1979-01-01

Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

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

PubMed

Kurganov, A

2007-05-25

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

Estimating volume, biomass, and potential emissions of hand-piled fuels

Treesearch

Clinton S. Wright; Cameron S. Balog; Jeffrey W. Kelly

2009-01-01

Dimensions, volume, and biomass were measured for 121 hand-constructed piles composed primarily of coniferous (n = 63) and shrub/hardwood (n = 58) material at sites in Washington and California. Equations using pile dimensions, shape, and type allow users to accurately estimate the biomass of hand piles. Equations for estimating true pile volume from simple geometric...

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

NASA Astrophysics Data System (ADS)

Polimeridis, Athanasios G.; Reid, M. T. H.; Jin, Weiliang; Johnson, Steven G.; White, Jacob K.; Rodriguez, Alejandro W.

2015-10-01

We describe a fluctuating volume-current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, Phys. Rev. B 88, 054305 (2013), 10.1103/PhysRevB.88.054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike previous scattering formulations based on field and/or surface unknowns, our work exploits powerful techniques from the volume-integral equation (VIE) method, in which electromagnetic scattering is described in terms of volumetric, current unknowns throughout the bodies. The resulting trace formulas (boxed equations) involve products of well-studied VIE matrices and describe power and momentum transfer between objects with spatially varying material properties and fluctuation characteristics. We demonstrate that thanks to the low-rank properties of the associated matrices, these formulas are susceptible to fast-trace computations based on iterative methods, making practical calculations tractable. We apply our techniques to study thermal radiation, heat transfer, and fluorescence in complicated geometries, checking our method against established techniques best suited for homogeneous bodies as well as applying it to obtain predictions of radiation from complex bodies with spatially varying permittivities and/or temperature profiles.

CrystalMoM: a tool for modeling the evolution of Crystals Size Distributions in magmas with the Method of Moments

NASA Astrophysics Data System (ADS)

Colucci, Simone; de'Michieli Vitturi, Mattia; Landi, Patrizia

2016-04-01

It is well known that nucleation and growth of crystals play a fundamental role in controlling magma ascent dynamics and eruptive behavior. Size- and shape-distribution of crystal populations can affect mixture viscosity, causing, potentially, transitions between effusive and explosive eruptions. Furthermore, volcanic samples are usually characterized in terms of Crystal Size Distribution (CSD), which provide a valuable insight into the physical processes that led to the observed distributions. For example, a large average size can be representative of a slow magma ascent, and a bimodal CSD may indicate two events of nucleation, determined by two degassing events within the conduit. The Method of Moments (MoM), well established in the field of chemical engineering, represents a mesoscopic modeling approach that rigorously tracks the polydispersity by considering the evolution in time and space of integral parameters characterizing the distribution, the moments, by solving their transport differential-integral equations. One important advantage of this approach is that the moments of the distribution correspond to quantities that have meaningful physical interpretations and are directly measurable in natural eruptive products, as well as in experimental samples. For example, when the CSD is defined by the number of particles of size D per unit volume of the magmatic mixture, the zeroth moment gives the total number of crystals, the third moment gives the crystal volume fraction in the magmatic mixture and ratios between successive moments provide different ways to evaluate average crystal length. Tracking these quantities, instead of volume fraction only, will allow using, for example, more accurate viscosity models in numerical code for magma ascent. Here we adopted, for the first time, a quadrature based method of moments to track the temporal evolution of CSD in a magmatic mixture and we verified and calibrated the model again experimental data. We also show how the equations and the tool developed can be integrated in a magma ascent numerical model, with application to eruptive events occurred at Stromboli volcano (Italy).

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions.

PubMed

Latella, Ivan; Pérez-Madrid, Agustín

2013-10-01

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

THERMOS. 30-Group ENDF/B Scattered Kernels

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

McCrosson, F.J.; Finch, D.R.

1973-12-01

These data are 30-group THERMOS thermal scattering kernels for P0 to P5 Legendre orders for every temperature of every material from s(alpha,beta) data stored in the ENDF/B library. These scattering kernels were generated using the FLANGE2 computer code. To test the kernels, the integral properties of each set of kernels were determined by a precision integration of the diffusion length equation and compared to experimental measurements of these properties. In general, the agreement was very good. Details of the methods used and results obtained are contained in the reference. The scattering kernels are organized into a two volume magnetic tapemore » library from which they may be retrieved easily for use in any 30-group THERMOS library.« less

Body composition estimation from selected slices: equations computed from a new semi-automatic thresholding method developed on whole-body CT scans

PubMed Central

Villa, Chiara; Brůžek, Jaroslav

2017-01-01

Background Estimating volumes and masses of total body components is important for the study and treatment monitoring of nutrition and nutrition-related disorders, cancer, joint replacement, energy-expenditure and exercise physiology. While several equations have been offered for estimating total body components from MRI slices, no reliable and tested method exists for CT scans. For the first time, body composition data was derived from 41 high-resolution whole-body CT scans. From these data, we defined equations for estimating volumes and masses of total body AT and LT from corresponding tissue areas measured in selected CT scan slices. Methods We present a new semi-automatic approach to defining the density cutoff between adipose tissue (AT) and lean tissue (LT) in such material. An intra-class correlation coefficient (ICC) was used to validate the method. The equations for estimating the whole-body composition volume and mass from areas measured in selected slices were modeled with ordinary least squares (OLS) linear regressions and support vector machine regression (SVMR). Results and Discussion The best predictive equation for total body AT volume was based on the AT area of a single slice located between the 4th and 5th lumbar vertebrae (L4-L5) and produced lower prediction errors (|PE| = 1.86 liters, %PE = 8.77) than previous equations also based on CT scans. The LT area of the mid-thigh provided the lowest prediction errors (|PE| = 2.52 liters, %PE = 7.08) for estimating whole-body LT volume. We also present equations to predict total body AT and LT masses from a slice located at L4-L5 that resulted in reduced error compared with the previously published equations based on CT scans. The multislice SVMR predictor gave the theoretical upper limit for prediction precision of volumes and cross-validated the results. PMID:28533960

Body composition estimation from selected slices: equations computed from a new semi-automatic thresholding method developed on whole-body CT scans.

PubMed

Lacoste Jeanson, Alizé; Dupej, Ján; Villa, Chiara; Brůžek, Jaroslav

2017-01-01

Estimating volumes and masses of total body components is important for the study and treatment monitoring of nutrition and nutrition-related disorders, cancer, joint replacement, energy-expenditure and exercise physiology. While several equations have been offered for estimating total body components from MRI slices, no reliable and tested method exists for CT scans. For the first time, body composition data was derived from 41 high-resolution whole-body CT scans. From these data, we defined equations for estimating volumes and masses of total body AT and LT from corresponding tissue areas measured in selected CT scan slices. We present a new semi-automatic approach to defining the density cutoff between adipose tissue (AT) and lean tissue (LT) in such material. An intra-class correlation coefficient (ICC) was used to validate the method. The equations for estimating the whole-body composition volume and mass from areas measured in selected slices were modeled with ordinary least squares (OLS) linear regressions and support vector machine regression (SVMR). The best predictive equation for total body AT volume was based on the AT area of a single slice located between the 4th and 5th lumbar vertebrae (L4-L5) and produced lower prediction errors (|PE| = 1.86 liters, %PE = 8.77) than previous equations also based on CT scans. The LT area of the mid-thigh provided the lowest prediction errors (|PE| = 2.52 liters, %PE = 7.08) for estimating whole-body LT volume. We also present equations to predict total body AT and LT masses from a slice located at L4-L5 that resulted in reduced error compared with the previously published equations based on CT scans. The multislice SVMR predictor gave the theoretical upper limit for prediction precision of volumes and cross-validated the results.

Analysis of historical and recent PBX 9404 cylinder tests using FLAG

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

Wooten, Hasani Omar; Whitley, Von Howard

2017-01-31

Cylinder test experiments using aged PBX-9404 were recently conducted. When compared to similar historical tests using the same materials, but different diagnostics, the data indicate that PBX 9404 imparts less energy to surrounding copper. The purpose of this work was to simulate historical and recent cylinder tests using the Lagrangian hydrodynamics code, FLAG, and identify any differences in the energetic behavior of the material. Nine experiments spanning approximately 4.5 decades were simulated, and radial wall expansions and velocities were compared. Equation-of-state parameters were adjusted to obtain reasonable matches with experimental data. Pressure-volume isentropes were integrated, and resultant energies at specificmore » volume expansions were compared. FLAG simulations matched to experimental data indicate energetic changes of approximately -0.57% to -0.78% per decade.« less

FastMag: Fast micromagnetic simulator for complex magnetic structures (invited)

NASA Astrophysics Data System (ADS)

Chang, R.; Li, S.; Lubarda, M. V.; Livshitz, B.; Lomakin, V.

2011-04-01

A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle multiscale problems with a high computational efficiency. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel graphics processing unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus, discretized superposition integrals are computed using a nonuniform grid interpolation method, which evaluates the field from N sources at N collocated observers in O(N) operations. This approach allows handling objects of arbitrary shape, allows easily calculating of the field outside the magnetized domains, does not require solving a linear system of equations, and requires little memory. FastMag is implemented on GPUs with ?> GPU-central processing unit speed-ups of 2 orders of magnitude. Simulations are shown of a large array of magnetic dots and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.

The sudden coalescene model of the boiling crisis

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

Carrica, P.M.; Clausse, A.

1995-09-01

A local two-phase flow integral model of nucleate boiling and crisis is presented. The model is based on average balances on a control volume, yielding to a set of three nonlinear differential equations for the local void fraction, bubble number density and velocity. Boiling crisis as critical heat flux is interpreted as a dynamic transition caused by the coalescence of bubbles near the heater. The theoretical dynamic model is compared with experimental results obtained for linear power ramps in a horizontal plate heater in R-113, showing an excellent qualitative agreement.

Two-dimensional thermal modeling of power monolithic microwave integrated circuits (MMIC's)

NASA Technical Reports Server (NTRS)

Fan, Mark S.; Christou, Aris; Pecht, Michael G.

1992-01-01

Numerical simulations of the two-dimensional temperature distributions for a typical GaAs MMIC circuit are conducted, aiming at understanding the heat conduction process of the circuit chip and providing temperature information for device reliability analysis. The method used is to solve the two-dimensional heat conduction equation with a control-volume-based finite difference scheme. In particular, the effects of the power dissipation and the ambient temperature are examined, and the criterion for the worst operating environment is discussed in terms of the allowed highest device junction temperature.

Drag Minimization for Wings and Bodies in Supersonic Flow

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Fuller, Franklyn B

1958-01-01

The minimization of inviscid fluid drag is studied for aerodynamic shapes satisfying the conditions of linearized theory, and subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining two-dimensional potential flows satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. A general method for determining integral relations between perturbation velocity components is developed. This analysis is not restricted in application to optimum cases; it may be used for any supersonic wing problem.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method

NASA Astrophysics Data System (ADS)

Choudhury, A. Ghose; Guha, Partha; Khanra, Barun

2009-10-01

The Darboux integrability method is particularly useful to determine first integrals of nonplanar autonomous systems of ordinary differential equations, whose associated vector fields are polynomials. In particular, we obtain first integrals for a variant of the generalized Raychaudhuri equation, which has appeared in string inspired modern cosmology.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

Taper and volume equations for selected Appalachian hardwood species

Treesearch

A. Jeff Martin

1981-01-01

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

Complex compatible taper and volume estimation systems for red and loblolly pine

Treesearch

John C. Byrne; David D. Reed

1986-01-01

Five equation systems are described which can be used to estimate upper stem diameter, total individual tree cubic-foot volume, and merchantable cubic-foot volumes to any merchantability imit (expressed in terms of diameter or height), both inside and outside bark. The equations provide consistent results since they are mathematically related and are fit using stem...

Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.

Method for Measuring the Volume-Scattering Function of Water

NASA Technical Reports Server (NTRS)

Agrawal, Yogesh C.

2009-01-01

The volume scattering function (VSF) of seawater affects visibility, remote sensing properties, in-water light propagation, lidar performance, and the like. Currently, it s possible to measure only small forward angles of VSF, or to use cumbersome, large, and non-autonomous systems. This innovation is a method of measuring the full range of VSF using a portable instrument. A single rapid-sensing photosensor is used to scan a green laser beam, which delivers the desired measurement. By using a single sensor, inter-calibration is avoided. A compact design is achieved by using drift-free detector electronics, fiber optics, and a new type of photomultiplier. This provides a high angular resolution of 1 or better, as well as the ability to focus in on a VSF region of particular interest. Currently, the total scattering of light is measured as a difference from the other two parts of the light budget equation. This innovation will allow the direct calculation of the total scattering of light by taking an integral of the VSF over all angles. This directly provides one of the three components of the light budget equation, allowing greater versatility in its calculation.

Verification of conventional equations of state for tantalum under quasi-isentropic compression

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

Binqiang, Luo; Guiji, Wang; Jianjun, Mo

2014-11-21

Shock Hugoniot data have been widely used to calibrate analytic equations of state (EOSs) of condensed matter at high pressures. However, the suitability of particular analytic EOSs under off-Hugoniot states has not been sufficiently verified using experimental data. We have conducted quasi-isentropic compression experiments (ICEs) of tantalum using the compact pulsed power generator CQ-4, and explored the relation of longitudinal stress versus volume of tantalum under quasi-isentropic compression using backward integration and characteristic inverse methods. By subtracting the deviatoric stress and additional pressure caused by irreversible plastic dissipation, the isentropic pressure can be extracted from the longitudinal stress. Several theoreticalmore » isentropes are deduced from analytic EOSs and compared with ICE results to validate the suitability of these analytic EOSs in isentropic compression states. The comparisons show that the Gruneisen EOS with Gruneisen Gamma proportional to volume is accurate, regardless whether the Hugoniot or isentrope is used as the reference line. The Vinet EOS yields better accuracy in isentropic compression states. Theoretical isentropes derived from Tillotson, PUFF, and Birch-Murnaghan EOSs well agree with the experimental isentrope in the range of 0–100 GPa, but deviate gradually with pressure increasing further.« less

Compatible taper and volume equations for young longleaf pine plantations in southwest Georgia

Treesearch

Lichun Jiang; John R. Brooks; Alexander Clark

2010-01-01

Inside and outside bark taper equations as well as compatible cubic foot volume equations were developed from felled tree data selected from young longleaf pine plantations that are part of an existing growth and yield study located in the Flint River drainage of southwest Georgia. A Max-Burkhart taper model was selected as the basic model form due to the accuracy...

Comprehensive analysis of heat transfer of gold-blood nanofluid (Sisko-model) with thermal radiation

NASA Astrophysics Data System (ADS)

Eid, Mohamed R.; Alsaedi, Ahmed; Muhammad, Taseer; Hayat, Tasawar

Characteristics of heat transfer of gold nanoparticles (Au-NPs) in flow past a power-law stretching surface are discussed. Sisko bio-nanofluid flow (with blood as a base fluid) in existence of non-linear thermal radiation is studied. The resulting equations system is abbreviated to model the suggested problem in non-linear PDEs. Along with initial and boundary-conditions, the equations are made non-dimensional and then resolved numerically utilizing 4th-5th order Runge-Kutta-Fehlberg (RKF45) technique with shooting integration procedure. Various flow quantities behaviors are examined for parametric consideration such as the Au-NPs volume fraction, the exponentially stretching and thermal radiation parameters. It is observed that radiation drives to shortage the thermal boundary-layer thickness and therefore resulted in better heat transfer at surface.

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

PubMed

Abbasi, Mahdi

2014-01-01

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

Quaternion regularization in celestial mechanics, astrodynamics, and trajectory motion control. III

NASA Astrophysics Data System (ADS)

Chelnokov, Yu. N.

2015-09-01

The present paper1 analyzes the basic problems arising in the solution of problems of the optimum control of spacecraft (SC) trajectory motion (including the Lyapunov instability of solutions of conjugate equations) using the principle of the maximum. The use of quaternion models of astrodynamics is shown to allow: (1) the elimination of singular points in the differential phase and conjugate equations and in their partial analytical solutions; (2) construction of the first integrals of the new quaternion; (3) a considerable decrease of the dimensions of systems of differential equations of boundary value optimization problems with their simultaneous simplification by using the new quaternion variables related with quaternion constants of motion by rotation transformations; (4) construction of general solutions of differential equations for phase and conjugate variables on the sections of SC passive motion in the simplest and most convenient form, which is important for the solution of optimum pulse SC transfers; (5) the extension of the possibilities of the analytical investigation of differential equations of boundary value problems with the purpose of identifying the basic laws of optimum control and motion of SC; (6) improvement of the computational stability of the solution of boundary value problems; (7) a decrease in the required volume of computation.

Geometry, Heat Equation and Path Integrals on the Poincaré Upper Half-Plane

NASA Astrophysics Data System (ADS)

Kubo, R.

1988-01-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincaré upper half-plane. The fundamental solution to the heat equation partial f/partial t = Delta_{H} f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrödinger equation is also valid for our case.

FLiT: a field line trace code for magnetic confinement devices

NASA Astrophysics Data System (ADS)

Innocente, P.; Lorenzini, R.; Terranova, D.; Zanca, P.

2017-04-01

This paper presents a field line tracing code (FLiT) developed to study particle and energy transport as well as other phenomena related to magnetic topology in reversed-field pinch (RFP) and tokamak experiments. The code computes magnetic field lines in toroidal geometry using curvilinear coordinates (r, ϑ, ϕ) and calculates the intersections of these field lines with specified planes. The code also computes the magnetic and thermal diffusivity due to stochastic magnetic field in the collisionless limit. Compared to Hamiltonian codes, there are no constraints on the magnetic field functional formulation, which allows the integration of whichever magnetic field is required. The code uses the magnetic field computed by solving the zeroth-order axisymmetric equilibrium and the Newcomb equation for the first-order helical perturbation matching the edge magnetic field measurements in toroidal geometry. Two algorithms are developed to integrate the field lines: one is a dedicated implementation of a first-order semi-implicit volume-preserving integration method, and the other is based on the Adams-Moulton predictor-corrector method. As expected, the volume-preserving algorithm is accurate in conserving divergence, but slow because the low integration order requires small amplitude steps. The second algorithm proves to be quite fast and it is able to integrate the field lines in many partially and fully stochastic configurations accurately. The code has already been used to study the core and edge magnetic topology of the RFX-mod device in both the reversed-field pinch and tokamak magnetic configurations.

New Mathematical Functions for Vacuum System Analysis

NASA Technical Reports Server (NTRS)

Woronowicz, Michael S.

2017-01-01

A new bivariate function has been found that provides solutions of integrals having the form u (sup minus eta) e (sup u) du which arise when developing predictions for the behavior of pressure within a rigid volume under high vacuum conditions in the presence of venting as well as sources characterized by power law transient decay over the range [0,1] for eta and for u greater than or equal to 0. A few properties of the new function are explored in this work. For instance the eta equals 1/2 case reproduces the Dawson function. In addition, a slight variation of the solution technique reproduces the exponential integral for eta equals 1. The technique used to generate these functions leads to an approach for solving a more general class of nonlinear ordinary differential equations, with the potential for identifying other new functions that solve other integrals.

A spectral geometric model for Compton single scatter in PET based on the single scatter simulation approximation

NASA Astrophysics Data System (ADS)

Kazantsev, I. G.; Olsen, U. L.; Poulsen, H. F.; Hansen, P. C.

2018-02-01

We investigate the idealized mathematical model of single scatter in PET for a detector system possessing excellent energy resolution. The model has the form of integral transforms estimating the distribution of photons undergoing a single Compton scattering with a certain angle. The total single scatter is interpreted as the volume integral over scatter points that constitute a rotation body with a football shape, while single scattering with a certain angle is evaluated as the surface integral over the boundary of the rotation body. The equations for total and sample single scatter calculations are derived using a single scatter simulation approximation. We show that the three-dimensional slice-by-slice filtered backprojection algorithm is applicable for scatter data inversion provided that the attenuation map is assumed to be constant. The results of the numerical experiments are presented.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

The use of numerical programs in research and academic institutions

NASA Astrophysics Data System (ADS)

Scupi, A. A.

2016-08-01

This paper is conceived on the idea that numerical programs using computer models of physical processes can be used both for scientific research and academic teaching to study different phenomena. Computational Fluid Dynamics (CFD) is used today on a large scale in research and academic institutions. CFD development is not limited to computer simulations of fluid flow phenomena. Analytical solutions for most fluid dynamics problems are already available for ideal or simplified situations for different situations. CFD is based on the Navier- Stokes (N-S) equations characterizing the flow of a single phase of any liquid. For multiphase flows the integrated N-S equations are complemented with equations of the Volume of Fluid Model (VOF) and with energy equations. Different turbulent models were used in the paper, each one of them with practical engineering applications: the flow around aerodynamic surfaces used as unconventional propulsion system, multiphase flows in a settling chamber and pneumatic transport systems, heat transfer in a heat exchanger etc. Some of them numerical results were validated by experimental results. Numerical programs are also used in academic institutions where certain aspects of various phenomena are presented to students (Bachelor, Master and PhD) for a better understanding of the phenomenon itself.

Validation of Volume and Taper Equations For Loblolly Shortleaf and Slash Pine

Treesearch

Allan E. Tiarks; V. Clark Baldwin

1999-01-01

Inside-bark diameter measurements at 6.64 intervals of 137 loblolly, 52 shortleaf, and 64 slash pines were used to calculate the actual volume and taper of each species for comparison with volumes and tapers predicted from published equations. The loblolly pine were cut in Texas (TX) and Louisiana (LA) while the shortleaf was sampled only in TX. The slash pine were...

Comparison of estimates of hardwood bole volume using importance sampling, the centroid method, and some taper equations

Treesearch

Harry V., Jr. Wiant; Michael L. Spangler; John E. Baumgras

2002-01-01

Various taper systems and the centroid method were compared to unbiased volume estimates made by importance sampling for 720 hardwood trees selected throughout the state of West Virginia. Only the centroid method consistently gave volumes estimates that did not differ significantly from those made by importance sampling, although some taper equations did well for most...

Integrability: mathematical methods for studying solitary waves theory

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2014-03-01

In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the real features in a variety of vital areas in science, technology and engineering. In recognition of the importance of solitary waves theory and the underlying concept of integrable equations, a variety of powerful methods have been developed to carry out the required analysis. Examples of such methods which have been advanced are the inverse scattering method, the Hirota bilinear method, the simplified Hirota method, the Bäcklund transformation method, the Darboux transformation, the Pfaffian technique, the Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method, the coupled amplitude-phase formulation, the sine-cosine method, the sech-tanh method, the mapping and deformation approach and many new other methods. The inverse scattering method, viewed as a nonlinear analogue of the Fourier transform method, is a powerful approach that demonstrates the existence of soliton solutions through intensive computations. At the center of the theory of integrable equations lies the bilinear forms and Hirota's direct method, which can be used to obtain soliton solutions by using exponentials. The Bäcklund transformation method is a useful invariant transformation that transforms one solution into another of a differential equation. The Darboux transformation method is a well known tool in the theory of integrable systems. It is believed that there is a connection between the Bäcklund transformation and the Darboux transformation, but it is as yet not known. Archetypes of integrable equations are the Korteweg-de Vries (KdV) equation, the modified KdV equation, the sine-Gordon equation, the Schrödinger equation, the Vakhnenko equation, the KdV6 equation, the Burgers equation, the fifth-order Lax equation and many others. These equations yield soliton solutions, multiple soliton solutions, breather solutions, quasi-periodic solutions, kink solutions, homo-clinic solutions and other solutions as well. The couplings of linear and nonlinear equations were recently discovered and subsequently received considerable attention. The concept of couplings forms a new direction for developing innovative construction methods. The recently obtained results in solitary waves theory highlight new approaches for additional creative ideas, promising further achievements and increased progress in this field. We are grateful to all of the authors who accepted our invitation to contribute to this comment section.

Volume Equations for Plantation Cottonwood Trees (Populusdeltoides)

Treesearch

Roger M. Krinard

1988-01-01

Equations and tables for cubic-foot volume of outside bark to the top of the tree and inside bark to a3-inchtop are given for plantation-grown cottonwoods (Populus delfoidesBartr. ex Marsh.) from 5 to 22 inches in d.b.h.

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe; Kwak, Dochan; Vinokur, Marcel

1992-01-01

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

NASA Astrophysics Data System (ADS)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D ( x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Euler equation computations for the flow over a hovering helicopter rotor

NASA Technical Reports Server (NTRS)

Roberts, Thomas Wesley

1988-01-01

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

Non-invasive method and apparatus for monitoring intracranial pressure and pressure volume index in humans

NASA Technical Reports Server (NTRS)

Cantrell, John H. (Inventor); Yost, William T. (Inventor)

1994-01-01

Non-invasive measuring devices responsive to changes in a patient's intracranial pressure (ICP) can be accurately calibrated for monitoring purposes by providing known changes in ICP by non-invasive methods, such as placing the patient on a tilting bed and calculating a change in ICP from the tilt angle and the length of the patient's cerebrospinal column, or by placing a pressurized skull cap on the patient and measuring the inflation pressure. Absolute values for the patient's pressure-volume index (PVI) and the steady state ICP can then be determined by inducing two known changes in the volume of cerebrospinal fluid while recording the corresponding changes in ICP by means of the calibrated measuring device. The two pairs of data for pressure change and volume change are entered into an equation developed from an equation describing the relationship between ICP and cerebrospinal fluid volume. PVI and steady state ICP are then determined by solving the equation. Methods for inducing known changes in cerebrospinal fluid volume are described.

Non-invasive method and apparatus for monitoring intracranial pressure and pressure volume index in humans

NASA Technical Reports Server (NTRS)

Yost, William T. (Inventor); Cantrell, Jr., John H. (Inventor)

1997-01-01

Non-invasive measuring devices responsive to changes in a patient's intracranial pressure (ICP) can be accurately calibrated for monitoring purposes by providing known changes in ICP by non-invasive methods, such as placing the patient on a tilting bed and calculating a change in ICP from the tilt angle and the length of the patient's cerebrospinal column, or by placing a pressurized skull cap on the patient and measuring the inflation pressure. Absolute values for the patient's pressure-volume index (PVI) and the steady state ICP can then be determined by inducing two known changes in the volume of cerebrospinal fluid while recording the corresponding changes in ICP by means of the calibrated measuring device. The two pairs of data for pressure change and volume change are entered into an equation developed from an equation describing the relationship between ICP and cerebrospinal fluid volume. PVI and steady state ICP are then determined by solving the equation. Methods for inducing known changes in cerebrospinal fluid volume are described.

The development of a volume element model for energy systems engineering and integrative thermodynamic optimization

NASA Astrophysics Data System (ADS)

Yang, Sam

The dissertation presents the mathematical formulation, experimental validation, and application of a volume element model (VEM) devised for modeling, simulation, and optimization of energy systems in their early design stages. The proposed model combines existing modeling techniques and experimental adjustment to formulate a reduced-order model, while retaining sufficient accuracy to serve as a practical system-level design analysis and optimization tool. In the VEM, the physical domain under consideration is discretized in space using lumped hexahedral elements (i.e., volume elements), and the governing equations for the variable of interest are applied to each element to quantify diverse types of flows that cross it. Subsequently, a system of algebraic and ordinary differential equations is solved with respect to time and scalar (e.g., temperature, relative humidity, etc.) fields are obtained in both spatial and temporal domains. The VEM is capable of capturing and predicting dynamic physical behaviors in the entire system domain (i.e., at system level), including mutual interactions among system constituents, as well as with their respective surroundings and cooling systems, if any. The VEM is also generalizable; that is, the model can be easily adapted to simulate and optimize diverse systems of different scales and complexity and attain numerical convergence with sufficient accuracy. Both the capability and generalizability of the VEM are demonstrated in the dissertation via thermal modeling and simulation of an Off-Grid Zero Emissions Building, an all-electric ship, and a vapor compression refrigeration (VCR) system. Furthermore, the potential of the VEM as an optimization tool is presented through the integrative thermodynamic optimization of a VCR system, whose results are used to evaluate the trade-offs between various objective functions, namely, coefficient of performance, second law efficiency, pull-down time, and refrigerated space temperature, in both transient and steady-state operations.

Bone Balance within a Cortical BMU: Local Controls of Bone Resorption and Formation

PubMed Central

Smith, David W.; Gardiner, Bruce S.; Dunstan, Colin

2012-01-01

Maintaining bone volume during bone turnover by a BMU is known as bone balance. Balance is required to maintain structural integrity of the bone and is often dysregulated in disease. Consequently, understanding how a BMU controls bone balance is of considerable interest. This paper develops a methodology for identifying potential balance controls within a single cortical BMU. The theoretical framework developed offers the possibility of a directed search for biological processes compatible with the constraints of balance control. We first derive general control constraint equations and then introduce constitutive equations to identify potential control processes that link key variables that describe the state of the BMU. The paper describes specific local bone volume balance controls that may be associated with bone resorption and bone formation. Because bone resorption and formation both involve averaging over time, short-term fluctuations in the environment are removed, leaving the control systems to manage deviations in longer-term trends back towards their desired values. The length of time for averaging is much greater for bone formation than for bone resorption, which enables more filtering of variability in the bone formation environment. Remarkably, the duration for averaging of bone formation may also grow to control deviations in long-term trends of bone formation. Providing there is sufficient bone formation capacity by osteoblasts, this leads to an extraordinarily robust control mechanism that is independent of either osteoblast number or the cellular osteoid formation rate. A complex picture begins to emerge for the control of bone volume. Different control relationships may achieve the same objective, and the ‘integration of information’ occurring within a BMU may be interpreted as different sets of BMU control systems coming to the fore as different information is supplied to the BMU, which in turn leads to different observable BMU behaviors. PMID:22844401

Principles of Considering the Effect of the Limited Volume of a System on Its Thermodynamic State

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-01-01

The features of a system with a finite volume that affect its thermodynamic state are considered in comparison to describing small bodies in macroscopic phases. Equations for unary and pair distribution functions are obtained using difference derivatives of a discrete statistical sum. The structure of the equation for the free energy of a system consisting of an ensemble of volume-limited regions with different sizes and a full set of equations describing a macroscopic polydisperse system are discussed. It is found that the equations can be applied to molecular adsorption on small faces of microcrystals, to bound and isolated pores of a polydisperse material, and to describe the spinodal decomposition of a fluid in brief periods of time and high supersaturations of the bulk phase when each local region functions the same on average. It is shown that as the size of a system diminishes, corrections must be introduced for the finiteness of the system volume and fluctuations of the unary and pair distribution functions.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

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

PubMed

Grima, R

2010-07-21

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

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

2004-01-01

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

Kinetics of diffusional droplet growth in a liquid/liquid two-phase system

NASA Technical Reports Server (NTRS)

Baird, James K.

1992-01-01

In the case of the diaphragm cell transport equation where the interdiffusion coefficient is a function of concentration, we have derived an integral of the form, t = B(sub 0) + B(sub L)ln(delta(c)) + B(sub 1)(delta(c)) + B(sub 2)(delta(c))(exp 2) +... where t is the time and (delta(c)) is the concentration difference across the frit. The coefficient, B(sub 0), is a constant of integration, while the coefficient, B(sub L), B(sub 1), B(sub 2), ..., depend in general upon the cell constant, the compartment volumes, the interdiffusion coefficient, and various of its concentration derivatives evaluated at the mean concentration for the cell. Explicit formulae for B(sub L), B(sub 1), B(sub 2), ... are given.

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

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

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

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

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

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Equations for total, wood, and saw-log volume for thirteen California hardwoods.

Treesearch

Norman H. Pillsbury; Michael L. Kirkley

1984-01-01

Volume equations for thirteen species of California hardwoods were developed from measurements of 766 sample trees from all parts of the state. The species included: bigleaf maple (Acer macrophyllum Pursh), Pacific madrone (Arbutus menziesii Pursh), giant chinkapin (Castanopsis chrysophylla (Dougl.) A. DC...

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

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

PubMed Central

Howard, Jesse J.

2011-01-01

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

HYDRA-II: A hydrothermal analysis computer code: Volume 3, Verification/validation assessments

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

McCann, R.A.; Lowery, P.S.

1987-10-01

HYDRA-II is a hydrothermal computer code capable of three-dimensional analysis of coupled conduction, convection, and thermal radiation problems. This code is especially appropriate for simulating the steady-state performance of spent fuel storage systems. The code has been evaluated for this application for the US Department of Energy's Commercial Spent Fuel Management Program. HYDRA-II provides a finite difference solution in cartesian coordinates to the equations governing the conservation of mass, momentum, and energy. A cylindrical coordinate system may also be used to enclose the cartesian coordinate system. This exterior coordinate system is useful for modeling cylindrical cask bodies. The difference equationsmore » for conservation of momentum are enhanced by the incorporation of directional porosities and permeabilities that aid in modeling solid structures whose dimensions may be smaller than the computational mesh. The equation for conservation of energy permits modeling of orthotropic physical properties and film resistances. Several automated procedures are available to model radiation transfer within enclosures and from fuel rod to fuel rod. The documentation of HYDRA-II is presented in three separate volumes. Volume I - Equations and Numerics describes the basic differential equations, illustrates how the difference equations are formulated, and gives the solution procedures employed. Volume II - User's Manual contains code flow charts, discusses the code structure, provides detailed instructions for preparing an input file, and illustrates the operation of the code by means of a model problem. This volume, Volume III - Verification/Validation Assessments, provides a comparison between the analytical solution and the numerical simulation for problems with a known solution. This volume also documents comparisons between the results of simulations of single- and multiassembly storage systems and actual experimental data. 11 refs., 55 figs., 13 tabs.« less

Predictive equations for lung volumes from computed tomography for size matching in pulmonary transplantation.

PubMed

Konheim, Jeremy A; Kon, Zachary N; Pasrija, Chetan; Luo, Qingyang; Sanchez, Pablo G; Garcia, Jose P; Griffith, Bartley P; Jeudy, Jean

2016-04-01

Size matching for lung transplantation is widely accomplished using height comparisons between donors and recipients. This gross approximation allows for wide variation in lung size and, potentially, size mismatch. Three-dimensional computed tomography (3D-CT) volumetry comparisons could offer more accurate size matching. Although recipient CT scans are universally available, donor CT scans are rarely performed. Therefore, predicted donor lung volumes could be used for comparison to measured recipient lung volumes, but no such predictive equations exist. We aimed to use 3D-CT volumetry measurements from a normal patient population to generate equations for predicted total lung volume (pTLV), predicted right lung volume (pRLV), and predicted left lung volume (pLLV), for size-matching purposes. Chest CT scans of 400 normal patients were retrospectively evaluated. 3D-CT volumetry was performed to measure total lung volume, right lung volume, and left lung volume of each patient, and predictive equations were generated. The fitted model was tested in a separate group of 100 patients. The model was externally validated by comparison of total lung volume with total lung capacity from pulmonary function tests in a subset of those patients. Age, gender, height, and race were independent predictors of lung volume. In the test group, there were strong linear correlations between predicted and actual lung volumes measured by 3D-CT volumetry for pTLV (r = 0.72), pRLV (r = 0.72), and pLLV (r = 0.69). A strong linear correlation was also observed when comparing pTLV and total lung capacity (r = 0.82). We successfully created a predictive model for pTLV, pRLV, and pLLV. These may serve as reference standards and predict donor lung volume for size matching in lung transplantation. Copyright © 2016 The American Association for Thoracic Surgery. Published by Elsevier Inc. All rights reserved.

Philipp Frank, Richard von Mises, and the Frank-Mises

NASA Astrophysics Data System (ADS)

Siegmund-Schultze, Reinhard

2007-01-01

The theoretical physicist Philipp Frank (1884 1966) and the applied mathematician Richard von Mises (1883 1953) both received their university education in Vienna shortly after 1900 and became friends at the latest during the Great War.They were attached to the Vienna Circle of Logical Positivists and wrote an influential two-part work on the differential and integral equations of mechanics and physics, the Frank-Mises, of 1925 and 1927, with its second edition following in 1930 and 1935.This work originated in the lectures that the mathematician Bernhard Riemann (1826 1866) delivered on partial differential equations and their applications to physical questions at the University of Göttingen between 1854 and 1862, which were edited and published posthumously in1869 by the physicist Karl Hattendorff (1834 1882).The immediate precursor of the Frank-Mises, however, was the extensive revision of Hattendorff’s edition of Riemann’s lectures that the mathematician Heinrich Weber (1842 1913) published in two volumes, the Riemann-Weber, of 1900 and 1901, with its second edition following in 1910 and 1912. I trace this historical lineage, explore the nature and contents of the Frank-Mises, and discuss its complementary relationship to the first volume of the text that the mathematicians Richard Courant (1888 1972) and David Hilbert (1862 1943) published on the methods of mathematical physics in 1924, the Courant-Hilbert,which, when it and its second volume of 1937 were translated into English and extensively revised in 1953 and 1961, eclipsed the classic Frank-Mises.

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

Finite-volume scheme for anisotropic diffusion

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

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

Equation of State for Solid Phase I of Carbon Dioxide Valid for Temperatures up to 800 K and Pressures up to 12 GPa

NASA Astrophysics Data System (ADS)

Martin Trusler, J. P.

2011-12-01

The available thermodynamic-property data for solid phase I of carbon dioxide ("dry ice") are reviewed and used to determine the parameters of a new fundamental equation of state constructed in the form of a Helmholtz energy function with temperature and molar volume as the independent variables. The experimental data considered include the pressure, molar volume, and isobaric heat capacity along the sublimation curve, the melting-pressure curve, and molar volume in the compressed solid at temperatures from 295 to 764 K and pressures up to 12 GPa. The equation of state is based on the quasi-harmonic approximation, incorporating a Debye oscillator distribution for the vibrons, two discrete modes for the librons and a further three distinct modes for the internal vibrations of the CO2 molecule. A small anharmonic correction term is included, which is significant mainly in the region of the triple point. The estimated relative uncertainty of molar volume at specified temperature and pressure calculated from the equation of state is 0.02% on the sublimation curve and 1.5% in the compressed solid; for isobaric heat capacity on the sublimation curve, the uncertainty varies from 5.0% to 0.5% between 2 and 195 K. Auxiliary equations for the pressure and molar volume on the sublimation and melting curves are given. The equation of state is valid at temperatures from 0 to 800 K and at pressures from the solid-fluid phase boundary to 12 GPa.

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

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.

Hydromagnetic flow of a Cu-water nanofluid past a moving wedge with viscous dissipation

NASA Astrophysics Data System (ADS)

M. Salem, A.; Galal, Ismail; Rania, Fathy

2014-04-01

A numerical study is performed to investigate the flow and heat transfer at the surface of a permeable wedge immersed in a copper (Cu)-water-based nanofluid in the presence of magnetic field and viscous dissipation using a nanofluid model proposed by Tiwari and Das (Tiwari I K and Das M K 2007 Int. J. Heat Mass Transfer 50 2002). A similarity solution for the transformed governing equation is obtained, and those equations are solved by employing a numerical shooting technique with a fourth-order Runge-Kutta integration scheme. A comparison with previously published work is carried out and shows that they are in good agreement with each other. The effects of velocity ratio parameter λ, solid volume fraction φ, magnetic field M, viscous dissipation Ec, and suction parameter Fw on the fluid flow and heat transfer characteristics are discussed. The unique and dual solutions for self-similar equations of the flow and heat transfer are analyzed numerically. Moreover, the range of the velocity ratio parameter for which the solution exists increases in the presence of magnetic field and suction parameter.

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

NASA Astrophysics Data System (ADS)

Gjennestad, Magnus Aa.; Gruber, Andrea; Lervåg, Karl Yngve; Johansen, Øyvind; Ervik, Åsmund; Hammer, Morten; Munkejord, Svend Tollak

2017-11-01

We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas-liquid or gas-solid) and three-phase (gas-liquid-solid) flow of CO2 whose thermodynamic properties are calculated using the Span-Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge-Kutta method. We demonstrate close to fifth-order convergence for advection-diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO2 jets.

Aircraft Landing Dynamic Analysis. Volume 1. Equations of Motion

DTIC Science & Technology

1987-11-09

aQh Xp* (WB 1I H 3 Hh pg esd r f, d X, r B dIp ~ b X aH Hf (a, B + b B 3 b) + F d el 1N + b 60 The fB 2 equation is fBEB N G B f2B (M )CS a 1, N ] B...1 a a TBB (A s a’ Ga 3bg a=I a ah a C + F Hb ( B/eB ) B d 6be d H c + e TBg C l e H e 3 Hh Pg esdr x f ?Hd (a r + b XBr) 8 s ) H 3 f TB 1 b VB BY + g...nondecreasing on [a,b] then f is g integrable on [a,b] (Reference (3)). This is denoted by Jb f dg. In the special case where g = I (the identity

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

A Rate-Theory-Phase-Field Model of Irradiation-Induced Recrystallization in UMo Nuclear Fuels

NASA Astrophysics Data System (ADS)

Hu, Shenyang; Joshi, Vineet; Lavender, Curt A.

2017-12-01

In this work, we developed a recrystallization model to study the effect of microstructures and radiation conditions on recrystallization kinetics in UMo fuels. The model integrates the rate theory of intragranular gas bubble and interstitial loop evolutions and a phase-field model of recrystallization zone evolution. A first passage method is employed to describe one-dimensional diffusion of interstitials with a diffusivity value several orders of magnitude larger than that of fission gas xenons. With the model, the effect of grain sizes on recrystallization kinetics is simulated. The results show that (1) recrystallization in large grains starts earlier than that in small grains, (2) the recrystallization kinetics (recrystallization volume fraction) decrease as the grain size increases, (3) the predicted recrystallization kinetics are consistent with the experimental results, and (4) the recrystallization kinetics can be described by the modified Avrami equation, but the parameters of the Avrami equation strongly depend on the grain size.

Predicting volumes in four Hawaii hardwoods...first multivariate equations developed

Treesearch

David A. Sharpnack

1966-01-01

Multivariate regression equations were developed for predicting board-foot (Int. 1/ 4-inch log rule ) and cubic-foot volumes in each 8.15-foot section of trees of four Hawaii hardwood species. The species are koa (Acacia koa), ohia (Metrosideros polymorpha), robusta eucalyptus (Eucalyptus robusta), and...

Predicting lumber volume and value of young-growth true firs: user's guide.

Treesearch

Susan Ernst; W.Y. Pong

1982-01-01

Equations are presented for predicting the volume and value of young-growth red, white, and grand firs. Examples of how to use them are also given. These equations were developed on trees less than 140 years old from areas in southern Oregon, northern California, and Idaho.

A panning DLT procedure for three-dimensional videography.

PubMed

Yu, B; Koh, T J; Hay, J G

1993-06-01

The direct linear transformation (DLT) method [Abdel-Aziz and Karara, APS Symposium on Photogrammetry. American Society of Photogrammetry, Falls Church, VA (1971)] is widely used in biomechanics to obtain three-dimensional space coordinates from film and video records. This method has some major shortcomings when used to analyze events which take place over large areas. To overcome these shortcomings, a three-dimensional data collection method based on the DLT method, and making use of panning cameras, was developed. Several small single control volumes were combined to construct a large total control volume. For each single control volume, a regression equation (calibration equation) is developed to express each of the 11 DLT parameters as a function of camera orientation, so that the DLT parameters can then be estimated from arbitrary camera orientations. Once the DLT parameters are known for at least two cameras, and the associated two-dimensional film or video coordinates of the event are obtained, the desired three-dimensional space coordinates can be computed. In a laboratory test, five single control volumes (in a total control volume of 24.40 x 2.44 x 2.44 m3) were used to test the effect of the position of the single control volume on the accuracy of the computed three dimensional space coordinates. Linear and quadratic calibration equations were used to test the effect of the order of the equation on the accuracy of the computed three dimensional space coordinates. For four of the five single control volumes tested, the mean resultant errors associated with the use of the linear calibration equation were significantly larger than those associated with the use of the quadratic calibration equation. The position of the single control volume had no significant effect on the mean resultant errors in computed three dimensional coordinates when the quadratic calibration equation was used. Under the same data collection conditions, the mean resultant errors in the computed three dimensional coordinates associated with the panning and stationary DLT methods were 17 and 22 mm, respectively. The major advantages of the panning DLT method lie in the large image sizes obtained and in the ease with which the data can be collected. The method also has potential for use in a wide variety of contexts. The major shortcoming of the method is the large amount of digitizing necessary to calibrate the total control volume. Adaptations of the method to reduce the amount of digitizing required are being explored.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

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

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

DOE PAGES

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett; ...

2017-01-01

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.

2004-01-01

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation. Volume 1: Study results

NASA Technical Reports Server (NTRS)

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

1982-01-01

A variety of artificial intelligence techniques which could be used with regard to NASA space applications and robotics were evaluated. The techniques studied were decision tree manipulators, problem solvers, rule based systems, logic programming languages, representation language languages, and expert systems. The overall structure of a robotic simulation tool was defined and a framework for that tool developed. Nonlinear and linearized dynamics equations were formulated for n link manipulator configurations. A framework for the robotic simulation was established which uses validated manipulator component models connected according to a user defined configuration.

Unstructured Euler flow solutions using hexahedral cell refinement

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1991-01-01

An attempt is made to extend grid refinement into three dimensions by using unstructured hexahedral grids. The flow solver is developed using the TIGER (topologically Independent Grid, Euler Refinement) as the starting point. The program uses an unstructured hexahedral mesh and a modified version of the Jameson four-stage, finite-volume Runge-Kutta algorithm for integration of the Euler equations. The unstructured mesh allows for local refinement appropriate for each freestream condition, thereby concentrating mesh cells in the regions of greatest interest. This increases the computational efficiency because the refinement is not required to extend throughout the entire flow field.

Gastric residual volume (GRV) and gastric contents measurement by refractometry.

PubMed

Chang, Wei-Kuo; McClave, Stephen A; Hsieh, Chung-Bao; Chao, You-Chen

2007-01-01

Traditional use of gastric residual volumes (GRVs), obtained by aspiration from a nasogastric tube, is inaccurate and cannot differentiate components of the gastric contents (gastric secretion vs delivered formula). The use of refractometry and 3 mathematical equations has been proposed as a method to calculate the formula concentration, GRV, and formula volume. In this paper, we have validated these mathematical equations so that they can be implemented in clinical practice. Each of 16 patients receiving a nasogastric tube had 50 mL of water followed by 100 mL of dietary formula (Osmolite HN, Abbott Laboratories, Columbus, OH) infused into the stomach. After mixing, gastric content was aspirated for the first Brix value (BV) measurement by refractometry. Then, 50 mL of water was infused into the stomach and a second BV was measured. The procedure of infusion of dietary formula (100 mL) and then water (50 mL) was repeated and followed by subsequent BV measurement. The same procedure was performed in an in vitro experiment. Formula concentration, GRV, and formula volume were calculated from the derived mathematical equations. The formula concentrations, GRVs, and formula volumes calculated by using refractometry and the mathematical equations were close to the true values obtained from both in vivo and in vitro validation experiments. Using this method, measurement of the BV of gastric contents is simple, reproducible, and inexpensive. Refractometry and the derived mathematical equations may be used to measure formula concentration, GRV, and formula volume, and also to serve as a tool for monitoring the gastric contents of patients receiving nasogastric feeding.

The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

Scaling and scale invariance of conservation laws in Reynolds transport theorem framework

NASA Astrophysics Data System (ADS)

Haltas, Ismail; Ulusoy, Suleyman

2015-07-01

Scale invariance is the case where the solution of a physical process at a specified time-space scale can be linearly related to the solution of the processes at another time-space scale. Recent studies investigated the scale invariance conditions of hydrodynamic processes by applying the one-parameter Lie scaling transformations to the governing equations of the processes. Scale invariance of a physical process is usually achieved under certain conditions on the scaling ratios of the variables and parameters involved in the process. The foundational axioms of hydrodynamics are the conservation laws, namely, conservation of mass, conservation of linear momentum, and conservation of energy from continuum mechanics. They are formulated using the Reynolds transport theorem. Conventionally, Reynolds transport theorem formulates the conservation equations in integral form. Yet, differential form of the conservation equations can also be derived for an infinitesimal control volume. In the formulation of the governing equation of a process, one or more than one of the conservation laws and, some times, a constitutive relation are combined together. Differential forms of the conservation equations are used in the governing partial differential equation of the processes. Therefore, differential conservation equations constitute the fundamentals of the governing equations of the hydrodynamic processes. Applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework instead of applying to the governing partial differential equations may lead to more fundamental conclusions on the scaling and scale invariance of the hydrodynamic processes. This study will investigate the scaling behavior and scale invariance conditions of the hydrodynamic processes by applying the one-parameter Lie scaling transformation to the conservation laws in the Reynolds transport theorem framework.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations

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

Maccari, A.

1996-12-01

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}

Coupled 2-dimensional cascade theory for noise an d unsteady aerodynamics of blade row interaction in turbofans. Volume 2: Documentation for computer code CUP2D

NASA Technical Reports Server (NTRS)

Hanson, Donald B.

1994-01-01

A two dimensional linear aeroacoustic theory for rotor/stator interaction with unsteady coupling was derived and explored in Volume 1 of this report. Computer program CUP2D has been written in FORTRAN embodying the theoretical equations. This volume (Volume 2) describes the structure of the code, installation and running, preparation of the input file, and interpretation of the output. A sample case is provided with printouts of the input and output. The source code is included with comments linking it closely to the theoretical equations in Volume 1.

A CORRELATION BETWEEN RADIATION TOLERANCE AND NUCLEAR SURFACE AREA

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

Iversen, S.

1962-09-22

Sparrow and Miksche (Science, 134:282) determined the dose (r/day) required to produce severe growth inhibition in 23 species of plants and found a linear relationship between log nuclear volume and log dose. The following equations hold for 6 species: log nuclear volume - 4.42 -0.82 log dose and log nuclear volume = 1.66 + 0.66 log (DNA content). If all the nuclear DNA is distributed in two peripheral zones, the equations also hold: 2(log nuclear surface area) - 1.33(log nuclear volume) - 2.21 + 0.88 log(DNA content) and 5.88-- 1.09 log dose. For the 23 species, the equation was obtained:more » 2(log nuclear surface area) = 5.41 -- 0.97 log dose. All the slopes are close to the expected value of 1.00. (D.L.C.)« less

Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.

PubMed

Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan

2017-04-07

In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Water-budget methods

USGS Publications Warehouse

Healy, Richard W.; Scanlon, Bridget R.

2010-01-01

A water budget is an accounting of water movement into and out of, and storage change within, some control volume. Universal and adaptable are adjectives that reflect key features of water-budget methods for estimating recharge. The universal concept of mass conservation of water implies that water-budget methods are applicable over any space and time scales (Healy et al., 2007). The water budget of a soil column in a laboratory can be studied at scales of millimeters and seconds. A water-budget equation is also an integral component of atmospheric general circulation models used to predict global climates over periods of decades or more. Water-budget equations can be easily customized by adding or removing terms to accurately portray the peculiarities of any hydrologic system. The equations are generally not bound by assumptions on mechanisms by which water moves into, through, and out of the control volume of interest. So water-budget methods can be used to estimate both diffuse and focused recharge, and recharge estimates are unaffected by phenomena such as preferential flow paths within the unsaturated zone.Water-budget methods represent the largest class of techniques for estimating recharge. Most hydrologic models are derived from a water-budget equation and can therefore be classified as water-budget models. It is not feasible to address all water-budget methods in a single chapter. This chapter is limited to discussion of the “residual” water-budget approach, whereby all variables in a water-budget equation, except for recharge, are independently measured or estimated and recharge is set equal to the residual. This chapter is closely linked with Chapter 3, on modeling methods, because the equations presented here form the basis of many models and because models are often used to estimate individual components in water-budget studies. Water budgets for streams and other surface-water bodies are addressed in Chapter 4. The use of soil-water budgets and lysimeters for determining potential recharge and evapotranspiration from changes in water storage is discussed in Chapter 5. Aquifer water-budget methods based on the measurement of groundwater levels are described in Chapter 6.

Morphometric approach to thermodynamic quantities of solvation of complex molecules: Extension to multicomponent solvent

NASA Astrophysics Data System (ADS)

Kodama, Ryota; Roth, Roland; Harano, Yuichi; Kinoshita, Masahiro

2011-07-01

The morphometric approach (MA) is a powerful tool for calculating a solvation free energy (SFE) and related quantities of solvation thermodynamics of complex molecules. Here, we extend it to a solvent consisting of m components. In the integral equation theories, the SFE is expressed as the sum of m terms each of which comprises solute-component j correlation functions (j = 1, …, m). The MA is applied to each term in a formally separate manner: The term is expressed as a linear combination of the four geometric measures, excluded volume, solvent-accessible surface area, and integrated mean and Gaussian curvatures of the accessible surface, which are calculated for component j. The total number of the geometric measures or the coefficients in the linear combinations is 4m. The coefficients are determined in simple geometries, i.e., for spherical solutes with various diameters in the same multicomponent solvent. The SFE of the spherical solutes are calculated using the radial-symmetric integral equation theory. The extended version of the MA is illustrated for a protein modeled as a set of fused hard spheres immersed in a binary mixture of hard spheres. Several mixtures of different molecular-diameter ratios and compositions and 30 structures of the protein with a variety of radii of gyration are considered for the illustration purpose. The SFE calculated by the MA is compared with that by the direct application of the three-dimensional integral equation theory (3D-IET) to the protein. The deviations of the MA values from the 3D-IET values are less than 1.5%. The computation time required is over four orders of magnitude shorter than that in the 3D-IET. The MA thus developed is expected to be best suited to analyses concerning the effects of cosolvents such as urea on the structural stability of a protein.

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

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

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

NASA Astrophysics Data System (ADS)

Eden, Burkhard; Smirnov, Vladimir A.

2016-10-01

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

What Can We Learn from Hugoniot Temperature as a Function of Shock Velocity?

NASA Astrophysics Data System (ADS)

LI, M.; Jeanloz, R.

2015-12-01

Shock-wave experiments traditionally rely on impact techniques, whereby measured shock velocity (US) can be related to material velocity (up), determined from the impact velocity (= 2up for a symmetric impact), and resulting in the empirically observed linear US-up equation of state: US = c0 + s up. Modern experiments relying on laser-driven compression have the advantage of reaching higher pressures than laboratory impact experiments, but up is typically not determined; instead, Hugoniot temperature (TH) and shock velocity are more readily measured. Assuming a linear US-up equation of state and that the Grüneisen parameter has the volume dependence g(V) = g0 (V/V0), measurements of the Hugoniot temperature as a function of shock velocity provide constraints on the specific heat along the Hugoniot CVH(US) = V0 f(US)[c0 g0 TH - s US dTH/dUS]-1 where the Walsh-Christian (1955) function f(US) = - (US - c0)2 US/(V0 s c0) = TH dSH/dVH gives the entropy change along the Hugoniot (subscripts 0 and H indicate zero-pressure and Hugoniot states, respectively). In this sense, TH(US) measurements are similar to calorimetry experiments. If specific heat and Grüneisen parameter are determined independently (e.g., from wave-velocity measurements and experiments on porous samples), the TH(US) analog to the linear US-up equation of state is TH(US) = {T0 exp(g0 /s) - ò[V0 c0 f(x)/(s x CV)] exp[c0 g0 /(s x)] dx} exp[- c0 g0 /(s US)] where the integration is from x = c0 to x = US. In addition, experiments can be considered with: 1) different initial volume, as in a porous sample; 2) different initial internal energy, as in a sample heated at constant volume; and 3) different initial volume and internal energy, as in a sample initially heated at ambient pressure. From these four initial states, we get four different Hugoniot curves, and can also consider the effect of phase transition latent heat. Temperature as a function of shock velocity may thus be benefit the analysis of melting and other phase transitions with small volume change and finite latent heat.

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

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

Development of a 3D Soil-Plant-Atmosphere Continuum (SPAC) coupled to a Land Surface Model

NASA Astrophysics Data System (ADS)

Bisht, G.; Riley, W. J.; Lorenzetti, D.; Tang, J.

2015-12-01

Exchange of water between the atmosphere and biosphere via evapotranspiration (ET) influences global hydrological, energy, and biogeochemical cycles. Isotopic analysis has shown that evapotranspiration over the continents is largely dominated by transpiration. Water is taken up from soil by plant roots, transported through the plant's vascular system, and evaporated from the leaves. Yet current Land Surface Models (LSMs) integrated into Earth System Models (ESMs) treat plant roots as passive components. These models distribute the ET sink vertically over the soil column, neglect the vertical pressure distribution along the plant vascular system, and assume that leaves can directly access water from any soil layer within the root zone. Numerous studies have suggested that increased warming due to climate change will lead drought and heat-induced tree mortality. A more mechanistic treatment of water dynamics in the soil-plant-atmosphere continuum (SPAC) is essential for investigating the fate of ecosystems under a warmer climate. In this work, we describe a 3D SPAC model that can be coupled to a LSM. The SPAC model uses the variably saturated Richards equations to simulate water transport. The model uses individual governing equations and constitutive relationships for the various SPAC components (i.e., soil, root, and xylem). Finite volume spatial discretization and backward Euler temporal discretization is used to solve the SPAC model. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is used to numerically integrate the discretized system of equations. Furthermore, PETSc's multi-physics coupling capability (DMComposite) is used to solve the tightly coupled system of equations of the SPAC model. Numerical results are presented for multiple test problems.

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

Whole stand volume tables for quaking aspen in the Rocky Mountains

Treesearch

Wayne D. Shepperd; H. Todd Mowrer

1984-01-01

Linear regression equations were developed to predict stand volumes for aspen given average stand basal area and average stand height. Tables constructed from these equations allow easy field estimation of gross merchantable cubic and board foot Scribner Rules per acre, and cubic meters per hectare using simple prism cruise data.

Tables and equations for estimating volumes of trees in the Susitna River Basin, Alaska.

Treesearch

Frederic R. Larson; Kenneth C. Winterberger

1988-01-01

Scribner board-foot, merchantable cubic-foot, and total cubic-foot volume equations were derived from fall, buck, and scale data for 441 trees at 78 locations in the Susitna River basin, Alaska. Tree species included white and black spruce, paper birch, black cottonwood, and quaking aspen.

Individual tree, merchantable stem green weight and volume equations for four bottomland hardwood oak species in southeast Arkansas

Treesearch

Paul F. Doruska; David W. Patterson; Matthew B. Hurd; Jonathan I. Hartley

2013-01-01

Equations were developed to estimate outside-bark, merchantable stem green weight (lb) and inside-bark merchantable stem volume (ft3) for sawtimber-sized Nuttall oak (Quercus texana Buckley), overcup oak (Quercus lyrata Walt.), water oak (Quercus nigra L.), and willow oak (Quercus...

Application of integral equation theory to analyze stability of electric field in multimode microwave heating cavity

NASA Astrophysics Data System (ADS)

Tang, Zhengming; Hong, Tao; Chen, Fangyuan; Zhu, Huacheng; Huang, Kama

2017-10-01

Microwave heating uniformity is mainly dependent on and affected by electric field. However, little study has paid attention to its stability characteristics in multimode cavity. In this paper, this problem is studied by the theory of Freedholm integral equation. Firstly, Helmholtz equation and the electric dyadic Green's function are used to derive the electric field integral equation. Then, the stability of electric field is demonstrated as the characteristics of solutions to Freedholm integral equation. Finally, the stability characteristics are obtained and verified by finite element calculation. This study not only can provide a comprehensive interpretation of electric field in multimode cavity but also help us make better use of microwave energy.

Complementary effect of patient volume and quality of care on hospital cost efficiency.

PubMed

Choi, Jeong Hoon; Park, Imsu; Jung, Ilyoung; Dey, Asoke

2017-06-01

This study explores the direct effect of an increase in patient volume in a hospital and the complementary effect of quality of care on the cost efficiency of U.S. hospitals in terms of patient volume. The simultaneous equation model with three-stage least squares is used to measure the direct effect of patient volume and the complementary effect of quality of care and volume. Cost efficiency is measured with a data envelopment analysis method. Patient volume has a U-shaped relationship with hospital cost efficiency and an inverted U-shaped relationship with quality of care. Quality of care functions as a moderator for the relationship between patient volume and efficiency. This paper addresses the economically important question of the relationship of volume with quality of care and hospital cost efficiency. The three-stage least square simultaneous equation model captures the simultaneous effects of patient volume on hospital quality of care and cost efficiency.

A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system

NASA Astrophysics Data System (ADS)

Li, Chun-Xia; Lafortune, Stéphane; Shen, Shou-Feng

2016-05-01

We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation, respectively. Among these equations, we are mainly concerned with the semi-discrete bilinear Kadomtsev-Petviashvili (KP) equation which is seldomly studied in literature. We present both of its Casorati and Grammian determinant solutions. Through the Pfaffianization procedure proposed by Hirota and Ohta, we are able to derive the coupled integrable system for the semi-discrete KP equation.

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Stochastic modeling of cell growth with symmetric or asymmetric division

NASA Astrophysics Data System (ADS)

Marantan, Andrew; Amir, Ariel

2016-07-01

We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

Fluid-particle characteristics in fully-developed cluster-induced turbulence

NASA Astrophysics Data System (ADS)

Capecelatro, Jesse; Desjardins, Olivier; Fox, Rodney

2014-11-01

In this study, we present a theoretical framework for collisional fluid-particle turbulence. To identify the key mechanisms responsible for energy exchange between the two phases, an Eulerian-Lagrangian strategy is used to simulate fully-developed cluster-inudced turbulence (CIT) under a range of Reynolds numbers, where fluctuations in particle concentration generate and sustain the carrier-phase turbulence. Using a novel filtering approach, a length-scale separation between the correlated particle velocity and uncorrelated granular temperature (GT) is achieved. This separation allows us to extract the instantaneous Eulerian volume fraction, velocity and GT fields from the Lagrangian data. Direct comparisons can thus be made with the relevant terms that appear in the multiphase turbulence model. It is shown that the granular pressure is highly anisotropic, and thus additional transport equations (as opposed to a single equation for GT) are necessary in formulating a predictive multiphase turbulence model. In addition to reporting the relevant contributions to the Reynolds stresses of each phase, two-point statistics, integral length/timescales, averages conditioned on the local volume fraction, and PDFs of the key multiphase statistics are presented and discussed. The research reported in this paper is partially supported by the HPC equipment purchased through U.S. National Science Foundation MRI Grant Number CNS 1229081 and CRI Grant Number 1205413.

Green's function solution to heat transfer of a transparent gas through a tube

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1989-01-01

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

First integrals of the axisymmetric shape equation of lipid membranes

NASA Astrophysics Data System (ADS)

Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun

2018-03-01

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

Plasma volume methodology: Evans blue, hemoglobin-hematocrit, and mass density transformations

NASA Technical Reports Server (NTRS)

Greenleaf, J. E.; Hinghofer-Szalkay, H.

1985-01-01

Methods for measuring absolute levels and changes in plasma volume are presented along with derivations of pertinent equations. Reduction in variability of the Evans blue dye dilution technique using chromatographic column purification suggests that the day-to-day variability in the plasma volume in humans is less than + or - 20 m1. Mass density determination using the mechanical-oscillator technique provides a method for measuring vascular fluid shifts continuously for assessing the density of the filtrate, and for quantifying movements of protein across microvascular walls. Equations for the calculation of volume and density of shifted fluid are presented.

Prognostic Value of Residual Urine Volume, GFR by 24-hour Urine Collection, and eGFR in Patients Receiving Dialysis.

PubMed

Lee, Mi Jung; Park, Jung Tak; Park, Kyoung Sook; Kwon, Young Eun; Oh, Hyung Jung; Yoo, Tae-Hyun; Kim, Yong-Lim; Kim, Yon Su; Yang, Chul Woo; Kim, Nam-Ho; Kang, Shin-Wook; Han, Seung Hyeok

2017-03-07

Residual kidney function can be assessed by simply measuring urine volume, calculating GFR using 24-hour urine collection, or estimating GFR using the proposed equation (eGFR). We aimed to investigate the relative prognostic value of these residual kidney function parameters in patients on dialysis. Using the database from a nationwide prospective cohort study, we compared differential implications of the residual kidney function indices in 1946 patients on dialysis at 36 dialysis centers in Korea between August 1, 2008 and December 31, 2014. Residual GFR calculated using 24-hour urine collection was determined by an average of renal urea and creatinine clearance on the basis of 24-hour urine collection. eGFR-urea, creatinine and eGFR β 2 -microglobulin were calculated from the equations using serum urea and creatinine and β 2 -microglobulin, respectively. The primary outcome was all-cause death. During a mean follow-up of 42 months, 385 (19.8%) patients died. In multivariable Cox analyses, residual urine volume (hazard ratio, 0.96 per 0.1-L/d higher volume; 95% confidence interval, 0.94 to 0.98) and GFR calculated using 24-hour urine collection (hazard ratio, 0.98; 95% confidence interval, 0.95 to 0.99) were independently associated with all-cause mortality. In 1640 patients who had eGFR β 2 -microglobulin data, eGFR β 2 -microglobulin (hazard ratio, 0.98; 95% confidence interval, 0.96 to 0.99) was also significantly associated with all-cause mortality as well as residual urine volume (hazard ratio, 0.96 per 0.1-L/d higher volume; 95% confidence interval, 0.94 to 0.98) and GFR calculated using 24-hour urine collection (hazard ratio, 0.97; 95% confidence interval, 0.95 to 0.99). When each residual kidney function index was added to the base model, only urine volume improved the predictability for all-cause mortality (net reclassification index =0.11, P =0.01; integrated discrimination improvement =0.01, P =0.01). Higher residual urine volume was significantly associated with a lower risk of death and exhibited a stronger association with mortality than GFR calculated using 24-hour urine collection and eGFR-urea, creatinine. These results suggest that determining residual urine volume may be beneficial to predict patient survival in patients on dialysis. Copyright © 2017 by the American Society of Nephrology.

Power Flow in Phonation

NASA Astrophysics Data System (ADS)

Zhang, Lucy; Yu, Feimi; Krane, Michael

2017-11-01

The control volume analysis of power flow during sustained phonation is performed using results of a fully-coupled aeroelastic-aeroacoustic simulation. The control volumes consist of the laryngeal region, and the larynx and the vocal tract. Two cases are considered: an effectively infinite length vocal tract, where sound produced in the larynx radiates away and is not reflected back, and a constant-area vocal tract of normal adult human dimensions, in which phonatory sound resonates before radiating from the mouth opening. In both cases the lungs are modeled to absorb all incident sound, while providing a constant volume flow toward the larynx. Control of the acoustic boundary conditions is accomplished using perfectly matched- layers, and flow from the lungs is provided by a source distribution near the entrance to the trachea region. For both cases the power flow for the larynx and larynx plus vocal tract control volumes are computed using the integral form of the mechanical energy equation, expanded to consider power exchanges between slightly compressible flow in the larynx and the acoustic fields in the vocal tract and trachea. The funding from NIH 2R01DC005642-10A1 is greatly acknowledged.

Cubic-foot tree volumes and product recoveries for eastern redcedar in the Ozarks

Treesearch

Leland F. Hanks

1979-01-01

Tree volume tables and equations for eastern redcedar are presented for gross volume, cant volume, and volume of sawmill residue. These volumes, when multiplied by the average value per cubic foot of cants and residue, provide a way to estimate tree value.

Full-wave Nonlinear Inverse Scattering for Acoustic and Electromagnetic Breast Imaging

NASA Astrophysics Data System (ADS)

Haynes, Mark Spencer

Acoustic and electromagnetic full-wave nonlinear inverse scattering techniques are explored in both theory and experiment with the ultimate aim of noninvasively mapping the material properties of the breast. There is evidence that benign and malignant breast tissue have different acoustic and electrical properties and imaging these properties directly could provide higher quality images with better diagnostic certainty. In this dissertation, acoustic and electromagnetic inverse scattering algorithms are first developed and validated in simulation. The forward solvers and optimization cost functions are modified from traditional forms in order to handle the large or lossy imaging scenes present in ultrasonic and microwave breast imaging. An antenna model is then presented, modified, and experimentally validated for microwave S-parameter measurements. Using the antenna model, a new electromagnetic volume integral equation is derived in order to link the material properties of the inverse scattering algorithms to microwave S-parameters measurements allowing direct comparison of model predictions and measurements in the imaging algorithms. This volume integral equation is validated with several experiments and used as the basis of a free-space inverse scattering experiment, where images of the dielectric properties of plastic objects are formed without the use of calibration targets. These efforts are used as the foundation of a solution and formulation for the numerical characterization of a microwave near-field cavity-based breast imaging system. The system is constructed and imaging results of simple targets are given. Finally, the same techniques are used to explore a new self-characterization method for commercial ultrasound probes. The method is used to calibrate an ultrasound inverse scattering experiment and imaging results of simple targets are presented. This work has demonstrated the feasibility of quantitative microwave inverse scattering by way of a self-consistent characterization formalism, and has made headway in the same area for ultrasound.

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

NASA Astrophysics Data System (ADS)

Guerrero-García, Guillermo Iván; González-Tovar, Enrique; Olvera de la Cruz, Mónica

2011-08-01

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-elec-trolytes with different ion sizes.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Finite volume model for two-dimensional shallow environmental flow

USGS Publications Warehouse

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

Predictive modeling of multicellular structure formation by using Cellular Particle Dynamics simulations

NASA Astrophysics Data System (ADS)

McCune, Matthew; Shafiee, Ashkan; Forgacs, Gabor; Kosztin, Ioan

2014-03-01

Cellular Particle Dynamics (CPD) is an effective computational method for describing and predicting the time evolution of biomechanical relaxation processes of multicellular systems. A typical example is the fusion of spheroidal bioink particles during post bioprinting structure formation. In CPD cells are modeled as an ensemble of cellular particles (CPs) that interact via short-range contact interactions, characterized by an attractive (adhesive interaction) and a repulsive (excluded volume interaction) component. The time evolution of the spatial conformation of the multicellular system is determined by following the trajectories of all CPs through integration of their equations of motion. CPD was successfully applied to describe and predict the fusion of 3D tissue construct involving identical spherical aggregates. Here, we demonstrate that CPD can also predict tissue formation involving uneven spherical aggregates whose volumes decrease during the fusion process. Work supported by NSF [PHY-0957914]. Computer time provided by the University of Missouri Bioinformatics Consortium.

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Frederickson, Paul O.

1990-01-01

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.

Exponential Methods for the Time Integration of Schroedinger Equation

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

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

3D Material Response Analysis of PICA Pyrolysis Experiments

NASA Technical Reports Server (NTRS)

Oliver, A. Brandon

2017-01-01

The PICA decomposition experiments of Bessire and Minton are investigated using 3D material response analysis. The steady thermoelectric equations have been added to the CHAR code to enable analysis of the Joule-heated experiments and the DAKOTA optimization code is used to define the voltage boundary condition that yields the experimentally observed temperature response. This analysis has identified a potential spatial non-uniformity in the PICA sample temperature driven by the cooled copper electrodes and thermal radiation from the surface of the test article (Figure 1). The non-uniformity leads to a variable heating rate throughout the sample volume that has an effect on the quantitative results of the experiment. Averaging the results of integrating a kinetic reaction mechanism with the heating rates seen across the sample volume yield a shift of peak species production to lower temperatures that is more significant for higher heating rates (Figure 2) when compared to integrating the same mechanism at the reported heating rate. The analysis supporting these conclusions will be presented along with a proposed analysis procedure that permits quantitative use of the existing data. Time permitting, a status on the in-development kinetic decomposition mechanism based on this data will be presented as well.

Discreteness-induced concentration inversion in mesoscopic chemical systems.

PubMed

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

2012-04-10

Molecular discreteness is apparent in small-volume chemical systems, such as biological cells, leading to stochastic kinetics. Here we present a theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network. We consider independent realizations of the same chemical system in compartments of different volumes. Rate equations ignore molecular discreteness and predict the same average steady-state concentrations in all compartments. However, our theory predicts that the average steady state of the system varies with volume: if a species is more abundant than another for large volumes, then the reverse occurs for volumes below a critical value, leading to a concentration inversion effect. The addition of extrinsic noise increases the size of the critical volume. We theoretically predict the critical volumes and verify, by exact stochastic simulations, that rate equations are qualitatively incorrect in sub-critical volumes.

A Growth and Yield Model for Thinned Stands of Yellow-Poplar

Treesearch

Bruce R. Knoebel; Harold E. Burkhart; Donald E. Beck

1986-01-01

Simultaneous growth and yield equations were developed for predicting basal area growth and cubic-foot volume growth and yield in thinned stands of yellow-poplar. A joint loss function involving both volume and basal area was used to estimate the coefficients in the system of equations. The estimates obtained were analytically compatible, invariant for projection...

Development of equations for predicting Puerto Rican subtropical dry forest biomass and volume

Treesearch

Thomas J. Brandeis; Matthew Delaney; Bernard R. Parresol; Larry Royer

2006-01-01

Carbon accounting, forest health monitoring and sustainable management of the subtropical dry forests of Puerto Rico and other Caribbean Islands require an accurate assessment of forest aboveground biomass (AGB) and stem volume. One means of improving assessment accuracy is the development of predictive equations derived from locally collected data. Forest inventory...

Development of equations for predicting Puerto Rican subtropical dry forest biomass and volume.

Treesearch

Thomas J. Brandeis; Matthew Delaney; Bernard R. Parresol; Larry Royer

2006-01-01

Carbon accounting, forest health monitoring and sustainable management of the subtropical dry forests of Puerto Rico and other Caribbean Islands require an accurate assessment of forest aboveground biomass (AGB) and stem volume. One means of improving assessment accuracy is the development of predictive equations derived from locally collected data. Forest inventory...

Ratio equations for loblolly pine trees

Treesearch

Dehai Zhao; Michael Kane; Daniel Markewitz; Robert Teskey

2015-01-01

The conversion factors (CFs) or expansion factors (EFs) are often used to convert volume to green or dry weight, or from one component biomass to estimate total biomass or other component biomass. These factors might be inferred from the previously developed biomass and volume equations with or without destructive sampling data. However, how the factors are related to...

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Integrability and structural stability of solutions to the Ginzburg-Landau equation

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1986-01-01

The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).

Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

NASA Technical Reports Server (NTRS)

Geddes, K. O.

1977-01-01

If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

An Integrated Computational Materials Engineering Method for Woven Carbon Fiber Composites Preforming Process

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

Zhang, Weizhao; Ren, Huaqing; Wang, Zequn

2016-10-19

An integrated computational materials engineering method is proposed in this paper for analyzing the design and preforming process of woven carbon fiber composites. The goal is to reduce the cost and time needed for the mass production of structural composites. It integrates the simulation methods from the micro-scale to the macro-scale to capture the behavior of the composite material in the preforming process. In this way, the time consuming and high cost physical experiments and prototypes in the development of the manufacturing process can be circumvented. This method contains three parts: the micro-scale representative volume element (RVE) simulation to characterizemore » the material; the metamodeling algorithm to generate the constitutive equations; and the macro-scale preforming simulation to predict the behavior of the composite material during forming. The results show the potential of this approach as a guidance to the design of composite materials and its manufacturing process.« less

Permeable Surface Corrections for Ffowcs Williams and Hawkings Integrals

NASA Technical Reports Server (NTRS)

Lockard, David P.; Casper, Jay H.

2005-01-01

The acoustic prediction methodology discussed herein applies an acoustic analogy to calculate the sound generated by sources in an aerodynamic simulation. Sound is propagated from the computed flow field by integrating the Ffowcs Williams and Hawkings equation on a suitable control surface. Previous research suggests that, for some applications, the integration surface must be placed away from the solid surface to incorporate source contributions from within the flow volume. As such, the fluid mechanisms in the input flow field that contribute to the far-field noise are accounted for by their mathematical projection as a distribution of source terms on a permeable surface. The passage of nonacoustic disturbances through such an integration surface can result in significant error in an acoustic calculation. A correction for the error is derived in the frequency domain using a frozen gust assumption. The correction is found to work reasonably well in several test cases where the error is a small fraction of the actual radiated noise. However, satisfactory agreement has not been obtained between noise predictions using the solution from a three-dimensional, detached-eddy simulation of flow over a cylinder.

Anthropometrically estimated total body water volumes are larger than modeled urea volume in chronic hemodialysis patients: effects of age, race, and gender.

PubMed

Daugirdas, John T; Greene, Tom; Depner, Thomas A; Chumlea, Cameron; Rocco, Michael J; Chertow, Glenn M

2003-09-01

The modeled volume of urea distribution (Vm) in intermittently hemodialyzed patients is often compared with total body water (TBW) volume predicted from population studies of patient anthropometrics (Vant). Using data from the HEMO Study, we compared Vm determined by both blood-side and dialysate-side urea kinetic models with Vant as calculated by the Watson, Hume-Weyers, and Chertow anthropometric equations. Median levels of dialysate-based Vm and blood-based Vm agreed (43% and 44% of body weight, respectively). These volumes were lower than anthropometric estimates of TBW, which had median values of 52% to 55% of body weight for the three formulas evaluated. The difference between the Watson equation for TBW and modeled urea volume was greater in Caucasians (19%) than in African Americans (13%). Correlations between Vm and Vant determined by each of the three anthropometric estimation equations were similar; but Vant derived from the Watson formula had a slightly higher correlation with Vm. The difference between Vm and the anthropometric formulas was greatest with the Chertow equation, less with the Hume-Weyers formula, and least with the Watson estimate. The age term in the Watson equation for men that adjusts Vant downward with increasing age reduced an age effect on the difference between Vant and Vm in men. The findings show that kinetically derived values for V from blood-side and dialysate-side modeling are similar, and that these modeled urea volumes are lower by a substantial amount than anthropometric estimates of TBW. The higher values for anthropometry-derived TBW in hemodialyzed patients could be due to measurement errors. However, the possibility exists that TBW space is contracted in patients with end-stage renal disease (ESRD) or that the TBW space and the urea distribution space are not identical.

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

An integrable family of Monge-Ampère equations and their multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sarioǧlu, Ö.

1993-02-01

We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the first.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics

DTIC Science & Technology

2007-09-30

sub-processor must be added as shown in the blue box of Fig. 1. We first consider the Kadomtsev - Petviashvili (KP) equation ηt + coηx +αηηx + βη ...analytic integration of the so-called “soliton equations ,” I have discovered how the GFT can be used to solved higher order equations for which study...analytical study and extremely fast numerical integration of the extended nonlinear Schroedinger equation for fully three dimensional wave motion

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

ERIC Educational Resources Information Center

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

FIA's volume-to-biomass conversion method (CRM) generally underestimates biomass in comparison to published equations

Treesearch

David. C. Chojnacky

2012-01-01

An update of the Jenkins et al. (2003) biomass estimation equations for North American tree species resulted in 35 generalized equations developed from published equations. These 35 equations, which predict aboveground biomass of individual species grouped according to a taxa classification (based on genus or family and sometimes specific gravity), generally predicted...

Continuous properties of the data-to-solution map for a generalized μ-Camassa-Holm integrable equation

NASA Astrophysics Data System (ADS)

Yu, Shengqi

2018-05-01

This work studies a generalized μ-type integrable equation with both quadratic and cubic nonlinearities; the μ-Camassa-Holm and modified μ-Camassa-Holm equations are members of this family of equations. It has been shown that the Cauchy problem for this generalized μ-Camassa-Holm integrable equation is locally well-posed for initial data u0 ∈ Hs, s > 5/2. In this work, we further investigate the continuity properties to this equation. It is proved in this work that the data-to-solution map of the proposed equation is not uniformly continuous. It is also found that the solution map is Hölder continuous in the Hr-topology when 0 ≤ r < s with Hölder exponent α depending on both s and r.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Diffusion in Brain Extracellular Space

PubMed Central

Syková, Eva; Nicholson, Charles

2009-01-01

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is about 20% and the tortuosity about 1.6 (i.e. free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties are valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain. PMID:18923183

On a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong

2017-02-01

In this paper, a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation is investigated. The underlying integrable structures like the Lax pair, the infinite number of conservation laws, the Darboux-Bäcklund transformation, and the solutions are presented in the explicit form. The theory of the semi-discrete equation including integrable properties yields the corresponding theory of the continuous counterpart in the continuous limit. Finally, numerical experiments are provided to demonstrate the effectiveness of the developed integrable semi-discretization algorithms.

Calculation of Moment Matrix Elements for Bilinear Quadrilaterals and Higher-Order Basis Functions

DTIC Science & Technology

2016-01-06

methods are known as boundary integral equation (BIE) methods and the present study falls into this category. The numerical solution of the BIE is...iterated integrals. The inner integral involves the product of the free-space Green’s function for the Helmholtz equation multiplied by an appropriate...Website: http://www.wipl-d.com/ 5. Y. Zhang and T. K. Sarkar, Parallel Solution of Integral Equation -Based EM Problems in the Frequency Domain. New

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Quantification of pleural effusion on CT by simple measurement.

PubMed

Hazlinger, Martin; Ctvrtlik, Filip; Langova, Katerina; Herman, Miroslav

2014-01-01

To find the simplest method for quantifying pleural effusion volume from CT scans. Seventy pleural effusions found on chest CT examination in 50 consecutive adult patients with the presence of free pleural effusion were included. The volume of pleural effusion was calculated from a three-dimensional reconstruction of CT scans. Planar measurements were made on CT scans and their two-dimensional reconstructions in the sagittal plane and at three levels on transversal scans. Individual planar measurements were statistically compared with the detected volume of pleural effusion. Regression equations, averaged absolute difference between observed and predicted values and determination coefficients were found for all measurements and their combinations. A tabular expression of the best single planar measurement was created. The most accurate correlation between the volume and a single planar measurement was found in the dimension measured perpendicular to the parietal pleura on transversal scan with the greatest depth of effusion. Conversion of this measurement to the appropriate volume is possible by regression equation: Volume = 0.365 × b(3) - 4.529 × b(2) + 159.723 × b - 88.377. We devised a simple method of conversion of a single planar measurement on CT scan to the volume of pleural effusion. The tabular expression of our equation can be easily and effectively used in routine practice.

Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study

PubMed Central

Urbic, Tomaz

2016-01-01

Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures. PMID:27875894

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

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

Maccari, A.

1997-08-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large classmore » of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}« less

Comment on "Symplectic integration of magnetic systems" by Stephen D. Webb [J. Comput. Phys. 270 (2014) 570-576

NASA Astrophysics Data System (ADS)

Zhang, Shuangxi; Jia, Yuesong; Sun, Qizhi

2015-02-01

Webb [1] proposed a method to get symplectic integrators of magnetic systems by Taylor expanding the discrete Euler-Lagrangian equations (DEL) which resulted from variational symplectic method by making the variation of the discrete action [2], and approximating the results to the order of O (h2), where h is the time step. And in that paper, Webb thought that the integrators obtained by that method are symplectic ones, especially, he treated Boris integrator (BI) as the symplectic one. However, we have questions about Webb's results. Theoretically the transformation of phase-space coordinates between two adjacent points induced by symplectic algorithm should conserve a symplectic 2-form [2-5]. As proved in Refs. [2,3], the transformations induced by the standard symplectic integrator derived from Hamilton and the variational symplectic integrator (VSI) [2,6] from Lagrangian should conserve a symplectic 2-forms. But the approximation of VSI to O (h2) obtained by that paper is hard to conserve a symplectic 2-form, contrary to the claim of [1]. In the next section, we will use BI as an example to support our point and will prove BI not to be a symplectic one but an integrator conserving discrete phase-space volume.

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

NASA Technical Reports Server (NTRS)

Gatewood, B. E.

1971-01-01

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

A novel multiphysic model for simulation of swelling equilibrium of ionized thermal-stimulus responsive hydrogels

NASA Astrophysics Data System (ADS)

Li, Hua; Wang, Xiaogui; Yan, Guoping; Lam, K. Y.; Cheng, Sixue; Zou, Tao; Zhuo, Renxi

2005-03-01

In this paper, a novel multiphysic mathematical model is developed for simulation of swelling equilibrium of ionized temperature sensitive hydrogels with the volume phase transition, and it is termed the multi-effect-coupling thermal-stimulus (MECtherm) model. This model consists of the steady-state Nernst-Planck equation, Poisson equation and swelling equilibrium governing equation based on the Flory's mean field theory, in which two types of polymer-solvent interaction parameters, as the functions of temperature and polymer-network volume fraction, are specified with or without consideration of the hydrogen bond interaction. In order to examine the MECtherm model consisting of nonlinear partial differential equations, a meshless Hermite-Cloud method is used for numerical solution of one-dimensional swelling equilibrium of thermal-stimulus responsive hydrogels immersed in a bathing solution. The computed results are in very good agreements with experimental data for the variation of volume swelling ratio with temperature. The influences of the salt concentration and initial fixed-charge density are discussed in detail on the variations of volume swelling ratio of hydrogels, mobile ion concentrations and electric potential of both interior hydrogels and exterior bathing solution.

A comparison of upwind schemes for computation of three-dimensional hypersonic real-gas flows

NASA Technical Reports Server (NTRS)

Gerbsch, R. A.; Agarwal, R. K.

1992-01-01

The method of Suresh and Liou (1992) is extended, and the resulting explicit noniterative upwind finite-volume algorithm is applied to the integration of 3D parabolized Navier-Stokes equations to model 3D hypersonic real-gas flowfields. The solver is second-order accurate in the marching direction and employs flux-limiters to make the algorithm second-order accurate, with total variation diminishing in the cross-flow direction. The algorithm is used to compute hypersonic flow over a yawed cone and over the Ames All-Body Hypersonic Vehicle. The solutions obtained agree well with other computational results and with experimental data.

SMD-based numerical stochastic perturbation theory

NASA Astrophysics Data System (ADS)

Dalla Brida, Mattia; Lüscher, Martin

2017-05-01

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously established and the use of higher-order symplectic integration schemes is shown to be highly profitable in this context. For illustration, the gradient-flow coupling in finite volume with Schrödinger functional boundary conditions is computed to two-loop (i.e. NNL) order in the SU(3) gauge theory. The scaling behaviour of the algorithm turns out to be rather favourable in this case, which allows the computations to be driven close to the continuum limit.

An analytical approach for the calculation of stress-intensity factors in transformation-toughened ceramics

NASA Astrophysics Data System (ADS)

Müller, W. H.

1990-12-01

Stress-induced transformation toughening in Zirconia-containing ceramics is described analytically by means of a quantitative model: A Griffith crack which interacts with a transformed, circular Zirconia inclusion. Due to its volume expansion, a ZrO2-particle compresses its flanks, whereas a particle in front of the crack opens the flanks such that the crack will be attracted and finally absorbed. Erdogan's integral equation technique is applied to calculate the dislocation functions and the stress-intensity-factors which correspond to these situations. In order to derive analytical expressions, the elastic constants of the inclusion and the matrix are assumed to be equal.

Partial drift volume due to a self-propelled swimmer

NASA Astrophysics Data System (ADS)

Chisholm, Nicholas G.; Khair, Aditya S.

2018-01-01

We assess the ability of a self-propelled swimmer to displace a volume of fluid that is large compared to its own volume via the mechanism of partial drift. The swimmer performs rectilinear locomotion in an incompressible, unbounded Newtonian fluid. The partial drift volume D is the volume of fluid enclosed between the initial and final profiles of an initially flat circular disk of marked fluid elements; the disk is initially aligned perpendicular to the direction of locomotion and subsequently distorted due to the passage of the swimmer, which travels a finite distance. To focus on the possibility of large-scale drift, we model the swimmer simply as a force dipole aligned with the swimming direction. At zero Reynolds number (Re =0 ), we demonstrate that D grows without limit as the radius of the marked fluid disk h is made large, indicating that a swimmer at Re =0 can generate a partial drift volume much larger than its own volume. Next, we consider a steady swimmer at small Re , which is modeled as the force-dipole solution to Oseen's equation. Here, we find that D no longer diverges with h , which is due to inertial screening of viscous forces, and is effectively proportional to the magnitude of the force dipole exerted by the swimmer. The validity of this result is extended to Re ≥O (1 ) —the realm of intermediate-Re swimmers such as copepods—by taking advantage of the fact that, in this case, the flow is also described by Oseen's equations at distances much larger than the characteristic linear dimension of the swimmer. Next, we utilize an integral momentum balance to demonstrate that our analysis for a steady inertial swimmer also holds, in a time-averaged sense, for an unsteady swimmer that does not experience a net acceleration over a stroke cycle. Finally, we use experimental data to estimate D for a few real swimmers. Interestingly, we find that D depends heavily on the kinematics of swimming, and, in certain cases, D can be significantly greater than the volume of the swimmer at Re ≥O (1 ) . Our work also highlights that D due to a self-propelled body is fundamentally different than that due to a body towed by an external force. In particular, predictions of D in the latter case cannot be utilized to estimate D for a self-propelled swimmer.

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

Kleinert, H; Zatloukal, V

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

NASA Technical Reports Server (NTRS)

Sloss, J. M.; Kranzler, S. K.

1972-01-01

The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Analysis of Hydraulic Servo Equations for WRDRF Prototype Control System : Volume I

DOT National Transportation Integrated Search

1971-10-01

A set of dynamic performance equations derived by Wylie Labs., Huntsville, Alabama, were independently rederived and checked. These equations describe the perfromance of the prototype electro hydraulic servo actuator system selected by Wylie as repre...

Stem Profile for Southern Equations for Southern Tree Species

Treesearch

Alexander Clark; Ray A. Souter; Bryce E. Schlaegel

1991-01-01

Form-class segmented-profile equations for 58 southern tree species and species groups are presented.The profile equations are based on taper data for 13,469 trees sampled in natural stands in many locations across the South.The profile equations predict diameter at any given height, height to give diameter, and volume between two heights.Equation coefficients for use...

Temperature Dependence of Densities and Excess Molar Volumes of the Ternary Mixture (1-Butanol + Chloroform + Benzene) and its Binary Constituents (1-Butanol + Chloroform and 1-Butanol + Benzene)

NASA Astrophysics Data System (ADS)

Smiljanić, Jelena D.; Kijevčanin, Mirjana Lj.; Djordjević, Bojan D.; Grozdanić, Dušan K.; Šerbanović, Slobodan P.

2008-04-01

Densities ρ of the 1-butanol + chloroform + benzene ternary mixture and the 1-butanol + chloroform and 1-butanol + benzene binaries have been measured at six temperatures (288.15, 293.15, 298.15, 303.15, 308.15, and 313.15) K and atmospheric pressure, using an oscillating U-tube densimeter. From these densities, excess molar volumes ( V E) were calculated and fitted to the Redlich Kister equation for all binary mixtures and to the Nagata and Tamura equation for the ternary system. The Radojković et al. equation has been used to predict excess molar volumes of the ternary mixtures. Also, V E data of the binary systems were correlated by the van der Waals (vdW1) and Twu Coon Bluck Tilton (TCBT) mixing rules coupled with the Peng Robinson Stryjek Vera (PRSV) equation of state. The prediction and correlation of V E data for the ternary system were performed by the same models.

FOSSIL2 energy policy model documentation: FOSSIL2 documentation

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

None

1980-10-01

This report discusses the structure, derivations, assumptions, and mathematical formulation of the FOSSIL2 model. Each major facet of the model - supply/demand interactions, industry financing, and production - has been designed to parallel closely the actual cause/effect relationships determining the behavior of the United States energy system. The data base for the FOSSIL2 program is large, as is appropriate for a system dynamics simulation model. When possible, all data were obtained from sources well known to experts in the energy field. Cost and resource estimates are based on DOE data whenever possible. This report presents the FOSSIL2 model at severalmore » levels. Volumes II and III of this report list the equations that comprise the FOSSIL2 model, along with variable definitions and a cross-reference list of the model variables. Volume II provides the model equations with each of their variables defined, while Volume III lists the equations, and a one line definition for equations, in a shorter, more readable format.« less

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

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

Wei, Guowei; Baker, Nathan A.

2016-11-11

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

Nonzero solutions of nonlinear integral equations modeling infectious disease

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

Williams, L.R.; Leggett, R.W.

1982-01-01

Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, x(t) = ..integral../sup t//sub t-tau/f(s,x(s))ds, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if x(t) is the proportion of infectives at time t and f(t,x(t)) is the proportion of new infectives per unit time.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Electrokinetic coupling in unsaturated porous media.

PubMed

Revil, A; Linde, N; Cerepi, A; Jougnot, D; Matthäi, S; Finsterle, S

2007-09-01

We consider a charged porous material that is saturated by two fluid phases that are immiscible and continuous on the scale of a representative elementary volume. The wetting phase for the grains is water and the nonwetting phase is assumed to be an electrically insulating viscous fluid. We use a volume-averaging approach to derive the linear constitutive equations for the electrical current density as well as the seepage velocities of the wetting and nonwetting phases on the scale of a representative elementary volume. These macroscopic constitutive equations are obtained by volume-averaging Ampère's law together with the Nernst-Planck equation and the Stokes equations. The material properties entering the macroscopic constitutive equations are explicitly described as functions of the saturation of the water phase, the electrical formation factor, and parameters that describe the capillary pressure function, the relative permeability functions, and the variation of electrical conductivity with saturation. New equations are derived for the streaming potential and electro-osmosis coupling coefficients. A primary drainage and imbibition experiment is simulated numerically to demonstrate that the relative streaming potential coupling coefficient depends not only on the water saturation, but also on the material properties of the sample, as well as the saturation history. We also compare the predicted streaming potential coupling coefficients with experimental data from four dolomite core samples. Measurements on these samples include electrical conductivity, capillary pressure, the streaming potential coupling coefficient at various levels of saturation, and the permeability at saturation of the rock samples. We found very good agreement between these experimental data and the model predictions.

Multistep integration formulas for the numerical integration of the satellite problem

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Tapley, B. D.

1981-01-01

The use of two Class 2/fixed mesh/fixed order/multistep integration packages of the PECE type for the numerical integration of the second order, nonlinear, ordinary differential equation of the satellite orbit problem. These two methods are referred to as the general and the second sum formulations. The derivation of the basic equations which characterize each formulation and the role of the basic equations in the PECE algorithm are discussed. Possible starting procedures are examined which may be used to supply the initial set of values required by the fixed mesh/multistep integrators. The results of the general and second sum integrators are compared to the results of various fixed step and variable step integrators.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

The Algorithm Theoretical Basis Document for the Atmospheric Delay Correction to GLAS Laser Altimeter Ranges. Volume 8

NASA Technical Reports Server (NTRS)

Herring, Thomas A.; Quinn, Katherine J.

2012-01-01

NASA s Ice, Cloud, and Land Elevation Satellite (ICESat) mission will be launched late 2001. It s primary instrument is the Geoscience Laser Altimeter System (GLAS) instrument. The main purpose of this instrument is to measure elevation changes of the Greenland and Antarctic icesheets. To accurately measure the ranges it is necessary to correct for the atmospheric delay of the laser pulses. The atmospheric delay depends on the integral of the refractive index along the path that the laser pulse travels through the atmosphere. The refractive index of air at optical wavelengths is a function of density and molecular composition. For ray paths near zenith and closed form equations for the refractivity, the atmospheric delay can be shown to be directly related to surface pressure and total column precipitable water vapor. For ray paths off zenith a mapping function relates the delay to the zenith delay. The closed form equations for refractivity recommended by the International Union of Geodesy and Geophysics (IUGG) are optimized for ground based geodesy techniques and in the next section we will consider whether these equations are suitable for satellite laser altimetry.

A 3D model for rain-induced landslides based on molecular dynamics with fractal and fractional water diffusion

NASA Astrophysics Data System (ADS)

Martelloni, Gianluca; Bagnoli, Franco; Guarino, Alessio

2017-09-01

We present a three-dimensional model of rain-induced landslides, based on cohesive spherical particles. The rainwater infiltration into the soil follows either the fractional or the fractal diffusion equations. We analytically solve the fractal partial differential equation (PDE) for diffusion with particular boundary conditions to simulate a rainfall event. We developed a numerical integration scheme for the PDE, compared with the analytical solution. We adapt the fractal diffusion equation obtaining the gravimetric water content that we use as input of a triggering scheme based on Mohr-Coulomb limit-equilibrium criterion. This triggering is then complemented by a standard molecular dynamics algorithm, with an interaction force inspired by the Lennard-Jones potential, to update the positions and velocities of particles. We present our results for homogeneous and heterogeneous systems, i.e., systems composed by particles with same or different radius, respectively. Interestingly, in the heterogeneous case, we observe segregation effects due to the different volume of the particles. Finally, we analyze the parameter sensibility both for the triggering and the propagation phases. Our simulations confirm the results of a previous two-dimensional model and therefore the feasible applicability to real cases.

Finite element code development for modeling detonation of HMX composites

NASA Astrophysics Data System (ADS)

Duran, Adam V.; Sundararaghavan, Veera

2017-01-01

In this work, we present a hydrodynamics code for modeling shock and detonation waves in HMX. A stable efficient solution strategy based on a Taylor-Galerkin finite element (FE) discretization was developed to solve the reactive Euler equations. In our code, well calibrated equations of state for the solid unreacted material and gaseous reaction products have been implemented, along with a chemical reaction scheme and a mixing rule to define the properties of partially reacted states. A linear Gruneisen equation of state was employed for the unreacted HMX calibrated from experiments. The JWL form was used to model the EOS of gaseous reaction products. It is assumed that the unreacted explosive and reaction products are in both pressure and temperature equilibrium. The overall specific volume and internal energy was computed using the rule of mixtures. Arrhenius kinetics scheme was integrated to model the chemical reactions. A locally controlled dissipation was introduced that induces a non-oscillatory stabilized scheme for the shock front. The FE model was validated using analytical solutions for SOD shock and ZND strong detonation models. Benchmark problems are presented for geometries in which a single HMX crystal is subjected to a shock condition.

Molecular based equation of state for shocked liquid nitromethane.

PubMed

Desbiens, Nicolas; Bourasseau, Emeric; Maillet, Jean-Bernard; Soulard, Laurent

2009-07-30

An approach is proposed to obtain the equation of state of unreactive shocked liquid nitromethane. Unlike previous major works, this equation of state is not based on extended integration schemes [P.C. Lysne, D.R. Hardesty, Fundamental equation of state of liquid nitromethane to 100 kbar, J. Chem. Phys. 59 (1973) 6512]. It does not follow the way proposed by Winey et al. [J.M. Winey, G.E. Duvall, M.D. Knudson, Y.M. Gupta, Equation of state and temperature measurements for shocked nitromethane, J. Chem. Phys. 113 (2000) 7492] where the specific heat C(v), the isothermal bulk modulus B(T) and the coefficient of thermal pressure (deltaP/deltaT)(v) are modeled as functions of temperature and volume using experimental data. In this work, we compute the complete equation of state by microscopic calculations. Indeed, by means of Monte Carlo molecular simulations, we have proposed a new force field for nitromethane that lead to a good description of shock properties [N. Desbiens, E. Bourasseau, J.-B. Maillet, Potential optimization for the calculation of shocked liquid nitromethane properties, Mol. Sim. 33 (2007) 1061; A. Hervouët, N. Desbiens, E. Bourasseau, J.-B. Maillet, Microscopic approaches to liquid nitromethane detonation properties, J. Phys. Chem. B 112 (2008) 5070]. Particularly, it has been shown that shock temperatures and second shock temperatures are accurately reproduced which is significative of the quality of the potential. Here, thermodynamic derivative properties are computed: specific heats, Grüneisen parameter, sound velocity among others, along the Hugoniot curve. This work constitutes to our knowledge the first determination of the equation of state of an unreactive shocked explosive by molecular simulations.

Theory for the three-dimensional Mercedes-Benz model of water.

PubMed

Bizjak, Alan; Urbic, Tomaz; Vlachy, Vojko; Dill, Ken A

2009-11-21

The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the "right answer," we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim's Ornstein-Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation.

Theory for the three-dimensional Mercedes-Benz model of water

PubMed Central

Bizjak, Alan; Urbic, Tomaz; Vlachy, Vojko; Dill, Ken A.

2009-01-01

The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the “right answer,” we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim’s Ornstein–Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation. PMID:19929057

Theory for the three-dimensional Mercedes-Benz model of water

NASA Astrophysics Data System (ADS)

Bizjak, Alan; Urbic, Tomaz; Vlachy, Vojko; Dill, Ken A.

2009-11-01

The two-dimensional Mercedes-Benz (MB) model of water has been widely studied, both by Monte Carlo simulations and by integral equation methods. Here, we study the three-dimensional (3D) MB model. We treat water as spheres that interact through Lennard-Jones potentials and through a tetrahedral Gaussian hydrogen bonding function. As the "right answer," we perform isothermal-isobaric Monte Carlo simulations on the 3D MB model for different pressures and temperatures. The purpose of this work is to develop and test Wertheim's Ornstein-Zernike integral equation and thermodynamic perturbation theories. The two analytical approaches are orders of magnitude more efficient than the Monte Carlo simulations. The ultimate goal is to find statistical mechanical theories that can efficiently predict the properties of orientationally complex molecules, such as water. Also, here, the 3D MB model simply serves as a useful workbench for testing such analytical approaches. For hot water, the analytical theories give accurate agreement with the computer simulations. For cold water, the agreement is not as good. Nevertheless, these approaches are qualitatively consistent with energies, volumes, heat capacities, compressibilities, and thermal expansion coefficients versus temperature and pressure. Such analytical approaches offer a promising route to a better understanding of water and also the aqueous solvation.

Simultaneous temporally resolved DPIV and pressure measurements of symmetric oscillations in a scaled-up vocal fold model

NASA Astrophysics Data System (ADS)

Ringenberg, Hunter; Rogers, Dylan; Wei, Nathaniel; Krane, Michael; Wei, Timothy

2017-11-01

The objective of this study is to apply experimental data to theoretical framework of Krane (2013) in which the principal aeroacoustic source is expressed in terms of vocal fold drag, glottal jet dynamic head, and glottal exit volume flow, reconciling formal theoretical aeroacoustic descriptions of phonation with more traditional lumped-element descriptions. These quantities appear in the integral equations of motion for phonatory flow. In this way time resolved velocity field measurements can be used to compute time-resolved estimates of the relevant terms in the integral equations of motion, including phonation aeroacoustic source strength. A simplified 10x scale vocal fold model from Krane, et al. (2007) was used to examine symmetric, i.e. `healthy', oscillatory motion of the vocal folds. By using water as the working fluid, very high spatial and temporal resolution was achieved. Temporal variation of transglottal pressure was simultaneously measured with flow on the vocal fold model mid-height. Experiments were dynamically scaled to examine a range of frequencies corresponding to male and female voice. The simultaneity of the pressure and flow provides new insights into the aeroacoustics associated with vocal fold oscillations. Supported by NIH Grant No. 2R01 DC005642-11.

Integrability of the Kruskal--Zabusky Discrete Equation by Multiscale Expansion

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

Levi, Decio; Scimiterna, Christian

2010-03-08

In 1965 Kruskal and Zabusky in a very famous article in Physical Review Letters introduced the notion of 'soliton' to describe the interaction of solitary waves solutions of the Korteweg de Vries equation (KdV). To do so they introduced a discrete approximation to the KdV, the Kruskal-Zabusky equation (KZ). Here we analyze the KZ equation using the multiscale expansion and show that the equation is only A{sub 2} integrable.

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

NASA Astrophysics Data System (ADS)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

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

Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K.

2016-12-15

Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.

The preliminary exploration of 64-slice volume computed tomography in the accurate measurement of pleural effusion.

PubMed

Guo, Zhi-Jun; Lin, Qiang; Liu, Hai-Tao; Lu, Jun-Ying; Zeng, Yan-Hong; Meng, Fan-Jie; Cao, Bin; Zi, Xue-Rong; Han, Shu-Ming; Zhang, Yu-Huan

2013-09-01

Using computed tomography (CT) to rapidly and accurately quantify pleural effusion volume benefits medical and scientific research. However, the precise volume of pleural effusions still involves many challenges and currently does not have a recognized accurate measuring. To explore the feasibility of using 64-slice CT volume-rendering technology to accurately measure pleural fluid volume and to then analyze the correlation between the volume of the free pleural effusion and the different diameters of the pleural effusion. The 64-slice CT volume-rendering technique was used to measure and analyze three parts. First, the fluid volume of a self-made thoracic model was measured and compared with the actual injected volume. Second, the pleural effusion volume was measured before and after pleural fluid drainage in 25 patients, and the volume reduction was compared with the actual volume of the liquid extract. Finally, the free pleural effusion volume was measured in 26 patients to analyze the correlation between it and the diameter of the effusion, which was then used to calculate the regression equation. After using the 64-slice CT volume-rendering technique to measure the fluid volume of the self-made thoracic model, the results were compared with the actual injection volume. No significant differences were found, P = 0.836. For the 25 patients with drained pleural effusions, the comparison of the reduction volume with the actual volume of the liquid extract revealed no significant differences, P = 0.989. The following linear regression equation was used to compare the pleural effusion volume (V) (measured by the CT volume-rendering technique) with the pleural effusion greatest depth (d): V = 158.16 × d - 116.01 (r = 0.91, P = 0.000). The following linear regression was used to compare the volume with the product of the pleural effusion diameters (l × h × d): V = 0.56 × (l × h × d) + 39.44 (r = 0.92, P = 0.000). The 64-slice CT volume-rendering technique can accurately measure the volume in pleural effusion patients, and a linear regression equation can be used to estimate the volume of the free pleural effusion.

The exit-time problem for a Markov jump process

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

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Converting international ¼ inch tree volume to Doyle

Treesearch

Aaron Holley; John R. Brooks; Stuart A. Moss

2014-01-01

An equation for converting Mesavage and Girard's International ¼ inch tree volumes to the Doyle log rule is presented as a function of tree diameter. Volume error for trees having less than four logs exhibited volume prediction errors within a range of ±10 board feet. In addition, volume prediction error as a percent of actual Doyle tree volume...

On the solution of integral equations with a generalized cauchy kernal

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strong ly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1985-01-01

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

Partitioning standard base excess: a new approach.

PubMed

Morgan, Thomas John

2011-12-01

'Standard' or 'extracellular' base excess (SBE) is a modified calculation using one-third the normal hemoglobin concentration. It is a 'CO(2)-invariant' expression of meta- bolic acid-base status integrated across interstitial, plasma and erythrocytic compartments (IPE). SBE also integrates conflicting physical chemical influences on metabolic acid-base status. Until recently attempts to quantify individual contributions to SBE, for example the plasma strong ion gap, failed to span the 'CO(2-)stable' IPE dimension. The first breakthrough was from Anstey, who determined the con- centration of unmeasured charged species referenced to the IPE domain using Wooten's physical chemical version of the Van Slyke equation. In this issue Drs Wolf and DeLand present a diagnostic tool based on an IPE model which dissects a version of SBE (BEnet) into nine independent (BEind) components, all referenced to the IPE domain. The reported components are excess/deficits of free water, chlo- ride, albumin, unmeasured ions, sodium, potassium, lactate, 'Ca-Mg' (a composite divalent cation entity), and phosphate. The model also reports individualised volumes of plasma, erythrocytes and interstitial fluid. The tool is an original contribution, but there are concerns. The impact of assum- ing fixed relationships between arterial and venous acid-base and saturation values in sepsis, anaemia and in differing shock states is unclear. Clinicians are also unlikely to accept that unique, accurate IPE volume determinations can be derived from a single set of blood gas and biochemistry results. Nevertheless, volume determinations aside, the tool is likely to become a valuable addition to the diagnostic armamentarium.

A point-value enhanced finite volume method based on approximate delta functions

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

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

Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si; Dias, Cristiano L.

The thermodynamic and structural properties of the planar soft-sites dumbbell fluid are examined by Monte Carlo simulations and integral equation theory. The dimers are built of two Lennard-Jones segments. Site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions for a range of elongations and densities and the results are compared with Monte Carlo simulations. The critical parameters for selected types of dimers were also estimated. We analyze the influence of the bond length on critical point as well as tested correctness of site-site integral equation theory with different closures. The integral equations canmore » be used to predict the phase diagram of dimers whose molecular parameters are known.« less

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System

NASA Technical Reports Server (NTRS)

Mager, Arthur

1952-01-01

The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

A Bid Price Equation For Timber Sales on the Ouachita and Ozark National Forests

Treesearch

Michael M. Huebschmann; Thomas B. Lynch; David K. Lewis; Daniel S. Tilley; James M. Guldin

2004-01-01

Data from 150 timber sales on the Ouachita and Ozark National Forests in Arkansas and southeaster n Oklahoma were used to develop an equation that relates bid prices to timber sale variables. Variables used to predict the natural logarithm of the real, winning total bid price are the natural logarithms of total sawtimber volume per sale, total pulpwood volume per sale...

Volume growth and response to thinning and fertilizing of Douglas-fir stands in southwestern Oregon.

Treesearch

R.E. Miller; G.W. Clendenen; D. Bruce

1987-01-01

From data for 114 thinning and fertilizing trials in forests of southwestern Oregon and northern California with 5 or more years of observation, we produced equations to estimate gross cubic volume growth of 10- to 70-year-old Douglas-fir stands. These equations use stand escriptors (breast-height age, site index, and relative density) and treatment descriptors to...

Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations

NASA Astrophysics Data System (ADS)

Rosu, Haret C.; Mancas, Stefan C.

2017-04-01

A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

Evaluation of atomic pressure in the multiple time-step integration algorithm.

PubMed

Andoh, Yoshimichi; Yoshii, Noriyuki; Yamada, Atsushi; Okazaki, Susumu

2017-04-15

In molecular dynamics (MD) calculations, reduction in calculation time per MD loop is essential. A multiple time-step (MTS) integration algorithm, the RESPA (Tuckerman and Berne, J. Chem. Phys. 1992, 97, 1990-2001), enables reductions in calculation time by decreasing the frequency of time-consuming long-range interaction calculations. However, the RESPA MTS algorithm involves uncertainties in evaluating the atomic interaction-based pressure (i.e., atomic pressure) of systems with and without holonomic constraints. It is not clear which intermediate forces and constraint forces in the MTS integration procedure should be used to calculate the atomic pressure. In this article, we propose a series of equations to evaluate the atomic pressure in the RESPA MTS integration procedure on the basis of its equivalence to the Velocity-Verlet integration procedure with a single time step (STS). The equations guarantee time-reversibility even for the system with holonomic constrants. Furthermore, we generalize the equations to both (i) arbitrary number of inner time steps and (ii) arbitrary number of force components (RESPA levels). The atomic pressure calculated by our equations with the MTS integration shows excellent agreement with the reference value with the STS, whereas pressures calculated using the conventional ad hoc equations deviated from it. Our equations can be extended straightforwardly to the MTS integration algorithm for the isothermal NVT and isothermal-isobaric NPT ensembles. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Some Exact Solutions of a Nonintegrable Toda-type Equation

NASA Astrophysics Data System (ADS)

Kim, Chanju

2018-05-01

We study a Toda-type equation with two scalar fields which is not integrable and construct two families of exact solutions which are expressed in terms of rational functions. The equation appears in U(1) Chern-Simons theories coupled to two nonrelativistic matter fields with opposite charges. One family of solutions is a trivial embedding of Liouville-type solutions. The other family is obtained by transforming the equation into the Taubes vortex equation on the hyperbolic space. Though the Taubes equation is not integrable, a trivial vacuum solution provides nontrivial solutions to the original Toda-type equation.

On the interpretation of the inverted kinetics equation and space-time calculations of the effectiveness of the VVER-1000 reactor scram system

NASA Astrophysics Data System (ADS)

Zizin, M. N.; Ivanov, L. D.

2013-12-01

In the present paper, an attempt is made to analyze the accuracy of calculating the effectiveness of the VVER-1000 reactor scram system by means of the inverted solution of the kinetics equation (ISKE). In the numerical studies in the intellectual ShIPR software system, the actuation of the reactor scram system with the possible jamming of one of the two most effective rods is simulated. First, the connection of functionals calculated in the space-time computation in different approximations with the kinetics equation is considered on the theoretical level. The formulas are presented in a manner facilitating their coding. Then, the results of processing of several such functions by the ISKE are presented. For estimating the effectiveness of the VVER-1000 reactor scram system, it is proposed to use the measured currents of ionization chambers (IC) jointly with calculated readings of IC imitators. In addition, the integral of the delayed neutron (DN) generation rate multiplied by the adjoint DN source over the volume of the reactor, calculated for the instant of time when insertion of safety rods ends, is used. This integral is necessary for taking into account the spatial reactivity effects. Reasonable agreement was attained for the considered example between the effectiveness of the scram system evaluated by this method and the values obtained by steady-state calculations as the difference of the reciprocal effective multiplication factors with withdrawn and inserted control rods. This agreement was attained with the use of eight-group DN parameters.

PROTEUS two-dimensional Navier-Stokes computer code, version 1.0. Volume 1: Analysis description

NASA Technical Reports Server (NTRS)

Towne, Charles E.; Schwab, John R.; Benson, Thomas J.; Suresh, Ambady

1990-01-01

A new computer code was developed to solve the two-dimensional or axisymmetric, Reynolds averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The thin-layer or Euler equations may also be solved. Turbulence is modeled using an algebraic eddy viscosity model. The objective was to develop a code for aerospace applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The equations are written in nonorthogonal body-fitted coordinates, and solved by marching in time using a fully-coupled alternating direction-implicit procedure with generalized first- or second-order time differencing. All terms are linearized using second-order Taylor series. The boundary conditions are treated implicitly, and may be steady, unsteady, or spatially periodic. Simple Cartesian or polar grids may be generated internally by the program. More complex geometries require an externally generated computational coordinate system. The documentation is divided into three volumes. Volume 1 is the Analysis Description, and describes in detail the governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models.

Equation of State for Detonation Product Gases

NASA Astrophysics Data System (ADS)

Nagayama, Kunihito; Kubota, Shiro

2013-06-01

Based on the empirical linear relationship between detonation velocity and loading density, an approximate description for the Chapman-Jouguet state for detonation product gases of solid phase high explosives has been developed. Provided that the Grüneisen parameter is a function only of volume, systematic and closed system of equations for the Grüneisen parameter and CJ volume have been formulated. These equations were obtained by combining this approximation with the Jones-Stanyukovich-Manson relation together with JWL isentrope for detonation of crystal density PETN. A thermodynamic identity between the Grüneisen parameter and another non-dimensional material parameter introduced by Wu and Jing can be used to derive the enthalpy-pressure-volume equation of state for detonation gases. This Wu-Jing parameter is found to be the ratio of the Grüneisen parameter and the adiabatic index. Behavior of this parameter as a function of pressure was calculated and revealed that their change with pressure is very gradual. By using this equation of state, several isentropes down from the Chapman-Jouguet states reached by four different lower initial density PETN have been calculated and compared with available cylinder expansion tests.

Painlevé equations, elliptic integrals and elementary functions

NASA Astrophysics Data System (ADS)

Żołądek, Henryk; Filipuk, Galina

2015-02-01

The six Painlevé equations can be written in the Hamiltonian form, with time dependent Hamilton functions. We present a rather new approach to this result, leading to rational Hamilton functions. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems with two degrees of freedom. We realize the Bäcklund transformations of the Painlevé equations as symplectic birational transformations in C4 and we interpret the cases with classical solutions as the cases of partial integrability of the extended Hamiltonian systems. We prove that the extended Hamiltonian systems do not have any additional algebraic first integral besides the known special cases of the third and fifth Painlevé equations. We also show that the original Painlevé equations admit the first integrals expressed in terms of the elementary functions only in the special cases mentioned above. In the proofs we use equations in variations with respect to a parameter and Liouville's theory of elementary functions.

OPS MCC level B/C formulation requirements: Area targets and space volumes processor

NASA Technical Reports Server (NTRS)

Bishop, M. J., Jr.

1979-01-01

The level B/C mathematical specifications for the area targets and space volumes processor (ATSVP) are described. The processor is designed to compute the acquisition-of-signal (AOS) and loss-of-signal (LOS) times for area targets and space volumes. The characteristics of the area targets and space volumes are given. The mathematical equations necessary to determine whether the spacecraft lies within the area target or space volume are given. These equations provide a detailed model of the target geometry. A semianalytical technique for predicting the AOS and LOS time periods is disucssed. This technique was designed to bound the actual visibility period using a simplified target geometry model and unperturbed orbital motion. Functional overview of the ATSVP is presented and it's detailed logic flow is described.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

A nodal domain theorem for integrable billiards in two dimensions

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

Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a familymore » are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.« less

Oblique scattering from radially inhomogeneous dielectric cylinders: An exact Volterra integral equation formulation

NASA Astrophysics Data System (ADS)

Tsalamengas, John L.

2018-07-01

We study plane-wave electromagnetic scattering by radially and strongly inhomogeneous dielectric cylinders at oblique incidence. The method of analysis relies on an exact reformulation of the underlying field equations as a first-order 4 × 4 system of differential equations and on the ability to restate the associated initial-value problem in the form of a system of coupled linear Volterra integral equations of the second kind. The integral equations so derived are discretized via a sophisticated variant of the Nyström method. The proposed method yields results accurate up to machine precision without relying on approximations. Numerical results and case studies ably demonstrate the efficiency and high accuracy of the algorithms.

Spontaneous Imbibition Process in Micro-Nano Fractal Capillaries Considering Slip Flow

NASA Astrophysics Data System (ADS)

Shen, Yinghao; Li, Caoxiong; Ge, Hongkui; Guo, Xuejing; Wang, Shaojun

An imbibition process of water into a matrix is required to investigate the influences of large-volume fracturing fluids on gas production of unconventional formations. Slip flow has been recognized by recent studies as a major mechanism of fluid transport in nanotubes. For nanopores in shale, a slip boundary is nonnegligible in the imbibition process. In this study, we established an analytic equation of spontaneous imbibition considering slip effects in capillaries. A spontaneous imbibition model that couples the analytic equation considering the slip effect was constructed based on fractal theory. We then used a model for various conditions, such as slip boundary, pore structure, and fractal dimension of pore tortuosity, to capture the imbibition characteristics considering the slip effect. A dynamic contact angle was integrated into the modeling. Results of our study verify that the slip boundary influences water imbibition significantly. The imbibition speed is significantly improved when slip length reaches the equivalent diameter of a tube. Therefore, disregarding the slip effect will underestimate the imbibition speed in shale samples.

A general numerical model for wave rotor analysis

NASA Technical Reports Server (NTRS)

Paxson, Daniel W.

1992-01-01

Wave rotors represent one of the promising technologies for achieving very high core temperatures and pressures in future gas turbine engines. Their operation depends upon unsteady gas dynamics and as such, their analysis is quite difficult. This report describes a numerical model which has been developed to perform such an analysis. Following a brief introduction, a summary of the wave rotor concept is given. The governing equations are then presented, along with a summary of the assumptions used to obtain them. Next, the numerical integration technique is described. This is an explicit finite volume technique based on the method of Roe. The discussion then focuses on the implementation of appropriate boundary conditions. Following this, some results are presented which first compare the numerical approximation to the governing differential equations and then compare the overall model to an actual wave rotor experiment. Finally, some concluding remarks are presented concerning the limitations of the simplifying assumptions and areas where the model may be improved.

A two-dimensional model of water: Theory and computer simulations

NASA Astrophysics Data System (ADS)

Urbič, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Southall, N. T.; Dill, K. A.

2000-02-01

We develop an analytical theory for a simple model of liquid water. We apply Wertheim's thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the MB model, which is among the simplest models of water. Water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz (MB) logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation function of the model water at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.

Spectral method for the static electric potential of a charge density in a composite medium

NASA Astrophysics Data System (ADS)

Bergman, David J.; Farhi, Asaf

2018-04-01

A spectral representation for the static electric potential field in a two-constituent composite medium is presented. A theory is developed for calculating the quasistatic eigenstates of Maxwell's equations for such a composite. The local physical potential field produced in the system by a given source charge density is expanded in this set of orthogonal eigenstates for any position r. The source charges can be located anywhere, i.e., inside any of the constituents. This is shown to work even if the eigenfunctions are normalized in an infinite volume. If the microstructure consists of a cluster of separate inclusions in a uniform host medium, then the quasistatic eigenstates of all the separate isolated inclusions can be used to calculate the eigenstates of the total structure as well as the local potential field. Once the eigenstates are known for a given host and a given microstructure, then calculation of the local field only involves calculating three-dimensional integrals of known functions and solving sets of linear algebraic equations.

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Schallhorn, Paul

1998-01-01

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

Integrated modeling of second phase precipitation in cold-worked 316 stainless steels under irradiation

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

Mamivand, Mahmood; Yang, Ying; Busby, Jeremy T.

The current work combines the Cluster Dynamics (CD) technique and CALPHAD-based precipitation modeling to address the second phase precipitation in cold-worked (CW) 316 stainless steels (SS) under irradiation at 300–400 °C. CD provides the radiation enhanced diffusion and dislocation evolution as inputs for the precipitation model. The CALPHAD-based precipitation model treats the nucleation, growth and coarsening of precipitation processes based on classical nucleation theory and evolution equations, and simulates the composition, size and size distribution of precipitate phases. We benchmark the model against available experimental data at fast reactor conditions (9.4 × 10 –7 dpa/s and 390 °C) and thenmore » use the model to predict the phase instability of CW 316 SS under light water reactor (LWR) extended life conditions (7 × 10 –8 dpa/s and 275 °C). The model accurately predicts the γ' (Ni 3Si) precipitation evolution under fast reactor conditions and that the formation of this phase is dominated by radiation enhanced segregation. The model also predicts a carbide volume fraction that agrees well with available experimental data from a PWR reactor but is much higher than the volume fraction observed in fast reactors. We propose that radiation enhanced dissolution and/or carbon depletion at sinks that occurs at high flux could be the main sources of this inconsistency. The integrated model predicts ~1.2% volume fraction for carbide and ~3.0% volume fraction for γ' for typical CW 316 SS (with 0.054 wt% carbon) under LWR extended life conditions. Finally, this work provides valuable insights into the magnitudes and mechanisms of precipitation in irradiated CW 316 SS for nuclear applications.« less

Integrated modeling of second phase precipitation in cold-worked 316 stainless steels under irradiation

DOE PAGES

Mamivand, Mahmood; Yang, Ying; Busby, Jeremy T.; ...

2017-03-11

The current work combines the Cluster Dynamics (CD) technique and CALPHAD-based precipitation modeling to address the second phase precipitation in cold-worked (CW) 316 stainless steels (SS) under irradiation at 300–400 °C. CD provides the radiation enhanced diffusion and dislocation evolution as inputs for the precipitation model. The CALPHAD-based precipitation model treats the nucleation, growth and coarsening of precipitation processes based on classical nucleation theory and evolution equations, and simulates the composition, size and size distribution of precipitate phases. We benchmark the model against available experimental data at fast reactor conditions (9.4 × 10 –7 dpa/s and 390 °C) and thenmore » use the model to predict the phase instability of CW 316 SS under light water reactor (LWR) extended life conditions (7 × 10 –8 dpa/s and 275 °C). The model accurately predicts the γ' (Ni 3Si) precipitation evolution under fast reactor conditions and that the formation of this phase is dominated by radiation enhanced segregation. The model also predicts a carbide volume fraction that agrees well with available experimental data from a PWR reactor but is much higher than the volume fraction observed in fast reactors. We propose that radiation enhanced dissolution and/or carbon depletion at sinks that occurs at high flux could be the main sources of this inconsistency. The integrated model predicts ~1.2% volume fraction for carbide and ~3.0% volume fraction for γ' for typical CW 316 SS (with 0.054 wt% carbon) under LWR extended life conditions. Finally, this work provides valuable insights into the magnitudes and mechanisms of precipitation in irradiated CW 316 SS for nuclear applications.« less

Abdominal girth and vertebral column length aid in predicting intrathecal hyperbaric bupivacaine dose for elective cesarean section

PubMed Central

Wei, Chang-Na; Zhou, Qing-He; Wang, Li-Zhong

2017-01-01

Abstract Currently, there is no consensus on how to determine the optimal dose of intrathecal bupivacaine for an individual undergoing an elective cesarean section. In this study, we developed a regression equation between intrathecal 0.5% hyperbaric bupivacaine volume and abdominal girth and vertebral column length, to determine a suitable block level (T5) for elective cesarean section patients. In phase I, we analyzed 374 parturients undergoing an elective cesarean section that received a suitable dose of intrathecal 0.5% hyperbaric bupivacaine after a combined spinal-epidural (CSE) was performed at the L3/4 interspace. Parturients with T5 blockade to pinprick were selected for establishing the regression equation between 0.5% hyperbaric bupivacaine volume and vertebral column length and abdominal girth. Six parturient and neonatal variables, intrathecal 0.5% hyperbaric bupivacaine volume, and spinal anesthesia spread were recorded. Bivariate line correlation analyses, multiple line regression analyses, and 2-tailed t tests or chi-square test were performed, as appropriate. In phase II, another 200 parturients with CSE for elective cesarean section were enrolled to verify the accuracy of the regression equation. In phase I, a total of 143 parturients were selected to establish the following regression equation: YT5 = 0.074X1 − 0.022X2 − 0.017 (YT5 = 0.5% hyperbaric bupivacaine volume for T5 block level; X1 = vertebral column length; and X2 = abdominal girth). In phase II, a total of 189 participants were enrolled in the study to verify the accuracy of the regression equation, and 155 parturients with T5 blockade were deemed eligible, which accounted for 82.01% of all participants. This study evaluated parturients with T5 blockade to pinprick after a CSE for elective cesarean section to establish a regression equation between parturient vertebral column length and abdominal girth and 0.5% hyperbaric intrathecal bupivacaine volume. This equation can accurately predict the suitable intrathecal hyperbaric bupivacaine dose for elective cesarean section. PMID:28834913

Abdominal girth and vertebral column length aid in predicting intrathecal hyperbaric bupivacaine dose for elective cesarean section.

PubMed

Wei, Chang-Na; Zhou, Qing-He; Wang, Li-Zhong

2017-08-01

Currently, there is no consensus on how to determine the optimal dose of intrathecal bupivacaine for an individual undergoing an elective cesarean section. In this study, we developed a regression equation between intrathecal 0.5% hyperbaric bupivacaine volume and abdominal girth and vertebral column length, to determine a suitable block level (T5) for elective cesarean section patients.In phase I, we analyzed 374 parturients undergoing an elective cesarean section that received a suitable dose of intrathecal 0.5% hyperbaric bupivacaine after a combined spinal-epidural (CSE) was performed at the L3/4 interspace. Parturients with T5 blockade to pinprick were selected for establishing the regression equation between 0.5% hyperbaric bupivacaine volume and vertebral column length and abdominal girth. Six parturient and neonatal variables, intrathecal 0.5% hyperbaric bupivacaine volume, and spinal anesthesia spread were recorded. Bivariate line correlation analyses, multiple line regression analyses, and 2-tailed t tests or chi-square test were performed, as appropriate. In phase II, another 200 parturients with CSE for elective cesarean section were enrolled to verify the accuracy of the regression equation.In phase I, a total of 143 parturients were selected to establish the following regression equation: YT5 = 0.074X1 - 0.022X2 - 0.017 (YT5 = 0.5% hyperbaric bupivacaine volume for T5 block level; X1 = vertebral column length; and X2 = abdominal girth). In phase II, a total of 189 participants were enrolled in the study to verify the accuracy of the regression equation, and 155 parturients with T5 blockade were deemed eligible, which accounted for 82.01% of all participants.This study evaluated parturients with T5 blockade to pinprick after a CSE for elective cesarean section to establish a regression equation between parturient vertebral column length and abdominal girth and 0.5% hyperbaric intrathecal bupivacaine volume. This equation can accurately predict the suitable intrathecal hyperbaric bupivacaine dose for elective cesarean section.

Estimating peak discharges, flood volumes, and hydrograph shapes of small ungaged urban streams in Ohio

USGS Publications Warehouse

Sherwood, J.M.

1986-01-01

Methods are presented for estimating peak discharges, flood volumes and hydrograph shapes of small (less than 5 sq mi) urban streams in Ohio. Examples of how to use the various regression equations and estimating techniques also are presented. Multiple-regression equations were developed for estimating peak discharges having recurrence intervals of 2, 5, 10, 25, 50, and 100 years. The significant independent variables affecting peak discharge are drainage area, main-channel slope, average basin-elevation index, and basin-development factor. Standard errors of regression and prediction for the peak discharge equations range from +/-37% to +/-41%. An equation also was developed to estimate the flood volume of a given peak discharge. Peak discharge, drainage area, main-channel slope, and basin-development factor were found to be the significant independent variables affecting flood volumes for given peak discharges. The standard error of regression for the volume equation is +/-52%. A technique is described for estimating the shape of a runoff hydrograph by applying a specific peak discharge and the estimated lagtime to a dimensionless hydrograph. An equation for estimating the lagtime of a basin was developed. Two variables--main-channel length divided by the square root of the main-channel slope and basin-development factor--have a significant effect on basin lagtime. The standard error of regression for the lagtime equation is +/-48%. The data base for the study was established by collecting rainfall-runoff data at 30 basins distributed throughout several metropolitan areas of Ohio. Five to eight years of data were collected at a 5-min record interval. The USGS rainfall-runoff model A634 was calibrated for each site. The calibrated models were used in conjunction with long-term rainfall records to generate a long-term streamflow record for each site. Each annual peak-discharge record was fitted to a Log-Pearson Type III frequency curve. Multiple-regression techniques were then used to analyze the peak discharge data as a function of the basin characteristics of the 30 sites. (Author 's abstract)

Gas Flow in the Capillary of the Atmosphere-to-Vacuum Interface of Mass Spectrometers

NASA Astrophysics Data System (ADS)

Skoblin, Michael; Chudinov, Alexey; Soulimenkov, Ilia; Brusov, Vladimir; Kozlovskiy, Viacheslav

2017-10-01

Numerical simulations of a gas flow through a capillary being a part of mass spectrometer atmospheric interface were performed using a detailed laminar flow model. The simulated interface consisted of atmospheric and forevacuum volumes connected via a thin capillary. The pressure in the forevacuum volume where the gas was expanding after passing through the capillary was varied in the wide range from 10 to 900 mbar in order to study the volume flow rate as well as the other flow parameters as functions of the pressure drop between the atmospheric and forevacuum volumes. The capillary wall temperature was varied in the range from 24 to 150 °C. Numerical integration of the complete system of Navier-Stokes equations for a viscous compressible gas taking into account the heat transfer was performed using the standard gas dynamic simulation software package ANSYS CFX. The simulation results were compared with experimental measurements of gas flow parameters both performed using our experimental setup and taken from the literature. The simulated volume flow rates through the capillary differed no more than by 10% from the measured ones over the entire pressure and temperatures ranges. A conclusion was drawn that the detailed digital laminar model is able to quantitatively describe the measured gas flow rates through the capillaries under conditions considered. [Figure not available: see fulltext.

Gas Flow in the Capillary of the Atmosphere-to-Vacuum Interface of Mass Spectrometers.

PubMed

Skoblin, Michael; Chudinov, Alexey; Soulimenkov, Ilia; Brusov, Vladimir; Kozlovskiy, Viacheslav

2017-10-01

Numerical simulations of a gas flow through a capillary being a part of mass spectrometer atmospheric interface were performed using a detailed laminar flow model. The simulated interface consisted of atmospheric and forevacuum volumes connected via a thin capillary. The pressure in the forevacuum volume where the gas was expanding after passing through the capillary was varied in the wide range from 10 to 900 mbar in order to study the volume flow rate as well as the other flow parameters as functions of the pressure drop between the atmospheric and forevacuum volumes. The capillary wall temperature was varied in the range from 24 to 150 °C. Numerical integration of the complete system of Navier-Stokes equations for a viscous compressible gas taking into account the heat transfer was performed using the standard gas dynamic simulation software package ANSYS CFX. The simulation results were compared with experimental measurements of gas flow parameters both performed using our experimental setup and taken from the literature. The simulated volume flow rates through the capillary differed no more than by 10% from the measured ones over the entire pressure and temperatures ranges. A conclusion was drawn that the detailed digital laminar model is able to quantitatively describe the measured gas flow rates through the capillaries under conditions considered. Graphical Abstract ᅟ.

Predictive equations for total lung capacity and residual volume calculated from radiographs in a random sample of the Michigan population.

PubMed Central

Kilburn, K H; Warshaw, R H; Thornton, J C; Thornton, K; Miller, A

1992-01-01

BACKGROUND: Published predicted values for total lung capacity and residual volume are often based on a small number of subjects and derive from different populations from predicted spirometric values. Equations from the only two large studies gave smaller predicted values for total lung capacity than the smaller studies. A large number of subjects have been studied from a population which has already provided predicted values for spirometry and transfer factor for carbon monoxide. METHODS: Total lung capacity was measured from standard posteroanterior and lateral chest radiographs and forced vital capacity by spirometry in a population sample of 771 subjects. Prediction equations were developed for total lung capacity (TLC), residual volume (RV) and RV/TLC in two groups--normal and total. Subjects with signs or symptoms of cardiopulmonary disease were combined with the normal subjects and equations for all subjects were also modelled. RESULTS: Prediction equations for TLC and RV in non-smoking normal men and women were square root transformations which included height and weight but not age. They included a coefficient for duration of smoking in current smokers. The predictive equation for RV/TLC included weight, age, age and duration of smoking for current smokers and ex-smokers of both sexes. For the total population the equations took the same form but the height coefficients and constants were slightly different. CONCLUSION: These population based prediction equations for TLC, RV and RV/TLC provide reference standards in a population that has provided reference standards for spirometry and single breath transfer factor for carbon monoxide. PMID:1412094

Estimating merchantable volumes of second growth Douglas-fir stands from total cubic volume and associated stand characteristics.

Treesearch

Richard L. Williamson; Robert O. Curtis

1980-01-01

Equations are given for estimating merchantable volumes of second-growth Douglas-fir stands to specified breast-high and top-diameter limits, in cubic feet or board feet, from total volume in cubic feet and certain associated stand characteristics.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

High-temperature viscoelastic creep constitutive equations for polymer composites: Homogenization theory and experiments

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

Skontorp, A.; Wang, S.S.; Shibuya, Y.

1994-12-31

In this paper, a homogenization theory is developed to determine high-temperature effective viscoelastic constitutive equations for fiber-reinforced polymer composites. The homogenization theory approximates the microstructure of a fiber composite, and determine simultaneously effective macroscopic constitutive properties of the composite and the associated microscopic strain and stress in the heterogeneous material. The time-temperature dependent homogenization theory requires that the viscoelastic constituent properties of the matrix phase at elevated temperatures, the governing equations for the composites, and the boundary conditions of the problem be Laplace transformed to a conjugate problem. The homogenized effective properties in the transformed domain are determined, using amore » two-scale asymptotic expansion of field variables and an averaging procedure. Field solutions in the unit cell are determined from basic and first-order governing equations with the aid of a boundary integral method (BIM). Effective viscoelastic constitutive properties of the composite at elevated temperatures are determined by an inverse transformation, as are the microscopic stress and deformation in the composite. Using this method, interactions among fibers and between the fibers and the matrix can be evaluated explicitly, resulting in accurate solutions for composites with high-volume fraction of reinforcing fibers. Examples are given for the case of a carbon-fiber reinforced thermoplastic polyamide composite in an elevated temperature environment. The homogenization predictions are in good agreement with experimental data available for the composite.« less

Solving Ordinary Differential Equations

NASA Technical Reports Server (NTRS)

Krogh, F. T.

1987-01-01

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

FAST TRACK COMMUNICATION: On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

NASA Astrophysics Data System (ADS)

Man, Yiu-Kwong

2010-10-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided.

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

NASA Astrophysics Data System (ADS)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

Friction factor and heat transfer of nanofluids containing cylindrical nanoparticles in laminar pipe flow

NASA Astrophysics Data System (ADS)

Lin, Jianzhong; Xia, Yi; Ku, Xiaoke

2014-10-01

Numerical simulations of polyalphaolefins-Al2O3 nanofluids containing cylindrical nanoparticles in a laminar pipe flow are performed by solving the Navier-Stokes equation with term of cylindrical nanoparticles, the general dynamic equation for cylindrical nanoparticles, and equation for nanoparticle orientation. The distributions of particle number and volume concentration, the friction factor, and heat transfer are obtained and analyzed. The results show that distributions of nanoparticle number and volume concentration are non-uniform across the section, with larger and smaller values in the region near the pipe center and near the wall, respectively. The non-uniformity becomes significant with the increase in the axial distance from the inlet. The friction factor decreases with increasing Reynolds number. The relationships between the friction factor and the nanoparticle volume concentration as well as particle aspect ratio are dependent on the Reynolds number. The Nusselt number of nanofluids, directly proportional to the Reynolds number, particle volume concentration, and particle aspect ratio, is higher near the pipe entrance than at the downstream locations. The rate of increase in Nusselt number at lower particle volume concentration is more than that at higher concentration. Finally, the expressions of friction factor and Nusselt number as a function of particle volume concentration, particle aspect ratio, and Reynolds number are derived based on the numerical data.

A mathematical model of intestinal oedema formation.

PubMed

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

2014-03-01

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

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

NASA Astrophysics Data System (ADS)

Kari, Leif

2017-09-01

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

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

On the solution of integral equations with a generalized cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

NASA Technical Reports Server (NTRS)

Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

1986-01-01

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Davidenko’s Method for the Solution of Nonlinear Operator Equations.

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), OPERATORS(MATHEMATICS), BANACH SPACE , MAPPING (TRANSFORMATIONS), NUMERICAL METHODS AND PROCEDURES, INTEGRALS, SET THEORY, CONVERGENCE, MATRICES(MATHEMATICS)

Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

DTIC Science & Technology

1987-02-01

equation [18]. It should be noted that the 80 equation has more similarities [19] with the Kadomtsev - Petviashvili (KP...Cimento, 39B, 1 (1977). [31] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation , preprint U.M.I.S.T. (1985). II ’AI D p-I 4, - -- - -- - - -w 4 ...TOM NONLINEAR STUDIES IDTIC I IELEC )// MAR 2 51988 I / \\ / Integrable Equations in Multi- dimensions (2+1) are Bi-Hamiltonian Systems by A.S.

The non-autonomous YdKN equation and generalized symmetries of Boll equations

NASA Astrophysics Data System (ADS)

Gubbiotti, G.; Scimiterna, C.; Levi, D.

2017-05-01

In this paper, we study the integrability of a class of nonlinear non-autonomous quad graph equations compatible around the cube introduced by Boll in the framework of the generalized Adler, Bobenko, and Suris (ABS) classification. We show that all these equations possess three-point generalized symmetries which are subcases of either the Yamilov discretization of the Krichever-Novikov equation or of its non-autonomous extension. We also prove that all those symmetries are integrable as they pass the algebraic entropy test.

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

Treesearch

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

2003-01-01

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

Project SQUID: The Foundations of Nonequilibrium Statistical Mechanics. Volume 1

DTIC Science & Technology

1963-06-01

equations available (Boltzmann, Landau,, Bogolubov- Balescu -Lenard) are essentially exact and cannot be improved. That isv for kinetic gases (those...effects) as well as to the newly obtained kinetic equation for plasmas (8) (Bogolubov- Balescu -Lenard equation). The hope of ob- taining correctly

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Solving Simple Kinetics without Integrals

ERIC Educational Resources Information Center

de la Pen~a, Lisandro Herna´ndez

2016-01-01

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

One- and two-dimensional search of an equation of state using a newly released 2DRoptimize package

NASA Astrophysics Data System (ADS)

Jamal, M.; Reshak, A. H.

2018-05-01

A new package called 2DRoptimize has been released for performing two-dimensional searches of the equation of state (EOS) for rhombohedral, tetragonal, and hexagonal compounds. The package is compatible and available with the WIEN2k package. The 2DRoptimize package performs a convenient volume and c/a structure optimization. First, the package finds the best value for c/a and the associated energy for each volume. In the second step, it calculates the EoS. The package then finds the equation of the c/a ratio vs. volume to calculate the c/a ratio at the optimized volume. In the last stage, by using the optimized volume and c/a ratio, the 2DRoptimize package calculates a and c lattice constants for tetragonal and hexagonal compounds, as well as the a lattice constant with the α angle for rhombohedral compounds. We tested our new package based on several hexagonal, tetragonal, and rhombohedral structures, and the 2D search results for the EOS showed that this method is more accurate than 1D search. Our results agreed very well with the experimental data and they were better than previous theoretical calculations.

Effect of three-body interactions on the zero-temperature equation of state of HCP solid 4He

NASA Astrophysics Data System (ADS)

Barnes, Ashleigh L.; Hinde, Robert J.

2017-03-01

Previous studies have pointed to the importance of three-body interactions in high density 4He solids. However the computational cost often makes it unfeasible to incorporate these interactions into the simulation of large systems. We report the implementation and evaluation of a computationally efficient perturbative treatment of three-body interactions in hexagonal close packed solid 4He utilizing the recently developed nonadditive three-body potential of Cencek et al. This study represents the first application of the Cencek three-body potential to condensed phase 4He systems. Ground state energies from quantum Monte Carlo simulations, with either fully incorporated or perturbatively treated three-body interactions, are calculated in systems with molar volumes ranging from 21.3 cm3/mol down to 2.5 cm3/mol. These energies are used to derive the zero-temperature equation of state for comparison against existing experimental and theoretical data. The equations of state derived from both perturbative and fully incorporated three-body interactions are found to be in very good agreement with one another, and reproduce the experimental pressure-volume data with significantly better accuracy than is obtained when only two-body interactions are considered. At molar volumes below approximately 4.0 cm3/mol, neither two-body nor three-body equations of state are able to accurately reproduce the experimental pressure-volume data, suggesting that below this molar volume four-body and higher many-body interactions are becoming important.

Experimental analysis and numerical modeling of mollusk shells as a three dimensional integrated volume.

PubMed

Faghih Shojaei, M; Mohammadi, V; Rajabi, H; Darvizeh, A

2012-12-01

In this paper, a new numerical technique is presented to accurately model the geometrical and mechanical features of mollusk shells as a three dimensional (3D) integrated volume. For this purpose, the Newton method is used to solve the nonlinear equations of shell surfaces. The points of intersection on the shell surface are identified and the extra interior parts are removed. Meshing process is accomplished with respect to the coordinate of each point of intersection. The final 3D generated mesh models perfectly describe the spatial configuration of the mollusk shells. Moreover, the computational model perfectly matches with the actual interior geometry of the shells as well as their exterior architecture. The direct generation technique is employed to generate a 3D finite element (FE) model in ANSYS 11. X-ray images are taken to show the close similarity of the interior geometry of the models and the actual samples. A scanning electron microscope (SEM) is used to provide information on the microstructure of the shells. In addition, a set of compression tests were performed on gastropod shell specimens to obtain their ultimate compressive strength. A close agreement between experimental data and the relevant numerical results is demonstrated. Copyright © 2012 Elsevier Ltd. All rights reserved.

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

Integral equation approach to time-dependent kinematic dynamos in finite domains

NASA Astrophysics Data System (ADS)

Xu, Mingtian; Stefani, Frank; Gerbeth, Gunter

2004-11-01

The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples—the α2 dynamo model with radially varying α and the Bullard-Gellman model—illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α2 dynamo in rectangular domains.

A boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies

NASA Technical Reports Server (NTRS)

Gallman, Judith M.; Myers, M. K.; Farassat, F.

1990-01-01

The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.

A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume 1: The generalized method of averaging applied to the artificial satellite problem

NASA Technical Reports Server (NTRS)

Mcclain, W. D.

1977-01-01

A recursively formulated, first-order, semianalytic artificial satellite theory, based on the generalized method of averaging is presented in two volumes. Volume I comprehensively discusses the theory of the generalized method of averaging applied to the artificial satellite problem. Volume II presents the explicit development in the nonsingular equinoctial elements of the first-order average equations of motion. The recursive algorithms used to evaluate the first-order averaged equations of motion are also presented in Volume II. This semianalytic theory is, in principle, valid for a term of arbitrary degree in the expansion of the third-body disturbing function (nonresonant cases only) and for a term of arbitrary degree and order in the expansion of the nonspherical gravitational potential function.

Emerging Technologies Program Integration Report. Volume 2. Background, Delphi and Workshop Data. Appendices

DTIC Science & Technology

1987-05-04

FTIILE COP’ AD-A196 840 EMERGING TECHNOLOGIES PROGRAM INTEGRATION REPORT VOLUME II BACKGROUND, DELPHI AND WORKSHOP DATA, APPENDICES . -- PREPARED...Security Classification) Emerging Technologies Program Integration Report Volume II: Background, Delphi and Workshop Data; Appendices (U) 12 PERSONAL...volumes of this integration report assess and synthesize information gathered through a Delphi survey, defense needs prioritization workshops, and

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

The application of the integral equation theory to study the hydrophobic interaction

PubMed Central

Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

2014-01-01

The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy. PMID:24437891

Algorithms For Integrating Nonlinear Differential Equations

NASA Technical Reports Server (NTRS)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

NASA Technical Reports Server (NTRS)

Radhakrishnan, K.

1984-01-01

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

DOE PAGES

McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; ...

2015-09-04

We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

Technology requirements for future Earth-to-geosynchronous orbit transportation systems. Volume 3: Appendices

NASA Technical Reports Server (NTRS)

Caluori, V. A.; Conrad, R. T.; Jenkins, J. C.

1980-01-01

Technological requirements and forecasts of rocket engine parameters and launch vehicles for future Earth to geosynchronous orbit transportation systems are presented. The parametric performance, weight, and envelope data for the LOX/CH4, fuel cooled, staged combustion cycle and the hydrogen cooled, expander bleed cycle engine concepts are discussed. The costing methodology and ground rules used to develop the engine study are summarized. The weight estimating methodology for winged launched vehicles is described and summary data, used to evaluate and compare weight data for dedicated and integrated O2/H2 subsystems for the SSTO, HLLV and POTV are presented. Detail weights, comparisons, and weight scaling equations are provided.

International Symposium on Numerical Methods in Engineering, 5th, Ecole Polytechnique Federale de Lausanne, Switzerland, Sept. 11-15, 1989, Proceedings. Volumes 1 & 2

NASA Astrophysics Data System (ADS)

Gruber, Ralph; Periaux, Jaques; Shaw, Richard Paul

Recent advances in computational mechanics are discussed in reviews and reports. Topics addressed include spectral superpositions on finite elements for shear banding problems, strain-based finite plasticity, numerical simulation of hypersonic viscous continuum flow, constitutive laws in solid mechanics, dynamics problems, fracture mechanics and damage tolerance, composite plates and shells, contact and friction, metal forming and solidification, coupling problems, and adaptive FEMs. Consideration is given to chemical flows, convection problems, free boundaries and artificial boundary conditions, domain-decomposition and multigrid methods, combustion and thermal analysis, wave propagation, mixed and hybrid FEMs, integral-equation methods, optimization, software engineering, and vector and parallel computing.

Two-Dimensional Computational Model for Wave Rotor Flow Dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

1996-01-01

A two-dimensional (theta,z) Navier-Stokes solver for multi-port wave rotor flow simulation is described. The finite-volume form of the unsteady thin-layer Navier-Stokes equations are integrated in time on multi-block grids that represent the stationary inlet and outlet ports and the moving rotor passages of the wave rotor. Computed results are compared with three-port wave rotor experimental data. The model is applied to predict the performance of a planned four-port wave rotor experiment. Two-dimensional flow features that reduce machine performance and influence rotor blade and duct wall thermal loads are identified. The performance impact of rounding the inlet port wall, to inhibit separation during passage gradual opening, is assessed.

Differential equations for loop integrals in Baikov representation

NASA Astrophysics Data System (ADS)

Bosma, Jorrit; Larsen, Kasper J.; Zhang, Yang

2018-05-01

We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.

Monograph - The Numerical Integration of Ordinary Differential Equations.

ERIC Educational Resources Information Center

Hull, T. E.

The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

Estimating aspen volume and weight for individual trees, diameter classes, or entire stands.

Treesearch

Bryce E. Schlaegel

1975-01-01

Presents allometric volume and weight equations for Minnesota quaking aspen. Volume, green weight, and dry weight estimates can be made for wood, bark, and limbs on the basis of individual trees, diameter classes, or entire stands.

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications. Volume 24. Note on Numerical Fluid Mechanics

DTIC Science & Technology

1989-01-01

Calculations and Experiments (B.van den Berg/ D.A. Humphreysl E. Krause /J.P. F. Lindhout) Volume 20 Proceedings of the Seventh GAMM-Conference on...GRID METHODS FOR HYPERBOLIC PROBLEMS Wolfgang Hackbusch Sigrid Hagemann Institut fUr Informatik und Praktische Mathematik Christian-Albrechts...Euler Equations. Proceedings of the 8th Inter- national Conference on Numerical Methods in Fluid Dynamics (E. Krause , ed.), Aachen, 1988. Springer

A Model for Estimating Current and Future Timber Volume Loss from Stem Decay Caused by Heterobasidion annosum and Other Fungi in Stands of True Fir

Treesearch

Gregory M. Filip

1989-01-01

In 1979, an equation was developed to estimate the percentage of current and future timber volume loss due to stem decay caused by Heterobasidion annosum and other fungi in advance regeneration stands of grand and white fir in eastern Oregon and Washington. Methods for using and testing the equation are presented. Extensive testing in 1988 showed the...

A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Wu, Li-Xin; Rui, Wen-Juan

2015-05-01

With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03), and the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

High-order finite-volume solutions of the steady-state advection-diffusion equation with nonlinear Robin boundary conditions

NASA Astrophysics Data System (ADS)

Lin, Zhi; Zhang, Qinghai

2017-09-01

We propose high-order finite-volume schemes for numerically solving the steady-state advection-diffusion equation with nonlinear Robin boundary conditions. Although the original motivation comes from a mathematical model of blood clotting, the nonlinear boundary conditions may also apply to other scientific problems. The main contribution of this work is a generic algorithm for generating third-order, fourth-order, and even higher-order explicit ghost-filling formulas to enforce nonlinear Robin boundary conditions in multiple dimensions. Under the framework of finite volume methods, this appears to be the first algorithm of its kind. Numerical experiments on boundary value problems show that the proposed fourth-order formula can be much more accurate and efficient than a simple second-order formula. Furthermore, the proposed ghost-filling formulas may also be useful for solving other partial differential equations.

Crystal structure optimisation using an auxiliary equation of state

NASA Astrophysics Data System (ADS)

Jackson, Adam J.; Skelton, Jonathan M.; Hendon, Christopher H.; Butler, Keith T.; Walsh, Aron

2015-11-01

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other "beyond" density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu2ZnSnS4 and the magnetic metal-organic framework HKUST-1.

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship.

PubMed

Yan, Zai You; Hung, Kin Chew; Zheng, Hui

2003-05-01

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Reply to "Comment on 'Defocusing complex short-pulse equation and its multi-dark-soliton solution' ".

PubMed

Feng, Bao-Feng; Ling, Liming; Zhu, Zuonong

2017-08-01

Our paper [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.1103/PhysRevE.93.052227], proposing an integrable model for the propagation of ultrashort pulses, has recently received a Comment by Youssoufa et al. [Phys. Rev. E 96, 026201 (2017)10.1103/PhysRevE.96.026201] about a possible flaw in its derivation. We point out that their claim is incorrect since we have stated explicitly that a term is neglected to derive our model equation in our paper. Furthermore, the integrable model is validated by comparing with the normalized Maxwell equation and other known integrable models. Moreover, we show that a similar approximation has to be performed in deriving the same integrable equation as explained in the Comment.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Applications of Black Scholes Complexity Concepts to Combat Modelling

DTIC Science & Technology

2009-03-01

Lauren, G C McIntosh, N D Perry and J Moffat, Chaos 17, 2007. 4 Lanchester Models of Warfare Volumes 1 and 2, J G Taylor, Operations Research Society...transformation matrix A Lanchester Equation solution parameter bi Dependent model variables b(x,t) Variable variance rate B Lanchester Equation solution...distribution. The similarity between this equation and the Lanchester Equations (equation 1) is clear. This suggests an obvious solution to the question of

A single-stage flux-corrected transport algorithm for high-order finite-volume methods

DOE PAGES

Chaplin, Christopher; Colella, Phillip

2017-05-08

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. Here, we modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge-Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered- differencemore » and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.« less

A time-dependent model to determine the thermal conductivity of a nanofluid

NASA Astrophysics Data System (ADS)

Myers, T. G.; MacDevette, M. M.; Ribera, H.

2013-07-01

In this paper, we analyse the time-dependent heat equations over a finite domain to determine expressions for the thermal diffusivity and conductivity of a nanofluid (where a nanofluid is a fluid containing nanoparticles with average size below 100 nm). Due to the complexity of the standard mathematical analysis of this problem, we employ a well-known approximate solution technique known as the heat balance integral method. This allows us to derive simple analytical expressions for the thermal properties, which appear to depend primarily on the volume fraction and liquid properties. The model is shown to compare well with experimental data taken from the literature even up to relatively high concentrations and predicts significantly higher values than the Maxwell model for volume fractions approximately >1 %. The results suggest that the difficulty in reproducing the high values of conductivity observed experimentally may stem from the use of a static heat flow model applied over an infinite domain rather than applying a dynamic model over a finite domain.

Viscous wing theory development. Volume 1: Analysis, method and results

NASA Technical Reports Server (NTRS)

Chow, R. R.; Melnik, R. E.; Marconi, F.; Steinhoff, J.

1986-01-01

Viscous transonic flows at large Reynolds numbers over 3-D wings were analyzed using a zonal viscid-inviscid interaction approach. A new numerical AFZ scheme was developed in conjunction with the finite volume formulation for the solution of the inviscid full-potential equation. A special far-field asymptotic boundary condition was developed and a second-order artificial viscosity included for an improved inviscid solution methodology. The integral method was used for the laminar/turbulent boundary layer and 3-D viscous wake calculation. The interaction calculation included the coupling conditions of the source flux due to the wing surface boundary layer, the flux jump due to the viscous wake, and the wake curvature effect. A method was also devised incorporating the 2-D trailing edge strong interaction solution for the normal pressure correction near the trailing edge region. A fully automated computer program was developed to perform the proposed method with one scalar version to be used on an IBM-3081 and two vectorized versions on Cray-1 and Cyber-205 computers.

A monotonicity preserving conservative sharp interface flow solver for high density ratio two-phase flows

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

Le Chenadec, Vincent, E-mail: vlechena@stanford.edu; Pitsch, Heinz; Institute for Combustion Technology, RWTH Aachen, Templergraben 64, 52056 Aachen

2013-09-15

This paper presents a novel approach for solving the conservative form of the incompressible two-phase Navier–Stokes equations. In order to overcome the numerical instability induced by the potentially large density ratio encountered across the interface, the proposed method includes a Volume-of-Fluid type integration of the convective momentum transport, a monotonicity preserving momentum rescaling, and a consistent and conservative Ghost Fluid projection that includes surface tension effects. The numerical dissipation inherent in the Volume-of-Fluid treatment of the convective transport is localized in the interface vicinity, enabling the use of a kinetic energy conserving discretization away from the singularity. Two- and three-dimensionalmore » tests are presented, and the solutions shown to remain accurate at arbitrary density ratios. The proposed method is then successfully used to perform the detailed simulation of a round water jet emerging in quiescent air, therefore suggesting the applicability of the proposed algorithm to the computation of realistic turbulent atomization.« less

A Riccati model for Denmark Strait overflow variability

NASA Astrophysics Data System (ADS)

Käse, R. H.

2006-10-01

A controlled volume box model of the western basins of the Nordic Seas for water denser than 1027.8 kg m-3 is constructed, where accumulation in volume ($\\frac{dV}{dt) is driven by net imbalances between prescribed net inflow from the northern, eastern and top boundaries (Qs) and hydraulically limited outflow through the Denmark Strait. The resulting Riccati equation is solved analytically for filling and flushing experiments with constant Qs and numerically for stochastic forcing Qs(t). For small perturbations to Qs with white noise spectrum, the overflow response is red noise with a time scale between 5 and 15 years depending on the mean interface height and area. For Qs proportional to the NAO index, the overflow is positively correlated with the NAO. A 140 years integration reveals variations in the overflow between 2.5 Sv in the 1970s and a maximum of 4 Sv in the 1990s. Hydraulic transport calculations from hydrographic data north of Iceland show good agreement with the model hindcast.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the ;equations of motion; on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

Analytical expressions for the correlation function of a hard sphere dimer fluid

NASA Astrophysics Data System (ADS)

Kim, Soonho; Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.

Analytical expression for the correlation function of a hard sphere chain fluid

NASA Astrophysics Data System (ADS)

Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

New integrable model of propagation of the few-cycle pulses in an anisotropic microdispersed medium

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2018-03-01

We investigate the propagation of the few-cycle electromagnetic pulses in the anisotropic microdispersed medium. The effects of the anisotropy and spatial dispersion of the medium are created by the two sorts of the two-level atoms. The system of the material equations describing an evolution of the states of the atoms and the wave equations for the ordinary and extraordinary components of the pulses is derived. By applying the approximation of the sudden excitation to exclude the material variables, we reduce this system to the single nonlinear wave equation that generalizes the modified sine-Gordon equation and the Rabelo-Fokas equation. It is shown that this equation is integrable by means of the inverse scattering transformation method if an additional restriction on the parameters is imposed. The multisoliton solutions of this integrable generalization are constructed and investigated.

A plane wave model for direct simulation of reflection and transmission by discretely inhomogeneous plane parallel media

NASA Astrophysics Data System (ADS)

Mackowski, Daniel; Ramezanpour, Bahareh

2018-07-01

A formulation is developed for numerically solving the frequency domain Maxwell's equations in plane parallel layers of inhomogeneous media. As was done in a recent work [1], the plane parallel layer is modeled as an infinite square lattice of W × W × H unit cells, with W being a sample width of the layer and H the layer thickness. As opposed to the 3D volume integral/discrete dipole formulation, the derivation begins with a Fourier expansion of the electric field amplitude in the lateral plane, and leads to a coupled system of 1D ordinary differential equations in the depth direction of the layer. A 1D dyadic Green's function is derived for this system and used to construct a set of coupled 1D integral equations for the field expansion coefficients. The resulting mathematical formulation is considerably simpler and more compact than that derived, for the same system, using the discrete dipole approximation applied to the periodic plane lattice. Furthermore, the fundamental property variable appearing in the formulation is the Fourier transformed complex permittivity distribution in the unit cell, and the method obviates any need to define or calculate a dipole polarizability. Although designed primarily for random media calculations, the method is also capable of predicting the single scattering properties of individual particles; comparisons are presented to demonstrate that the method can accurately reproduce, at scattering angles not too close to 90°, the polarimetric scattering properties of single and multiple spheres. The derivation of the dyadic Green's function allows for an analytical preconditioning of the equations, and it is shown that this can result in significantly accelerated solution times when applied to densely-packed systems of particles. Calculation results demonstrate that the method, when applied to inhomogeneous media, can predict coherent backscattering and polarization opposition effects.

Novel Numerical Approaches to Loop Quantum Cosmology

NASA Astrophysics Data System (ADS)

Diener, Peter

2015-04-01

Loop Quantum Gravity (LQG) is an (as yet incomplete) approach to the quantization of gravity. When applied to symmetry reduced cosmological spacetimes (Loop Quantum Cosmology or LQC) one of the predictions of the theory is that the Big Bang is replaced by a Big Bounce, i.e. a previously existing contracting universe underwent a bounce at finite volume before becoming our expanding universe. The evolution equations of LQC take the form of difference equations (with the discretization given by the theory) that in the large volume limit can be approximated by partial differential equations (PDEs). In this talk I will first discuss some of the unique challenges encountered when trying to numerically solve these difference equations. I will then present some of the novel approaches that have been employed to overcome the challenges. I will here focus primarily on the Chimera scheme that takes advantage of the fact that the LQC difference equations can be approximated by PDEs in the large volume limit. I will finally also briefly discuss some of the results that have been obtained using these numerical techniques by performing simulations in regions of parameter space that were previously unreachable. This work is supported by a grant from the John Templeton Foundation and by NSF grant PHYS1068743.

First integrals and parametric solutions of third-order ODEs admitting {\\mathfrak{sl}(2, {R})}

NASA Astrophysics Data System (ADS)

Ruiz, A.; Muriel, C.

2017-05-01

A complete set of first integrals for any third-order ordinary differential equation admitting a Lie symmetry algebra isomorphic to sl(2, {R}) is explicitly computed. These first integrals are derived from two linearly independent solutions of a linear second-order ODE, without additional integration. The general solution in parametric form can be obtained by using the computed first integrals. The study includes a parallel analysis of the four inequivalent realizations of sl(2, {R}) , and it is applied to several particular examples. These include the generalized Chazy equation, as well as an example of an equation which admits the most complicated of the four inequivalent realizations.

The ε-form of the differential equations for Feynman integrals in the elliptic case

NASA Astrophysics Data System (ADS)

Adams, Luise; Weinzierl, Stefan

2018-06-01

Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral family that an ε-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The ε-form is obtained by a (non-algebraic) change of basis for the master integrals.

De-Aliasing Through Over-Integration Applied to the Flux Reconstruction and Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Spiegel, Seth C.; Huynh, H. T.; DeBonis, James R.

2015-01-01

High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).

Divergence of activity expansions: Is it actually a problem?

NASA Astrophysics Data System (ADS)

Ushcats, M. V.; Bulavin, L. A.; Sysoev, V. M.; Ushcats, S. Yu.

2017-12-01

For realistic interaction models, which include both molecular attraction and repulsion (e.g., Lennard-Jones, modified Lennard-Jones, Morse, and square-well potentials), the asymptotic behavior of the virial expansions for pressure and density in powers of activity has been studied taking power terms of high orders into account on the basis of the known finite-order irreducible integrals as well as the recent approximations of infinite irreducible series. Even in the divergence region (at subcritical temperatures), this behavior stays thermodynamically adequate (in contrast to the behavior of the virial equation of state with the same set of irreducible integrals) and corresponds to the beginning of the first-order phase transition: the divergence yields the jump (discontinuity) in density at constant pressure and chemical potential. In general, it provides a statistical explanation of the condensation phenomenon, but for liquid or solid states, the physically proper description (which can turn the infinite discontinuity into a finite jump of density) still needs further study of high-order cluster integrals and, especially, their real dependence on the system volume (density).

Estimating sugar maple bark thickness and volume.

Treesearch

Charles L. Stayton; Michael Hoffman

1970-01-01

Sugar maple bark thickness and volume were estimated using first a published method, then equations developed by the authors. Both methods gave estimates that compared closely with measured values. Information is also presented on variation in bark thickness and on weight and volume of bark as a percentage of total merchantable stem weight and volume.

Distribution theory for Schrödinger’s integral equation

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

Lange, Rutger-Jan, E-mail: rutger-jan.lange@cantab.net

2015-12-15

Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger’s equation. This paper, in contrast, investigates the integral form of Schrödinger’s equation. While both forms are known to be equivalent for smooth potentials, this is not true for distributional potentials. Here, we assume that the potential is given by a distribution defined on the space of discontinuous test functions. First, by using Schrödinger’s integral equation, we confirm a seminal result by Kurasov, which was originally obtained in the context of Schrödinger’s differential equation. This hints at a possible deeper connection between bothmore » forms of the equation. We also sketch a generalisation of Kurasov’s [J. Math. Anal. Appl. 201(1), 297–323 (1996)] result to hypersurfaces. Second, we derive a new closed-form solution to Schrödinger’s integral equation with a delta prime potential. This potential has attracted considerable attention, including some controversy. Interestingly, the derived propagator satisfies boundary conditions that were previously derived using Schrödinger’s differential equation. Third, we derive boundary conditions for “super-singular” potentials given by higher-order derivatives of the delta potential. These boundary conditions cannot be incorporated into the normal framework of self-adjoint extensions. We show that the boundary conditions depend on the energy of the solution and that probability is conserved. This paper thereby confirms several seminal results and derives some new ones. In sum, it shows that Schrödinger’s integral equation is a viable tool for studying singular interactions in quantum mechanics.« less

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

3D robust Chan-Vese model for industrial computed tomography volume data segmentation

NASA Astrophysics Data System (ADS)

Liu, Linghui; Zeng, Li; Luan, Xiao

2013-11-01

Industrial computed tomography (CT) has been widely applied in many areas of non-destructive testing (NDT) and non-destructive evaluation (NDE). In practice, CT volume data to be dealt with may be corrupted by noise. This paper addresses the segmentation of noisy industrial CT volume data. Motivated by the research on the Chan-Vese (CV) model, we present a region-based active contour model that draws upon intensity information in local regions with a controllable scale. In the presence of noise, a local energy is firstly defined according to the intensity difference within a local neighborhood. Then a global energy is defined to integrate local energy with respect to all image points. In a level set formulation, this energy is represented by a variational level set function, where a surface evolution equation is derived for energy minimization. Comparative analysis with the CV model indicates the comparable performance of the 3D robust Chan-Vese (RCV) model. The quantitative evaluation also shows the segmentation accuracy of 3D RCV. In addition, the efficiency of our approach is validated under several types of noise, such as Poisson noise, Gaussian noise, salt-and-pepper noise and speckle noise.

Turbofan Volume Dynamics Model for Investigations of Aero-Propulso-Servo-Elastic Effects in a Supersonic Commercial Transport

NASA Technical Reports Server (NTRS)

Connolly, Joseph W.; Kopasakis, George; Lemon, Kimberly A.

2010-01-01

A turbofan simulation has been developed for use in aero-propulso-servo-elastic coupling studies, on supersonic vehicles. A one-dimensional lumped volume approach is used whereby each component (fan, high-pressure compressor, combustor, etc.) is represented as a single volume using characteristic performance maps and conservation equations for continuity, momentum and energy. The simulation is developed in the MATLAB/SIMULINK (The MathWorks, Inc.) environment in order to facilitate controls development, and ease of integration with a future aero-servo-elastic vehicle model being developed at NASA Langley. The complete simulation demonstrated steady state results that closely match a proposed engine suitable for a supersonic business jet at the cruise condition. Preliminary investigation of the transient simulation revealed expected trends for fuel flow disturbances as well as upstream pressure disturbances. A framework for system identification enables development of linear models for controller design. Utilizing this framework, a transfer function modeling an upstream pressure disturbance s impacts on the engine speed is developed as an illustrative case of the system identification. This work will eventually enable an overall vehicle aero-propulso-servo-elastic model